Article: 5895 of sci.physics.particle Path: senator-bedfellow.mit.edu!bloom-beacon.mit.edu!paperboy.osf.org!mogul.osf.org!columbus From: columbus@osf.org Newsgroups: sci.physics,sci.physics.research,sci.physics.cond-matter,sci.physics.particle,alt.sci.physics.new-theories,sci.answers,alt.answers,news.answers Subject: sci.physics Frequently Asked Questions (Part 1 of 4) Supersedes: Followup-To: sci.physics Date: 13 Oct 1995 14:40:48 GMT Organization: Open Software Foundation Lines: 1532 Approved: news-answers-request@MIT.EDU Distribution: world Expires: 17-Nov 1995 Message-ID: Reply-To: columbus@osf.org (Michael Weiss) NNTP-Posting-Host: mogul.osf.org Summary: This posting contains a list of Frequently Asked Questions (and their answers) about physics, and should be read by anyone who wishes to post to the sci.physics.* newsgroups. Keywords: Sci.physics FAQ X-Posting-Frequency: posted monthly Originator: columbus@mogul.osf.org Xref: senator-bedfellow.mit.edu sci.physics:147070 sci.physics.research:3040 sci.physics.cond-matter:555 sci.physics.particle:5895 alt.sci.physics.new-theories:21138 sci.answers:3263 alt.answers:12764 news.answers:55201 Posted-By: auto-faq 3.1.1.2 Archive-name: physics-faq/part1 -------------------------------------------------------------------------------- FREQUENTLY ASKED QUESTIONS ON SCI.PHYSICS - Part 1/4 -------------------------------------------------------------------------------- This Frequently Asked Questions List is posted monthly to the USENET newsgroups sci.physics, sci.physics.cond-matter, sci.physics.research, sci.physics.particle, and alt.sci.physics.new-theories in an attempt to provide good answers to frequently asked questions and other reference material which is worth preserving. If you have corrections or answers to other frequently asked questions that you would like included in this posting, send E-mail to columbus@osf.org (Michael Weiss). The originator and original maintainer of this FAQ was Scott I. Chase. This document, as a collection, is Copyright (c) 1994 by Scott I. Chase. The individual articles are Copyright (c) 1994/5 by the individual authors listed. All rights are reserved. Permission to use, copy and distribute this unmodified document by any means and for any purpose EXCEPT PROFIT PURPOSES is hereby granted, provided that both the above Copyright notice and this permission notice appear in all copies of the FAQ itself. Reproducing this FAQ by any means, included, but not limited to, printing, copying existing prints, publishing by electronic or other means, implies full agreement to the above non-profit-use clause, unless upon explicit prior written permission of the authors. This FAQ is provided by the authors "as is," with all its faults. Any express or implied warranties, including, but not limited to, any implied warranties of merchantability, accuracy, or fitness for any particular purpose, are disclaimed. If you use the information in this document, in any way, you do so at your own risk. This document is probably out of date if you are reading it more than 30 days after the date which appears in the header. You can get it by FTP from rtfm.mit.edu or one of its mirror sites: North America: ftp.uu.net /usenet/news.answers mirrors.aol.com /pub/rtfm/usenet ftp.seas.gwu.edu /pub/rtfm rtfm.mit.edu /pub/usenet/news.answers Europe: ftp.uni-paderborn.de /pub/FAQ ftp.Germany.EU.net /pub/newsarchive/news.answers ftp.sunet.se /pub/usenet Asia: nctuccca.edu.tw /USENET/FAQ hwarang.postech.ac.kr /pub/usenet/news.answers ftp.hk.super.net /mirror/faqs Look for the files physics-faq/part1 physics-faq/part2 physics-faq/part3 physics-faq/part4 If you are a new reader of the Physics newsgroups, please read item #1, below. If you do not wish to read the FAQ at all, add "Frequently Asked Questions" to your .KILL file. A listing of new items can be found above the subject index, so that you can quickly identify new subjects of interest. To locate old items which have been updated since the last posting, look for the stars (*) in the subject index, which indicate new material (other than minor corrections). Items which have been submitted by a single individual are attributed to the original author. All other contributors have been thanked privately. New Item: #25. Can You See the Lorentz Contraction? Index of Subjects ----------------- FAQ 1/4 - Administriva and Reference 1. An Introduction to the Physics Newsgroups on USENET 2. The Care and Feeding of Kill Files 3. Accessing and Using Online Physics Resources 4. A Physics Booklist - Recommendations from the Net 5. The Nobel Prize for Physics FAQ 2/4 - Cosmology and Astrophysics 6. Gravitational Radiation 7. Is Energy Conserved in General Relativity? 8. Olbers' Paradox 9. What is Dark Matter? 10. Some Frequently Asked Questions About Black Holes 11. The Solar Neutrino Problem 12. The Expanding Universe FAQ 3/4 - General Physics 13. Apparent Superluminal Velocity of Galaxies 14. Hot Water Freezes Faster than Cold! 15. Why are Golf Balls Dimpled? 16. How to Change Nuclear Decay Rates 17. What is a Dippy Bird, and how is it used? 18. Below Absolute Zero - What Does Negative Temperature Mean? 19. Which Way Will my Bathtub Drain? 20. Why do Mirrors Reverse Left and Right? 21. Why Do Stars Twinkle While Planets Do Not? 22. Time Travel - Fact or Fiction? 23. Open Questions FAQ 4/4 - Particles, Special Relativity and Quantum Mechanics 24. Special Relativistic Paradoxes and Puzzles (a) The Barn and the Pole (b) The Twin Paradox (c) The Superluminal Scissors *25. Can You See the Lorentz-Fitzgerald Contraction? 26. Tachyons 27. The Particle Zoo 28. Does Antimatter Fall Up or Down? 29. What is the Mass of a Photon? 30. Baryogenesis - Why Are There More Protons Than Antiprotons? 31. The EPR Paradox and Bell's Inequality Principle 32. Some Frequently Asked Questions About Virtual Particles ******************************************************************************** Item 1. updated 10-APR-1994 by SIC original by Scott I. Chase An Introduction to the Physics Newsgroups on USENET --------------------------------------------------- The USENET hierarchy contains a number of newsgroups dedicated to the discussion of physics and physics-related topics. These include sci.physics, sci.physics.research, sci.physics.cond-matter, sci.physics.particle and alt.sci.physics.new-theories, to all of which this general physics FAQ is cross-posted. Some of the more narrowly focussed physics newsgroups have their own FAQs, which can, of course, be found in the appropriate newsgroups. Sci.Physics is an unmoderated newsgroup dedicated to the discussion of physics, news from the physics community, and physics-related social issues. Sci.Physics.Research is a moderated newgroup designed to offer an environment with less traffic and more opportunity for discussion of serious topics in physics among experts and beginners alike. The current moderators of sci.physics.research are John Baez (baez@math.ucr.edu), William Johnson (mwj@beta.lanl.gov), Cameron Randale (Dale) Bass (crb7q@kelvin.seas.Virginia.edu), and Lee Sawyer (sawyer@utahep.uta.edu). Sci.physics.cond-matter is an unmoderated newsgroup dedicated to the discussion of the physics of condensed matter. Sci.physics.particle is an unmoderated newsgroup dedicated to the discussion of all aspects of particle physics by people with all levels of expertise. Alt.sci.physics.new-theories is an open forum for discussion of any topics related to conventional or unconventional physics. In this context, "unconventional physics" includes any ideas on physical science, whether or not they are widely accepted by the mainstream physics community. People from a wide variety of non-physics backgrounds, as well as students and experts in all areas of physics participate in the ongoing discussions on these newsgroups. Professors, industrial scientists, graduate students, etc., are all on hand to bring physics expertise to bear on almost any question. But the only requirement for participation is interest in physics, so feel free to post -- but before you do, please do the following: (1) Read this posting, a.k.a., the FAQ. It contains good answers, contributed by the readership, to some of the most frequently asked questions. (2) Understand "netiquette." If you are not sure what this means, subscribe to news.announce.newusers and read the excellent discussion of proper net behavior that is posted there periodically. (3) Be aware that there is another newsgroup dedicated to the discussion of "alternative" physics. It is alt.sci.physics.new-theories, and is the appropriate forum for discussion of physics ideas which are not widely accepted by the physics community. Sci.Physics is not the group for such discussions. A quick look at articles posted to both groups will make the distinction apparent. (4) Read the responses already posted in the thread to which you want to contribute. If a good answer is already posted, or the point you wanted to make has already been made, let it be. Old questions have probably been thoroughly discussed by the time you get there -- save bandwidth by posting only new information. Post to as narrow a geographic region as is appropriate. If your comments are directed at only one person, try E-mail. (5) Get the facts right! Opinions may differ, but facts should not. It is very tempting for new participants to jump in with quick answers to physics questions posed to the group. But it is very easy to end up feeling silly when people barrage you with corrections. So before you give us all a physics lesson you'll regret -- look it up. (6) Don't post textbook problems in the hope that someone will do your homework for you. Do your own homework; it's good for you. On the other hand, questions, even about elementary physics, are always welcome. So if you want to discuss the physics which is relevent to your homework, feel free to do so. Be warned that you may still have plenty of work to do, trying to figure out which of the many answers you get are correct. (7) Be prepared for heated discussion. People have strong opinions about the issues, and discussions can get a little "loud" at times. Don't take it personally if someone seems to always jump all over everything you say. Everyone was jumping all over everybody long before you got there! You can keep the discussion at a low boil by trying to stick to the facts. Clearly separate facts from opinion -- don't let people think you are confusing your opinions with scientific truth. And keep the focus of discussion on the ideas, not the people who post them. (8) Tolerate everyone. People of many different points of view, and widely varying educational backgrounds from around the world participate in this newsgroup. Respect for others will be returned in kind. Personal criticism is usually not welcome. ******************************************************************************** Item 2. The Care and Feeding of Kill Files updated 28-SEP-1993 by SIC ---------------------------------- original by Scott I. Chase With most newsreaders, it is possible for you to selectively ignore articles with certain title words, or by a certain author. This feature is implemented as a "kill file," which contains instructions to your newsreader about how to filter out unwanted articles. The exact details on how to specify articles you want to ignore varies from program to program, so you should check the documentation for your particular newsreader. Some examples are given below for a few common newsreaders. If your newsreader does not support kill files, you may want to consider upgrading to one that does. Some of the more popular newsreaders that support kill files are rn, trn, nn, xrn, gnews, and gnus. Let's say that you wish to `kill' all posts made by a certain user. Using the `rn' or `trn' newsreader, you would type a [CTRL]-K while in read mode to begin editing the kill file, and then type the following: /From: username@sitename.com/h:j This will look for articles that come with "From: username@sitename.com" in the header, junk them, and then display the subject lines of titles that just got zapped. To kill articles by Subject titles, you would type something like this: /: *The Big Bang Never Happened/:j /: *Space Potatoes Have Inertia/:j When finished, save the kill file in the normal manner for the editor you're using. In trn 3.0 and higher you can use the faster command /username@sitename\.com/f:j to kill all of username's postings. In trn change the 'j' to ',' to kill all the replies as well. Note the '\' to escape the '.'. This is needed in any search string in a kill file (although they usually work if you forget). Also in [t]rn you can simply hit K to automatically killfile the current subject without directly editing the file. For the `nn' newsreader, type a capital K when viewing the contents of a newsgroup. nn will then ask you a few questions on whether it is a Subject or a Name, duration of time that the posts are to be killed, etc. Simply answer the questions accordingly. There's a lot more to it, of course, when you become proficient. You can kill all articles cross-posted to specific groups, for example, or kill any article with a particular name or phrase appearing anywhere in the header. A good primer is in the "rn KILL file FAQ" which appears periodically in news.answers. You should also check the man pages for your particular newsreader. ******************************************************************************** Item 3. slightly updated 1-AUG-1995 by MW updated 5-DEC-1994 by SIC original by Scott I. Chase Accessing and Using Online Physics Resources -------------------------------------------- (I) Physical Constants These are available on the Web, at URL http://physics.nist.gov/PhysRefData/codata86/codata86.html (II) Particle Physics Databases The Full Listings of the Review of Particle Properties (RPP), as well as other particle physics databases, are accessible on-line. Here is a summary of the major ones, as described in the RPP: (A) SLAC Databases PARTICLES - Full listings of the RPP HEP - Guide to particle physics preprints, journal articles, reports, theses, conference papers, etc. CONF - Listing of past and future conferences in particle physics HEPNAMES - E-mail addresses of many HEP people INST - Addresses of HEP institutions DATAGUIDE - Adjunct to HEP, indexes papers REACTIONS - Numerical data on reactions (cross-sections, polarizations, etc) EXPERIMENTS - Guide to current and past experiments Anyone with a SLAC account can access these databases. Alternately, most of us can access them via QSPIRES. You can access QSPIRES via BITNET with the 'send' command ('tell','bsend', or other system-specific command) or by using E-mail. For example, send QSPIRES@SLACVM FIND TITLE Z0 will get you a search of HEP for all papers which reference the Z0 in the title. By E-mail, you would send the one line message "FIND TITLE Z0" with a blank subject line to QSPIRES@SLACVM.BITNET or QSPIRES@VM.SLAC.STANFORD.EDU. QSPIRES is free. Help can be obtained by mailing "HELP" to QSPIRES. For more detailed information, see the RPP, p.I.12, or contact: Louise Addis (ADDIS@SLACVM.BITNET) or Harvey Galic (GALIC@SLACVM.BITNET). (B) CERN Databases on ALICE LIB - Library catalogue of books, preprints, reports, etc. PREP - Subset of LIB containing preprints, CERN publications, and conference papers. CONF - Subset of LIB containing upcoming and past conferences since 1986 DIR - Directory of Research Institutes in HEP, with addresses, fax, telex, e-mail addresses, and info on research programs ALICE can be accessed via DECNET or INTERNET. It runs on the CERN library's VXLIB, alias ALICE.CERN.CH (IP# 128.141.201.44). Use Username ALICE (no password required.) Remote users with no access to the CERN Ethernet can use QALICE, similar to QSPIRES. Send E-mail to QALICE@VXLIB.CERN.CH, put the query in the subject field and leave the message field blank. For more information, send the subject "HELP" to QALICE or contact CERN Scientific Information Service, CERN, CH-1211 Geneva 23, Switzerland, or E-mail MALICE@VXLIB.CERN.CH. Regular weekly or monthly searches of the CERN databases can be arranged according to a personal search profile. Contact David Dallman, CERN SIS (address above) or E-mail CALLMAN@CERNVM.CERN.CH. DIR is available in Filemaker PRO format for Macintosh. Contact Wolfgang Simon (ISI@CERNVM.CERN.CH). (C) Particle Data Group Online Service The Particle Data Group is maintaining a new user-friendly computer database of the Full Listings from the Review of Particle Properties. Users may query by paper, particle, mass range, quantum numbers, or detector and can select specific properties or classes of properties like masses or decay parameters. All other relevant information (e.g. footnotes and references) is included. Complete instructions are available online. The last complete update of the RPP database was a copy of the Full Listings from the Review of Particle Properties which was published as Physical Review D45, Part 2 (1 June 1992). A subsequent update made on 27 April 1993 was complete for unstable mesons, less complete for the W, Z, D mesons, and stable baryons, and otherwise was unchanged from the 1992 version. DECNET access: SET HOST MUSE or SET HOST 42062 TCP/IP access: TELNET MUSE.LBL.GOV or TELNET 131.243.48.11 Login to: PDG_PUBLIC with password HEPDATA. Contact: Gary S. Wagman, (510)486-6610. Email: (GSWagman@LBL.GOV). (D) Other Databases Durham-RAL and Serpukhov both maintain large databases containing Particle Properties, reaction data, experiments, E-mail ID's, cross-section compilations (CS), etc. Except for the Serpukhov CS, these databases overlap SPIRES at SLAC considerably, though they are not the same and may be more up-to-date. For details, see the RPP, p.I.14, or contact: For Durham-RAL, Mike Whalley (MRW@UKACRL.BITNET,MRW@CERNVM.BITNET) or Dick Roberts (RGR@UKACRL.BITNET). For Serpukhov, contact Sergey Alekhin (ALEKHIN@M9.IHEP.SU) or Vladimir Exhela (EZHELA@M9.IHEP.SU). (III) Online Preprint Sources There are a number of online sources of preprints: alg-geom@publications.math.duke.edu (algebraic geometry) astro-ph@babbage.sissa.it (astrophysics) cond-mat@babbage.sissa.it (condensed matter) funct-an@babbage.sissa.it (functional analysis) e-mail@babbage.sissa.it (e-mail address database) hep-lat@ftp.scri.fsu.edu (computational and lattice physics) hep-ph@xxx.lanl.gov (high energy physics phenomenological) hep-th@xxx.lanl.gov (high energy physics theoretical) hep-ex@xxx.lanl.gov (high energy physics experimental) lc-om@alcom-p.cwru.edu (liquid crystals, optical materials) gr-qc@xxx.lanl.gov (general relativity, quantum cosmology) nucl-th@xxx.lanl.gov, (nuclear physics theory) nlin-sys@xyz.lanl.gov (nonlinear science) Note that babbage.sissa.it also mirrors hep-ph, hep-th and gr-qc. To get things if you know the preprint number, send a message to the appropriate address with subject header "get (preprint number)" and no message body. If you *don't* know the preprint number, or want to get preprints regularly, or want other information, send a message with subject header "help" and no message body. On the Web, some of these preprint archive databases are accessible at url http://xxx.lanl.gov/. The following GOPHER servers which are concerned with physics are currently running on the Internet. They mainly provide a full-text indexed archive to the preprint mailing lists: xyz.lanl.gov, port 70 (LANL Nonlinear Sciences) mentor.lanl.gov,70 ('traditional' preprint lists) babbage.sissa.it,70 ('traditional' preprint lists) physinfo.uni-augsburg.de,70 (all lists, but only abstracts) (IV) Mailing Lists In addition to the preprint services already described, there are several mailing lists that allow one to regularly receive material via email. To get a long list of many of them, send mail to LISTSERV@LISTSERV.NET with the following command in the text (not the subject) of your message: LISTS global To subscribe, send mail to LISTSERV@LISTSERV.NET with the following command in the text (not the subject) of your message: SUBSCRIBE where is the name of the list. Example: SUBSCRIBE PHYSICS Isaac Newton Here are a few of the physics-related lists: ACC-PHYS Preprint server for Accelerator Physics ALPHA-L L3 Alpha physics block analysis diagram group ASTRO-PH Preprint server for Astrophysics FUSION Redistribution of sci.physics.fusion OPTICS-L Optics Newsletter PHYS-L Forum for Physics Teachers PHYS-STU Physics Student Discussion List PHYSHARE Sharing resources for high school physics PHYSIC-L Physics List PHYSICS Physics Discussion POLYMER Polymer-related discussions and announcements POLYMERP Polymer Physics discussions SPACE sci.space.tech Digest SUP-COND SuperConductivity List WKSPHYS Workshop Physics List The AIP runs several mailing lists. The server is "listserv@aip.org". Leave the subject line blank, and send text of "help" and "longindex" on separate lines for a general help file and description of the mailing lists. Three mailing lists are physnews a digest of physics news items arising from physics meetings, physics journals, newspapers and magazines, and other news sources. Physics News Update appears approximately once a week. pen summarizes information on resources, national initiatives, outreach programs, grants, professional development opportunities, and publications related to physics and science education. It is issued twice a month. fyi summarizes science policy developments in Washington affecting the physics and astronomy community. It is issued between two and five times every week. To add yourself to a mailing list, send the command add
in the text of a message to the server. Example: add user@aip.org fyi (V) The World Wide Web There is a wealth of information, on all sorts of topics, available on the World Wide Web [WWW], a distributed HyperText system (a network of documents connected by links which can be activated electronically). Subject matter includes some physics areas such as High Energy Physics, Astrophysics abstracts, and Space Science, but also includes such diverse subjects as bioscience, music, and the law. * How to get to the Web If you have no clue what WWW is, you can go over the Internet with telnet to info.cern.ch (no login required) which brings you to the WWW Home Page at CERN. You are now using the simple line mode browser. To move around the Web, enter the number given after an item. * Browsing the Web If you have a WWW browser up and running, you can move around more easily. The by far nicest way of "browsing" through WWW uses the X-Terminal based tool "XMosaic". Binaries for many platforms (ready for use) and sources are available via anonymous FTP from ftp.ncsa.uiuc.edu in directory Web/xmosaic. The general FTP repository for browser software is info.cern.ch (including a hypertext browser/editor for NeXTStep 3.0) * For Further Information For questions related to WWW, try consulting the WWW-FAQ: Its most recent version is available via anonymous FTP on rtfm.mit.edu in /pub/usenet/news.answers/www-faq , or on WWW at http://www.vuw.ac.nz:80/non-local/gnat/www-faq.html The official contact (in fact the midwife of the World Wide Web) is Tim Berners-Lee, timbl@info.cern.ch. For general matters on WWW, try www-request@info.cern.ch or Robert Cailliau (responsible for the "physics" content of the Web, cailliau@cernnext.cern.ch). * Finding stuff on the Web The URL http://www.yahoo.com is one good starting place for locating information; for example, http://www.yahoo.com/Reference/Scientific_Constants will get you to a list of scientific constants. (V) Other Archive Sites http://pdg.lbl.gov/cpep/adventure.html This page is part of the Contemporary Physics Education Project. (A) FreeHEP The FreeHEP collection of software, useful to high energy physicists is available on the Web as http://heplibw3.slac.stanford.edu:80/FIND/FHMAIN.HTML or anonymous ftp to freehep.scri.fsu.edu. This is high-energy oriented but has much which is useful to other fields also. Contact Saul Youssef (youssef@scri.fsu.edu) for more information. (B) AIP Archives An archive of the electronic newsletters of the American Institute of Physics is now available on nic.hep.net. The three publications are "For Your Information", "The Physics News Update" written by Dr. Phil Schewe, and "What's New" written by Dr. Robert Park". FYI is archived as [ANON_FTP.AIP-FYI.199*]AIPFYI-nnn-mmmddyyyy.TXT. PNU is archived as [ANON_FTP.PHYSICS-NEWS.199*]PHYSICS-NEWS-yyyy-mm-dd.TXT. WN is archived as [ANON_FTP.WHATS-NEW.199*]WHATS-NEW-yyyy-mm-dd.TXT In each case, the last issue received is always available as: latest.txt. (C) There is an FTP archive site of preprints and programs for nonlinear dynamics, signal processing, and related subjects on node lyapunov.ucsd.edu (132.239.86.10) at the Institute for Nonlinear Science, UCSD. Just login anonymously, using your host id as your password. Contact Matt Kennel (mbk@inls1.ucsd.edu) for more information. (VI) Physics Education Online (A) Mailing Lists PHYS-L PHYS-L@UWF Forum for Physics Teachers PHYS-STU PHYS-STU@UWF Physics Student Discussion List (B) On the Web The Computers in Physics Education Committee of the AAPT has endorsed a project to have a site which would point to the all the known physics education resources on the net. Alan Cairns has agreed to maintain the site until the AAPT is convinced to put some funding into maintaining it. The current URL is: http://www.halcyon.com/cairns/physics.html This project is still in its infancy - anyone with an interest in physics education is invited to take a look. Your submissions will allow the site to grow into a mature resource. Contact: acairns@halcyon.com. ******************************************************************************** Item 4. original Vijay D. Fafat updated 28-JUL-1994 by SIC A Physics Booklist - Recommendations from the Net ------------------------------------------------- This article is a complilation of books recommended by sci.physics participants as the 'standard' or 'classic' texts on a wide variety of topics of general interest to physicists and physics students. As a guide to finding the right book for you, many of the comments from the contributors have been retained. This document is still under construction. Many entries are incomplete, and many good books are not yet listed. Please feel free to contribute to this project. Contact pvfafat@GSB.UChicago.EDU, who will compile the information for future updates. The formatting and organization of this article will also be reviewed and improved in future updates. This is the first try, and it shows. Please bear with us. Subject Index ------------- You can find books in the area of your choice by searching forward for the following keywords: General Physics Classical Mechanics Classical Electromagnetism Quantum Mechanics Statistical Mechanics Condensed Matter Special Relativity Particle Physics General Relativity Mathematical Methods Nuclear Physics Cosmology Astronomy Plasma Physics Numerical Methods/Simulations Fluid Dynamics Nonlinear Dynamics, Complexity and Chaos Optics (Classical and Quantum), Lasers Mathematical Phyiscs Atomic Phyiscs Low Temperature Physics, Superconductivity ------------------------------ Subject: General Physics (so even mathematicians can understand it!) 1] M. S. Longair, Theoretical concepts in physics, 1986. An alternative view of theoretical reasoning in Physics for final year undergrads. 2] Sommerfeld, Arnold - Lectures on Theoretical Physics Sommerfeld is God for mathematical physics. 3] Feynman, R: The Feynman lectures on Physics - 3 vols. 4] Walker, Jearle: The Flying Circus of Physics Note: There is the entire Landau and Lifshitz series. They have volumes on classical mechanics, classical field theory, E&M, QM, QFT, Statistical Physics, and more. Very good series that spans entire graduate level curriculum. 5] The New physics / edited by Paul Davies. This is one *big* book to go through and takes time to look through topics as diverse as general relativity, astrophysics, particle theory, quantum mechanics, chaos and nonlinearity, low temperature physics and phase transitions. Nevertheless, this is one excellent book of recent (1989) physics articles, written by several physicists/astrophysicists. 6] QED : The strange theory of light and matter / Richard P. Feynman. One need no longer be confused by this beautiful theory. Richard Feynman gives an exposition that is once again and by itself a beautiful explanation of the theory of photon-matter interactions. ------------------------------ Subject: Classical Mechanics 1] Goldstein, Herbert "Classical Mechanics", 2nd ed, 1980. intermediate to advanced; excellent bibliography 2] Introductory: The Feyman Lectures, vol 1. 3] Symon, Keith - Mechanics, 3rd ed., 1971 undergrad level. 4] Corbin, H and Stehle, P - Classical Mechanics, 2nd ed., 1960 5] V.I. Arnold, Mathematical methods of classical mechanics, translated by K. Vogtmann and A. Weinstein, 2nd ed., 1989. The appendices are somewhat more advanced and cover all sorts of nifty topics. Deals with Geometrical aspects of classical mechanics 6] Resnick, R and Halliday, D - Physics, vol 1, 4th Ed., 1993 Excellent introduction without much calculus. Lots of problems and review questions. 7] Marion, J & Thornton, "Classical Dynamics of Particles and Systems", 2nd ed., 1970. Undergrad level. A useful intro to classical dynamics. Not as advanced as Goldstein, but with real worked-out examples. 8] Fetter, A and Walecka, J: Theoretical mechanics of particles and continua. graduate level text, a little less impressive than Goldstein (and sometimes a little less obtuse) 9] Many-Particle Physics, G. Mahan 10] Fetter & Walecka: Theoretical Mechanics of Particles and Continua. ------------------------------ Subject: Classical Electromagnetism 1] Jackson, J. D. "Classical Electrodynamics", 2nd ed., 1975 intermediate to advanced. 2] a] Edward Purcell, Berkely Physics Series Vol 2. You can't beat this for the intelligent, reasonably sophisticated beginning physics student. He tells you on the very first page about the experimental proof of how charge does not vary with speed. b] Chen, Min, Berkeley Physics problems with solutions. 3] Reitz, J, Milford, F and Christy, R: Foundations of Electromagnetic Theory 3rd ed., 1979 Undergraduate level. Pretty difficult to learn from at first, but good reference, for some calculations involving stacks of thin films and their reflectance and transmission properties, for eg. It's a good, rigorous text as far as it goes, which is pretty far, but not all the way. For example, they have a great section on optical properties of a single thin film between two dielectric semi-infinate media, but no generalization to stacks of films. 4] Feynman, R: Feynman Lectures, vol 2 5] Lorrain, P & Corson D: Electromagnetism, Principles and Applications, 1979 6] Resnick, R and Halliday, D: Physics, vol 2, 4th ed., 1993 7] Igor Irodov, Problems in Physics. Excellent and extensive collection of EM problems for undergrads. 8] Smythe, William: Static and Dynamic Electricity, 3rd ed., 1968 For the extreme masochists. Some of the most hair-raising EM problems you'll ever see. Definitely not for the weak-of-heart. 9] Landau, Lifschitz, and Pitaevskii, "Electrodynamics of Continuous Media," 2nd ed., 1984 same level as Jackson and with lots of material not in Jackson. 10] Marion, J and Heald, M: "Classical Electromagnetic Radiation," 2nd ed., 1980 undergraduate or low-level graduate level ------------------------------ Subject: Quantum Mechanics 1] Cohen-Tannoudji, "Quantum Mechanics I & II", 1977. introductory to intermediate. 2] Liboff - Introductory Quantum Mechanics, 2nd ed., 1992 elementary level. Makes a few mistakes. 3] Sakurai, J - Modern Quantum Mechanics, 1985 4] Sakurai, J - Advanced Quantum Mechanics, 1967 Good as an introduction to the very basic beginnings of quantum field theory, except that it has the unfortunate feature of using 'imaginary time' to make Minkowski space look Euclidean. 5] Wheeler, J and Zurek, W (eds.) Quantum Theory and Measurement, 1983 On the philosophical end. People who want to know about interpretations of quantum mechanics should definitely look at this collection of relevant articles. 6] DeWitt, C and Neill Graham: The Many Worlds Interpretation of Quantum Mechanics Philosophical. Collection of articles. 7] Everett, H: "Theory of the Universal Wavefunction" An exposition which has some gems on thermodynamics and probability. Worth reading for this alone. 8] Bjorken, J and Drell, S - Relativistic Quantum Mechanics/ Relativistic Quantum Fields (for comments, see under Particle Physics) 9] Ryder, Lewis - Quantum Field Theory, 1984 10] Guidry, M - Gauge Field Theories : an introduction with applications, 1991 11] Messiah, A: Quantum Mechanics, 1961 12] Dirac, Paul: a] Principles of QM, 4th ed., 1958 b] Lectures in QM, 1964 c] Lectures on Quantum Field Theory, 1966 13] Itzykson, C and Zuber, J: Quantum Field Theory, 1980 Very advanced level. 14] Slater, J: "Quantum theory: Address, essays, lectures. Good follow on to Schiff. note: Schiff, Bjorken and Drell, Fetter and Walecka, and Slater are all volumes in "International Series in pure and Applied Physics" published by McGraw Hill. 15] Pierre Ramond, Field Theory: A Modern Primer, 2nd edition. Volume 74 in the FiP series. The so-called "revised printing" is a must, as they must've rushed the first printing of the 2nd edition, and it's full of inexcusable mistakes. 16] Feynman, R: Lectures - vol III : A non-traditional approach. A good place to get an intuitive feel for QM, if one already knows the traditional approach. &&&&&&& 17] Heitler & London, "Quantum theory of molecules"?? 18] Bell: Speakable and Unspeakable in Quantum Mechanics, 1987 An excellent collection of essays on the philosophical aspects of QM. 19] Milonni: The quantum vacuum: an introduction to quantum electrodynamics 1994. 20] Holland: The Quantum Theory of Motion A good bet for strong foundation in QM. 21] John Von Neumann: Mathematical foundations of quantum mechanics, 1955. For the more mathematical side of quantum theory, especially for those who are going to be arguing about measurement theory. 22] Schiff, Leonard, L: Quantum Mechanics, 3rd ed., 1968 A little old. Not much emphasis on airy-fairy things like many worlds or excessive angst over Heisenberg UP. Straight up QM for people who want to do calculations. Introductory gradauate level. Mostly Schrod. eqn. Spin included, but only in an adjunct to Schrod. Not much emphasis on things like Dirac eqn., etc. 23] "Quantum Physics of Atoms, Molecules, Solids, Nuclei, and Particles" by Eisberg and Resnick, 2nd ed., 1985. This is a basic intro. to QM, and it is excellent for undergrads. It is not thorough with math, but fills in a lot of the intuitive stuff that most textbooks do not present. 24] Elementary Quantum Mechanics, David Saxon It's a decent undergraduate (senior level) text. 25] Intermediate Quantum Mechanics, Bethe and Jackiw ------------------------------ Subject: Statistical Mechanics 1] David Chandler, "Introduction to Modern Statistical Mechanics", 1987 2] Kittel & Kroemer: Statistical Thermodynamics. Best of a bad lot. 3] Reif, F : Principles of statistical and thermal physics. the big and little Reif stat mech books. Big Reif is much better than Kittel & Kroemer. He uses clear language but avoids the handwaving that thermodynamics often gives rise to. More classical than QM oriented. 4] Bloch, Felix: Fundamentals of Statistical Mechanics. 5] Radu Balescu "Statistical Physics" Graduate Level. Good description of non-equilibrium stat. mech. but difficult to read. It is all there, but often you don't realize it until after you have learned it somewhere else. Nice development in early chapters about parallels between classical and quantum Stat. Mech. 6] Huang (grad) The following 6 books deal with modern topics in (mostly) classical statistical mechanics, namely, the central notions of linear response theory (Forster) and critical phenomena (the rest) at level suitable for beginning graduate students. 7] Thermodynamics, by H. Callen. 8] Statistical Mechanics, by R. K. Pathria 9] Hydrodynamic Fluctuations, Broken Symmetry, and Correlation Functions, by D. Forster 10] Introduction to Phase Transitions and Critical Phenomena, by H. E. Stanley 11] Modern Theory of Critical Phenomena, by S. K. Ma 12] Lectures on Phase Transitions and the Renormalization Group, by N. Goldenfeld 13] Methods of Quantum Field Theory in Statistical Physics, Abrikosov, Gorkov, and Dyzaloshinski ------------------------------ Subject: Condensed Matter 1] Charles Kittel, "Introduction to Solid State Physics" (ISSP), introductory 2] Ashcroft and Mermin, "Solid State Physics", interm to advanced 3] Charles Kittel, Quantum Theory of Solids. This is from before the days of his ISSP; it is a more advanced book. At a similar level... 4] Solid State Theory, by W. A. Harrison (a great bargain now that it's published by Dover) 5] Theory of Solids, by Ziman. 6] Fundamentals of the Theory of Metals, by Abrikosov Half of the book is on superconductivity. ------------------------------ Subject: Special Relativity 1] Taylor and Wheeler, _Spacetime Physics_ Still the best introduction out there. 2] "Relativity" : Einstein's popular exposition. 3] Wolfgang Rindler, Essential Relativity. Springer 1977 With a heavy bias towards astrophysics and therefore on a more moderate level formally. Quite strong on intuition. 4] A P French: Special Relativity A through introductory text. Good discussion of the twin paradox, pole and the barn etc. Plenty of diagrams illustrating lorentz transformed co-ordinates, giving both an algebraic and geometrical insight to SR. ------------------------------ Subject: Particle Physics 1] Kerson Huang, Quarks, leptons & gauge fields, World Scientific, 1982. Good on mathematical aspects of gauge theory and topology. 2] L. B. Okun, Leptons and quarks, translated from Russian by V. I. Kisin, North-Holland, 1982. 3] T. D. Lee, Particle physics and introduction to field theory. 4] Itzykson: Particle Physics 5] Bjorken & Drell: "Relativistic Quantum Mechanics" One of the more terse books. The first volume on Relativistic quantum mechanics covers the subject in a blinding 300 pages. Very good if you *really* want to know the subject. 6] Francis Halzen & Alan D. Martin, "Quarks & Leptons", beginner to intermediate, this is a standard textbook for graduate level courses. Good knowledge of quantum mechanics and special relativity is assumed. A very good introduction to the concepts of particle physics. Good examples, but not a lot of Feynman diagram calculation. For this, see Bjorken & Drell. 7] Donald H. Perkins: Introduction to high energy physics Regarded by many people in the field as the best introductory text at the undergraduate level. Covers basically everything with almost no mathematics. 8] Close,Marten, and Sutton: The Particle Explosion. A popular exposition of the history of particle physics with terrific photography. 9] Christine Sutton: Spaceship Neutrino A good, historical, largely intuitive introduction to particle physics, seen from the neutrino viewpoint. ------------------------------ Subject: General Relativity 1] The telephone book, er, that is, MTW, Meisner, Thorne and Wheeler. The "bible". W. H. Freeman & Co., San Francisco 1973 2] Robert M. Wald, Space, Time, and Gravity : the Theory of the Big Bang and Black Holes. A good nontechnical introduction, with a nice mix of mathematical rigor and comprehensible physics. 3] Schutz: First Course in General Relativity. 4] Weinberg: Gravitation and Cosmology Good reference book, but not a very good read. 5] Hans Ohanian: Gravitation & Spacetime (recently back in print) For someone who actually wants to learn to work problems, ideal for self-teaching, and math is introduced as needed, rather than in a colossal blast. 6] Robert Wald, General Relativity It's a more advanced textbook than Wald's earlier book, appropriate for an introductory graduate course in GR. It strikes just the right balance, in my opinion, between mathematical rigor and physical intuition. It has great mathematics appendices for those who care about proving theorems carefully, and a good introduction to the problems behind quantum gravity (although not to their solutions). I think it's MUCH better than either MTW or Weinberg. ------------------------------ Subject: Mathematical Methods (so that even physicists can understand it!) 1] Morse and Feshbach - Methods of Theoretical Physics (can be hard to find) 2] Mathews and Walker, Mathematical Methods for Physicists. An absolute joy for those who love math, and very informative even for those who don't. 3] Arfken "Mathematical Methods for Physicists" Academic Press Good introduction at graduate level. Not comprehensive in any area, but covers many areas widely. Arfken is to math methods what numerical recipes is to numerical methods -- good intro, but not the last word. 4] Zwillinger "Handbook of Differential Equations." Academic Press Kind of like CRC tables but for ODE's and PDE's. Good reference book when you've got a Diff. Eq. and wnat to find a solution. 5] Gradshteyn and Ryzhik "Table of Integrals, Series, and Products" Academic THE book of integrals. Huge, but useful when you need an integral. ------------------------------ Subject: Nuclear Physics 1] Preston and Bhaduri, "Structure of the Nucleus" 2] Blatt and Weisskopf - Theoretical Nuclear Physics 3] DeShalit and Feshbach - Theoretical Nuclear Physics This is serious stuff. Also quite expensive even in paper. I think the hard cover is out of print. This is volume I (structure). Volume II (scattering) is also available. 4] Satchler: "Direct Nuclear Reactions". ------------------------------ Subject: Cosmology 1] J. V. Narlikar, Introduction to Cosmology.1983 Jones & Bartlett Publ. For people with a solid background in physics and higher math, THE introductory text, IMHO, because it hits the balance between mathematical accuracy (tensor calculus and stuff) and intuitive clarity/geometrical models very well for grad student level. Of course, it has flaws but only noticeable by the Real Experts (TM) ... 2] Hawking: Brief History of Time Popular Science 3] Weinberg: First Three Minutes A very good book. It's pretty old, but most of the information in it is still correct. 4] Timothy Ferris: Coming of Age in the Milky Way. Popular Science. 5] Kolb and Turner: The Early Universe. At a more advanced level, a standard reference. As the title implies, K&T cover mostly the strange physics of very early times: it's heavy on the particle physics, and skimps on the astrophysics. There's a primer on large-scale structure, which is the most active area of cosmological research, but it's really not all that good. 6] Peebles: Principles of Physical Cosmology. Comprehensive, and on the whole it's quite a good book, but it's rather poorly organized. I find myself jumping back and forth through the book whenever I want to find anything. 7] "Black Holes and Warped Spacetime", by William J. Kaufmann, III. This is a great, fairly thorough, though non-mathematical description of black holes and spacetime as it relates to cosmology. I was impressed by how few mistakes Kaufmann makes in simplifying, while most such books tend to sacrifice accuracy for simplicity. 8] "Principles of Cosmology and Gravitation", Berry, M. V. This is very well-written, and useful as an undergrad text. 9] Dennis Overbye: Lonely Hearts of the Cosmos The unfinished history of converge on Hubble's constant is presented, from the perspective of competing astrophysics rival teams and institute, along with a lot of background on cosmology (a lot on inflation, for instance). A good insight into the scientific process. 10] The big bang / Joseph Silk. I consider Silk's book an absolute must for those who want a quick run at the current state of big bang cosmology and some of the recent (1988)issues which have given so many of us lots of problems to solve. 10] Bubbles, voids, and bumps in time : the new cosmology / edited by James Cornell. This is quite a nice and relatively short read for some of the pressing issues (as of 1987-88) in astrophysical cosmology. 11] Structure formation in the universe / T. Padmanabhan. A no-nonsense book for those who want to calculate some problems strictly related to the formation of structure in the universe. The book even comes complete with problems at the end of each chapter. A bad thing about this book is that there isn't any coverage on clusters of galaxies and the one really big thing that annoys the hell outta me is that the bibliography for *each* chapter is all combined in one big bibliography towards the end of the book which makes for lots of page flipping. 12] The large-scale structure of the universe / by P. J. E. Peebles. This is a definitive book for anyone who desires an understanding of the mathematics required to develop the theory for models of large scale structure. The essential techniques in the description of how mass is able to cluster under gravity from a smooth early universe are discussed. While I find it dry in some places, there are noteworthy sections (e.g. statistical tests, n-point correlation functions, etc.). ------------------------------ Subject: Astronomy 1] Hannu Karttunen et al. (eds.): Fundamental Astronomy. The best book covering all of astronomy (also for absolute beginners) AND still going into a lot of detail for special work for people more involved AND presenting excellent graphics and pictures. 2] Pasachoff: Contemporary Astronomy Good introductory textbook for the nontechnical reader. It gives a pretty good overview of the important topics, and it has good pictures. 3] Shu, Frank: The physical universe : an introduction to astronomy, 4] Astrophysical formulae : a compendium for the physicist and astrophysicist / Kenneth R. Lang. Here is everything you wanted to know (and more!) about astrophysical formulae on a one-line/one-parargraph/one-shot deal. Of course, the formulae come complete with references (a tad old, mind you) but it's a must for everyone who's working in astronomy and astrophysics. You learn something new everytime you flip through the pages! ------------------------------ Subject: Plasma Physics (See Robert Heeter's sci.phys.fusion FAQ for details) ------------------------------ Subject: Numerical Methods/Simulations 1] Johnson and Rees "Numerical Analysis" Addison Wesley Undergrad. level broad intro. 2] Numerical Recipes in X (X=c,fortran,pascal,etc) Tueklosky and Press 3] Young and Gregory "A survey of Numerical Mathmematics" Dover 2 volumes. Excellent overview at grad. level. Emphasis toward solution of elliptic PDE's, but good description of methods to get there including linear algebra, Matrix techniques, ODE solving methods, and interpolation theory. Biggest strength is it provides a coherent framework and structure to attach most commonly used num. methods. This helps understanding about why to use one method or another. 2 volumes. 4]Hockney and Eastwood "Computer Simulation Using Particles" Adam Hilger Good exposition of particle-in-cell (PIC) method and extensions. Applications to plasmas, astronmy, and solid state are discussed. Emphasis is on description of algortihms. Some results shown. 5] Birdsall and Langdon "Plasma Physics via Computer Simulations" PIC simulation applied to plasmas. Source codes shown. First part is almost a tutorial on how to do PIC. Second part is like a series of review articles on different PIC methods. 6] Tajima "Computational Plasma Physics: With Applications to Fusion and Astrophysics" Addison Wesley Frontiers in physics Series. Algorthims described. Emphasis on physics that can be simulated. Applications limited to plasmas, but subjest areas very broad, fusion, cosmology, solar astrophysics, magnetospheric physics, plasma turbulence, general astrophysics. ------------------------------ Subject: Fluid Dynamics 1] Triton "Physical Fluid Dynamics" 2] Batchelor 3] Chandreshekar ------------------------------ Subject: Nonlinear Dynamics, Complexity, and Chaos There is a FAQ posted regularly to sci.nonlinear. 1] Prigogine, "Exploring Complexity" Or any other Prigogine book. If you've read one, you read most of all of them (A Poincare recurrance maybe?) 2] Guckenheimer and Holmes "Nonlinear Oscillations, Dynamical Systems, and Bifurcations of Vector Fields" Springer Borderline phys/math. Advanced level. Nuts and bolts how to textbook. No Saganesque visionary thing from the authors. They let the topic provide all the razz-ma-tazz, which is plenty if you pay attention and remember the physics that it applies to. 3] Lichtenberg, A. J. and M. A. Lieberman (1982). Regular and Stochastic Motion. New York, Springer-Verlag. 4] "The Dreams Of Reason" by Heinz Pagels. He is a very clear and interesting, captivating writer, and presents the concepts in a very intuitive way. The level is popular science, but it is still useful for physicists who know little of complexity. 5] M.Mitchell Waldrop: Complexity. A popular intro to the subject of spontaneous orders, complexity and so on. Covers implications for economics, biology etc and not just physics. ------------------------------ Subject: Optics (Classical and Quantum), Lasers 1] Born and Wolf standard reference. 2] Sommerfeld, A: For the more classically minded 3] Allen and Eberly's Optical Resonance and Two-Level Atoms. For quantum optics, the most readable but most limited. 4] Quantum Optics and Electronics (Les Houches summer school 1963-or-4, but someone has claimed that Gordon and Breach, NY, are going to republish it in 1995), edited by DeWitt, Blandin, and Cohen- Tannoudji, is noteworthy primarily for Glauber's lectures, which form the basis of quantum optics as it is known today. 5] Sargent, Scully, & Lamb: Laser Physics 6] Yariv: Quantum Electronics 7] Siegman: Lasers 8] Shen: The Principles of Nonlinear Optics 9] Meystre & Sargent: Elements of Quantum Optics 10] Cohen-Tannoudji, Dupont-Roc, & Grynberg: Photons, Atoms and Atom-Photon Interactions. 11] Hecht: Optics A very good intro optics book (readable by a smart college freshman, but useful as a reference to the graduate student) 12] "Practical Holography" by Graham Saxby, Prentice Hall: New York; 1988. This is a very clear and detailed book that is an excellent introduction to holography for interested undergraduate physics people, as well as advanced readers, esp. those who are interested in the practical details of making holograms and the theory behind them. ------------------------------ Subject: Mathematical Physics (Lie Algebra, Topology, Knot Theory, Tensors, etc.) These are books that are sort of talky and fun to read (but still substantial - some harder than others). These include things mathematicians can read about physics as well as vice versa. These books are different than the "bibles" one must have on hand at all times to do mathematical physics. 1] Yvonne Choquet-Bruhat, Cecile DeWitt-Morette, and Margaret Dillard-Bleick, Analysis, manifolds, and physics (2 volumes) Something every mathematical physicist should have at her bedside until she knows it inside and out - but some people say it's not especially easy to read. 2] Jean Dieudonne, A panorama of pure mathematics, as seen by N. Bourbaki, translated by I.G. Macdonald. Gives the big picture in math. 3] Robert Hermann, Lie groups for physicists, Benjamin-Cummings, 1966. 4] George Mackey, Quantum mechanics from the point of view of the theory of group representations, Mathematical Sciences Research Institute, 1984. 5] George Mackey, Unitary group representations in physics, probability, and number theory. 6] Charles Nash and S. Sen, Topology and geometry for physicists. 7] B. Booss and D.D. Bleecker, Topology and analysis: the Atiyah-Singer index formula and gauge-theoretic physics. 8] Bamberg and S. Sternberg, A Course of Mathematics for Students of Physics. 9] Bishop & Goldberg: Tensor Analysis on Manifolds. 10] Flanders : Differential Forms with applications to the Physical Sciences. 11] Dodson & Poston Tensor Geometry. 12] von Westenholz: Differential forms in Mathematical Physics. 13] Abraham, Marsden & Ratiu: Manifolds, Tensor Analysis and Applications. 14] M. Nakahara, Topology, Geometry and Physics. 15] Morandi: The Role of Topology in Classical and Quantum Physics 16] Singer, Thorpe: Lecture Notes on Elemetary Topology and Geometry 17] L. Kauffman: Knots and Physics, World Scientific, Singapore, 1991. 18] Yang, C and Ge, M: Braid group, Knot Theory & Statistical Mechanics. 19] Kastler, D: C-algebras and their applications to Statistical Mechanics and Quantum Field Theory. 20] Courant and Hilbert "Methods of Mathematical Physics" Wiley Really a math book in disguise. Emphasis on ODE's and PDE's. Proves existence, etc. Very comprehensive. 2 volumes. 21] Cecille Dewitt: is publishing a book on manifolds that should be out soon (maybe already is). Very high level, but supposedly of great importance for anyone needing to set the Feynman path integral in a firm foundation. 22] Howard Georgi, "Lie Groups for Particle Phyiscs" Addison Wesley Frontiers in Physics Series. 23] Synge and Schild ------------------------------ Subject: Atomic Physics 1] Born and Wolf: A classic, though a little old. ------------------------------ Subject: Low Temperature Physics, Superconductivity (high and low Tc), etc. 1] The Theory of Quantum Liquids, by D. Pines and P. Nozieres 2] Superconductivity of Metals and Alloys, P. G. DeGennes A classic introduction. 3] Theory of Superconductivity, J. R. Schrieffer 4] Superconductivity, M. Tinkham 5] Experimental techniques in low-temperature physics / by Guy K. White. This is considered by many as a "bible" for those working in experimental low temperature physics. Thanks to the contributors who made this compilation possible, including, but not limited to olivers@physics.utoronto.ca, cpf@alchemy.ithaca.NY.US, glowboy@robot.nuceng.ufl.edu, jgh1@iucf.indiana.edu, p675cen@mpifr-bonn. mpg.de, ted@physics.Berkeley.EDU, Jeremy_Caplan@postoffice.brown.edu, baez@ucrmath.UCR.EDU, greason@ptdcs2.intel.com, dbd@utkux.utcc.utk.edu, roberts@alpha.brooks.af.mil, rev@NBSENH.BITNET, cotera@aspen.uml.edu, panetta@cithe503.cithep.caltech.edu, johncobb@emx.cc.utexas.edu, exunikh @exu.ericsson.se, bergervo@prl.philips.nl, aephraim@physics5.berkeley.edu, zowie@daedalus.stanford.edu, jean@sitka.triumf.ca, price@price.demon.co.uk, palmer@sfu.ca, Benjamin.J.Tilly@dartmouth.edu, jac@ds8.scri.fsu.edu, BLYTHE@BrandonU.CA, alec@phys.oxy.edu, gelfand@lamar.ColoState.EDU, lee@aries.yorku.ca ******************************************************************************** Item 5. The Nobel Prize for Physics (1901-1993) updated 12-OCT-1994 by SIC --------------------------------------- original by Scott I. Chase The following is a complete listing of Nobel Prize awards, from the first award in 1901. Prizes were not awarded in every year. The description following the names is an abbreviation of the official citation. 1901 Wilhelm Konrad Roentgen X-rays 1902 Hendrik Antoon Lorentz Magnetism in radiation phenomena Pieter Zeeman 1903 Antoine Henri Bequerel Spontaneous radioactivity Pierre Curie Marie Sklodowska-Curie 1904 Lord Rayleigh Density of gases and (a.k.a. John William Strutt) discovery of argon 1905 Pilipp Eduard Anton von Lenard Cathode rays 1906 Joseph John Thomson Conduction of electricity by gases 1907 Albert Abraham Michelson Precision meteorological investigations 1908 Gabriel Lippman Reproducing colors photographically based on the phenomenon of interference 1909 Guglielmo Marconi Wireless telegraphy Carl Ferdinand Braun 1910 Johannes Diderik van der Waals Equation of state of fluids 1911 Wilhelm Wien Laws of radiation of heat 1912 Nils Gustaf Dalen Automatic gas flow regulators 1913 Heike Kamerlingh Onnes Matter at low temperature 1914 Max von Laue Crystal diffraction of X-rays 1915 William Henry Bragg X-ray analysis of crystal structure William Lawrence Bragg 1917 Charles Glover Barkla Characteristic X-ray spectra of elements 1918 Max Planck Energy quanta 1919 Johannes Stark Splitting of spectral lines in E fields 1920 Charles-Edouard Guillaume Anomalies in nickel steel alloys 1921 Albert Einstein Photoelectric Effect 1922 Niels Bohr Structure of atoms 1923 Robert Andrew Millikan Elementary charge of electricity 1924 Karl Manne Georg Siegbahn X-ray spectroscopy 1925 James Franck Impact of an electron upon an atom Gustav Hertz 1926 Jean Baptiste Perrin Sedimentation equilibrium 1927 Arthur Holly Compton Compton effect Charles Thomson Rees Wilson Invention of the Cloud chamber 1928 Owen Willans Richardson Thermionic phenomena, Richardson's Law 1929 Prince Louis-Victor de Broglie Wave nature of electrons 1930 Sir Chandrasekhara Venkata Raman Scattering of light, Raman effect 1932 Werner Heisenberg Quantum Mechanics 1933 Erwin Schrodinger Atomic theory Paul Adrien Maurice Dirac 1935 James Chadwick The neutron 1936 Victor Franz Hess Cosmic rays Carl D. Anderson The positron 1937 Clinton Joseph Davisson Crystal diffraction of electrons George Paget Thomson 1938 Enrico Fermi New radioactive elements 1939 Ernest Orlando Lawrence Invention of the Cyclotron 1943 Otto Stern Proton magnetic moment 1944 Isador Isaac Rabi Magnetic resonance in atomic nuclei 1945 Wolfgang Pauli The Exclusion principle 1946 Percy Williams Bridgman Production of extremely high pressures 1947 Sir Edward Victor Appleton Physics of the upper atmosphere 1948 Patrick Maynard Stuart Blackett Cosmic ray showers in cloud chambers 1949 Hideki Yukawa Prediction of Mesons 1950 Cecil Frank Powell Photographic emulsion for meson studies 1951 Sir John Douglas Cockroft Artificial acceleration of atomic Ernest Thomas Sinton Walton particles and transmutation of nuclei 1952 Felix Bloch Nuclear magnetic precision methods Edward Mills Purcell 1953 Frits Zernike Phase-contrast microscope 1954 Max Born Fundamental research in QM Walther Bothe Coincidence counters 1955 Willis Eugene Lamb Hydrogen fine structure Polykarp Kusch Electron magnetic moment 1956 William Shockley Transistors John Bardeen Walter Houser Brattain 1957 Chen Ning Yang Parity violation Tsung Dao Lee 1958 Pavel Aleksejevic Cerenkov Interpretation of the Cerenkov effect Il'ja Mickajlovic Frank Igor' Evgen'evic Tamm 1959 Emilio Gino Segre The Antiproton Owen Chamberlain 1960 Donald Arthur Glaser The Bubble Chamber 1961 Robert Hofstadter Electron scattering on nucleons Rudolf Ludwig Mossbauer Resonant absorption of photons 1962 Lev Davidovic Landau Theory of liquid helium 1963 Eugene P. Wigner Fundamental symmetry principles Maria Goeppert Mayer Nuclear shell structure J. Hans D. Jensen 1964 Charles H. Townes Maser-Laser principle Nikolai G. Basov Alexander M. Prochorov 1965 Sin-Itiro Tomonaga Quantum electrodynamics Julian Schwinger Richard P. Feynman 1966 Alfred Kastler Study of Hertzian resonance in atoms 1967 Hans Albrecht Bethe Energy production in stars 1968 Luis W. Alvarez Discovery of many particle resonances 1969 Murray Gell-Mann Quark model for particle classification 1970 Hannes Alfven Magneto-hydrodynamics in plasma physics Louis Neel Antiferromagnetism and ferromagnetism 1971 Dennis Gabor Principles of holography 1972 John Bardeen Theory of superconductivity Leon N. Cooper J. Robert Schrieffer 1973 Leo Esaki Tunneling in superconductors Ivar Giaever Brian D. Josephson Super-current through tunnel barriers 1974 Antony Hewish Discovery of pulsars Sir Martin Ryle Pioneering radioastronomy work 1975 Aage Bohr Structure of the atomic nucleus Ben Mottelson James Rainwater 1976 Burton Richter Discovery of the J/Psi particle Samual Chao Chung Ting 1977 Philip Warren Anderson Electronic structure of magnetic and Nevill Francis Mott disordered solids John Hasbrouck Van Vleck 1978 Pyotr Kapitsa Liquefaction of helium Arno A. Penzias Cosmic Microwave Background Radiation Robert W. Wilson 1979 Sheldon Glashow Electroweak Theory, especially Steven Weinberg weak neutral currents Abdus Salam 1980 James Cronin Discovery of CP violation in the Val Fitch asymmetric decay of neutral K-mesons 1981 Kai M. Seigbahn High resolution electron spectroscopy Nicolaas Bloembergen Laser spectroscopy Arthur L. Schawlow 1982 Kenneth G. Wilson Critical phenomena in phase transitions 1983 Subrahmanyan Chandrasekhar Evolution of stars William A. Fowler 1984 Carlo Rubbia Discovery of W,Z Simon van der Meer Stochastic cooling for colliders 1985 Klaus von Klitzing Discovery of quantum Hall effect 1986 Gerd Binning Scanning Tunneling Microscopy Heinrich Rohrer Ernst August Friedrich Ruska Electron microscopy 1987 Georg Bednorz High-temperature superconductivity Alex K. Muller 1988 Leon Max Lederman Discovery of the muon neutrino leading Melvin Schwartz to classification of particles in Jack Steinberger families 1989 Hans Georg Dehmelt Penning Trap for charged particles Wolfgang Paul Paul Trap for charged particles Norman F. Ramsey Control of atomic transitions by the separated oscillatory fields method 1990 Jerome Isaac Friedman Deep inelastic scattering experiments Henry Way Kendall leading to the discovery of quarks Richard Edward Taylor 1991 Pierre-Gilles de Gennes Order-disorder transitions in liquid crystals and polymers 1992 Georges Charpak Multiwire Proportional Chamber 1993 Russell A. Hulse Discovery of the first binary pulsar Joseph H. Taylor and subsequent tests of GR 1994 Bertram N. Brockhouse Neutron scattering experiments Clifford G. Shull ******************************************************************************** END OF PART 1/4 Article: 5896 of sci.physics.particle Path: senator-bedfellow.mit.edu!bloom-beacon.mit.edu!paperboy.osf.org!mogul.osf.org!columbus From: columbus@osf.org Newsgroups: sci.physics,sci.physics.research,sci.physics.cond-matter,sci.physics.particle,alt.sci.physics.new-theories,sci.answers,alt.answers,news.answers Subject: sci.physics Frequently Asked Questions (Part 2 of 4) Supersedes: Followup-To: sci.physics Date: 13 Oct 1995 14:40:54 GMT Organization: Open Software Foundation Lines: 1355 Approved: news-answers-request@MIT.EDU Distribution: world Expires: 17-Nov 1995 Message-ID: References: Reply-To: columbus@osf.org (Michael Weiss) NNTP-Posting-Host: mogul.osf.org Summary: This posting contains a list of Frequently Asked Questions (and their answers) about physics, and should be read by anyone who wishes to post to the sci.physics.* newsgroups. Keywords: Sci.physics FAQ X-Posting-Frequency: posted monthly Originator: columbus@mogul.osf.org Xref: senator-bedfellow.mit.edu sci.physics:147071 sci.physics.research:3041 sci.physics.cond-matter:556 sci.physics.particle:5896 alt.sci.physics.new-theories:21139 sci.answers:3264 alt.answers:12765 news.answers:55202 Posted-By: auto-faq 3.1.1.2 Archive-name: physics-faq/part2 -------------------------------------------------------------------------------- FREQUENTLY ASKED QUESTIONS ON SCI.PHYSICS - Part 2/4 -------------------------------------------------------------------------------- Item 6. Gravitational Radiation updated 20-May-1992 by SIC ----------------------- original by Scott I. Chase Gravitational Radiation is to gravity what light is to electromagnetism. It is produced when massive bodies accelerate. You can accelerate any body so as to produce such radiation, but due to the feeble strength of gravity, it is entirely undetectable except when produced by intense astrophysical sources such as supernovae, collisions of black holes, etc. These are quite far from us, typically, but they are so intense that they dwarf all possible laboratory sources of such radiation. Gravitational waves have a polarization pattern that causes objects to expand in one direction, while contracting in the perpendicular direction. That is, they have spin two. This is because gravity waves are fluctuations in the tensorial metric of space-time. All oscillating radiation fields can be quantized, and in the case of gravity, the intermediate boson is called the "graviton" in analogy with the photon. But quantum gravity is hard, for several reasons: (1) The quantum field theory of gravity is hard, because gauge interactions of spin-two fields are not renormalizable. See Cheng and Li, Gauge Theory of Elementary Particle Physics (search for "power counting"). (2) There are conceptual problems - what does it mean to quantize geometry, or space-time? It is possible to quantize weak fluctuations in the gravitational field. This gives rise to the spin-2 graviton. But full quantum gravity has so far escaped formulation. It is not likely to look much like the other quantum field theories. In addition, there are models of gravity which include additional bosons with different spins. Some are the consequence of non-Einsteinian models, such as Brans-Dicke which has a spin-0 component. Others are included by hand, to give "fifth force" components to gravity. For example, if you want to add a weak repulsive short range component, you will need a massive spin-1 boson. (Even-spin bosons always attract. Odd-spin bosons can attract or repel.) If antigravity is real, then this has implications for the boson spectrum as well. The spin-two polarization provides the method of detection. Most experiments to date use a "Weber bar." This is a cylindrical, very massive, bar suspended by fine wire, free to oscillate in response to a passing graviton. A high-sensitivity, low noise, capacitive transducer can turn the oscillations of the bar into an electric signal for analysis. So far such searches have failed. But they are expected to be insufficiently sensitive for typical radiation intensity from known types of sources. A more sensitive technique uses very long baseline laser interferometry. This is the principle of LIGO (Laser Interferometric Gravity wave Observatory). This is a two-armed detector, with perpendicular laser beams each travelling several km before meeting to produce an interference pattern which fluctuates if a gravity wave distorts the geometry of the detector. To eliminate noise from seismic effects as well as human noise sources, two detectors separated by hundreds to thousands of miles are necessary. A coincidence measurement then provides evidence of gravitational radiation. In order to determine the source of the signal, a third detector, far from either of the first two, would be necessary. Timing differences in the arrival of the signal to the three detectors would allow triangulation of the angular position in the sky of the signal. The first stage of LIGO, a two detector setup in the U.S., has been approved by Congress in 1992. LIGO researchers have started designing a prototype detector, and are hoping to enroll another nation, probably in Europe, to fund and be host to the third detector. The speed of gravitational radiation (C_gw) depends upon the specific model of Gravitation that you use. There are quite a few competing models (all consistent with all experiments to date) including of course Einstein's but also Brans-Dicke and several families of others. All metric models can support gravity waves. But not all predict radiation travelling at C_gw = C_em. (C_em is the speed of electromagnetic waves.) There is a class of theories with "prior geometry", in which, as I understand it, there is an additional metric which does not depend only on the local matter density. In such theories, C_gw != C_em in general. However, there is good evidence that C_gw is in fact at least almost C_em. We observe high energy cosmic rays in the 10^20-10^21 eV region. Such particles are travelling at up to (1-10^-18)*C_em. If C_gw < C_em, then particles with C_gw < v < C_em will radiate Cerenkov gravitational radiation into the vacuum, and decelerate from the back reaction. So evidence of these very fast cosmic rays is good evidence that C_gw >= (1-10^-18)*C_em, very close indeed to C_em. Bottom line: in a purely Einsteinian universe, C_gw = C_em. However, a class of models not yet ruled out experimentally does make other predictions. A definitive test would be produced by LIGO in coincidence with optical measurements of some catastrophic event which generates enough gravitational radiation to be detected. Then the "time of flight" of both gravitons and photons from the source to the Earth could be measured, and strict direct limits could be set on C_gw. For more information, see Gravitational Radiation (NATO ASI - Les Houches 1982), specifically the introductory essay by Kip Thorne. ******************************************************************************** Item 7. IS ENERGY CONSERVED IN GENERAL RELATIVITY? original by Michael Weiss ------------------------------------------ and John Baez In special cases, yes. In general--- it depends on what you mean by "energy", and what you mean by "conserved". In flat spacetime (the backdrop for special relativity) you can phrase energy conservation in two ways: as a differential equation, or as an equation involving integrals (gory details below). The two formulations are mathematically equivalent. But when you try to generalize this to curved spacetimes (the arena for general relativity) this equivalence breaks down. The differential form extends with nary a hiccup; not so the integral form. The differential form says, loosely speaking, that no energy is created in any infinitesimal piece of spacetime. The integral form says the same for a finite-sized piece. (This may remind you of the "divergence" and "flux" forms of Gauss's law in electrostatics, or the equation of continuity in fluid dynamics. Hold on to that thought!) An infinitesimal piece of spacetime "looks flat", while the effects of curvature become evident in a finite piece. (The same holds for curved surfaces in space, of course). GR relates curvature to gravity. Now, even in Newtonian physics, you must include gravitational potential energy to get energy conservation. And GR introduces the new phenomenon of gravitational waves; perhaps these carry energy as well? Perhaps we need to include gravitational energy in some fashion, to arrive at a law of energy conservation for finite pieces of spacetime? Casting about for a mathematical expression of these ideas, physicists came up with something called an energy pseudo-tensor. (In fact, several of 'em!) Now, GR takes pride in treating all coordinate systems equally. Mathematicians invented tensors precisely to meet this sort of demand--- if a tensor equation holds in one coordinate system, it holds in all. Pseudo-tensors are not tensors (surprise!), and this alone raises eyebrows in some circles. In GR, one must always guard against mistaking artifacts of a particular coordinate system for real physical effects. (See the FAQ entry on black holes for some examples.) These pseudo-tensors have some rather strange properties. If you choose the "wrong" coordinates, they are non-zero even in flat empty spacetime. By another choice of coordinates, they can be made zero at any chosen point, even in a spacetime full of gravitational radiation. For these reasons, most physicists who work in general relativity do not believe the pseudo-tensors give a good *local* definition of energy density, although their integrals are sometimes useful as a measure of total energy. One other complaint about the pseudo-tensors deserves mention. Einstein argued that all energy has mass, and all mass acts gravitationally. Does "gravitational energy" itself act as a source of gravity? Now, the Einstein field equations are G_{mu,nu} = 8pi T_{mu,nu} Here G_{mu,nu} is the Einstein curvature tensor, which encodes information about the curvature of spacetime, and T_{mu,nu} is the so-called stress-energy tensor, which we will meet again below. T_{mu,nu} represents the energy due to matter and electromagnetic fields, but includes NO contribution from "gravitational energy". So one can argue that "gravitational energy" does NOT act as a source of gravity. On the other hand, the Einstein field equations are non-linear; this implies that gravitational waves interact with each other (unlike light waves in Maxwell's (linear) theory). So one can argue that "gravitational energy" IS a source of gravity. In certain special cases, energy conservation works out with fewer caveats. The two main examples are static spacetimes and asymptotically flat spacetimes. Let's look at four examples before plunging deeper into the math. Three examples involve redshift, the other, gravitational radiation. (1) Very fast objects emitting light. According to *special* relativity, you will see light coming from a receding object as redshifted. So if you, and someone moving with the source, both measure the light's energy, you'll get different answers. Note that this has nothing to do with energy conservation per se. Even in Newtonian physics, kinetic energy (mv^2/2) depends on the choice of reference frame. However, relativity serves up a new twist. In Newtonian physics, energy conservation and momentum conservation are two separate laws. Special relativity welds them into one law, the conservation of the *energy-momentum 4-vector*. To learn the whole scoop on 4-vectors, read a text on SR, for example Taylor and Wheeler (see refs.) For our purposes, it's enough to remark that 4-vectors are vectors in spacetime, which most people privately picture just like ordinary vectors (unless they have *very* active imaginations). (2) Very massive objects emitting light. Light from the Sun appears redshifted to an Earthbound astronomer. In quasi-Newtonian terms, we might say that light loses kinetic energy as it climbs out of the gravitational well of the Sun, but gains potential energy. General relativity looks at it differently. In GR, gravity is described not by a "potential" but by the "metric" of spacetime. But "no problem", as the saying goes. The Schwarzschild metric describes spacetime around a massive object, if the object is spherically symmetrical, uncharged, and "alone in the universe". The Schwarzschild metric is both static and asymptotically flat, and energy conservation holds without major pitfalls. For further details, consult MTW, chapter 25. (3) Gravitational waves. A binary pulsar emits gravitational waves, according to GR, and one expects (innocent word!) that these waves will carry away energy. So its orbital period should change. Einstein derived a formula for the rate of change (known as the quadrapole formula), and in the centenary of Einstein's birth, Russell Hulse and Joseph Taylor reported that the binary pulsar PSR1913+16 bore out Einstein's predictions within a few percent. Hulse and Taylor were awarded the Nobel prize in 1993. Despite this success, Einstein's formula remained controversial for many years, partly because of the subtleties surrounding energy conservation in GR. The need to understand this situation better has kept GR theoreticians busy over the last few years. Einstein's formula now seems well-established, both theoretically and observationally. (4) Expansion of the universe leading to cosmological redshift. The Cosmic Background Radiation (CBR) has red-shifted over billions of years. Each photon gets redder and redder. What happens to this energy? Cosmologists model the expanding universe with Friedmann-Robertson-Walker (FRW) spacetimes. (The familiar "expanding balloon speckled with galaxies" belongs to this class of models.) The FRW spacetimes are neither static nor asymptotically flat. Those who harbor no qualms about pseudo-tensors will say that radiant energy becomes gravitational energy. Others will say that the energy is simply lost. It's time to look at mathematical fine points. There are many to choose from! The definition of asymptotically flat, for example, calls for some care (see Stewart); one worries about "boundary conditions at infinity". (In fact, both spatial infinity and "null infinity" clamor for attention--- leading to different kinds of total energy.) The static case has close connections with Noether's theorem (see Goldstein or Arnold). If the catch-phrase "time translation symmetry implies conservation of energy" rings a bell (perhaps from quantum mechanics), then you're on the right track. (Check out "Killing vector" in the index of MTW, Wald, or Sachs and Wu.) But two issues call for more discussion. Why does the equivalence between the two forms of energy conservation break down? How do the pseudo-tensors slide around this difficulty? We've seen already that we should be talking about the energy-momentum 4-vector, not just its time-like component (the energy). Let's consider first the case of flat Minkowski spacetime. Recall that the notion of "inertial frame" corresponds to a special kind of coordinate system (Minkowskian coordinates). Pick an inertial reference frame. Pick a volume V in this frame, and pick two times t=t_0 and t=t_1. One formulation of energy-momentum conservation says that the energy-momentum inside V changes only because of energy-momentum flowing across the boundary surface (call it S). It is "conceptually difficult, mathematically easy" to define a quantity T so that the captions on the Equation 1 (below) are correct. (The quoted phrase comes from Sachs and Wu.) Equation 1: (valid in flat Minkowski spacetime, when Minkowskian coordinates are used) t=t_1 / / / | | | | T dV - | T dV = | T dt dS / / / V,t=t_0 V,t=t_1 t=t_0 p contained p contained p flowing out through in volume V - in volume V = boundary S of V at time t_0 at time t_1 during t=t_0 to t=t_1 (Note: p = energy-momentum 4-vector) T is called the stress-energy tensor. You don't need to know what that means! ---just that you can integrate T, as shown, to get 4-vectors. Equation 1 may remind you of Gauss's theorem, which deals with flux across a boundary. If you look at Equation 1 in the right 4-dimensional frame of mind, you'll discover it really says that the flux across the boundary of a certain 4-dimensional hypervolume is zero. (The hypervolume is swept out by V during the interval t=t_0 to t=t_1.) MTW, chapter 7, explains this with pictures galore. (See also Wheeler.) A 4-dimensional analogue to Gauss's theorem shows that Equation 1 is equivalent to: Equation 2: (valid in flat Minkowski spacetime, with Minkowskian coordinates) coord_div(T) = sum_mu (partial T/partial x_mu) = 0 We write "coord_div" for the divergence, for we will meet another divergence in a moment. Proof? Quite similar to Gauss's theorem: if the divergence is zero throughout the hypervolume, then the flux across the boundary must also be zero. On the other hand, the flux out of an infinitesimally small hypervolume turns out to be the divergence times the measure of the hypervolume. Pass now to the general case of any spacetime satisfying Einstein's field equation. It is easy to generalize the differential form of energy-momentum conservation, Equation 2: Equation 3: (valid in any GR spacetime) covariant_div(T) = sum_mu nabla_mu(T) = 0 (where nabla_mu = covariant derivative) (Side comment: Equation 3 is the correct generalization of Equation 1 for SR when non-Minkowskian coordinates are used.) GR relies heavily on the covariant derivative, because the covariant derivative of a tensor is a tensor, and as we've seen, GR loves tensors. Equation 3 follows from Einstein's field equation (because something called Bianchi's identity says that covariant_div(G)=0). But Equation 3 is no longer equivalent to Equation 1! Why not? Well, the familiar form of Gauss's theorem (from electrostatics) holds for any spacetime, because essentially you are summing fluxes over a partition of the volume into infinitesimally small pieces. The sum over the faces of one infinitesimal piece is a divergence. But the total contribution from an interior face is zero, since what flows out of one piece flows into its neighbor. So the integral of the divergence over the volume equals the flux through the boundary. "QED". But for the equivalence of Equations 1 and 3, we would need an extension of Gauss's theorem. Now the flux through a face is not a scalar, but a vector (the flux of energy-momentum through the face). The argument just sketched involves adding these vectors, which are defined at different points in spacetime. Such "remote vector comparison" runs into trouble precisely for curved spacetimes. The mathematician Levi-Civita invented the standard solution to this problem, and dubbed it "parallel transport". It's easy to picture parallel transport: just move the vector along a path, keeping its direction "as constant as possible". (Naturally, some non-trivial mathematics lurks behind the phrase in quotation marks. But even pop-science expositions of GR do a good job explaining parallel transport.) The parallel transport of a vector depends on the transportation path; for the canonical example, imagine parallel transporting a vector on a sphere. But parallel transportation over an "infinitesimal distance" suffers no such ambiguity. (It's not hard to see the connection with curvature.) To compute a divergence, we need to compare quantities (here vectors) on opposite faces. Using parallel transport for this leads to the covariant divergence. This is well-defined, because we're dealing with an infinitesimal hypervolume. But to add up fluxes all over a finite-sized hypervolume (as in the contemplated extension of Gauss's theorem) runs smack into the dependence on transportation path. So the flux integral is not well-defined, and we have no analogue for Gauss's theorem. One way to get round this is to pick one coordinate system, and transport vectors so their *components* stay constant. Partial derivatives replace covariant derivatives, and Gauss's theorem is restored. The energy pseudo-tensors take this approach (at least some of them do). If you can mangle Equation 3 (covariant_div(T) = 0) into the form: coord_div(Theta) = 0 then you can get an "energy conservation law" in integral form. Einstein was the first to do this; Dirac, Landau and Lifshitz, and Weinberg all came up with variations on this theme. We've said enough already on the pros and cons of this approach. We will not delve into definitions of energy in general relativity such as the Hamiltonian (amusingly, the energy of a closed universe always works out to zero according to this definition), various kinds of energy one hopes to obtain by "deparametrizing" Einstein's equations, or "quasilocal energy". There's quite a bit to say about this sort of thing! Indeed, the issue of energy in general relativity has a lot to do with the notorious "problem of time" in quantum gravity.... but that's another can of worms. References (vaguely in order of difficulty): Clifford Will, "The renaissance of general relativity", in "The New Physics" (ed. Paul Davies) gives a semi-technical discussion of the controversy over gravitational radiation. Wheeler, "A Journey into Gravity and Spacetime". Wheeler's try at a "pop-science" treatment of GR. Chapters 6 and 7 are a tour-de-force: Wheeler tries for a non-technical explanation of Cartan's formulation of Einstein's field equation. It might be easier just to read MTW!) Taylor and Wheeler, "Spacetime Physics". Goldstein, "Classical Mechanics". Arnold, "Mathematical Methods in Classical Mechanics". Misner, Thorne, and Wheeler (MTW), "Gravitation", chapters 7, 20, and 25 Wald, "General Relativity", Appendix E. This has the Hamiltonian formalism and a bit about deparametrizing, and chapter 11 discusses energy in asymptotically flat spacetimes. H. A. Buchdahl, "Seventeen Simple Lectures on General Relativity Theory" Lecture 15 derives the energy-loss formula for the binary star, and criticizes the derivation. Sachs and Wu, "General Relativity for Mathematicians", chapter 3 John Stewart, "Advanced General Relativity". Chapter 3 ("Asymptopia") shows just how careful one has to be in asymptotically flat spacetimes to recover energy conservation. Stewart also discusses the Bondi-Sachs mass, another contender for "energy". Damour, in "300 Years of Gravitation" (ed. Hawking and Israel). Damour heads the "Paris group", which has been active in the theory of gravitational radiation. Penrose and Rindler, "Spinors and Spacetime", vol II, chapter 9. The Bondi-Sachs mass generalized. J. David Brown and James York Jr., "Quasilocal energy in general relativity", in "Mathematical Aspects of Classical Field Theory". ******************************************************************************** Item 8. Olbers' Paradox updated: 24-JAN-1993 by SIC --------------- original by Scott I. Chase Why isn't the night sky as uniformly bright as the surface of the Sun? If the Universe has infinitely many stars, then it should be. After all, if you move the Sun twice as far away from us, we will intercept one-fourth as many photons, but the Sun will subtend one-fourth of the angular area. So the areal intensity remains constant. With infinitely many stars, every angular element of the sky should have a star, and the entire heavens should be as bright as the sun. We should have the impression that we live in the center of a hollow black body whose temperature is about 6000 degrees Centigrade. This is Olbers' paradox. It can be traced as far back as Kepler in 1610. It was rediscussed by Halley and Cheseaux in the eighteen century, but was not popularized as a paradox until Olbers took up the issue in the nineteenth century. There are many possible explanations which have been considered. Here are a few: (1) There's too much dust to see the distant stars. (2) The Universe has only a finite number of stars. (3) The distribution of stars is not uniform. So, for example, there could be an infinity of stars, but they hide behind one another so that only a finite angular area is subtended by them. (4) The Universe is expanding, so distant stars are red-shifted into obscurity. (5) The Universe is young. Distant light hasn't even reached us yet. The first explanation is just plain wrong. In a black body, the dust will heat up too. It does act like a radiation shield, exponentially damping the distant starlight. But you can't put enough dust into the universe to get rid of enough starlight without also obscuring our own Sun. So this idea is bad. The premise of the second explanation may technically be correct. But the number of stars, finite as it might be, is still large enough to light up the entire sky, i.e., the total amount of luminous matter in the Universe is too large to allow this escape. The number of stars is close enough to infinite for the purpose of lighting up the sky. The third explanation might be partially correct. We just don't know. If the stars are distributed fractally, then there could be large patches of empty space, and the sky could appear dark except in small areas. But the final two possibilities are are surely each correct and partly responsible. There are numerical arguments that suggest that the effect of the finite age of the Universe is the larger effect. We live inside a spherical shell of "Observable Universe" which has radius equal to the lifetime of the Universe. Objects more than about 15 billion years old are too far away for their light ever to reach us. Historically, after Hubble discovered that the Universe was expanding, but before the Big Bang was firmly established by the discovery of the cosmic background radiation, Olbers' paradox was presented as proof of special relativity. You needed the red-shift (an SR effect) to get rid of the starlight. This effect certainly contributes. But the finite age of the Universe is the most important effect. References: Ap. J. _367_, 399 (1991). The author, Paul Wesson, is said to be on a personal crusade to end the confusion surrounding Olbers' paradox. _Darkness at Night: A Riddle of the Universe_, Edward Harrison, Harvard University Press, 1987 ******************************************************************************** Item 9. What is Dark Matter? updated 11-MAY-1993 by SIC -------------------- original by Scott I. Chase The story of dark matter is best divided into two parts. First we have the reasons that we know that it exists. Second is the collection of possible explanations as to what it is. Why the Universe Needs Dark Matter ---------------------------------- We believe that that the Universe is critically balanced between being open and closed. We derive this fact from the observation of the large scale structure of the Universe. It requires a certain amount of matter to accomplish this result. Call it M. We can estimate the total BARYONIC matter of the universe by studying Big Bang nucleosynthesis. This is done by connecting the observed He/H ratio of the Universe today to the amount of baryonic matter present during the early hot phase when most of the helium was produced. Once the temperature of the Universe dropped below the neutron-proton mass difference, neutrons began decaying into protons. If the early baryon density was low, then it was hard for a proton to find a neutron with which to make helium before too many of the neutrons decayed away to account for the amount of helium we see today. So by measuring the He/H ratio today, we can estimate the necessary baryon density shortly after the Big Bang, and, consequently, the total number of baryons today. It turns out that you need about 0.05 M total baryonic matter to account for the known ratio of light isotopes. So only 1/20 of the total mass of the Universe is baryonic matter. Unfortunately, the best estimates of the total mass of everything that we can see with our telescopes is roughly 0.01 M. Where is the other 99% of the stuff of the Universe? Dark Matter! So there are two conclusions. We only see 0.01 M out of 0.05 M baryonic matter in the Universe. The rest must be in baryonic dark matter halos surrounding galaxies. And there must be some non-baryonic dark matter to account for the remaining 95% of the matter required to give omega, the mass of the Universe, in units of critical mass, equal to unity. For those who distrust the conventional Big Bang models, and don't want to rely upon fancy cosmology to derive the presence of dark matter, there are other more direct means. It has been observed in clusters of galaxies that the motion of galaxies within a cluster suggests that they are bound by a total gravitational force due to about 5-10 times as much matter as can be accounted for from luminous matter in said galaxies. And within an individual galaxy, you can measure the rate of rotation of the stars about the galactic center of rotation. The resultant "rotation curve" is simply related to the distribution of matter in the galaxy. The outer stars in galaxies seem to rotate too fast for the amount of matter that we see in the galaxy. Again, we need about 5 times more matter than we can see via electromagnetic radiation. These results can be explained by assuming that there is a "dark matter halo" surrounding every galaxy. What is Dark Matter ------------------- This is the open question. There are many possibilities, and nobody really knows much about this yet. Here are a few of the many published suggestions, which are being currently hunted for by experimentalists all over the world. Remember, you need at least one baryonic candidate and one non-baryonic candidate to make everything work out, so there there may be more than one correct choice among the possibilities given here. (1) Normal matter which has so far eluded our gaze, such as (a) dark galaxies (b) brown dwarfs (c) planetary material (rock, dust, etc.) (2) Massive Standard Model neutrinos. If any of the neutrinos are massive, then this could be the missing mass. On the other hand, if they are too heavy, as the purported 17 KeV neutrino would have been, massive neutrinos create almost as many problems as they solve in this regard. (3) Exotica (See the "Particle Zoo" FAQ entry for some details) Massive exotica would provide the missing mass. For our purposes, these fall into two classes: those which have been proposed for other reasons but happen to solve the dark matter problem, and those which have been proposed specifically to provide the missing dark matter. Examples of objects in the first class are axions, additional neutrinos, supersymmetric particles, and a host of others. Their properties are constrained by the theory which predicts them, but by virtue of their mass, they solve the dark matter problem if they exist in the correct abundance. Particles in the second class are generally classed in loose groups. Their properties are not specified, but they are merely required to be massive and have other properties such that they would so far have eluded discovery in the many experiments which have looked for new particles. These include WIMPS (Weakly Interacting Massive Particles), CHAMPS, and a host of others. References: _Dark Matter in the Universe_ (Jerusalem Winter School for Theoretical Physics, 1986-7), J.N. Bahcall, T. Piran, & S. Weinberg editors. _Dark Matter_ (Proceedings of the XXIIIrd Recontre de Moriond) J. Audouze and J. Tran Thanh Van. editors. ******************************************************************************** Item 10. Some Frequently Asked Questions About Black Holes updated 02-FEB-1995 by MM ------------------------------------------------- original by Matt McIrvin Contents: 1. What is a black hole, really? 2. What happens to you if you fall in? 3. Won't it take forever for you to fall in? Won't it take forever for the black hole to even form? 4. Will you see the universe end? 5. What about Hawking radiation? Won't the black hole evaporate before you get there? 6. How does the gravity get out of the black hole? 7. Where did you get that information? 1. What is a black hole, really? In 1916, when general relativity was new, Karl Schwarzschild worked out a useful solution to the Einstein equation describing the evolution of spacetime geometry. This solution, a possible shape of spacetime, would describe the effects of gravity *outside* a spherically symmetric, uncharged, nonrotating object (and would serve approximately to describe even slowly rotating objects like the Earth or Sun). It worked in much the same way that you can treat the Earth as a point mass for purposes of Newtonian gravity if all you want to do is describe gravity *outside* the Earth's surface. What such a solution really looks like is a "metric," which is a kind of generalization of the Pythagorean formula that gives the length of a line segment in the plane. The metric is a formula that may be used to obtain the "length" of a curve in spacetime. In the case of a curve corresponding to the motion of an object as time passes (a "timelike worldline,") the "length" computed by the metric is actually the elapsed time experienced by an object with that motion. The actual formula depends on the coordinates chosen in which to express things, but it may be transformed into various coordinate systems without affecting anything physical, like the spacetime curvature. Schwarzschild expressed his metric in terms of coordinates which, at large distances from the object, resembled spherical coordinates with an extra coordinate t for time. Another coordinate, called r, functioned as a radial coordinate at large distances; out there it just gave the distance to the massive object. Now, at small radii, the solution began to act strangely. There was a "singularity" at the center, r=0, where the curvature of spacetime was infinite. Surrounding that was a region where the "radial" direction of decreasing r was actually a direction in *time* rather than in space. Anything in that region, including light, would be obligated to fall toward the singularity, to be crushed as tidal forces diverged. This was separated >from the rest of the universe by a place where Schwarzschild's coordinates blew up, though nothing was wrong with the curvature of spacetime there. (This was called the Schwarzschild radius. Later, other coordinate systems were discovered in which the blow-up didn't happen; it was an artifact of the coordinates, a little like the problem of defining the longitude of the North Pole. The physically important thing about the Schwarzschild radius was not the coordinate problem, but the fact that within it the direction into the hole became a direction in time.) Nobody really worried about this at the time, because there was no known object that was dense enough for that inner region to actually be outside it, so for all known cases, this odd part of the solution would not apply. Arthur Stanley Eddington considered the possibility of a dying star collapsing to such a density, but rejected it as aesthetically unpleasant and proposed that some new physics must intervene. In 1939, Oppenheimer and Snyder finally took seriously the possibility that stars a few times more massive than the sun might be doomed to collapse to such a state at the end of their lives. Once the star gets smaller than the place where Schwarzschild's coordinates fail (called the Schwarzschild radius for an uncharged, nonrotating object, or the event horizon) there's no way it can avoid collapsing further. It has to collapse all the way to a singularity for the same reason that you can't keep from moving into the future! Nothing else that goes into that region afterward can avoid it either, at least in this simple case. The event horizon is a point of no return. In 1971 John Archibald Wheeler named such a thing a black hole, since light could not escape from it. Astronomers have many candidate objects they think are probably black holes, on the basis of several kinds of evidence (typically they are dark objects whose large mass can be deduced from their gravitational effects on other objects, and which sometimes emit X-rays, presumably from infalling matter). But the properties of black holes I'll talk about here are entirely theoretical. They're based on general relativity, which is a theory that seems supported by available evidence. 2. What happens to you if you fall in? Suppose that, possessing a proper spacecraft and a self-destructive urge, I decide to go black-hole jumping and head for an uncharged, nonrotating ("Schwarzschild") black hole. In this and other kinds of hole, I won't, before I fall in, be able to see anything within the event horizon. But there's nothing *locally* special about the event horizon; when I get there it won't seem like a particularly unusual place, except that I will see strange optical distortions of the sky around me from all the bending of light that goes on. But as soon as I fall through, I'm doomed. No bungee will help me, since bungees can't keep Sunday from turning into Monday. I have to hit the singularity eventually, and before I get there there will be enormous tidal forces-- forces due to the curvature of spacetime-- which will squash me and my spaceship in some directions and stretch them in another until I look like a piece of spaghetti. At the singularity all of present physics is mute as to what will happen, but I won't care. I'll be dead. For ordinary black holes of a few solar masses, there are actually large tidal forces well outside the event horizon, so I probably wouldn't even make it into the hole alive and unstretched. For a black hole of 8 solar masses, for instance, the value of r at which tides become fatal is about 400 km, and the Schwarzschild radius is just 24 km. But tidal stresses are proportional to M/r^3. Therefore the fatal r goes as the cube root of the mass, whereas the Schwarzschild radius of the black hole is proportional to the mass. So for black holes larger than about 1000 solar masses I could probably fall in alive, and for still larger ones I might not even notice the tidal forces until I'm through the horizon and doomed. 3. Won't it take forever for you to fall in? Won't it take forever for the black hole to even form? Not in any useful sense. The time I experience before I hit the event horizon, and even until I hit the singularity-- the "proper time" calculated by using Schwarzschild's metric on my worldline -- is finite. The same goes for the collapsing star; if I somehow stood on the surface of the star as it became a black hole, I would experience the star's demise in a finite time. On my worldline as I fall into the black hole, it turns out that the Schwarzschild coordinate called t goes to infinity when I go through the event horizon. That doesn't correspond to anyone's proper time, though; it's just a coordinate called t. In fact, inside the event horizon, t is actually a *spatial* direction, and the future corresponds instead to decreasing r. It's only outside the black hole that t even points in a direction of increasing time. In any case, this doesn't indicate that I take forever to fall in, since the proper time involved is actually finite. At large distances t *does* approach the proper time of someone who is at rest with respect to the black hole. But there isn't any non-arbitrary sense in which you can call t at smaller r values "the proper time of a distant observer," since in general relativity there is no coordinate-independent way to say that two distant events are happening "at the same time." The proper time of any observer is only defined locally. A more physical sense in which it might be said that things take forever to fall in is provided by looking at the paths of emerging light rays. The event horizon is what, in relativity parlance, is called a "lightlike surface"; light rays can remain there. For an ideal Schwarzschild hole (which I am considering in this paragraph) the horizon lasts forever, so the light can stay there without escaping. (If you wonder how this is reconciled with the fact that light has to travel at the constant speed c-- well, the horizon *is* traveling at c! Relative speeds in GR are also only unambiguously defined locally, and if you're at the event horizon you are necessarily falling in; it comes at you at the speed of light.) Light beams aimed directly outward from just outside the horizon don't escape to large distances until late values of t. For someone at a large distance from the black hole and approximately at rest with respect to it, the coordinate t does correspond well to proper time. So if you, watching from a safe distance, attempt to witness my fall into the hole, you'll see me fall more and more slowly as the light delay increases. You'll never see me actually *get to* the event horizon. My watch, to you, will tick more and more slowly, but will never reach the time that I see as I fall into the black hole. Notice that this is really an optical effect caused by the paths of the light rays. This is also true for the dying star itself. If you attempt to witness the black hole's formation, you'll see the star collapse more and more slowly, never precisely reaching the Schwarzschild radius. Now, this led early on to an image of a black hole as a strange sort of suspended-animation object, a "frozen star" with immobilized falling debris and gedankenexperiment astronauts hanging above it in eternally slowing precipitation. This is, however, not what you'd see. The reason is that as things get closer to the event horizon, they also get *dimmer*. Light from them is redshifted and dimmed, and if one considers that light is actually made up of discrete photons, the time of escape of *the last photon* is actually finite, and not very large. So things would wink out as they got close, including the dying star, and the name "black hole" is justified. As an example, take the eight-solar-mass black hole I mentioned before. If you start timing from the moment the you see the object half a Schwarzschild radius away from the event horizon, the light will dim exponentially from that point on with a characteristic time of about 0.2 milliseconds, and the time of the last photon is about a hundredth of a second later. The times scale proportionally to the mass of the black hole. If I jump into a black hole, I don't remain visible for long. Also, if I jump in, I won't hit the surface of the "frozen star." It goes through the event horizon at another point in spacetime from where/when I do. (Some have pointed out that I really go through the event horizon a little earlier than a naive calculation would imply. The reason is that my addition to the black hole increases its mass, and therefore moves the event horizon out around me at finite Schwarzschild t coordinate. This really doesn't change the situation with regard to whether an external observer sees me go through, since the event horizon is still lightlike; light emitted at the event horizon or within it will never escape to large distances, and light emitted just outside it will take a long time to get to an observer, timed, say, from when the observer saw me pass the point half a Schwarzschild radius outside the hole.) All this is not to imply that the black hole can't also be used for temporal tricks much like the "twin paradox" mentioned elsewhere in this FAQ. Suppose that I don't fall into the black hole-- instead, I stop and wait at a constant r value just outside the event horizon, burning tremendous amounts of rocket fuel and somehow withstanding the huge gravitational force that would result. If I then return home, I'll have aged less than you. In this case, general relativity can say something about the difference in proper time experienced by the two of us, because our ages can be compared *locally* at the start and end of the journey. 4. Will you see the universe end? If an external observer sees me slow down asymptotically as I fall, it might seem reasonable that I'd see the universe speed up asymptotically-- that I'd see the universe end in a spectacular flash as I went through the horizon. This isn't the case, though. What an external observer sees depends on what light does after I emit it. What I see, however, depends on what light does before it gets to me. And there's no way that light from future events far away can get to me. Faraway events in the arbitrarily distant future never end up on my "past light-cone," the surface made of light rays that get to me at a given time. That, at least, is the story for an uncharged, nonrotating black hole. For charged or rotating holes, the story is different. Such holes can contain, in the idealized solutions, "timelike wormholes" which serve as gateways to otherwise disconnected regions-- effectively, different universes. Instead of hitting the singularity, I can go through the wormhole. But at the entrance to the wormhole, which acts as a kind of inner event horizon, an infinite speed-up effect actually does occur. If I fall into the wormhole I see the entire history of the universe outside play itself out to the end. Even worse, as the picture speeds up the light gets blueshifted and more energetic, so that as I pass into the wormhole an "infinite blueshift" happens which fries me with hard radiation. There is apparently good reason to believe that the infinite blueshift would imperil the wormhole itself, replacing it with a singularity no less pernicious than the one I've managed to miss. In any case it would render wormhole travel an undertaking of questionable practicality. 5. What about Hawking radiation? Won't the black hole evaporate before you get there? (First, a caveat: Not a lot is really understood about evaporating black holes. The following is largely deduced from information in Wald's GR text, but what really happens-- especially when the black hole gets very small-- is unclear. So take the following with a grain of salt.) Short answer: No, it won't. This demands some elaboration. From thermodynamic arguments Stephen Hawking realized that a black hole should have a nonzero temperature, and ought therefore to emit blackbody radiation. He eventually figured out a quantum- mechanical mechanism for this. Suffice it to say that black holes should very, very slowly lose mass through radiation, a loss which accelerates as the hole gets smaller and eventually evaporates completely in a burst of radiation. This happens in a finite time according to an outside observer. But I just said that an outside observer would *never* observe an object actually entering the horizon! If I jump in, will you see the black hole evaporate out from under me, leaving me intact but marooned in the very distant future from gravitational time dilation? You won't, and the reason is that the discussion above only applies to a black hole that is not shrinking to nil from evaporation. Remember that the apparent slowing of my fall is due to the paths of outgoing light rays near the event horizon. If the black hole *does* evaporate, the delay in escaping light caused by proximity to the event horizon can only last as long as the event horizon does! Consider your external view of me as I fall in. If the black hole is eternal, events happening to me (by my watch) closer and closer to the time I fall through happen divergingly later according to you (supposing that your vision is somehow not limited by the discreteness of photons, or the redshift). If the black hole is mortal, you'll instead see those events happen closer and closer to the time the black hole evaporates. Extrapolating, you would calculate my time of passage through the event horizon as the exact moment the hole disappears! (Of course, even if you could see me, the image would be drowned out by all the radiation from the evaporating hole.) I won't experience that cataclysm myself, though; I'll be through the horizon, leaving only my light behind. As far as I'm concerned, my grisly fate is unaffected by the evaporation. All of this assumes you can see me at all, of course. In practice the time of the last photon would have long been past. Besides, there's the brilliant background of Hawking radiation to see through as the hole shrinks to nothing. (Due to considerations I won't go into here, some physicists think that the black hole won't disappear completely, that a remnant hole will be left behind. Current physics can't really decide the question, any more than it can decide what really happens at the singularity. If someone ever figures out quantum gravity, maybe that will provide an answer.) 6. How does the gravity get out of the black hole? Purely in terms of general relativity, there is no problem here. The gravity doesn't have to get out of the black hole. General relativity is a local theory, which means that the field at a certain point in spacetime is determined entirely by things going on at places that can communicate with it at speeds less than or equal to c. If a star collapses into a black hole, the gravitational field outside the black hole may be calculated entirely from the properties of the star and its external gravitational field *before* it becomes a black hole. Just as the light registering late stages in my fall takes longer and longer to get out to you at a large distance, the gravitational consequences of events late in the star's collapse take longer and longer to ripple out to the world at large. In this sense the black hole *is* a kind of "frozen star": the gravitational field is a fossil field. The same is true of the electromagnetic field that a black hole may possess. Often this question is phrased in terms of gravitons, the hypothetical quanta of spacetime distortion. If things like gravity correspond to the exchange of "particles" like gravitons, how can they get out of the event horizon to do their job? Gravitons don't exist in general relativity, because GR is not a quantum theory. They might be part of a theory of quantum gravity when it is completely developed, but even then it might not be best to describe gravitational attraction as produced by virtual gravitons. See the FAQ on virtual particles for a discussion of this. Nevertheless, the question in this form is still worth asking, because black holes *can* have static electric fields, and we know that these may be described in terms of virtual photons. So how do the virtual photons get out of the event horizon? Well, for one thing, they can come from the charged matter prior to collapse, just like classical effects. In addition, however, virtual particles aren't confined to the interiors of light cones: they can go faster than light! Consequently the event horizon, which is really just a surface that moves at the speed of light, presents no barrier. I couldn't use these virtual photons after falling into the hole to communicate with you outside the hole; nor could I escape from the hole by somehow turning myself into virtual particles. The reason is that virtual particles don't carry any *information* outside the light cone. See the FAQ on virtual particles for details. 7. Where did you get that information? The numbers concerning fatal radii, dimming, and the time of the last photon came from Misner, Thorne, and Wheeler's _Gravitation_ (San Francisco: W. H. Freeman & Co., 1973), pp. 860-862 and 872-873. Chapters 32 and 33 (IMHO, the best part of the book) contain nice descriptions of some of the phenomena I've described. Information about evaporation and wormholes came from Robert Wald's _General Relativity_ (Chicago: University of Chicago Press, 1984). The famous conformal diagram of an evaporating hole on page 413 has resolved several arguments on sci.physics (though its veracity is in question). Steven Weinberg's _Gravitation and Cosmology_ (New York: John Wiley and Sons, 1972) provided me with the historical dates. It discusses some properties of the Schwarzschild solution in chapter 8 and describes gravitational collapse in chapter 11. ******************************************************************************** Item 11. The Solar Neutrino Problem original by Bruce Scott -------------------------- updated 5-JUN-1994 by SIC The Short Story: Fusion reactions in the core of the Sun produce a huge flux of neutrinos. These neutrinos can be detected on Earth using large underground detectors, and the flux measured to see if it agrees with theoretical calculations based upon our understanding of the workings of the Sun and the details of the Standard Model (SM) of particle physics. The measured flux is roughly one-half of the flux expected from theory. The cause of the deficit is a mystery. Is our particle physics wrong? Is our model of the Solar interior wrong? Are the experiments in error? This is the "Solar Neutrino Problem." There are precious few experiments which seem to stand in disagreement with the SM, which can be studied in the hope of making breakthroughs in particle physics. The study of this problem may yield important new insights which may help us go beyond the Standard Model. There are many experiments in progress, so stay tuned. The Long Story: A middle-aged main-sequence star like the Sun is in a slowly-evolving equilibrium, in which pressure exerted by the hot gas balances the self-gravity of the gas mass. Slow evolution results from the star radiating energy away in the form of light, fusion reactions occurring in the core heating the gas and replacing the energy lost by radiation, and slow structural adjustment to compensate the changes in entropy and composition. We cannot directly observe the center, because the mean-free path of a photon against absorption or scattering is very short, so short that the radiation-diffusion time scale is of order 10 million years. But the main proton-proton reaction (PP1) in the Sun involves emission of a neutrino: p + p --> D + positron + neutrino(0.26 MeV), which is directly observable since the cross-section for interaction with ordinary matter is so small (the 0.26 MeV is the average energy carried away by the neutrino). Essentially all the neutrinos make it to the Earth. Of course, this property also makes it difficult to detect the neutrinos. The first experiments by Davis and collaborators, involving large tanks of chloride fluid placed underground, could only detect higher-energy neutrinos from small side-chains in the solar fusion: PP2: Be(7) + electron --> Li(7) + neutrino(0.80 MeV), PP3: B(8) --> Be(8) + positron + neutrino(7.2 MeV). Recently, however, the GALLEX experiment, using a gallium-solution detector system, has observed the PP1 neutrinos to provide the first unambiguous confirmation of proton-proton fusion in the Sun. There is a "neutrino problem", however, and that is the fact that every experiment has measured a shortfall of neutrinos. About one- to two-thirds of the neutrinos expected are observed, depending on experimental error. In the case of GALLEX, the data read 80 units where 120 are expected, and the discrepancy is about two standard deviations. To explain the shortfall, one of two things must be the case: (1) either the temperature at the center is slightly less than we think it is, or (2) something happens to the neutrinos during their flight over the 150-million-km journey to Earth. A third possibility is that the Sun undergoes relaxation oscillations in central temperature on a time scale shorter than 10 Myr, but since no-one has a credible mechanism this alternative is not seriously entertained. (1) The fusion reaction rate is a very strong function of the temperature, because particles much faster than the thermal average account for most of it. Reducing the temperature of the standard solar model by 6 per cent would entirely explain GALLEX; indeed, Bahcall has recently published an article arguing that there may be no solar neutrino problem at all. However, the community of solar seismologists, who observe small oscillations in spectral line strengths due to pressure waves traversing through the Sun, argue that such a change is not permitted by their results. (2) A mechanism (called MSW, after its authors) has been proposed, by which the neutrinos self-interact to periodically change flavor between electron, muon, and tau neutrino types. Here, we would only expect to observe a fraction of the total, since only electron neutrinos are detected in the experiments. (The fraction is not exactly 1/3 due to the details of the theory.) Efforts continue to verify this theory in the laboratory. The MSW phenomenon, also called "neutrino oscillation", requires that the three neutrinos have finite and differing mass, which is also still unverified. To use explanation (1) with the Sun in thermal equilibrium generally requires stretching several independent observations to the limits of their errors, and in particular the earlier chloride results must be explained away as unreliable (there was significant scatter in the earliest ones, casting doubt in some minds on the reliability of the others). Further data over longer times will yield better statistics so that we will better know to what extent there is a problem. Explanation (2) depends of course on a proposal whose veracity has not been determined. Until the MSW phenomenon is observed or ruled out in the laboratory, the matter will remain open. In summary, fusion reactions in the Sun can only be observed through their neutrino emission. Fewer neutrinos are observed than expected, by two standard deviations in the best result to date. This can be explained either by a slightly cooler center than expected or by a particle-physics mechanism by which neutrinos oscillate between flavors. The problem is not as severe as the earliest experiments indicated, and further data with better statistics are needed to settle the matter. References: [0] The main-sequence Sun: D. D. Clayton, Principles of Stellar Evolution and Nucleosynthesis, McGraw-Hill, 1968. Still the best text. [0] Solar neutrino reviews: J. N. Bahcall and M. Pinsonneault, Reviews of Modern Physics, vol 64, p 885, 1992; S. Turck-Chieze and I. Lopes, Astrophysical Journal, vol 408, p 347, 1993. See also J. N. Bahcall, Neutrino Astrophysics (Cambridge, 1989). [1] Experiments by R. Davis et al: See October 1990 Physics Today, p 17. [2] The GALLEX team: two articles in Physics Letters B, vol 285, p 376 and p 390. See August 1992 Physics Today, p 17. Note that 80 "units" correspond to the production of 9 atoms of Ge(71) in 30 tons of solution containing 12 tons Ga(71), after three weeks of run time! [3] Bahcall arguing for new physics: J. N. Bahcall and H. A. Bethe, Physical Review D, vol 47, p 1298, 1993; against new physics: J. N. Bahcall et al, "Has a Standard Model Solution to the Solar Neutrino Problem Been Found?", preprint IASSNS-94/13 received at the National Radio Astronomy Observatory, 1994. [4] The MSW mechanism, after Mikheyev, Smirnov, and Wolfenstein: See the second GALLEX paper. [5] Solar seismology and standard solar models: J. Christensen-Dalsgaard and W. Dappen, Astronomy and Astrophysics Reviews, vol 4, p 267, 1992; K. G. Librecht and M. F. Woodard, Science, vol 253, p 152, 1992. See also the second GALLEX paper. ******************************************************************************** Item 12. The Expanding Universe original by Michael Weiss ---------------------- updated 5-DEC-1994 by SIC Here are the answers to some commonly asked questions about exactly what it means to say that the Universe is expanding. (1) IF THE UNIVERSE IS EXPANDING, DOES THAT MEAN ATOMS ARE GETTING BIGGER? IS THE SOLAR SYSTEM EXPANDING? Mrs. Felix: Why don't you do your homework? Allen Felix: The Universe is expanding. Everything will fall apart, and we'll all die. What's the point? Mrs. Felix: We live in Brooklyn. Brooklyn is not expanding! Go do your homework. -from "Annie Hall" by Woody Allen. Mrs. Felix is right. Neither Brooklyn, nor its atoms, nor the solar system, nor even the galaxy, is expanding. The Universe expands (according to standard cosmological models) only when averaged over a very large scale. The phrase "expansion of the Universe" refers both to experimental observation and to theoretical cosmological models. Lets look at them one at a time, starting with the observations. Observation ----------- The observation is Hubble's redshift law. In 1929, Hubble reported that the light from distant galaxies is redshifted. If you interpret this redshift as a Doppler shift, then the galaxies are receding according to the law: (velocity of recession) = H * (distance from Earth) H is called Hubble's constant; Hubble's original value for H was 550 kilometers per second per megaparsec (km/s/Mpc). Current estimates range >from 40 to 100 km/s/Mpc. (Measuring redshift is easy; estimating distance is hard. Roughly speaking, astronomers fall into two "camps", some favoring an H around 80 km/s/Mpc, others an H around 40-55). Hubble's redshift formula does *not* imply that the Earth is in particularly bad oder in the universe. The familiar model of the universe as an expanding balloon speckled with galaxies shows that Hubble's alter ego on any other galaxy would make the same observation. But astronomical objects in our neck of the woods--- our solar system, our galaxy, nearby galaxies--- show no such Hubble redshifts. Nearby stars and galaxies *do* show motion with respect to the Earth (known as "peculiar velocities"), but this does not look like the "Hubble flow" that is seen for distant galaxies. For example, the Andromeda galaxy shows blueshift instead of redshift. So the verdict of observation is: our galaxy is not expanding. By the way, Hubble's constant, is not, in spite of its name, constant in time. In fact, it is decreasing. Imagine a galaxy D light-years from the Earth, receding at a velocity V = H*D. D is always increasing because of the recession. But does V increase? No. In fact, V is decreasing. (If you are fond of Newtonian analogies, you could say that "gravitational attraction" is causing this deceleration. But be warned: some general relativists would object strenuously to this way of speaking.) So H is going down over time. But it *is* constant over space, i.e., it is the same number for all distant objects as we observe them today. Theory ------ The theoretical models are, typically, Friedmann-Robertson-Walker (FRW) spacetimes. Cosmologists model the universe using "spacetimes", that is to say, solutions to the field equations of Einstein's theory of general relativity. The Russian mathematician Alexander Friedmann discovered an important class of global solutions in 1923. The familiar image of the universe as an expanding balloon speckled with galaxies is a "movie version" of one of Friedmann's solutions. Robertson and Walker later extended Friedmann's work, so you'll find references to "Friedmann-Robertson-Walker" (FRW) spacetimes in the literature. FRW spacetimes come in a great variety of styles--- expanding, contracting, flat, curved, open, closed, .... The "expanding balloon" picture corresponds to just a few of these. A concept called the metric plays a starring role in general relativity. The metric encodes a lot of information; the part we care about (for this FAQ entry) is distances between objects. In an FRW expanding universe, the distance between any two "points on the balloon" does increase over time. However, the FRW model is NOT meant to describe OUR spacetime accurately on a small scale--- where "small" is interpreted pretty liberally! You can picture this in a couple of ways. You may want to think of the "continuum approximation" in fluid dynamics--- by averaging the motion of individual molecules over a large enough scale, you obtain a continuous flow. (Droplets can condense even as a gas expands.) Similarly, it is generally believed that if we average the actual metric of the universe over a large enough scale, we'll get an FRW spacetime. Or you may want to alter your picture of the "expanding balloon". The galaxies are not just painted on, but form part of the substance of the balloon (poetically speaking), and locally affect its "elasticity". The FRW spacetimes ignore these small-scale variations. Think of a uniformly elastic balloon, with the galaxies modelled as mere points. "Points on the balloon" correspond to a mathematical concept known as a *comoving geodesic*. Any two comoving geodesics drift apart over time, in an expanding FRW spacetime. At the scale of the Solar System, we get a pretty good approximation to the spacetime metric by using another solution to Einstein's equations, known as the Schwarzschild metric. Using evocative but dubious terminology, we can say this models the gravitational field of the Sun. (Dubious because what does "gravitational field" mean in GR, if it's not just a synonym for "metric"?) The geodesics in the Schwarzschild metric do NOT display the "drifting apart" behavior typical of the FRW comoving geodesics--- or in more familiar terms, the Earth is not drifting away from the Sun. The "true metric" of the universe is, of course, fantastically complicated; you can't expect idealized simple solutions (like the FRW and Schwarzschild metrics) to capture all the complexity. Our knowledge of the large-scale structure of the universe is fragmentary and imprecise. In old-fashioned, Newtonian terms, one says that the Solar System is "gravitationally bound" (ditto the galaxy, the local group). So the Solar System is not expanding. The case for Brooklyn is even clearer: it is bound by atomic forces, and its atoms do not typically follow geodesics. So Brooklyn is not expanding. Now go do your homework. References: (My thanks to Jarle Brinchmann, who helped with this list.) Misner, Thorne, and Wheeler, "Gravitation", chapters 27 and 29. Page 719 discusses this very question; Box 29.4 outlines the "cosmic distance ladder" and the difficulty of measuring cosmic distances; Box 29.5 presents Hubble's work. MTW refer to Noerdlinger and Petrosian, Ap.J., vol. 168 (1971), pp. 1--9, for an exact mathematical treatment of gravitationally bound systems in an expanding universe. M.V.Berry, "Principles of Cosmology and Gravitation". Chapter 2 discusses the cosmic distance ladder; chapters 6 and 7 explain FRW spacetimes. Steven Weinberg, "The First Three Minutes", chapter 2. A non-technical treatment. Hubble's original paper: "A Relation Between Distance And Radial Velocity Among Extra-Galactic Nebulae", Proc. Natl. Acad. Sci., Vol. 15, No. 3, pp. 168-173, March 1929. Sidney van den Bergh, "The cosmic distance scale", Astronomy & Astrophysics Review 1989 (1) 111-139. M. Rowan-Robinson, "The Cosmological Distance Ladder", Freeman. A new method has been devised recently to estimate Hubble's constant, using gravitational lensing. The method is described in: \O Gr\on and Sjur Refsdal, "Gravitational Lenses and the age of the universe", Eur. J. Phys. 13, 1992 178-183. S. Refsdal & J. Surdej, Rep. Prog. Phys. 56, 1994 (117-185) and H is estimated with this method in: H.Dahle, S.J. Maddox, P.B. Lilje, to appear in ApJ Letters. Two books may be consulted for what is known (or believed) about the large-scale structure of the universe: P.J.E.Peebles, "An Introduction to Physical Cosmology". T. Padmanabhan, "Structure Formation in the Universe". ====================================================================== (2) WHAT CAUSES THE HUBBLE REDSHIFT? ARE THE LIGHT-WAVES "STRETCHED" AS THE UNIVERSE EXPANDS, OR IS THE LIGHT DOPPLER-SHIFTED BECAUSE DISTANT GALAXIES ARE MOVING AWAY FROM US? In a word: yes. In two sentences: the Doppler-shift explanation is a linear approximation to the "stretched-light" explanation. Switching >from one viewpoint to the other amounts to a change of coordinate systems in (curved) spacetime. A detailed explanation requires looking at Friedmann-Robertson-Walker (FRW) models of spacetime. The famous "expanding balloon speckled with galaxies" provides a visual analogy for one of these; like any analogy, it will mislead you if taken too literally, but handled with caution it can furnish some insight. Draw a latitude/longitude grid on the balloon. These define *co-moving* coordinates. Imagine a couple of speckles ("galaxies") imbedded in the rubber surface. The co-moving coordinates of the speckles don't change as the balloon expands, but the distance between the speckles steadily increases. In co-moving coordinates, we say that the speckles don't move, but "space itself" stretches between them. A bug starts crawling from one speckle to the other. A second after the first bug leaves, his brother follows him. (Think of the bugs as two light-pulses, or successive wave-crests in a beam of light.) Clearly the separation between the bugs will increase during their journey. In co-moving coordinates, light is "stretched" during its journey. Now we switch to a different coordinate system, this one valid only in a neighborhood (but one large enough to cover both speckles). Imagine a clear, flexible, non-stretching patch, attached to the balloon at one speckle. The patch clings to the surface of the balloon, which slides beneath it as the balloon inflates. (The bugs crawl along *under* the patch.) We draw a coordinate grid on the patch. In the patch coordinates, the second speckle recedes from the first speckle. And so in patch coordinates, we can regard the redshift as a Doppler shift. Is this visually appealing? I think so. However, this explanation glosses over one crucial point: the time coordinate. FRW spacetimes come fully-equipped with a specially distinguished time coordinate (called the co-moving or cosmological time). For example, a co-moving observer could set her clock by the average density of surrounding speckles, or by the temperature of the Cosmic Background Radiation. (From a purely mathematical standpoint, the co-moving time coordinate is singled out by a certain symmetry property.) We have many choices of time-coordinate to go with the space-coordinates drawn on our patch. Let's use cosmological time. Notice that this is *not* the choice usually made in Special Relativity: though the two speckles separate rapidly, their cosmological clocks remain synchronized. Bugs embarking on their journey from the "moving" speckle appear to crawl "upstream" against flowing space as they head towards the "home" speckle. The current diminishes as they approach home. (In other words, bug-speed is anisotropic in these coordinates.) These differences >from the usual SR picture are symptoms of a deeper fact: besides the obvious "spatial" curvature of the balloon's surface, FRW spacetimes have "temporal" curvature as well. Indeed, not all FRW spacetimes exhibit spatial curvature, but (with one exception) all have temporal curvature. You can work out the magnitude of the redshift using patch coordinates. I leave this as an exercise, with a couple of hints. (1) Since bug-speed is anisotropic far from the home speckle, consider also a patch attached to the "moving" speckle. Compute the initial distance between the bugs (the "wavelength") in both patch coordinate systems, using the standard *non-relativistic* Doppler formula for a stationary source, moving receiver. (2) Now think about how the bug-distance changes as the bugs journey to the home speckle (this time sticking with home patch coordinates). The bug-distance does *not* propagate unchanged. Consider instead the analog of the period of a lightwave: the time between bug-crossings of a grid line on the patch. This *does* propagate almost unchanged, *provided* the rate of balloon expansion stays pretty much the same throughout the bugs' perilous trek. The final result: the magnitude of the redshift, computed using Doppler's formula, agrees to first-order with magnitude computed using the "stretched-light" explanation. (To the cognoscenti: the assumptions are that Hx<<1 and (dH/dt)x<<1, where H(t)=dR(t)/dt, R(t) is the scale factor, t is cosmological time, and x is the average distance between the "speckles" (co-moving geodesics) during the course of the journey.) (This long-winded "proof of equivalence" between the Doppler and "stretched-light" explanations substitutes a paragraph of imagery for a half-page of calculus.) Let me close by emphasizing the word "approximation" from the first paragraph of this entry. The Doppler explanation fails for very large redshifts, for then we must consider how Hubble's "constant" changes over the course of the journey. References: Misner, Thorne, and Wheeler, "Gravitation", chapter 29. M.V.Berry, "Principles of Cosmology and Gravitation", chapter 6. Steven Weinberg, "The First Three Minutes", chapter 2, especially pp. 13 and 30. ******************************************************************************** END OF PART 2/4 Article: 5897 of sci.physics.particle Path: senator-bedfellow.mit.edu!bloom-beacon.mit.edu!paperboy.osf.org!mogul.osf.org!columbus From: columbus@osf.org Newsgroups: sci.physics,sci.physics.research,sci.physics.cond-matter,sci.physics.particle,alt.sci.physics.new-theories,sci.answers,alt.answers,news.answers Subject: sci.physics Frequently Asked Questions (Part 3 of 4) Supersedes: Followup-To: sci.physics Date: 13 Oct 1995 14:40:59 GMT Organization: Open Software Foundation Lines: 1082 Approved: news-answers-request@MIT.EDU Distribution: world Expires: 17-Nov 1995 Message-ID: References: Reply-To: columbus@osf.org (Michael Weiss) NNTP-Posting-Host: mogul.osf.org Summary: This posting contains a list of Frequently Asked Questions (and their answers) about physics, and should be read by anyone who wishes to post to the sci.physics.* newsgroups. Keywords: Sci.physics FAQ X-Posting-Frequency: posted monthly Originator: columbus@mogul.osf.org Xref: senator-bedfellow.mit.edu sci.physics:147072 sci.physics.research:3042 sci.physics.cond-matter:557 sci.physics.particle:5897 alt.sci.physics.new-theories:21140 sci.answers:3265 alt.answers:12766 news.answers:55203 Posted-By: auto-faq 3.1.1.2 Archive-name: physics-faq/part3 -------------------------------------------------------------------------------- FREQUENTLY ASKED QUESTIONS ON SCI.PHYSICS - Part 3/4 -------------------------------------------------------------------------------- Item 13. Apparent Superluminal Velocity of Galaxies updated 5-DEC-1994 by SIC ------------------------------------------ original by Scott I. Chase A distant object can appear to travel faster than the speed of light relative to us, provided that it has some component of motion towards us as well as perpendicular to our line of sight. Say that on Jan. 1 you make a position measurement of galaxy X. One month later, you measure it again. Assuming you know its distance from us by some independent measurement, you derive its linear speed, and conclude that it is moving faster than the speed of light. What have you forgotten? Let's say that on Jan. 1, the object is D km from us, and that between Jan. 1 and Feb. 1, the object has moved d km closer to us. You have assumed that the light you measured on Jan. 1 and Feb. 1 were emitted exactly one month apart. Not so. The first light beam had further to travel, and was actually emitted (1 + d/c) months before the second measurement, if we measure c in km/month. The object has traveled the given angular distance in more time than you thought. Similarly, if the object is moving away from us, the apparent angular velocity will be too slow, if you do not correct for this effect, which becomes significant when the object is moving along a line close to our line of sight. Note that most extragalactic objects are moving away from us due to the Hubble expansion. So for most objects, you don't get superluminal apparent velocities. But the effect is still there, and you need to take it into account if you want to measure velocities by this technique. References: Considerations about the Apparent 'Superluminal Expansions' in Astrophysics, E. Recami, A. Castellino, G.D. Maccarrone, M. Rodono, Nuovo Cimento 93B, 119 (1986). Apparent Superluminal Sources, Comparative Cosmology and the Cosmic Distance Scale, Mon. Not. R. Astr. Soc. 242, 423-427 (1990). ******************************************************************************** Item 14. Hot Water Freezes Faster than Cold! updated 11-May-1992 by SIC ----------------------------------- original by Richard M. Mathews You put two pails of water outside on a freezing day. One has hot water (95 degrees C) and the other has an equal amount of colder water (50 degrees C). Which freezes first? The hot water freezes first! Why? It is commonly argued that the hot water will take some time to reach the initial temperature of the cold water, and then follow the same cooling curve. So it seems at first glance difficult to believe that the hot water freezes first. The answer lies mostly in evaporation. The effect is definitely real and can be duplicated in your own kitchen. Every "proof" that hot water can't freeze faster assumes that the state of the water can be described by a single number. Remember that temperature is a function of position. There are also other factors besides temperature, such as motion of the water, gas content, etc. With these multiple parameters, any argument based on the hot water having to pass through the initial state of the cold water before reaching the freezing point will fall apart. The most important factor is evaporation. The cooling of pails without lids is partly Newtonian and partly by evaporation of the contents. The proportions depend on the walls and on temperature. At sufficiently high temperatures evaporation is more important. If equal masses of water are taken at two starting temperatures, more rapid evaporation from the hotter one may diminish its mass enough to compensate for the greater temperature range it must cover to reach freezing. The mass lost when cooling is by evaporation is not negligible. In one experiment, water cooling from 100C lost 16% of its mass by 0C, and lost a further 12% on freezing, for a total loss of 26%. The cooling effect of evaporation is twofold. First, mass is carried off so that less needs to be cooled from then on. Also, evaporation carries off the hottest molecules, lowering considerably the average kinetic energy of the molecules remaining. This is why "blowing on your soup" cools it. It encourages evaporation by removing the water vapor above the soup. Thus experiment and theory agree that hot water freezes faster than cold for sufficiently high starting temperatures, if the cooling is by evaporation. Cooling in a wooden pail or barrel is mostly by evaporation. In fact, a wooden bucket of water starting at 100C would finish freezing in 90% of the time taken by an equal volume starting at room temperature. The folklore on this matter may well have started a century or more ago when wooden pails were usual. Considerable heat is transferred through the sides of metal pails, and evaporation no longer dominates the cooling, so the belief is unlikely to have started from correct observations after metal pails became common. References: "Hot water freezes faster than cold water. Why does it do so?", Jearl Walker in The Amateur Scientist, Scientific American, Vol. 237, No. 3, pp 246-257; September, 1977. "The Freezing of Hot and Cold Water", G.S. Kell in American Journal of Physics, Vol. 37, No. 5, pp 564-565; May, 1969. ******************************************************************************** Item 15. Why are Golf Balls Dimpled? updated 17-NOV-1993 by CDF --------------------------- original by Craig DeForest The dimples, paradoxically, *do* increase drag slightly. But they also increase `Magnus lift', that peculiar lifting force experienced by rotating bodies travelling through a medium. Contrary to Freshman physics, golf balls do not travel in inverted parabolas. They follow an 'impetus trajectory': * * * * (golfer) * * * * <-- trajectory \O/ * * | * * -/ \-T---------------------------------------------------------------ground This is because of the combination of drag (which reduces horizontal speed late in the trajectory) and Magnus lift, which supports the ball during the initial part of the trajectory, making it relatively straight. The trajectory can even curve upwards at first, depending on conditions! Here is a cheesy diagram of a golf ball in flight, with some relevant vectors: F(magnus) ^ | F(drag) <--- O -------> V \ \----> (sense of rotation) The Magnus force can be thought of as due to the relative drag on the air on the top and bottom portions of the golf ball: the top portion is moving slower relative to the air around it, so there is less drag on the air that goes over the ball. The boundary layer is relatively thin, and air in the not-too-near region moves rapidly relative to the ball. The bottom portion moves fast relative to the air around it; there is more drag on the air passing by the bottom, and the boundary (turbulent) layer is relatively thick; air in the not-too-near region moves more slowly relative to the ball. The Bernoulli force produces lift. (Alternatively, one could say that `the flow lines past the ball are displaced down, so the ball is pushed up.') The difficulty comes near the transition region between laminar flow and turbulent flow. At low speeds, the flow around the ball is laminar. As speed is increased, the bottom part tends to go turbulent *first*. But turbulent flow can follow a surface much more easily than laminar flow. As a result, the (laminar) flow lines around the top break away >from the surface sooner than otherwise, and there is a net displacement *up* of the flow lines. The magnus lift goes *negative*. The dimples aid the rapid formation of a turbulent boundary layer around the golf ball in flight, giving more lift. Without 'em, the ball would travel in more of a parabolic trajectory, hitting the ground sooner (and not coming straight down). References: Lord Rayleigh, "On the Irregular Flight of a Tennis Ball", _Scientific Papers I_, p. 344 Briggs Lyman J., "Effect of Spin and Speed on the Lateral Deflection of a Baseball; and the Magnus Effect for Smooth Spheres", Am. J. Phys. _27_, 589 (1959). [Briggs was trying to explain the mechanism behind the `curve ball' in baseball, using specialized apparatus in a wind tunnel at the NBS. He stumbled on the reverse effect by accident, because his model `baseball' had no stitches on it. The stitches on a baseball create turbulence in flight in much the same way that the dimples on a golf ball do.] R. Watts and R. Ferver, "The Lateral Force on a Spinning Sphere" Aerodynamics of a Curveball", Am. J. Phys. _55_, 40 (1986) ******************************************************************************** Item 16. updated 9-DEC-1993 by SIC Original by Bill Johnson How to Change Nuclear Decay Rates --------------------------------- "I've had this idea for making radioactive nuclei decay faster/slower than they normally do. You do [this, that, and the other thing]. Will this work?" Short Answer: Possibly, but probably not usefully. Long Answer: "One of the paradigms of nuclear science since the very early days of its study has been the general understanding that the half-life, or decay constant, of a radioactive substance is independent of extranuclear considerations." (Emery, cited below.) Like all paradigms, this one is subject to some interpretation. Normal decay of radioactive stuff proceeds via one of four mechanisms: * Emission of an alpha particle -- a helium-4 nucleus -- reducing the number of protons and neutrons present in the parent nucleus by two each; * "Beta decay," encompassing several related phenomena in which a neutron in the nucleus turns into a proton, or a proton turns into a neutron -- along with some other things including emission of a neutrino. The "other things", as we shall see, are at the bottom of several questions involving perturbation of decay rates; * Emission of one or more gamma rays -- energetic photons -- that take a nucleus from an excited state to some other (typically ground) state; some of these photons may be replaced by "conversion electrons," of which more shortly; or *Spontaneous fission, in which a sufficiently heavy nucleus simply breaks in half. Most of the discussion about alpha particles will also apply to spontaneous fission. Gamma emission often occurs from the daughter of one of the other decay modes. We neglect *very* exotic processes like C-14 emission or double beta decay in this analysis. "Beta decay" refers most often to a nucleus with a neutron excess, which decays by converting a neutron into a proton: n ----> p + e- + anti-nu(e), where n means neutron, p means proton, e- means electron, and anti-nu(e) means an antineutrino of the electron type. The type of beta decay which involves destruction of a proton is not familiar to many people, so deserves a little elaboration. Either of two processes may occur when this kind of decay happens: p ----> n + e+ + nu(e), where e+ means positron and nu(e) means electron neutrino; or p + e- ----> n + nu(e), where e- means a negatively charged electron, which is captured from the neighborhood of the nucleus undergoing decay. These processes are called "positron emission" and "electron capture," respectively. A given nucleus which has too many protons for stability may undergo beta decay through either, and typically both, of these reactions. "Conversion electrons" are produced by the process of "internal conversion," whereby the photon that would normally be emitted in gamma decay is *virtual* and its energy is absorbed by an atomic electron. The absorbed energy is sufficient to unbind the electron from the nucleus (ignoring a few exceptional cases), and it is ejected from the atom as a result. Now for the tie-in to decay rates. Both the electron-capture and internal conversion phenomena require an electron somewhere close to the decaying nucleus. In any normal atom, this requirement is satisfied in spades: the innermost electrons are in states such that their probability of being close to the nucleus is both large and insensitive to things in the environment. The decay rate depends on the electronic wavefunctions, i.e, how much of their time the inner electrons spend very near the nucleus -- but only very weakly. For most nuclides that decay by electron capture or internal conversion, most of the time, the probability of grabbing or converting an electron is also insensitive to the environment, as the innermost electrons are the ones most likely to get grabbed/converted. However, there are exceptions, the most notable being the the astrophysically important isotope beryllium-7. Be-7 decays purely by electron capture (positron emission being impossible because of inadequate decay energy) with a half-life of somewhat over 50 days. It has been shown that differences in chemical environment result in half-life variations of the order of 0.2%, and high pressures produce somewhat similar changes. Other cases where known changes in decay rate occur are Zr-89 and Sr-85, also electron capturers; Tc-99m ("m" implying an excited state), which decays by both beta and gamma emission; and various other "metastable" things that decay by gamma emission with internal conversion. With all of these other cases the magnitude of the effect is less than is typically the case with Be-7. What makes these cases special? The answer is that one or more of the usual starting assumptions -- insensitivity of electron wave function near the nucleus to external forces, or availability of the innermost electrons for capture/conversion -- are not completely valid. Atomic beryllium only has 4 electrons to begin with, so that the "innermost electrons" are also practically the *outermost* ones and therefore much more sensitive to chemical effects than usual. With most of the other cases, there is so little energy available from the decay (as little as a few electron volts; compare most radioactive decays, where hundreds or thousands of *kilo*volts are released), courtesy of accidents of nuclear structure, that the innermost electrons can't undergo internal conversion. Remember that converting an electron requires dumping enough energy into it to expel it from the atom (more or less); "enough energy," in context, is typically some tens of keV, so they don't get converted at all in these cases. Conversion therefore works only on some of the outer electrons, which again are more sensitive to the environment. A real anomaly is the beta emitter Re-187. Its decay energy is only about 2.6 keV, practically nothing by nuclear standards. "That this decay occurs at all is an example of the effects of the atomic environment on nuclear decay: the bare nucleus Re-187 [i.e., stripped of all orbital electrons -- MWJ] is stable against beta decay [but not to bound state beta decay, in which the outgoing electron is captured by the daughter nucleus into a tightly bound orbital -SIC] and it is the difference of 15 keV in the total electronic binding energy of osmium [to which it decays -- MWJ] and rhenium ... which makes the decay possible" (Emery). The practical significance of this little peculiarity, of course, is low, as Re-187 already has a half life of over 10^10 years. Alpha decay and spontaneous fission might also be affected by changes in the electron density near the nucleus, for a different reason. These processes occur as a result of penetration of the "Coulomb barrier" that inhibits emission of charged particles from the nucleus, and their rate is *very* sensitive to the height of the barrier. Changes in the electron density could, in principle, affect the barrier by some tiny amount. However, the magnitude of the effect is *very* small, according to theoretical calculations; for a few alpha emitters, the change has been estimated to be of the order of 1 part in 10^7 (!) or less, which would be unmeasurable in view of the fact that the alpha emitters' half lives aren't known to that degree of accuracy to begin with. All told, the existence of changes in radioactive decay rates due to the environment of the decaying nuclei is on solid grounds both experimentally and theoretically. But the magnitude of the changes is nothing to get very excited about. Reference: The best review article on this subject is now 20 years old: G. T. Emery, "Perturbation of Nuclear Decay Rates," Annual Review of Nuclear Science vol. 22, p. 165 (1972). Papers describing specific experiments are cited in that article, which contains considerable arcane math but also gives a reasonable qualitative "feel" for what is involved. ******************************************************************************** Item 17. original by Blair P. Houghton (blair@world.std.com) What is a Dippy Bird, and how is it used? ----------------------------------------- The Anatomy and Habits of a Dippy Bird: 1. The armature: The body of the bird is a straight tube attached to two bulbs, approximately the same size, one at either end. The tube flows into the upper bulb, like the neck of a funnel, and extends almost to the bottom of the lower bulb, like the straw in a soda. 2. The pivot: At about the middle of the tube is clamped a transverse bar, which allows the apparatus to pivot on a stand (the legs). The bar is bent very slightly concave dorsally, to unbalance the bird in the forward direction (thus discouraging dips to the rear). The ends of the pivot have downward protrusions, which hit stops on the stand placed so that the bird is free to rock when in a vertical position, but can not quite rotate enough to be horizontal during a dip. 3. The wick: The upper bulb is coated in fuzzy material, and has extended >from it a beak, made of or covered in the same material. 4. The tail. The tail has no significant external features, except that it should not be insulated (skin-oil deposited on the bird's glass parts >from handling will insulate it and can affect its operation). 5. The guts: The bird is partially filled with a somewhat carefully measured amount of a fluid with suitable lack of viscosity and density and a low latent heat of evaporation (small d(energy)/d(mass), ld). For water, ld is 2250 kJ/kg; for methylene chloride, ld is 406; for mercury, ld is a wondrous 281; ethyl alcohol has an ld of 880, more than twice that of MC. Boiling point is not important, here; evaporation and condensation take place on the surface of a liquid at any temperature. 6. The frills: Any hats, eyes, feathers, or liquid coloring have been added purely for entertainment value. (An anecdote: as it stood pumping in the Arizona sun on my kitchen windowsill for several days, the rich, Kool-Aid red of my bird's motorwater faded to a pale peach. I have since retired him to the mantelpiece in the family room). 7. Shreddin': The bird is operated by getting the head wet, taking care not to make it so wet that it drips down the tube. (Water on the bottom bulb will reverse the thermodynamic processes.) The first cycle will take somewhat longer than the following cycles. If you can keep water where the bird can dip it, the bird will dip for as long as the ambient humidity remains favorable. Come on, how does it really work? --------------------------------- Short answer: Thermodynamics plus Mechanics. Medium answer (and essential clues): Evaporative cooling on the outside; pV=nRT, evaporation/condensation, and gravity on the inside. Long answer: Initially the system is at equilibrium, with T equal in both chambers and pV/n in each compensating for the fluid levels. Evaporation of water outside the head draws heat from inside it; the vapor inside condenses, reducing pV/RT. This imbalances the pressures, so the vapor in the abdomen pushes down, which pushes fluid up the thorax, which reduces V in the head. Since p is decreasing in the abdomen, evaporation occurs, increasing n, and drawing heat from outside the body. The rising fluid raises the CM above the pivot point; the hips are slightly concave dorsally, so the bird dips forward. Tabs on the legs and the pivot maintain the angle at full dip, for drainage. The amount of fluid is set so that at full dip the lower end of the tube is exposed to the vapor. (The tube reaches almost to the bottom of the abdomen, like a straw in a soda, but flows into the head like the neck of a funnel.) A bubble of vapor rises in the tube and fluid drains into the abdomen. The rising bubble transfers heat to the head and the falling fluid releases gravitational potential energy as heat into the rising bubble and the abdomen. The CM drops below the pivot point and the bird bobs up. The system is thus reset; it's not quite at equilibrium, but is close enough that the process can repeat this chain of events. The beak acts as a wick, if allowed to dip into a reservoir of water, to keep the head wet, although it is not necessary for the bird to drink on every dip. Is that all there is to know about dippy birds? ----------------------------------------------- Of course not. Research continues to unravel these unanswered questions about the amazing dippy-bird: 1. All of the energy gained by the rising fluid is returned to the system when the fluid drops; where does this energy go, in what proportions, and how does this affect the rate at which the bird operates? 2. The heat that evaporates the water comes from both the surrounding air and the inside of the head; but, in what proportion? 3. Exactly what should the fluid be? Methylene Chloride is an excellent candidate, since it's listed in the documentation for recent birds sold by Edmund Scientific Corp. (trade named Happy Drinking Bird), and because its latent heat of evaporation (ld) is 406 kJ/kg, compared to 2250 kJ/kg for water (a 5.5:1 ratio of condensed MC to evaporated water, if all water-evaporating heat comes from inside the bird). Ethanol, at 880 kJ/kG, is only half as efficient. Mercury would likewise be a good prospective choice, having an ld of 281 kJ/kG (8:1!), but is expensive and dangerous, and its density would require careful redesign and greater quality control in the abdomen and pivot-stops to ensure proper operation at full dip; this does, however, indicate that the apparatus could be made in miniature, filled with mercury, and sold through a catalog-store such as The Sharper Image as a wildly successful yuppie desk-toy (Consider the submission of this FAQ entry to be prior art for patent purposes). 4. Does ambient temperature have an effect on operation aside from the increase in rate of evaporation of water? I.e., if the temperature and humidity can be controlled independently such that the rate of evaporation can be kept constant, what effect does such a change in ambient temperature and humidity have on the operation of the bird? Is the response transient, permanent, or composed of both? Dippy Bird Tips: ---------------- They have real trouble working at all in humid climates (like around the U. of Md., where I owned my first one), but can drive you bats in dry climates (aside from the constant hammering, it's hard to keep the water up to a level where the bird can get at it...). The evaporation of water from the head depends on the diffusibility of water vapor into the atmosphere; high partial pressures of water vapor in the atmosphere translate to low rates of evaporation. If you handle your bird, clean the glass with alcohol or Windex or Dawn or something; the oil from your hands has a high specific heat, which damps the transfer of heat, and a low thermal conductivity, which attenuates the transfer of heat. Once it's clean, grasp the bird only by the legs or the tube, which are not thermodynamically significant, or wear rubber gloves, just like a real EMT. The hat is there for show; the dippy bird operates okay with or without it, even though it may reduce the area of evaporation slightly. Ditto the feathers and the eyes. Bibliography: ------------- Chemical data from Gieck, K., _Engineering Formulas_, 3d. Ed., McGraw-Hill, 1979, as translated by J. Walters, B. Sc. I've also heard that SciAm had an "Amateur Scientist" column on this technology a few years ago. Perhaps someone who understands how a library works could look up the yr and vol... Kool-Aid is a trademark of some huge corporation that makes its money a farthing at a time... ******************************************************************************** Item 18. Below Absolute Zero - What Does Negative Temperature Mean? updated 24-MAR-1993 ---------------------------------------------------------- by Scott I. Chase Questions: What is negative temperature? Can you really make a system which has a temperature below absolute zero? Can you even give any useful meaning to the expression 'negative absolute temperature'? Answer: Absolutely. :-) Under certain conditions, a closed system *can* be described by a negative temperature, and, surprisingly, be *hotter* than the same system at any positive temperature. This article describes how it all works. Step I: What is "Temperature"? ------------------------------ To get things started, we need a clear definition of "temperature." Actually various kinds of "temperature" appear in the literature of physics (e.g., kinetic temperature, color temperature). The relevant one here is the one from thermodynamics, in some sense the most fundamental. Our intuitive notion is that two systems in thermal contact should exchange no heat, on average, if and only if they are at the same temperature. Let's call the two systems S1 and S2. The combined system, treating S1 and S2 together, can be S3. The important question, consideration of which will lead us to a useful quantitative definition of temperature, is "How will the energy of S3 be distributed between S1 and S2?" I will briefly explain this below, but I recommend that you read K&K, referenced below, for a careful, simple, and thorough explanation of this important and fundamental result. With a total energy E, S has many possible internal states (microstates). The atoms of S3 can share the total energy in many ways. Let's say there are N different states. Each state corresponds to a particular division of the total energy in the two subsystems S1 and S2. Many microstates can correspond to the same division, E1 in S1 and E2 in S2. A simple counting argument tells you that only one particular division of the energy, will occur with any significant probability. It's the one with the overwhelmingly largest number of microstates for the total system S3. That number, N(E1,E2) is just the product of the number of states allowed in each subsystem, N(E1,E2) = N1(E1)*N2(E2), and, since E1 + E2 = E, N(E1,E2) reaches a maximum when N1*N2 is stationary with respect to variations of E1 and E2 subject to the total energy constraint. For convenience, physicists prefer to frame the question in terms of the logarithm of the number of microstates N, and call this the entropy, S. You can easily see from the above analysis that two systems are in equilibrium with one another when (dS/dE)_1 = (dS/dE)_2, i.e., the rate of change of entropy, S, per unit change in energy, E, must be the same for both systems. Otherwise, energy will tend to flow from one subsystem to another as S3 bounces randomly from one microstate to another, the total energy E3 being constant, as the combined system moves towards a state of maximal total entropy. We define the temperature, T, by 1/T = dS/dE, so that the equilibrium condition becomes the very simple T_1 = T_2. This statistical mechanical definition of temperature does in fact correspond to your intuitive notion of temperature for most systems. So long as dS/dE is always positive, T is always positive. For common situations, like a collection of free particles, or particles in a harmonic oscillator potential, adding energy always increases the number of available microstates, increasingly faster with increasing total energy. So temperature increases with increasing energy, from zero, asymptotically approaching positive infinity as the energy increases. Step II: What is "Negative Temperature"? ---------------------------------------- Not all systems have the property that the entropy increases monotonically with energy. In some cases, as energy is added to the system, the number of available microstates, or configurations, actually decreases for some range of energies. For example, imagine an ideal "spin-system", a set of N atoms with spin 1/2 on a one-dimensional wire. The atoms are not free to move from their positions on the wire. The only degree of freedom allowed to them is spin-flip: the spin of a given atom can point up or down. The total energy of the system, in a magnetic field of strength B, pointing down, is (N+ - N-)*uB, where u is the magnetic moment of each atom and N+ and N- are the number of atoms with spin up and down respectively. Notice that with this definition, E is zero when half of the spins are up and half are down. It is negative when the majority are down and positive when the majority are up. The lowest possible energy state, all the spins pointing down, gives the system a total energy of -NuB, and temperature of absolute zero. There is only one configuration of the system at this energy, i.e., all the spins must point down. The entropy is the log of the number of microstates, so in this case is log(1) = 0. If we now add a quantum of energy, size uB, to the system, one spin is allowed to flip up. There are N possibilities, so the entropy is log(N). If we add another quantum of energy, there are a total of N(N-1)/2 allowable configurations with two spins up. The entropy is increasing quickly, and the temperature is rising as well. However, for this system, the entropy does not go on increasing forever. There is a maximum energy, +NuB, with all spins up. At this maximal energy, there is again only one microstate, and the entropy is again zero. If we remove one quantum of energy from the system, we allow one spin down. At this energy there are N available microstates. The entropy goes on increasing as the energy is lowered. In fact the maximal entropy occurs for total energy zero, i.e., half of the spins up, half down. So we have created a system where, as we add more and more energy, temperature starts off positive, approaches positive infinity as maximum entropy is approached, with half of all spins up. After that, the temperature becomes negative infinite, coming down in magnitude toward zero, but always negative, as the energy increases toward maximum. When the system has negative temperature, it is *hotter* than when it is has positive temperature. If you take two copies of the system, one with positive and one with negative temperature, and put them in thermal contact, heat will flow from the negative-temperature system into the positive-temperature system. Step III: What Does This Have to Do With the Real World? --------------------------------------------------------- Can this system ever by realized in the real world, or is it just a fantastic invention of sinister theoretical condensed matter physicists? Atoms always have other degrees of freedom in addition to spin, usually making the total energy of the system unbounded upward due to the translational degrees of freedom that the atom has. Thus, only certain degrees of freedom of a particle can have negative temperature. It makes sense to define the "spin-temperature" of a collection of atoms, so long as one condition is met: the coupling between the atomic spins and the other degrees of freedom is sufficiently weak, and the coupling between atomic spins sufficiently strong, that the timescale for energy to flow from the spins into other degrees of freedom is very large compared to the timescale for thermalization of the spins among themselves. Then it makes sense to talk about the temperature of the spins separately from the temperature of the atoms as a whole. This condition can easily be met for the case of nuclear spins in a strong external magnetic field. Nuclear and electron spin systems can be promoted to negative temperatures by suitable radio frequency techniques. Various experiments in the calorimetry of negative temperatures, as well as applications of negative temperature systems as RF amplifiers, etc., can be found in the articles listed below, and the references therein. References: Kittel and Kroemer,_Thermal Physics_, appendix E. N.F. Ramsey, "Thermodynamics and statistical mechanics at negative absolute temperature," Phys. Rev. _103_, 20 (1956). M.J. Klein,"Negative Absolute Temperature," Phys. Rev. _104_, 589 (1956). ******************************************************************************** Item 19. Which Way Will my Bathtub Drain? updated 16-MAR-1993 by SIC -------------------------------- original by Matthew R. Feinstein Question: Does my bathtub drain differently depending on whether I live in the northern or southern hemisphere? Answer: No. There is a real effect, but it is far too small to be relevant when you pull the plug in your bathtub. Because the earth rotates, a fluid that flows along the earth's surface feels a "Coriolis" acceleration perpendicular to its velocity. In the northern hemisphere low pressure storm systems spin counterclockwise. In the southern hemisphere, they spin clockwise because the direction of the Coriolis acceleration is reversed. This effect leads to the speculation that the bathtub vortex that you see when you pull the plug >from the drain spins one way in the north and the other way in the south. But this acceleration is VERY weak for bathtub-scale fluid motions. The order of magnitude of the Coriolis acceleration can be estimated from size of the "Rossby number" (see below). The effect of the Coriolis acceleration on your bathtub vortex is SMALL. To detect its effect on your bathtub, you would have to get out and wait until the motion in the water is far less than one rotation per day. This would require removing thermal currents, vibration, and any other sources of noise. Under such conditions, never occurring in the typical home, you WOULD see an effect. To see what trouble it takes to actually see the effect, see the reference below. Experiments have been done in both the northern and southern hemispheres to verify that under carefully controlled conditions, bathtubs drain in opposite directions due to the Coriolis acceleration from the Earth's rotation. Coriolis accelerations are significant when the Rossby number is SMALL. So, suppose we want a Rossby number of 0.1 and a bathtub-vortex length scale of 0.1 meter. Since the earth's rotation rate is about 10^(-4)/second, the fluid velocity should be less than or equal to 2*10^(-6) meters/second. This is a very small velocity. How small is it? Well, we can take the analysis a step further and calculate another, more famous dimensionless parameter, the Reynolds number. The Reynolds number is = L*U*density/viscosity Assuming that physicists bathe in hot water the viscosity will be about 0.005 poise and the density will be about 1.0, so the Reynolds Number is about 4*10^(-2). Now, life at low Reynolds numbers is different from life at high Reynolds numbers. In particular, at low Reynolds numbers, fluid physics is dominated by friction and diffusion, rather than by inertia: the time it would take for a particle of fluid to move a significant distance due to an acceleration is greater than the time it takes for the particle to break up due to diffusion. The same effect has been accused of responsibility for the direction water circulates when you flush a toilet. This is surely nonsense. In this case, the water rotates in the direction which the pipe points which carries the water from the tank to the bowl. Reference: Trefethen, L.M. et al, Nature 207 1084-5 (1965). ******************************************************************************** Item 20. Why do Mirrors Reverse Left and Right? updated 04-MAR-1994 by SIC -------------------------------------- original by Scott I. Chase The simple answer is that they don't. Look in a mirror and wave your right hand. On which side of the mirror is the hand that waved? The right side, of course. Mirrors DO reverse In/Out. Imagine holding an arrow in your hand. If you point it up, it will point up in the mirror. If you point it to the left, it will point to the left in the mirror. But if you point it toward the mirror, it will point right back at you. In and Out are reversed. If you take a three-dimensional, rectangular, coordinate system, (X,Y,Z), and point the Z axis such that the vector equation X x Y = Z is satisfied, then the coordinate system is said to be right-handed. Imagine Z pointing toward the mirror. X and Y are unchanged (remember the arrows?) but Z will point back at you. In the mirror, X x Y = - Z. The image contains a left-handed coordinate system. This has an important effect, familiar mostly to chemists and physicists. It changes the chirality, or handedness, of objects viewed in the mirror. Your left hand looks like a right hand, while your right hand looks like a left hand. Molecules often come in pairs called stereoisomers, which differ not in the sequence or number of atoms, but only in that one is the mirror image of the other, so that no rotation or stretching can turn one into the other. Your hands make a good laboratory for this effect. They are distinct, even though they both have the same components connected in the same way. They are a stereo pair, identical except for "handedness". People sometimes think that mirrors *do* reverse left/right, and that the effect is due to the fact that our eyes are aligned horizontally on our faces. This can be easily shown to be untrue by looking in any mirror with one eye closed! Reference: _The Left Hand of the Electron_, by Isaac Asimov, contains a very readable discussion of handedness and mirrors in physics. ******************************************************************************** Item 21. updated 16-MAR-1992 by SIC Original by John Blanton Why Do Stars Twinkle While Planets Do Not? ----------------------------------------- Stars, except for the Sun, although they may be millions of miles in diameter, are very far away. They appear as point sources even when viewed by telescopes. The planets in our solar system, much smaller than stars, are closer and can be resolved as disks with a little bit of magnification (field binoculars, for example). Since the Earth's atmosphere is turbulent, all images viewed up through it tend to "swim." The result of this is that sometimes a single point in object space gets mapped to two or more points in image space, and also sometimes a single point in object space does not get mapped into any point in image space. When a star's single point in object space fails to map to at least one point in image space, the star seems to disappear temporarily. This does not mean the star's light is lost for that moment. It just means that it didn't get to your eye, it went somewhere else. Since planets represent several points in object space, it is highly likely that one or more points in the planet's object space get mapped to a points in image space, and the planet's image never winks out. Each individual ray is twinkling away as badly as any star, but when all of those individual rays are viewed together, the next effect is averaged out to something considerably steadier. The result is that stars tend to twinkle, and planets do not. Other extended objects in space, even very far ones like nebulae, do not twinkle if they are sufficiently large that they have non-zero apparent diameter when viewed from the Earth. ******************************************************************************** Item 22. TIME TRAVEL - FACT OR FICTION? updated 07-MAR-1994 ------------------------------ original by Jon J. Thaler We define time travel to mean departure from a certain place and time followed (from the traveller's point of view) by arrival at the same place at an earlier (from the sedentary observer's point of view) time. Time travel paradoxes arise from the fact that departure occurs after arrival according to one observer and before arrival according to another. In the terminology of special relativity time travel implies that the timelike ordering of events is not invariant. This violates our intuitive notions of causality. However, intuition is not an infallible guide, so we must be careful. Is time travel really impossible, or is it merely another phenomenon where "impossible" means "nature is weirder than we think?" The answer is more interesting than you might think. THE SCIENCE FICTION PARADIGM: The B-movie image of the intrepid chrononaut climbing into his time machine and watching the clock outside spin backwards while those outside the time machine watch the him revert to callow youth is, according to current theory, impossible. In current theory, the arrow of time flows in only one direction at any particular place. If this were not true, then one could not impose a 4-dimensional coordinate system on space-time, and many nasty consequences would result. Nevertheless, there is a scenario which is not ruled out by present knowledge. This usually requires an unusual spacetime topology (due to wormholes or strings in general relativity) which has not yet seen, but which may be possible. In this scenario the universe is well behaved in every local region; only by exploring the global properties does one discover time travel. CONSERVATION LAWS: It is sometimes argued that time travel violates conservation laws. For example, sending mass back in time increases the amount of energy that exists at that time. Doesn't this violate conservation of energy? This argument uses the concept of a global conservation law, whereas relativistically invariant formulations of the equations of physics only imply local conservation. A local conservation law tells us that the amount of stuff inside a small volume changes only when stuff flows in or out through the surface. A global conservation law is derived from this by integrating over all space and assuming that there is no flow in or out at infinity. If this integral cannot be performed, then global conservation does not follow. So, sending mass back in time might be all right, but it implies that something strange is happening. (Why shouldn't we be able to do the integral?) GENERAL RELATIVITY: One case where global conservation breaks down is in general relativity. It is well known that global conservation of energy does not make sense in an expanding universe. For example, the universe cools as it expands; where does the energy go? See FAQ article #7 - Energy Conservation in Cosmology, for details. It is interesting to note that the possibility of time travel in GR has been known at least since 1949 (by Kurt Godel, discussed in [1], page 168). The GR spacetime found by Godel has what are now called "closed timelike curves" (CTCs). A CTC is a worldline that a particle or a person can follow which ends at the same spacetime point (the same position and time) as it started. A solution to GR which contains CTCs cannot have a spacelike embedding - space must have "holes" (as in donut holes, not holes punched in a sheet of paper). A would-be time traveller must go around or through the holes in a clever way. The Godel solution is a curiosity, not useful for constructing a time machine. Two recent proposals, one by Morris, et al. [2] and one by Gott [3], have the possibility of actually leading to practical devices (if you believe this, I have a bridge to sell you). As with Godel, in these schemes nothing is locally strange; time travel results from the unusual topology of spacetime. The first uses a wormhole (the inner part of a black hole, see fig. 1 of [2]) which is held open and manipulated by electromagnetic forces. The second uses the conical geometry generated by an infinitely long string of mass. If two strings pass by each other, a clever person can go into the past by traveling a figure-eight path around the strings. In this scenario, if the string has non-zero diameter and finite mass density, there is a CTC without any unusual topology. GRANDFATHER PARADOXES: With the demonstration that general relativity contains CTCs, people began studying the problem of self-consistency. Basically, the problem is that of the "grandfather paradox": What happens if our time traveller kills her grandmother before her mother was born? In more readily analyzable terms, one can ask what are the implications of the quantum mechanical interference of the particle with its future self. Boulware [5] shows that there is a problem - unitarity is violated. This is related to the question of when one can do the global conservation integral discussed above. It is an example of the "Cauchy problem" [1, chapter 7]. OTHER PROBLEMS (and an escape hatch?): How does one avoid the paradox that a simple solution to GR has CTCs which QM does not like? This is not a matter of applying a theory in a domain where it is expected to fail. One relevant issue is the construction of the time machine. After all, infinite strings aren't easily obtained. In fact, it has been shown [4] that Gott's scenario implies that the total 4-momentum of spacetime must be spacelike. This seems to imply that one cannot build a time machine from any collection of non-tachyonic objects, whose 4-momentum must be timelike. There are implementation problems with the wormhole method as well. TACHYONS: Finally, a diversion on a possibly related topic. If tachyons exist as physical objects, causality is no longer invariant. Different observers will see different causal sequences. This effect requires only special relativity (not GR), and follows from the fact that for any spacelike trajectory, reference frames can be found in which the particle moves backward or forward in time. This is illustrated by the pair of spacetime diagrams below. One must be careful about what is actually observed; a particle moving backward in time is observed to be a forward moving anti-particle, so no observer interprets this as time travel. t One reference | Events A and C are at the same frame: | place. C occurs first. | | Event B lies outside the causal | B domain of events A and C. -----------A----------- x (The intervals are spacelike). | C In this frame, tachyon signals | travel from A-->B and from C-->B. | That is, A and C are possible causes of event B. Another t reference | Events A and C are not at the same frame: | place. C occurs first. | | Event B lies outside the causal -----------A----------- x domain of events A and C. (The | intervals are spacelike) | | C In this frame, signals travel from | B-->A and from B-->C. B is the cause | B of both of the other two events. The unusual situation here arises because conventional causality assumes no superluminal motion. This tachyon example is presented to demonstrate that our intuitive notion of causality may be flawed, so one must be careful when appealing to common sense. See FAQ article # 25 - Tachyons, for more about these weird hypothetical particles. CONCLUSION: The possible existence of time machines remains an open question. None of the papers criticizing the two proposals are willing to categorically rule out the possibility. Nevertheless, the notion of time machines seems to carry with it a serious set of problems. REFERENCES: 1: S.W. Hawking, and G.F.R. Ellis, "The Large Scale Structure of Space-Time," Cambridge University Press, 1973. 2: M.S. Morris, K.S. Thorne, and U. Yurtsever, PRL, v.61, p.1446 (1989). --> How wormholes can act as time machines. 3: J.R. Gott, III, PRL, v.66, p.1126 (1991). --> How pairs of cosmic strings can act as time machines. 4: S. Deser, R. Jackiw, and G. 't Hooft, PRL, v.66, p.267 (1992). --> A critique of Gott. You can't construct his machine. 5: D.G. Boulware, University of Washington preprint UW/PT-92-04. Available on the hep-th@xxx.lanl.gov bulletin board: item number 9207054. --> Unitarity problems in QM with closed timelike curves. 6: "Nature", May 7, 1992 --> Contains a very well written review with some nice figures. ******************************************************************************** Item 23. Open Questions updated 01-JUN-1993 by SIC -------------- original by John Baez While for the most part a FAQ covers the answers to frequently asked questions whose answers are known, in physics there are also plenty of simple and interesting questions whose answers are not known. Before you set about answering these questions on your own, it's worth noting that while nobody knows what the answers are, there has been at least a little, and sometimes a great deal, of work already done on these subjects. People have said a lot of very intelligent things about many of these questions. So do plenty of research and ask around before you try to cook up a theory that'll answer one of these and win you the Nobel prize! You can expect to really know physics inside and out before you make any progress on these. The following partial list of "open" questions is divided into two groups, Cosmology and Astrophysics, and Particle and Quantum Physics. However, given the implications of particle physics on cosmology, the division is somewhat artificial, and, consequently, the categorization is somewhat arbitrary. (There are many other interesting and fundamental questions in fields such as condensed matter physics, nonlinear dynamics, etc., which are not part of the set of related questions in cosmology and quantum physics which are discussed below. Their omission is not a judgement about importance, but merely a decision about the scope of this article.) Cosmology and Astrophysics -------------------------- 1. What happened at or before the Big Bang? Was there really an initial singularity? Of course, this question might not make sense, but it might. Does the history of the Universe go back in time forever, or only a finite amount? 2. Will the future of the universe go on forever or not? Will there be a "big crunch" in the future? Is the Universe infinite in spatial extent? 3. Why is there an arrow of time; that is, why is the future so much different from the past? 4. Is spacetime really four-dimensional? If so, why - or is that just a silly question? Or is spacetime not really a manifold at all if examined on a short enough distance scale? 5. Do black holes really exist? (It sure seems like it.) Do they really radiate energy and evaporate the way Hawking predicts? If so, what happens when, after a finite amount of time, they radiate completely away? What's left? Do black holes really violate all conservation laws except conservation of energy, momentum, angular momentum and electric charge? What happens to the information contained in an object that falls into a black hole? Is it lost when the black hole evaporates? Does this require a modification of quantum mechanics? 6. Is the Cosmic Censorship Hypothesis true? Roughly, for generic collapsing isolated gravitational systems are the singularities that might develop guaranteed to be hidden beyond a smooth event horizon? If Cosmic Censorship fails, what are these naked singularities like? That is, what weird physical consequences would they have? 7. Why are the galaxies distributed in clumps and filaments? Is most of the matter in the universe baryonic? Is this a matter to be resolved by new physics? 8. What is the nature of the missing "Dark Matter"? Is it baryonic, neutrinos, or something more exotic? Particle and Quantum Physics ---------------------------- 1. Why are the laws of physics not symmetrical between left and right, future and past, and between matter and antimatter? I.e., what is the mechanism of CP violation, and what is the origin of parity violation in Weak interactions? Are there right-handed Weak currents too weak to have been detected so far? If so, what broke the symmetry? Is CP violation explicable entirely within the Standard Model, or is some new force or mechanism required? 2. Why are the strengths of the fundamental forces (electromagnetism, weak and strong forces, and gravity) what they are? For example, why is the fine structure constant, which measures the strength of electromagnetism, about 1/137.036? Where did this dimensionless constant of nature come from? Do the forces really become Grand Unified at sufficiently high energy? 3. Why are there 3 generations of leptons and quarks? Why are their mass ratios what they are? For example, the muon is a particle almost exactly like the electron except about 207 times heavier. Why does it exist and why precisely that much heavier? Do the quarks or leptons have any substructure? 4. Is there a consistent and acceptable relativistic quantum field theory describing interacting (not free) fields in four spacetime dimensions? For example, is the Standard Model mathematically consistent? How about Quantum Electrodynamics? 5. Is QCD a true description of quark dynamics? Is it possible to calculate masses of hadrons (such as the proton, neutron, pion, etc.) correctly from the Standard Model? Does QCD predict a quark/gluon deconfinement phase transition at high temperature? What is the nature of the transition? Does this really happen in Nature? 6. Why is there more matter than antimatter, at least around here? Is there really more matter than antimatter throughout the universe? 7. What is meant by a "measurement" in quantum mechanics? Does "wavefunction collapse" actually happen as a physical process? If so, how, and under what conditions? If not, what happens instead? 8. What are the gravitational effects, if any, of the immense (possibly infinite) vacuum energy density seemingly predicted by quantum field theory? Is it really that huge? If so, why doesn't it act like an enormous cosmological constant? 9. Why doesn't the flux of solar neutrinos agree with predictions? Is the disagreement really significant? If so, is the discrepancy in models of the sun, theories of nuclear physics, or theories of neutrinos? Are neutrinos really massless? The Big Question (TM) --------------------- This last question sits on the fence between the two categories above: How do you merge Quantum Mechanics and General Relativity to create a quantum theory of gravity? Is Einstein's theory of gravity (classical GR) also correct in the microscopic limit, or are there modifications possible/required which coincide in the observed limit(s)? Is gravity really curvature, or what else -- and why does it then look like curvature? An answer to this question will necessarily rely upon, and at the same time likely be a large part of, the answers to many of the other questions above. ******************************************************************************** END OF FAQ PART 3/4 Article: 5898 of sci.physics.particle Path: senator-bedfellow.mit.edu!bloom-beacon.mit.edu!paperboy.osf.org!mogul.osf.org!columbus From: columbus@osf.org Newsgroups: sci.physics,sci.physics.research,sci.physics.cond-matter,sci.physics.particle,alt.sci.physics.new-theories,sci.answers,alt.answers,news.answers Subject: sci.physics Frequently Asked Questions (Part 4 of 4) Supersedes: Followup-To: sci.physics Date: 13 Oct 1995 14:41:04 GMT Organization: Open Software Foundation Lines: 1405 Approved: news-answers-request@MIT.EDU Distribution: world Expires: 17-Nov 1995 Message-ID: References: Reply-To: columbus@osf.org (Michael Weiss) NNTP-Posting-Host: mogul.osf.org Summary: This posting contains a list of Frequently Asked Questions (and their answers) about physics, and should be read by anyone who wishes to post to the sci.physics.* newsgroups. Keywords: Sci.physics FAQ X-Posting-Frequency: posted monthly Originator: columbus@mogul.osf.org Xref: senator-bedfellow.mit.edu sci.physics:147073 sci.physics.research:3043 sci.physics.cond-matter:558 sci.physics.particle:5898 alt.sci.physics.new-theories:21141 sci.answers:3266 alt.answers:12767 news.answers:55204 Posted-By: auto-faq 3.1.1.2 Archive-name: physics-faq/part4 -------------------------------------------------------------------------------- FREQUENTLY ASKED QUESTIONS ON SCI.PHYSICS - Part 4/4 -------------------------------------------------------------------------------- Item 24. Special Relativistic Paradoxes - part (a) The Barn and the Pole updated 4-AUG-1992 by SIC --------------------- original by Robert Firth These are the props. You own a barn, 40m long, with automatic doors at either end, that can be opened and closed simultaneously by a switch. You also have a pole, 80m long, which of course won't fit in the barn. Now someone takes the pole and tries to run (at nearly the speed of light) through the barn with the pole horizontal. Special Relativity (SR) says that a moving object is contracted in the direction of motion: this is called the Lorentz Contraction. So, if the pole is set in motion lengthwise, then it will contract in the reference frame of a stationary observer. You are that observer, sitting on the barn roof. You see the pole coming towards you, and it has contracted to a bit less than 40m. So, as the pole passes through the barn, there is an instant when it is completely within the barn. At that instant, you close both doors. Of course, you open them again pretty quickly, but at least momentarily you had the contracted pole shut up in your barn. The runner emerges from the far door unscathed. But consider the problem from the point of view of the runner. She will regard the pole as stationary, and the barn as approaching at high speed. In this reference frame, the pole is still 80m long, and the barn is less than 20 meters long. Surely the runner is in trouble if the doors close while she is inside. The pole is sure to get caught. Well does the pole get caught in the door or doesn't it? You can't have it both ways. This is the "Barn-pole paradox." The answer is buried in the misuse of the word "simultaneously" back in the first sentence of the story. In SR, that events separated in space that appear simultaneous in one frame of reference need not appear simultaneous in another frame of reference. The closing doors are two such separate events. SR explains that the two doors are never closed at the same time in the runner's frame of reference. So there is always room for the pole. In fact, the Lorentz transformation for time is t'=(t-v*x/c^2)/sqrt(1-v^2/c^2). It's the v*x term in the numerator that causes the mischief here. In the runner's frame the further event (larger x) happens earlier. The far door is closed first. It opens before she gets there, and the near door closes behind her. Safe again - either way you look at it, provided you remember that simultaneity is not a constant of physics. References: Taylor and Wheeler's _Spacetime Physics_ is the classic. Feynman's _Lectures_ are interesting as well. ******************************************************************************** Item 24. Special Relativistic Paradoxes - part (b) The Twin Paradox updated 04-MAR-1994 by SIC ---------------- original by Kurt Sonnenmoser A Short Story about Space Travel: Two twins, conveniently named A and B, both know the rules of Special Relativity. One of them, B, decides to travel out into space with a velocity near the speed of light for a time T, after which she returns to Earth. Meanwhile, her boring sister A sits at home posting to Usenet all day. When B finally comes home, what do the two sisters find? Special Relativity (SR) tells A that time was slowed down for the relativistic sister, B, so that upon her return to Earth, she knows that B will be younger than she is, which she suspects was the the ulterior motive of the trip from the start. But B sees things differently. She took the trip just to get away >from the conspiracy theorists on Usenet, knowing full well that from her point of view, sitting in the spaceship, it would be her sister, A, who was travelling ultrarelativistically for the whole time, so that she would arrive home to find that A was much younger than she was. Unfortunate, but worth it just to get away for a while. What are we to conclude? Which twin is really younger? How can SR give two answers to the same question? How do we avoid this apparent paradox? Maybe twinning is not allowed in SR? Read on. Paradox Resolved: Much of the confusion surrounding the so-called Twin Paradox originates from the attempts to put the two twins into different frames --- without the useful concept of the proper time of a moving body. SR offers a conceptually very clear treatment of this problem. First chose _one_ specific inertial frame of reference; let's call it S. Second define the paths that A and B take, their so-called world lines. As an example, take (ct,0,0,0) as representing the world line of A, and (ct,f(t),0,0) as representing the world line of B (assuming that the the rest frame of the Earth was inertial). The meaning of the above notation is that at time t, A is at the spatial location (x1,x2,x3)=(0,0,0) and B is at (x1,x2,x3)=(f(t),0,0) --- always with respect to S. Let us now assume that A and B are at the same place at the time t1 and again at a later time t2, and that they both carry high-quality clocks which indicate zero at time t1. High quality in this context means that the precision of the clock is independent of acceleration. [In principle, a bunch of muons provides such a device (unit of time: half-life of their decay).] The correct expression for the time T such a clock will indicate at time t2 is the following [the second form is slightly less general than the first, but it's the good one for actual calculations]: t2 t2 _______________ / / / 2 | T = | d\tau = | dt \/ 1 - [v(t)/c] (1) / / t1 t1 where d\tau is the so-called proper-time interval, defined by 2 2 2 2 2 (c d\tau) = (c dt) - dx1 - dx2 - dx3 . Furthermore, d d v(t) = -- (x1(t), x2(t), x3(t)) = -- x(t) dt dt is the velocity vector of the moving object. The physical interpretation of the proper-time interval, namely that it is the amount the clock time will advance if the clock moves by dx during dt, arises from considering the inertial frame in which the clock is at rest at time t --- its so-called momentary rest frame (see the literature cited below). [Notice that this argument is only of heuristic value, since one has to assume that the absolute value of the acceleration has no effect. The ultimate justification of this interpretation must come from experiment.] The integral in (1) can be difficult to evaluate, but certain important facts are immediately obvious. If the object is at rest with respect to S, one trivially obtains T = t2-t1. In all other cases, T must be strictly smaller than t2-t1, since the integrand is always less than or equal to unity. Conclusion: the traveling twin is younger. Furthermore, if she moves with constant velocity v most of the time (periods of acceleration short compared to the duration of the whole trip), T will approximately be given by ____________ / 2 | (t2-t1) \/ 1 - [v/c] . (2) The last expression is exact for a round trip (e.g. a circle) with constant velocity v. [At the times t1 and t2, twin B flies past twin A and they compare their clocks.] Now the big deal with SR, in the present context, is that T (or d\tau, respectively) is a so-called Lorentz scalar. In other words, its value does not depend on the choice of S. If we Lorentz transform the coordinates of the world lines of the twins to another inertial frame S', we will get the same result for T in S' as in S. This is a mathematical fact. It shows that the situation of the traveling twins cannot possibly lead to a paradox _within_ the framework of SR. It could at most be in conflict with experimental results, which is also not the case. Of course the situation of the two twins is not symmetric, although one might be tempted by expression (2) to think the opposite. Twin A is at rest in one and the same inertial frame for all times, whereas twin B is not. [Formula (1) does not hold in an accelerated frame.] This breaks the apparent symmetry of the two situations, and provides the clearest nonmathematical hint that one twin will in fact be younger than the other at the end of the trip. To figure out *which* twin is the younger one, use the formulae above in a frame in which they are valid, and you will find that B is in fact younger, despite her expectations. It is sometimes claimed that one has to resort to General Relativity in order to "resolve" the Twin "Paradox". This is not true. In flat, or nearly flat, space-time (no strong gravity), SR is completely sufficient, and it has also no problem with world lines corresponding to accelerated motion. References: Taylor and Wheeler, _Spacetime Physics_ (An *excellent* discussion) Goldstein, _Classical Mechanics_, 2nd edition, Chap.7 (for a good general discussion of Lorentz transformations and other SR basics.) ******************************************************************************** Item 24. Special Relativistic Paradoxes - part (c) The Superluminal Scissors updated 31-MAR-1993 ------------------------- original by Scott I.Chase A Gedankenexperiment: Imagine a huge pair of scissors, with blades one light-year long. The handle is only about two feet long, creating a huge lever arm, initially open by a few degrees. Then you suddenly close the scissors. This action takes about a tenth of a second. Doesn't the contact point where the two blades touch move down the blades *much* faster than the speed of light? After all, the scissors close in a tenth of a second, but the blades are a light-year long. That seems to mean that the contact point has moved down the blades at the remarkable speed of 10 light-years per second. This is more than 10^8 times the speed of light! But this seems to violate the most important rule of Special Relativity - no signal can travel faster than the speed of light. What's going on here? Explanation: We have mistakenly assumed that the scissors do in fact close when you close the handle. But, in fact, according to Special Relativity, this is not at all what happens. What *does* happen is that the blades of the scissors flex. No matter what material you use for the scissors, SR sets a theoretical upper limit to the rigidity of the material. In short, when you close the scissors, they bend. The point at which the blades bend propagates down the blade at some speed less than the speed of light. On the near side of this point, the scissors are closed. On the far side of this point, the scissors remain open. You have, in fact, sent a kind of wave down the scissors, carrying the information that the scissors have been closed. But this wave does not travel faster than the speed of light. It will take at least one year for the tips of the blades, at the far end of the scissors, to feel any force whatsoever, and, ultimately, to come together to completely close the scissors. As a practical matter, this theoretical upper limit to the rigidity of the metal in the scissors is *far* higher than the rigidity of any real material, so it would, in practice, take much much longer to close a real pair of metal scissors with blades as long as these. One can analyze this problem microscopically as well. The electromagnetic force which binds the atoms of the scissors together propagates at the speeds of light. So if you displace some set of atoms in the scissor (such as the entire handles), the force will not propagate down the scissor instantaneously, This means that a scissor this big *must* cease to act as a rigid body. You can move parts of it without other parts moving at the same time. It takes some finite time for the changing forces on the scissor to propagate from atom to atom, letting the far tip of the blades "know" that the scissors have been closed. Caveat: The contact point where the two blades meet is not a physical object. So there is no fundamental reason why it could not move faster than the speed of light, provided that you arrange your experiment correctly. In fact it can be done with scissors provided that your scissors are short enough and wide open to start, very different conditions than those spelled out in the gedankenexperiment above. In this case it will take you quite a while to bring the blades together - more than enough time for light to travel to the tips of the scissors. When the blades finally come together, if they have the right shape, the contact point can indeed move faster than light. Think about the simpler case of two rulers pinned together at an edge point at the ends. Slam the two rulers together and the contact point will move infinitely fast to the far end of the rulers at the instant they touch. So long as the rulers are short enough that contact does not happen until the signal propagates to the far ends of the rulers, the rulers will indeed be straight when they meet. Only if the rulers are too long will they be bent like our very long scissors, above, when they touch. The contact point can move faster than the speed of light, but the energy (or signal) of the closing force can not. An analogy, equivalent in terms of information content, is, say, a line of strobe lights. You want to light them up one at a time, so that the `bright' spot travels faster than light. To do so, you can send a _luminal_ signal down the line, telling each strobe light to wait a little while before flashing. If you decrease the wait time with each successive strobe light, the apparent bright spot will travel faster than light, since the strobes on the end didn't wait as long after getting the go-ahead, as did the ones at the beginning. But the bright spot can't pass the original signal, because then the strobe lights wouldn't know to flash. ******************************************************************************** Item 25. Can You See the Lorentz-Fitzgerald Contraction? 12-Oct-1995 Or: Penrose-Terrell Rotation by Michael Weiss People sometimes argue over whether the Lorentz-Fitzgerald contraction is "real" or not. That's a topic for another FAQ entry, but here's a short answer: the contraction can be measured, but the measurement is frame-dependent. Whether that makes it "real" or not has more to do with your choice of words than the physics. Here we ask a subtly different question. If you take a snapshot of a rapidly moving object, will it *look* flattened when you develop the film? What is the difference between measuring and photographing? Isn't seeing believing? Not always! When you take a snapshot, you capture the light-rays that hit the *film* at one instant (in the reference frame of the film). These rays may have left the *object* at different instants; if the object is moving with respect to the film, then the photograph may give a distorted picture. (Strictly speaking snapshots aren't instantaneous, but we're idealizing.) Oddly enough, though Einstein published his famous relativity paper in 1905, and Fitzgerald proposed his contraction several years earlier, no one seems to have asked this question until the late '50s. Then Roger Penrose and James Terrell independently discovered that the object will *not* appear flattened [1,2]. People sometimes say that the object appears rotated, so this effect is called the Penrose-Terrell rotation. Calling it a rotation can be a bit confusing though. Rotating an object brings its backside into view, but it's hard to see how a contraction could do that. Among other things, this entry will try to explain in just what sense the Penrose-Terrell effect is a "rotation". It will clarify matters to imagine *two* snapshots of the same object, taken by two cameras moving uniformly with respect to each other. We'll call them *his* camera and *her* camera. The cameras pass through each other at the origin at t=0, when they take their two snapshots. Say that the object is at rest with respect to his camera, and moving with respect to hers. By analysing the process of taking a snapshot, the meaning of "rotation" will become clearer. How should we think of a snapshot? Here's one way: consider a pinhole camera. (Just one camera, for the moment.) The pinhole is located at the origin, and the film occupies a patch on a sphere surrounding the origin. We'll ignore all technical difficulties(!), and pretend that the camera takes full spherical pictures: the film occupies the entire sphere. We need more than just a pinhole and film, though: we also need a shutter. At t=0, the shutter snaps open for an instant to let the light-rays through the pinhole; these spread out in all directions, and at t=1 (in the rest-frame of the camera) paint a picture on the spherical film. Let's call points in the snapshot *pixels*. Each pixel gets its color due to an event, namely a light-ray hitting the sphere at t=1. Now let's consider his & her cameras, as we said before. We'll use t for his time, and t' for hers. At t=t'=0, the two pinholes coincide at the origin, the two shutters snap simultaneously, and the light rays spread out. At t=1 for *his* camera, they paint *his* pixels; at t'=1 for *her* camera, they paint *hers*. So the definition of a snapshot is frame-dependent. But you already knew that. (Pop quiz: what shape does *he* think *her* film has? Not spherical!) (More technical difficulties: the rays have to pass right through one film to hit the other.) So there's a one-one correspondence between pixels in the two snapshots. Two pixels correspond if they are painted by the same light-ray. You can see now that her snapshot is just a distortion of his (and vice versa). You could take his snapshot, scan it into a computer, run an algorithm to move the pixels around, and print out hers. So what does the pixel mapping look like? Simple: if we put the usual latitude/longitude grid on the spheres, chosen so that the relative motion is along the north-south axis, then each pixel slides up towards the north pole along a line of longitude. (Or down towards the south pole, depending on various choices I haven't specified.) This should ring a bell if you know about the aberration of light: if our snapshots portray the night-sky, then the stars are white pixels, and aberration changes their apparent positions. Now let's consider the object--- let's say a galaxy. In passing from his snapshot to hers, the image of the galaxy slides up the sphere, keeping the same face to us. In this sense, it has rotated. Its apparent size will also change, but not its shape (to a first approximation). The mathematical details are beautiful, but best left to the textbooks [3,4]. Just to entice you if you have the background: if we regard the two spheres as Riemann spheres, then the pixel mapping is given by a fractional linear transformation. Well-known facts from complex analysis now tell us two things. First, circles go to circles under the pixel mapping, so a sphere will *always* photograph as a sphere. Second, shapes of objects are preserved in the infinitesimally small limit. (If you know about the double-covering of SL(2), that also comes into play. [3] is a good reference.) References: [1] and [2] are the original articles. [3] and [4] are textbook treatments. [5] has beautiful computer-generated pictures of the Penrose-Terrell rotation. The authors of [5] later made a video [6] of this and other effects of "SR photography". [1] Penrose, R.,"The Apparent Shape of a Relativistically Moving Sphere", Proc. Camb. Phil. Soc., vol 55 Jul 1958. [2] Terrell, J., "Invisibility of the Lorentz Contraction", Phys. Rev. vol 116 no. 4 pp. 1041-1045 (1959). [3] Penrose, R., and W. Rindler, "Spinors and Space-Time", vol I chapter 1. [4] Marion, "Classical Dynamics", Section 10.5. [5] Hsiung, Ping-Kang, Robert H. Thibadeau, and Robert H. P. Dunn, "Ray-Tracing Relativity", Pixel, vol 1 no. 1 (Jan/Feb 1990). [6] Hsiung, Ping-Kang, and Robert H. Thibadeau, "Spacetime Visualizations," a video, Imaging Systems Lab, Robotics Institute, Carnegie Mellon University. ******************************************************************************** Item 26. Tachyons updated: 22-MAR-1993 by SIC -------- original by Scott I. Chase There was a young lady named Bright, Whose speed was far faster than light. She went out one day, In a relative way, And returned the previous night! -Reginald Buller It is a well known fact that nothing can travel faster than the speed of light. At best, a massless particle travels at the speed of light. But is this really true? In 1962, Bilaniuk, Deshpande, and Sudarshan, Am. J. Phys. _30_, 718 (1962), said "no". A very readable paper is Bilaniuk and Sudarshan, Phys. Today _22_,43 (1969). I give here a brief overview. Draw a graph, with momentum (p) on the x-axis, and energy (E) on the y-axis. Then draw the "light cone", two lines with the equations E = +/- p. This divides our 1+1 dimensional space-time into two regions. Above and below are the "timelike" quadrants, and to the left and right are the "spacelike" quadrants. Now the fundamental fact of relativity is that E^2 - p^2 = m^2. (Let's take c=1 for the rest of the discussion.) For any non-zero value of m (mass), this is an hyperbola with branches in the timelike regions. It passes through the point (p,E) = (0,m), where the particle is at rest. Any particle with mass m is constrained to move on the upper branch of this hyperbola. (Otherwise, it is "off-shell", a term you hear in association with virtual particles - but that's another topic.) For massless particles, E^2 = p^2, and the particle moves on the light-cone. These two cases are given the names tardyon (or bradyon in more modern usage) and luxon, for "slow particle" and "light particle". Tachyon is the name given to the supposed "fast particle" which would move with v>c. Now another familiar relativistic equation is E = m*[1-(v/c)^2]^(-.5). Tachyons (if they exist) have v > c. This means that E is imaginary! Well, what if we take the rest mass m, and take it to be imaginary? Then E is negative real, and E^2 - p^2 = m^2 < 0. Or, p^2 - E^2 = M^2, where M is real. This is a hyperbola with branches in the spacelike region of spacetime. The energy and momentum of a tachyon must satisfy this relation. You can now deduce many interesting properties of tachyons. For example, they accelerate (p goes up) if they lose energy (E goes down). Futhermore, a zero-energy tachyon is "transcendent," or infinitely fast. This has profound consequences. For example, let's say that there were electrically charged tachyons. Since they would move faster than the speed of light in the vacuum, they should produce Cerenkov radiation. This would *lower* their energy, causing them to accelerate more! In other words, charged tachyons would probably lead to a runaway reaction releasing an arbitrarily large amount of energy. This suggests that coming up with a sensible theory of anything except free (noninteracting) tachyons is likely to be difficult. Heuristically, the problem is that we can get spontaneous creation of tachyon-antitachyon pairs, then do a runaway reaction, making the vacuum unstable. To treat this precisely requires quantum field theory, which gets complicated. It is not easy to summarize results here. However, one reasonably modern reference is _Tachyons, Monopoles, and Related Topics_, E. Recami, ed. (North-Holland, Amsterdam, 1978). However, tachyons are not entirely invisible. You can imagine that you might produce them in some exotic nuclear reaction. If they are charged, you could "see" them by detecting the Cerenkov light they produce as they speed away faster and faster. Such experiments have been done. So far, no tachyons have been found. Even neutral tachyons can scatter off normal matter with experimentally observable consequences. Again, no such tachyons have been found. How about using tachyons to transmit information faster than the speed of light, in violation of Special Relativity? It's worth noting that when one considers the relativistic quantum mechanics of tachyons, the question of whether they "really" go faster than the speed of light becomes much more touchy! In this framework, tachyons are *waves* that satisfy a wave equation. Let's treat free tachyons of spin zero, for simplicity. We'll set c = 1 to keep things less messy. The wavefunction of a single such tachyon can be expected to satisfy the usual equation for spin-zero particles, the Klein-Gordon equation: (BOX + m^2)phi = 0 where BOX is the D'Alembertian, which in 3+1 dimensions is just BOX = (d/dt)^2 - (d/dx)^2 - (d/dy)^2 - (d/dz)^2. The difference with tachyons is that m^2 is *negative*, and m is imaginary. To simplify the math a bit, let's work in 1+1 dimensions, with coordinates x and t, so that BOX = (d/dt)^2 - (d/dx)^2 Everything we'll say generalizes to the real-world 3+1-dimensional case. Now - regardless of m, any solution is a linear combination, or superposition, of solutions of the form phi(t,x) = exp(-iEt + ipx) where E^2 - p^2 = m^2. When m^2 is negative there are two essentially different cases. Either |p| >= |E|, in which case E is real and we get solutions that look like waves whose crests move along at the rate |p|/|E| >= 1, i.e., no slower than the speed of light. Or |p| < |E|, in which case E is imaginary and we get solutions that look waves that amplify exponentially as time passes! We can decide as we please whether or not we want to consider the second sort of solutions. They seem weird, but then the whole business is weird, after all. 1) If we *do* permit the second sort of solution, we can solve the Klein-Gordon equation with any reasonable initial data - that is, any reasonable values of phi and its first time derivative at t = 0. (For the precise definition of "reasonable," consult your local mathematician.) This is typical of wave equations. And, also typical of wave equations, we can prove the following thing: If the solution phi and its time derivative are zero outside the interval [-L,L] when t = 0, they will be zero outside the interval [-L-|t|, L+|t|] at any time t. In other words, localized disturbances do not spread with speed faster than the speed of light! This seems to go against our notion that tachyons move faster than the speed of light, but it's a mathematical fact, known as "unit propagation velocity". 2) If we *don't* permit the second sort of solution, we can't solve the Klein-Gordon equation for all reasonable initial data, but only for initial data whose Fourier transforms vanish in the interval [-|m|,|m|]. By the Paley-Wiener theorem this has an odd consequence: it becomes impossible to solve the equation for initial data that vanish outside some interval [-L,L]! In other words, we can no longer "localize" our tachyon in any bounded region in the first place, so it becomes impossible to decide whether or not there is "unit propagation velocity" in the precise sense of part 1). Of course, the crests of the waves exp(-iEt + ipx) move faster than the speed of light, but these waves were never localized in the first place! The bottom line is that you can't use tachyons to send information faster than the speed of light from one place to another. Doing so would require creating a message encoded some way in a localized tachyon field, and sending it off at superluminal speed toward the intended receiver. But as we have seen you can't have it both ways - localized tachyon disturbances are subluminal and superluminal disturbances are nonlocal. ******************************************************************************** Item 27. The Particle Zoo updated 4-JUL-1995 by MCW ---------------- original by Matt Austern If you look in the Particle Data Book, you will find more than 150 particles listed there. It isn't quite as bad as that, though... The (observed) particles are divided into two major classes: the material particles, and the gauge bosons. We'll discuss the gauge bosons further down. The material particles in turn fall into three categories: leptons, mesons, and baryons. Leptons are particles that are like the electron: they have spin 1/2, and they do not undergo the strong interaction. There are three charged leptons, the electron, muon, and tau, and three corresponding neutral leptons, or neutrinos. (The muon and the tau are both short-lived.) Mesons and baryons both undergo strong interactions. The difference is that mesons have integral spin (0, 1,...), while baryons have half-integral spin (1/2, 3/2,...). The most familiar baryons are the proton and the neutron; all others are short-lived. The most familiar meson is the pion; its lifetime is 26 nanoseconds, and all other mesons decay even faster. Most of those 150+ particles are mesons and baryons, or, collectively, hadrons. The situation was enormously simplified in the 1960s by the "quark model," which says that hadrons are made out of spin-1/2 particles called quarks. A meson, in this model, is made out of a quark and an anti-quark, and a baryon is made out of three quarks. We don't see free quarks, but only hadrons; nevertheless, the evidence for quarks is compelling. Quark masses are not very well defined, since they are not free particles, but we can give estimates. The masses below are in GeV; the first is current mass and the second constituent mass (which includes some of the effects of the binding energy): Generation: 1 2 3 U-like: u=.006/.311 c=1.50/1.65 t=91-200/91-200 D-like: d=.010/.315 s=.200/.500 b=5.10/5.10 In the quark model, there are only 12 elementary particles, which appear in three "generations." The first generation consists of the up quark, the down quark, the electron, and the electron neutrino. (Each of these also has an associated antiparticle.) These particles make up all of the ordinary matter we see around us. There are two other generations, which are essentially the same, but with heavier particles. The second consists of the charm quark, the strange quark, the muon, and the muon neutrino; and the third consists of the top quark, the bottom quark, the tau, and the tau neutrino. These three generations are sometimes called the "electron family", the "muon family", and the "tau family." Finally, according to quantum field theory, particles interact by exchanging "gauge bosons," which are also particles. The most familiar on is the photon, which is responsible for electromagnetic interactions. There are also eight gluons, which are responsible for strong interactions, and the W+, W-, and Z, which are responsible for weak interactions. The picture, then, is this: FUNDAMENTAL PARTICLES OF MATTER Charge ------------------------- -1 | e | mu | tau | 0 | nu(e) |nu(mu) |nu(tau)| ------------------------- + antiparticles -1/3 | down |strange|bottom | 2/3 | up | charm | top | ------------------------- GAUGE BOSONS Charge Force 0 photon electromagnetism 0 gluons (8 of them) strong force +-1 W+ and W- weak force 0 Z weak force The Standard Model of particle physics also predicts the existence of a "Higgs boson," which has to do with breaking a symmetry involving these forces, and which is responsible for the masses of all the other particles. It has not yet been found. More complicated theories predict additional particles, including, for example, gauginos and sleptons and squarks (from supersymmetry), W' and Z' (additional weak bosons), X and Y bosons (from GUT theories), Majorons, familons, axions, paraleptons, ortholeptons, technipions (from technicolor models), B' (hadrons with fourth generation quarks), magnetic monopoles, e* (excited leptons), etc. None of these "exotica" have yet been seen. The search is on! REFERENCES: The best reference for information on which particles exist, their masses, etc., is the Particle Data Book. It is published every two years; the most recent edition is Physical Review D vol.50 No.3 part 1 August 1994. The Web version can be accessed through http://pdg.lbl.gov/. There are several good books that discuss particle physics on a level accessible to anyone who knows a bit of quantum mechanics. One is _Introduction to High Energy Physics_, by Perkins. Another, which takes a more historical approach and includes many original papers, is _Experimental Foundations of Particle Physics_, by Cahn and Goldhaber. For a book that is accessible to non-physicists, you could try _The Particle Explosion_ by Close, Sutton, and Marten. This book has fantastic photography. For a Web introduction by the folks at Fermilab, take a look at http://fnnews.fnal.gov/hep_overview.html . ******************************************************************************** Item 28. original by Scott I. Chase Does Antimatter Fall Up or Down? -------------------------------- This question has never been subject to a successful direct experiment. In other words, nobody has ever directly measured the gravititational acceleration of antimatter. So the bottom line is that we don't know yet. However, there is a lot more to say than just that, with regard to both theory and experiment. Here is a summary of the current state of affairs. (1) Is is even theoretically possible for antimatter to fall up? Answer: According to GR, antimatter falls down. If you believe that General Relativity is the exact true theory of gravity, then there is only one possible conclusion - by the equivalence principle, antiparticles must fall down with the same acceleration as normal matter. On the other hand: there are other models of gravity which are not ruled out by direct experiment which are distinct from GR in that antiparticles can fall down at different rates than normal matter, or even fall up, due to additional forces which couple to the mass of the particle in ways which are different than GR. Some people don't like to call these new couplings 'gravity.' They call them, generically, the 'fifth force,' defining gravity to be only the GR part of the force. But this is mostly a semantic distinction. The bottom line is that antiparticles won't fall like normal particles if one of these models is correct. There are also a variety of arguments, based upon different aspects of physics, against the possibility of antigravity. These include constraints imposed by conservation of energy (the "Morrison argument"), the detectable effects of virtual antiparticles (the "Schiff argument"), and the absense of gravitational effect in kaon regeneration experiments. Each of these does in fact rule out *some* models of antigravity. But none of them absolutely excludes all possible models of antigravity. See the reference below for all the details on these issues. (2) Haven't people done experiments to study this question? There are no valid *direct* experimental tests of whether antiparticles fall up or down. There was one well-known experiment by Fairbank at Stanford in which he tried to measure the fall of positrons. He found that they fell normally, but later analyses of his experiment revealed that he had not accounted for all the sources of stray electromagnetic fields. Because gravity is so much weaker than EM, this is a difficult experimental problem. A modern assessment of the Fairbank experiment is that it was inconclusive. In order to reduce the effect of gravity, it would be nice to repeat the Fairbank experiment using objects with the same magnitude of electric charge as positrons, but with much more mass, to increase the relative effect of gravity on the motion of the particle. Antiprotons are 1836 times more massive than positrons, so give you three orders of magnitude more sensitivity. Unfortunately, making many slow antiprotons which you can watch fall is very difficult. An experiment is under development at CERN right now to do just that, and within the next couple of years the results should be known. Most people expect that antiprotons *will* fall. But it is important to keep an open mind - we have never directly observed the effect of gravity on antiparticles. This experiment, if successful, will definitely be "one for the textbooks." Reference: Nieto and Goldman, "The Arguments Against 'Antigravity' and the Gravitational Acceleration of Antimatter," Physics Reports, v.205, No. 5, p.221. ******************************************************************************** Item 29. What is the Mass of a Photon? updated 24-JUL-1992 by SIC original by Matt Austern Or, "Does the mass of an object depend on its velocity?" This question usually comes up in the context of wondering whether photons are really "massless," since, after all, they have nonzero energy. The problem is simply that people are using two different definitions of mass. The overwhelming consensus among physicists today is to say that photons are massless. However, it is possible to assign a "relativistic mass" to a photon which depends upon its wavelength. This is based upon an old usage of the word "mass" which, though not strictly wrong, is not used much today. The old definition of mass, called "relativistic mass," assigns a mass to a particle proportional to its total energy E, and involved the speed of light, c, in the proportionality constant: m = E / c^2. (1) This definition gives every object a velocity-dependent mass. The modern definition assigns every object just one mass, an invariant quantity that does not depend on velocity. This is given by m = E_0 / c^2, (2) where E_0 is the total energy of that object at rest. The first definition is often used in popularizations, and in some elementary textbooks. It was once used by practicing physicists, but for the last few decades, the vast majority of physicists have instead used the second definition. Sometimes people will use the phrase "rest mass," or "invariant mass," but this is just for emphasis: mass is mass. The "relativistic mass" is never used at all. (If you see "relativistic mass" in your first-year physics textbook, complain! There is no reason for books to teach obsolete terminology.) Note, by the way, that using the standard definition of mass, the one given by Eq. (2), the equation "E = m c^2" is *not* correct. Using the standard definition, the relation between the mass and energy of an object can be written as E = m c^2 / sqrt(1 -v^2/c^2), (3) or as E^2 = m^2 c^4 + p^2 c^2, (4) where v is the object's velocity, and p is its momentum. In one sense, any definition is just a matter of convention. In practice, though, physicists now use this definition because it is much more convenient. The "relativistic mass" of an object is really just the same as its energy, and there isn't any reason to have another word for energy: "energy" is a perfectly good word. The mass of an object, though, is a fundamental and invariant property, and one for which we do need a word. The "relativistic mass" is also sometimes confusing because it mistakenly leads people to think that they can just use it in the Newtonian relations F = m a (5) and F = G m1 m2 / r^2. (6) In fact, though, there is no definition of mass for which these equations are true relativistically: they must be generalized. The generalizations are more straightforward using the standard definition of mass than using "relativistic mass." Oh, and back to photons: people sometimes wonder whether it makes sense to talk about the "rest mass" of a particle that can never be at rest. The answer, again, is that "rest mass" is really a misnomer, and it is not necessary for a particle to be at rest for the concept of mass to make sense. Technically, it is the invariant length of the particle's four-momentum. (You can see this from Eq. (4).) For all photons this is zero. On the other hand, the "relativistic mass" of photons is frequency dependent. UV photons are more energetic than visible photons, and so are more "massive" in this sense, a statement which obscures more than it elucidates. Reference: Lev Okun wrote a nice article on this subject in the June 1989 issue of Physics Today, which includes a historical discussion of the concept of mass in relativistic physics. ******************************************************************************** Item 30. original by David Brahm Baryogenesis - Why Are There More Protons Than Antiprotons? ----------------------------------------------------------- (I) How do we really *know* that the universe is not matter-antimatter symmetric? (a) The Moon: Neil Armstrong did not annihilate, therefore the moon is made of matter. (b) The Sun: Solar cosmic rays are matter, not antimatter. (c) The other Planets: We have sent probes to almost all. Their survival demonstrates that the solar system is made of matter. (d) The Milky Way: Cosmic rays sample material from the entire galaxy. In cosmic rays, protons outnumber antiprotons 10^4 to 1. (e) The Universe at large: This is tougher. If there were antimatter galaxies then we should see gamma emissions from annihilation. Its absence is strong evidence that at least the nearby clusters of galaxies (e.g., Virgo) are matter-dominated. At larger scales there is little proof. However, there is a problem, called the "annihilation catastrophe" which probably eliminates the possibility of a matter-antimatter symmetric universe. Essentially, causality prevents the separation of large chucks of antimatter from matter fast enough to prevent their mutual annihilation in in the early universe. So the Universe is most likely matter dominated. (II) How did it get that way? Annihilation has made the asymmetry much greater today than in the early universe. At the high temperature of the first microsecond, there were large numbers of thermal quark-antiquark pairs. K&T estimate 30 million antiquarks for every 30 million and 1 quarks during this epoch. That's a tiny asymmetry. Over time most of the antimatter has annihilated with matter, leaving the very small initial excess of matter to dominate the Universe. Here are a few possibilities for why we are matter dominated today: a) The Universe just started that way. Not only is this a rather sterile hypothesis, but it doesn't work under the popular "inflation" theories, which dilute any initial abundances. b) Baryogenesis occurred around the Grand Unified (GUT) scale (very early). Long thought to be the only viable candidate, GUT's generically have baryon-violating reactions, such as proton decay (not yet observed). c) Baryogenesis occurred at the Electroweak Phase Transition (EWPT). This is the era when the Higgs first acquired a vacuum expectation value (vev), so other particles acquired masses. Pure Standard Model physics. Sakharov enumerated 3 necessary conditions for baryogenesis: (1) Baryon number violation. If baryon number is conserved in all reactions, then the present baryon asymmetry can only reflect asymmetric initial conditions, and we are back to case (a), above. (2) C and CP violation. Even in the presence of B-violating reactions, without a preference for matter over antimatter the B-violation will take place at the same rate in both directions, leaving no excess. (3) Thermodynamic Nonequilibrium. Because CPT guarantees equal masses for baryons and antibaryons, chemical equilibrium would drive the necessary reactions to correct for any developing asymmetry. It turns out the Standard Model satisfies all 3 conditions: (1) Though the Standard Model conserves B classically (no terms in the Lagrangian violate B), quantum effects allow the universe to tunnel between vacua with different values of B. This tunneling is _very_ suppressed at energies/temperatures below 10 TeV (the "sphaleron mass"), _may_ occur at e.g. SSC energies (controversial), and _certainly_ occurs at higher temperatures. (2) C-violation is commonplace. CP-violation (that's "charge conjugation" and "parity") has been experimentally observed in kaon decays, though strictly speaking the Standard Model probably has insufficient CP-violation to give the observed baryon asymmetry. (3) Thermal nonequilibrium is achieved during first-order phase transitions in the cooling early universe, such as the EWPT (at T = 100 GeV or so). As bubbles of the "true vacuum" (with a nonzero Higgs vev) percolate and grow, baryogenesis can occur at or near the bubble walls. A major theoretical problem, in fact, is that there may be _too_ _much_ B-violation in the Standard Model, so that after the EWPT is complete (and condition 3 above is no longer satisfied) any previously generated baryon asymmetry would be washed out. References: Kolb and Turner, _The Early Universe_; Dine, Huet, Singleton & Susskind, Phys.Lett.B257:351 (1991); Dine, Leigh, Huet, Linde & Linde, Phys.Rev.D46:550 (1992). ******************************************************************************** Item 31. The EPR Paradox and Bell's Inequality Principle updated 31-AUG-1993 by SIC ----------------------------------------------- original by John Blanton In 1935 Albert Einstein and two colleagues, Boris Podolsky and Nathan Rosen (EPR) developed a thought experiment to demonstrate what they felt was a lack of completeness in quantum mechanics. This so-called "EPR paradox" has led to much subsequent, and still on-going, research. This article is an introduction to EPR, Bell's inequality, and the real experiments which have attempted to address the interesting issues raised by this discussion. One of the principal features of quantum mechanics is that not all the classical physical observables of a system can be simultaneously known, either in practice or in principle. Instead, there may be several sets of observables which give qualitatively different, but nonetheless complete (maximal possible) descriptions of a quantum mechanical system. These sets are sets of "good quantum numbers," and are also known as "maximal sets of commuting observables." Observables from different sets are "noncommuting observables." A well known example of noncommuting observables is position and momentum. You can put a subatomic particle into a state of well-defined momentum, but then you cannot know where it is - it is, in fact, everywhere at once. It's not just a matter of your inability to measure, but rather, an intrinsic property of the particle. Conversely, you can put a particle in a definite position, but then its momentum is completely ill-defined. You can also create states of intermediate knowledge of both observables: If you confine the particle to some arbitrarily large region of space, you can define the momentum more and more precisely. But you can never know both, exactly, at the same time. Position and momentum are continuous observables. But the same situation can arise for discrete observables such as spin. The quantum mechanical spin of a particle along each of the three space axes is a set of mutually noncommuting observables. You can only know the spin along one axis at a time. A proton with spin "up" along the x-axis has undefined spin along the y and z axes. You cannot simultaneously measure the x and y spin projections of a proton. EPR sought to demonstrate that this phenomenon could be exploited to construct an experiment which would demonstrate a paradox which they believed was inherent in the quantum-mechanical description of the world. They imagined two physical systems that are allowed to interact initially so that they subsequently will be defined by a single Schrodinger wave equation (SWE). [For simplicity, imagine a simple physical realization of this idea - a neutral pion at rest in your lab, which decays into a pair of back-to-back photons. The pair of photons is described by a single two-particle wave function.] Once separated, the two systems [read: photons] are still described by the same SWE, and a measurement of one observable of the first system will determine the measurement of the corresponding observable of the second system. [Example: The neutral pion is a scalar particle - it has zero angular momentum. So the two photons must speed off in opposite directions with opposite spin. If photon 1 is found to have spin up along the x-axis, then photon 2 *must* have spin down along the x-axis, since the total angular momentum of the final-state, two-photon, system must be the same as the angular momentum of the intial state, a single neutral pion. You know the spin of photon 2 even without measuring it.] Likewise, the measurement of another observable of the first system will determine the measurement of the corresponding observable of the second system, even though the systems are no longer physically linked in the traditional sense of local coupling. However, QM prohibits the simultaneous knowledge of more than one mutually noncommuting observable of either system. The paradox of EPR is the following contradiction: For our coupled systems, we can measure observable A of system I [for example, photon 1 has spin up along the x-axis; photon 2 must therefore have x-spin down.] and observable B of system II [for example, photon 2 has spin down along the y-axis; therefore the y-spin of photon 1 must be up.] thereby revealing both observables for both systems, contrary to QM. QM dictates that this should be impossible, creating the paradoxical implication that measuring one system should "poison" any measurement of the other system, no matter what the distance between them. [In one commonly studied interpretation, the mechanism by which this proceeds is 'instantaneous collapse of the wavefunction'. But the rules of QM do not require this interpretation, and several other perfectly valid interpretations exist.] The second system would instantaneously be put into a state of well-defined observable A, and, consequently, ill-defined observable B, spoiling the measurement. Yet, one could imagine the two measurements were so far apart in space that special relativity would prohibit any influence of one measurement over the other. [After the neutral-pion decay, we can wait until the two photons are a light-year apart, and then "simultaneously" measure the x-spin of photon 1 and the y-spin of photon 2. QM suggests that if, for example, the measurement of the photon 1 x-spin happens first, this measurement must instantaneously force photon 2 into a state of ill-defined y-spin, even though it is light-years away from photon 1. How do we reconcile the fact that photon 2 "knows" that the x-spin of photon 1 has been measured, even though they are separated by light-years of space and far too little time has passed for information to have travelled to it according to the rules of Special Relativity? There are basically two choices. You can accept the postulates of QM as a fact of life, in spite of its seemingly uncomfortable coexistence with special relativity, or you can postulate that QM is not complete, that there *was* more information available for the description of the two-particle system at the time it was created, carried away by both photons, and that you just didn't know it because QM does not properly account for it. So, EPR postulated that the existence of hidden variables, some so-far unknown properties, of the systems should account for the discrepancy. Their claim was that QM theory is incomplete; it does not completely describe the physical reality. System II knows all about System I long before the scientist measures any of the observables, thereby supposedly consigning the other noncommuting observables to obscurity. No instantaneous action-at-a-distance is necessary in this picture, which postulates that each System has more parameters than are accounted by QM. Niels Bohr, one of the founders of QM, held the opposite view and defended a strict interpretation, the Copenhagen Interpretation, of QM. In 1964 John S. Bell proposed a mechanism to test for the existence of these hidden parameters, and he developed his inequality principle as the basis for such a test. Use the example of two photons configured in the singlet state, consider this: After separation, each photon will have spin values for each of the three axes of space, and each spin can have one of two values; call them up and down. Call the axes A, B and C and call the spin in the A axis A+ if it is up in that axis, otherwise call it A-. Use similar definitions for the other two axes. Now perform the experiment. Measure the spin in one axis of one particle and the spin in another axis of the other photon. If EPR were correct, each photon will simultaneously have properties for spin in each of axes A, B and C. Look at the statistics. Perform the measurements with a number of sets of photons. Use the symbol N(A+, B-) to designate the words "the number of photons with A+ and B-." Similarly for N(A+, B+), N(B-, C+), etc. Also use the designation N(A+, B-, C+) to mean "the number of photons with A+, B- and C+," and so on. It's easy to demonstrate that for a set of photons (1) N(A+, B-) = N(A+, B-, C+) + N(A+, B-, C-) because all of the (A+, B-, C+) and all of the (A+, B-, C-) photons are included in the designation (A+, B-), and nothing else is included in N(A+, B-). You can make this claim if these measurements are connected to some real properties of the photons. Let n[A+, B+] be the designation for "the number of measurements of pairs of photons in which the first photon measured A+, and the second photon measured B+." Use a similar designation for the other possible results. This is necessary because this is all it is possible to measure. You can't measure both A and B of the same photon. Bell demonstrated that in an actual experiment, if (1) is true (indicating real properties), then the following must be true: (2) n[A+, B+] <= n[A+, C+] + n[B+, C-]. Additional inequality relations can be written by just making the appropriate permutations of the letters A, B and C and the two signs. This is Bell's inequality principle, and it is proved to be true if there are real (perhaps hidden) parameters to account for the measurements. At the time Bell's result first became known, the experimental record was reviewed to see if any known results provided evidence against locality. None did. Thus an effort began to develop tests of Bell's inequality. A series of experiments was conducted by Aspect ending with one in which polarizer angles were changed while the photons were `in flight'. This was widely regarded at the time as being a reasonably conclusive experiment confirming the predictions of QM. Three years later Franson published a paper showing that the timing constraints in this experiment were not adequate to confirm that locality was violated. Aspect measured the time delays between detections of photon pairs. The critical time delay is that between when a polarizer angle is changed and when this affects the statistics of detecting photon pairs. Aspect estimated this time based on the speed of a photon and the distance between the polarizers and the detectors. Quantum mechanics does not allow making assumptions about *where* a particle is between detections. We cannot know *when* a particle traverses a polarizer unless we detect the particle *at* the polarizer. Experimental tests of Bell's inequality are ongoing but none has yet fully addressed the issue raised by Franson. In addition there is an issue of detector efficiency. By postulating new laws of physics one can get the expected correlations without any nonlocal effects unless the detectors are close to 90% efficient. The importance of these issues is a matter of judgement. The subject is alive theoretically as well. In the 1970's Eberhard derived Bell's result without reference to local hidden variable theories; it applies to all local theories. Eberhard also showed that the nonlocal effects that QM predicts cannot be used for superluminal communication. The subject is not yet closed, and may yet provide more interesting insights into the subtleties of quantum mechanics. REFERENCES: 1. A. Einstein, B. Podolsky, N. Rosen: "Can quantum-mechanical description of physical reality be considered complete?" Physical Review 41, 777 (15 May 1935). (The original EPR paper) 2. D. Bohm: Quantum Theory, Dover, New York (1957). (Bohm discusses some of his ideas concerning hidden variables.) 3. N. Herbert: Quantum Reality, Doubleday. (A very good popular treatment of EPR and related issues) 4. M. Gardner: Science - Good, Bad and Bogus, Prometheus Books. (Martin Gardner gives a skeptics view of the fringe science associated with EPR.) 5. J. Gribbin: In Search of Schrodinger's Cat, Bantam Books. (A popular treatment of EPR and the paradox of "Schrodinger's cat" that results from the Copenhagen interpretation) 6. N. Bohr: "Can quantum-mechanical description of physical reality be considered complete?" Physical Review 48, 696 (15 Oct 1935). (Niels Bohr's response to EPR) 7. J. Bell: "On the Einstein Podolsky Rosen paradox" Physics 1 #3, 195 (1964). 8. J. Bell: "On the problem of hidden variables in quantum mechanics" Reviews of Modern Physics 38 #3, 447 (July 1966). 9. D. Bohm, J. Bub: "A proposed solution of the measurement problem in quantum mechanics by a hidden variable theory" Reviews of Modern Physics 38 #3, 453 (July 1966). 10. B. DeWitt: "Quantum mechanics and reality" Physics Today p. 30 (Sept 1970). 11. J. Clauser, A. Shimony: "Bell's theorem: experimental tests and implications" Rep. Prog. Phys. 41, 1881 (1978). 12. A. Aspect, Dalibard, Roger: "Experimental test of Bell's inequalities using time- varying analyzers" Physical Review Letters 49 #25, 1804 (20 Dec 1982). 13. A. Aspect, P. Grangier, G. Roger: "Experimental realization of Einstein-Podolsky-Rosen-Bohm gedankenexperiment; a new violation of Bell's inequalities" Physical Review Letters 49 #2, 91 (12 July 1982). 14. A. Robinson: "Loophole closed in quantum mechanics test" Science 219, 40 (7 Jan 1983). 15. B. d'Espagnat: "The quantum theory and reality" Scientific American 241 #5 (November 1979). 16. "Bell's Theorem and Delayed Determinism", Franson, Physical Review D, pgs. 2529-2532, Vol. 31, No. 10, May 1985. 17. "Bell's Theorem without Hidden Variables", P. H. Eberhard, Il Nuovo Cimento, 38 B 1, pgs. 75-80, (1977). 18. "Bell's Theorem and the Different Concepts of Locality", P. H. Eberhard, Il Nuovo Cimento 46 B, pgs. 392-419, (1978). ******************************************************************************** Item 32. Some Frequently Asked Questions About Virtual Particles ------------------------------------------------------- original By Matt McIrvin Contents: 1. What are virtual particles? 2. How can they be responsible for attractive forces? 3. Do they violate energy conservation? 4. Do they go faster than light? Do virtual particles contradict relativity or causality? 5. I hear physicists saying that the "quantum of the gravitational force" is something called a graviton. Doesn't general relativity say that gravity isn't a force at all? 1. What are virtual particles? One of the first steps in the development of quantum mechanics was Max Planck's idea that a harmonic oscillator (classically, anything that wiggles like a mass bobbing on the end of an ideal spring) cannot have just any energy. Its possible energies come in a discrete set of equally spaced levels. An electromagnetic field wiggles in the same way when it possesses waves. Applying quantum mechanics to this oscillator reveals that it must also have discrete, evenly spaced energy levels. These energy levels are what we usually identify as different numbers of photons. The higher the energy level of a vibrational mode, the more photons there are. In this way, an electromagnetic wave acts as if it were made of particles. The electromagnetic field is a quantum field. Electromagnetic fields can do things other than vibration. For instance, the electric field produces an attractive or repulsive force between charged objects, which varies as the inverse square of distance. The force can change the momenta of the objects. Can this be understood in terms of photons as well? It turns out that, in a sense, it can. We can say that the particles exchange "virtual photons" which carry the transferred momentum. Here is a picture (a "Feynman diagram") of the exchange of one virtual photon. \ / \ <- p / >~~~ / ^ time / ~~~~ / | / ~~~< | / \ ---> space / \ The lines on the left and right represent two charged particles, and the wavy line (jagged because of the limitations of ASCII) is a virtual photon, which transfers momentum from one to the other. The particle that emits the virtual photon loses momentum p in the recoil, and the other particle gets the momentum. This is a seemingly tidy explanation. Forces don't happen because of any sort of action at a distance, they happen because of virtual particles that spew out of things and hit other things, knocking them around. However, this is misleading. Virtual particles are really not just like classical bullets. 2. How can they be responsible for attractive forces? The most obvious problem with a simple, classical picture of virtual particles is that this sort of behavior can't possibly result in attractive forces. If I throw a ball at you, the recoil pushes me back; when you catch the ball, you are pushed away from me. How can this attract us to each other? The answer lies in Heisenberg's uncertainty principle. Suppose that we are trying to calculate the probability (or, actually, the probability amplitude) that some amount of momentum, p, gets transferred between a couple of particles that are fairly well- localized. The uncertainty principle says that definite momentum is associated with a huge uncertainty in position. A virtual particle with momentum p corresponds to a plane wave filling all of space, with no definite position at all. It doesn't matter which way the momentum points; that just determines how the wavefronts are oriented. Since the wave is everywhere, the photon can be created by one particle and absorbed by the other, no matter where they are. If the momentum transferred by the wave points in the direction from the receiving particle to the emitting one, the effect is that of an attractive force. The moral is that the lines in a Feynman diagram are not to be interpreted literally as the paths of classical particles. Usually, in fact, this interpretation applies to an even lesser extent than in my example, since in most Feynman diagrams the incoming and outgoing particles are not very well localized; they're supposed to be plane waves too. 3. Do they violate energy conservation? We are really using the quantum-mechanical approximation method known as perturbation theory. In perturbation theory, systems can go through intermediate "virtual states" that normally have energies different >from that of the initial and final states. This is because of another uncertainty principle, which relates time and energy. In the pictured example, we consider an intermediate state with a virtual photon in it. It isn't classically possible for a charged particle to just emit a photon and remain unchanged (except for recoil) itself. The state with the photon in it has too much energy, assuming conservation of momentum. However, since the intermediate state lasts only a short time, the state's energy becomes uncertain, and it can actually have the same energy as the initial and final states. This allows the system to pass through this state with some probability without violating energy conservation. Some descriptions of this phenomenon instead say that the energy of the *system* becomes uncertain for a short period of time, that energy is somehow "borrowed" for a brief interval. This is just another way of talking about the same mathematics. However, it obscures the fact that all this talk of virtual states is just an approximation to quantum mechanics, in which energy is conserved at all times. The way I've described it also corresponds to the usual way of talking about Feynman diagrams, in which energy is conserved, but virtual particles can carry amounts of energy not normally allowed by the laws of motion. (General relativity creates a different set of problems for energy conservation; that's described elsewhere in the sci.physics FAQ.) 4. Do they go faster than light? Do virtual particles contradict relativity or causality? In section 2, the virtual photon's plane wave is seemingly created everywhere in space at once, and destroyed all at once. Therefore, the interaction can happen no matter how far the interacting particles are from each other. Quantum field theory is supposed to properly apply special relativity to quantum mechanics. Yet here we have something that, at least at first glance, isn't supposed to be possible in special relativity: the virtual photon can go from one interacting particle to the other faster than light! It turns out, if we sum up all possible momenta, that the amplitude for transmission drops as the virtual particle's final position gets further and further outside the light cone, but that's small consolation. This "superluminal" propagation had better not transmit any information if we are to retain the principle of causality. I'll give a plausibility argument that it doesn't in the context of a thought experiment. Let's try to send information faster than light with a virtual particle. Suppose that you and I make repeated measurements of a quantum field at distant locations. The electromagnetic field is sort of a complicated thing, so I'll use the example of a field with just one component, and call it F. To make things even simpler, we'll assume that there are no "charged" sources of the F field or real F particles initially. This means that our F measurements should fluctuate quantum- mechanically around an average value of zero. You measure F (really, an average value of F over some small region) at one place, and I measure it a little while later at a place far away. We do this over and over, and wait a long time between the repetitions, just to be safe. . . . ------X ------ X------ ^ time ------X me | ------ | you X------ ---> space After a large number of repeated field measurements we compare notes. We discover that our results are not independent; the F values are correlated with each other-- even though each individual set of measurements just fluctuates around zero, the fluctuations are not completely independent. This is because of the propagation of virtual quanta of the F field, represented by the diagonal lines. It happens even if the virtual particle has to go faster than light. However, this correlation transmits no information. Neither of us has any control over the results we get, and each set of results looks completely random until we compare notes (this is just like the resolution of the famous EPR "paradox"). You can do things to fields other than measure them. Might you still be able to send a signal? Suppose that you attempt, by some series of actions, to send information to me by means of the virtual particle. If we look at this from the perspective of someone moving to the right at a high enough speed, special relativity says that in that reference frame, the effect is going the other way: . . . X------ ------ ------X you X------ ^ time ------ | ------X me | ---> space Now it seems as if I'm affecting what happens to you rather than the other way around. (If the quanta of the F field are not the same as their antiparticles, then the transmission of a virtual F particle >from you to me now looks like the transmission of its antiparticle >from me to you.) If all this is to fit properly into special relativity, then it shouldn't matter which of these processes "really" happened; the two descriptions should be equally valid. We know that all of this was derived from quantum mechanics, using perturbation theory. In quantum mechanics, the future quantum state of a system can be derived by applying the rules for time evolution to its present quantum state. No measurement I make when I "receive" the particle can tell me whether you've "sent" it or not, because in one frame that hasn't happened yet! Since my present state must be derivable from past events, if I have your message, I must have gotten it by other means. The virtual particle didn't "transmit" any information that I didn't have already; it is useless as a means of faster-than-light communication. The order of events does *not* vary in different frames if the transmission is at the speed of light or slower. Then, the use of virtual particles as a communication channel is completely consistent with quantum mechanics and relativity. That's fortunate: since all particle interactions occur over a finite time interval, in a sense *all* particles are virtual to some extent. 5. I hear physicists saying that the "quantum of the gravitational force" is something called a graviton. Doesn't general relativity say that gravity isn't a force at all? You don't have to accept that gravity is a "force" in order to believe that gravitons might exist. According to QM, anything that behaves like a harmonic oscillator has discrete energy levels, as I said in part 1. General relativity allows gravitational waves, ripples in the geometry of spacetime which travel at the speed of light. Under a certain definition of gravitational energy (a tricky subject), the wave can be said to carry energy. If QM is ever successfully applied to GR, it seems sensible to expect that these oscillations will also possess discrete "gravitational energies," corresponding to different numbers of gravitons. Quantum gravity is not yet a complete, established theory, so gravitons are still speculative. It is also unlikely that individual gravitons will be detected anytime in the near future. Furthermore, it is not at all clear that it will be useful to think of gravitational "forces," such as the one that sticks you to the earth's surface, as mediated by virtual gravitons. The notion of virtual particles mediating static forces comes from perturbation theory, and if there is one thing we know about quantum gravity, it's that the usual way of doing perturbation theory doesn't work. Quantum field theory is plagued with infinities, which show up in diagrams in which virtual particles go in closed loops. Normally these infinities can be gotten rid of by "renormalization," in which infinite "counterterms" cancel the infinite parts of the diagrams, leaving finite results for experimentally observable quantities. Renormalization works for QED and the other field theories used to describe particle interactions, but it fails when applied to gravity. Graviton loops generate an infinite family of counterterms. The theory ends up with an infinite number of free parameters, and it's no theory at all. Other approaches to quantum gravity are needed, and they might not describe static fields with virtual gravitons. ******************************************************************************** END OF FAQ