DR. ANDREW S. FRIEDMAN
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(a) Animation 6a corresponds to Fig. 2a of Friedman+2013 for the case α = 180 degrees where the redshift of event A is fixed to zA=0.5 and the redshift of event B is allowed to vary in the range 0.5 < zB < 71.91. For zB < zB ~ 50, events A and B have intersecting past lightcones and a shared causal past. For zB > zB ~ 50, the events do not have a shared causal past. This corresponds to fixing zA and α = 180 degrees and increasing zB until the point (zA, zB) lies in the light gray region in Fig 3b of Friedman+2013. For zA <= zB <= 3.65, events A and B both have shared causal pasts with Earth's worldline, whereas event B does not when zB > 3.65. The critical redshift zB is computed from Eq. 30 of Friedman+2013 (substituting labels A <--> B), and using Eq. 12 of Friedman+2013 to determine redshift for a given comoving distance.

(b) Animation 6b corresponds to Fig. 2a of Friedman+2013 for the case α = 180 degrees with symmetric redshifts zA=zB, where both redshifts are increased in the range 1 <= zA=zB <= 24.47. The symmetric case illustrates the role of the causal independence redshift zind=3.65. For zA=zB <= zind=3.65, events A and B have intersecting past lightcones and shared causal pasts with each other and Earth's worldline. For zA=zB > zind=3.65, events A and B have no shared causal past with each other or our worldline. The finite redshift resolution of the movie shows a frame with zA=zB=3.62 where the past lightcones of A and B clearly intersect (green circles), while the next frame with zA=zB=3.67 clearly shows that the past lightcones of the events no longer intersect.

Massachusetts Institute of Technology Harvard University Astronomy Smithsonian Astrophysical Observatory UC Berkeley Astronomy NSF Graduate Research Fellowship NASA Graduate Student Research Program Peters Automated Infrared Imaging Telescope (PAIRITEL) NASA Swift Satellite
Last Updated: Andrew Samuel Friedman, 5/2014

This material is based upon work supported by the National Science Foundation under Grant # 1056580 through an NSF Science, Technology, and Society Postdoctoral Fellowship at MIT.

Original animations are shared under a
Creative Commons Attribution-NonCommercial-ShareAlike 3.0 US License