The Net Advance of Physics RETRO:

Ubi Crux, Ibi Lux

2013 July 15

Crookes tube with traditional Maltese-cross anode. Photograph by Z. Sándor, 2002.

"Where there is the Cross (Crux), there is Light."

Such was the motto chosen by William Crookes when Queen Victoria knighted him. The self-educated son of a tailor, never on any university's faculty, Crookes was an outsider made good, an enemy of the growing professionalism of science who nevertheless made his living as an independent scientist, educator, and industrial consultant: (see the excellent biography by William H. Brock, Sir William Crookes (1832-1919) and the Commercialization of Science [Burlington, Vermont: Ashgate, 2008]). He discovered thallium when he was 29, and went on to success after success in both pure and applied science. There are few areas of physical chemistry, chemical physics, and chemical engineering to which he did not contribute, often in groundbreaking ways. Knighthood was only of the many honours heaped on him throughout his career.

In the Twentieth Century, however, Crookes is less remembered than one would expect from his record of achievement. This is partly because he did the first tentative work in fields where others -- Ernest Rutherford, J. J. Thomson, Fritz Haber ... -- would harvest everlasting fame. It is partly because, at the end of his career, he proposed a revolutionary new paradigm for chemistry -- that the elements literally evolve, in response to Darwinian selection pressure -- which briefly fired the imagination of scientists throughout the English-speaking world, but in retrospect struck them as embarassingly naive when compared to quantum mechanics. (In the Twenty-first Century of multiverse cosmology and the Landscape, however, Crookes's quasi-biological atoms changing in time may perhaps seem less self-evidently inferior to Bohr's timeless Platonic harmonies than they did one hundred years before!)

Mainly, though, Crookes's reputation has suffered because he epitomised aspects of Victorian culture which succeeding generations found it difficult to believe had ever even existed. His personality was so alien to the Twentieth Century mind that he could only be remembered as a sort of clown or lucky fool who had stumbled over great discoveries by chance.

Wm. Crookes. [Popular Science 10, 640 (1877)]

Certainly Crookes did not conform to the stereotype of an unassuming English gentleman-scholar. He was by nature a showman, almost an intellectually sophisticated version of P. T. Barnum. He loved the limelight, and constantly sought to popularise his ideas and discoveries by emphasising their more sensational aspects.

Moreover, despite his high standing in the technical community, he seemed to feel no allegiance whatever to the rationalistic Enlightenment consensus. He was one of the very earliest members of the (surprisingly large) group of late Nineteenth-Century physicists who openly investigated psychic phenomena, but even in this group he stood out. Many distinguished scientists of the era attended seances and hunted ghosts, but few with Crookes's fervour of belief. He practised alchemy, at one point teaming up with an American inventor of high-pressure transmutation-machines ... he joined Mme. Blavatsky's Theosophical Society ... he was literally a wizard, practising qabbalistic magic at the Golden Dawn's Isis-Urania Temple with such mystical dreamers as the young William Butler Yeats.

Apart from a few shocked members of the Royal Society who wanted his Fellowship rescinded, more conventional Victorians seem to have taken all of this in stride as the eccentricity accompanying genius: Ubi Crookes, Ibi Spooks went a much-repeated in-joke. Besides, at the fin de siècle anything seemed possible; if Crookes's observations of protactinium changing into uranium were undisputed, why should he not dream of lead changing into gold?

And was ectoplasm any more eerie than the ghostly "radiant matter" which Crookes found hovering around electrodes in his low-pressure glassware?

Photograph by Marcin Białek

On a Fourth State of Matter by W. Crookes, F.R.S. [Phil. Trans. R. S. L. 30, 469 [1879/1880]. Crookes's words are in bold.

7, Kensington Park Gardens
London, W.

April 29, 1880.

Dear Professor Stokes,

In introducing the discussion on Mr. Spottiswoode and Mr. Moulton's paper on the " Sensitive State of Vacuum Discharges," at the meeting of the Royal Society on April 15th, Dr. De la Rue, who occupied the chair, good-naturedly challenged me to substantiate my statement that there is such a thing as a fourth or ultra-gaseous state of matter.

The good-natured Warren De la Rue

I had no time then to enter fully into the subject ; nor was I prepared, on the spur of the moment, to marshal all the facts and reasons which have led me to this conclusion. But as I find that many other scientific men besides Dr. De la Rue are in doubt as to whether matter has been shown to exist in a state beyond that of gas, I will now endeavour to substantiate my position.

I will commence by explaining what seems to me to be the constitution of matter in its three states of solid, liquid, and gas.

I. First as to Solids : --- These are composed of discontinuous molecules, separated from each other by a space which is relatively large --- possibly enormous --- in comparison with the diameter of the central nucleus we call molecule. These molecules, themselves built up of atoms, are governed by certain forces. Two of these forces I will here refer to --- attraction and motion.

Animation by Kai Nordlund, University of Helsinki

Attraction when exerted at sensible distances is known as gravitation, but when the distances are molecular it is called adhesion and cohesion. Attraction appears to be independent of absolute temperature ; it increases as the distance between the molecules diminishes ; and were there no other counteracting force the result would be a mass of molecules in actual contact, with no molecular movement whatever --- a state of things beyond our conception --- a state, too, which would probably result in the creation of something that, according to our present views, would not be matter.

This force of cohesion is counterbalanced by the movements of the individual molecules themselves, movements varying directly with the temperature, increasing and diminishing in amplitude as the temperature rises and falls. The molecules in solids do not travel from one part to another, but possess adhesion and retain fixity of position about their centres of oscillation. Matter, as we know it, has so high an absolute temperature that the movements of the molecules are large in comparison with their diameter, for the mass must be able to bear a reduction of temperature of nearly 300° C. before the amplitude of the molecular excursions would vanish.

The state of solidity therefore --- the state which we are in the habit of considering par excellence as that of matter --- is merely the effect on our senses of the motion of the discrete molecules among themselves.

Solids exist of all consistencies, from the hardest metal, the most elastic crystal, down to thinnest jelly. A perfect solid would have no viscosity, i.e., when rendered discontinuous or divided by the forcible passage of a harder solid, it would not close up behind and again become continuous.

In solid bodies the cohesion varies according to some unknown factor which we call chemical constitution ; hence each kind of solid matter requires raising to a different temperature before the oscillating molecules lose their fixed position with reference to one another. At this point, varying in different bodies through a very wide range of temperature, the solid becomes liquid.

II. In liquids the force of cohesion is very much reduced, and the adhesion or the fixity of position of the centres of oscillation of the molecules is destroyed. When artificially heated, the inter-molecular movements increase in proportion as the temperature rises, until at last cohesion is broken down, and the molecules fly off into space with enormous velocities.

Graphic by HellTchi for Wikipedia

Liquids possess the property of viscosity --- that is to say, they offer a certain opposition to the passage of solid bodies ; at the same time they cannot permanently resist such opposition, however slight, if continuously applied. Liquids vary in consistency from the hard, brittle, apparently solid pitch, to the lightest and most ethereal liquid capable of existing at any particular temperature.

The state of liquidity, therefore, is due to inter-molecular motions of a larger and more tumultuous character than those which characterise the solid state.

III. In gases the molecules fly about in every conceivable direction, with constant collisions and enormous and constantly varying velocities, and their mean free path is sufficiently great to release them from the force of adhesion. Being free to move, the molecules exert pressure in all directions, and were it not for gravitation they would fly off into space.

Animation by Greg L.

The gaseous state remains so long as the collisions continue to be almost infinite in number, and of inconceivable irregularity. The state of gaseity, therefore, is pre-eminently a state dependent on collisions. A given space contains millions of millions of molecules in rapid movement in all directions, each molecule having millions of encounters in a second. In such a case, the length of the mean free path of the molecules is exceedingly small compared with the dimensions of the containing vessel, and the properties which constitute the ordinary gaseous state of matter, which depend upon constant collisions, are observed.

Maxim gun. © C2builder, 2007. [30 sec]

What, then, are these molecules ? Take a single lone molecule in space. Is it solid, liquid, or gas ? Solid it cannot be, because the idea of solidity involves certain properties which are absent in the isolated molecule. In fact, an isolated molecule is an inconceivable entity, whether we try, like Newton, to visualize it as a little hard spherical body, or with Boscovich and Faraday, to regard it as a centre of force, or accept Sir William Thomson's vortex atom. But if the individual molecule is not solid, a` fortiori it cannot be regarded as a liquid or gas, for these states are even more due to inter-molecular collisions than is the solid state. The individual molecules, therefore, must be classed by themselves in a distinct state or category.

The same reasoning applies to two or to any number of contiguous molecules, provided their motion is arrested or controlled, so that no collisions occur between them ; and even supposing this aggregation of isolated non-colliding molecules to be bodily transferred from one part of space to another, that kind of movement would not thereby cause this molecular collocation to assume the properties of gas ; a molecular wind may still be supposed to consist of isolated molecules, in the same way as the discharge from a mitrailleuse consists of isolated bullets.

Graphic by Belromain.

Matter in the fourth state is the ultimate result of gaseous expansion. By great rarefaction the free path of the molecules is made so long that the hits in a given time may be disregarded in comparison to the misses, in which case the average molecule is allowed to obey its own motions or laws without interference ; and if the mean free path is comparable to the dimensions of the containing vessel, the properties which constitute gaseity are reduced to a minimum, and the matter then becomes exalted to an ultra-gaseous state.

But the same condition of things will be produced if by any means we can take a portion of gas, and by some extraneous force infuse order into the apparently disorderly jostling of the molecules in every direction, by coercing them into a methodical rectilinear movement. This I have shown to be the case in the phenomena which cause the movements of the radiometer, and I have rendered such motion visible in my later researches on the negative discharge in vacuum tubes. In the one case the heated lamp-black and in the other the electrically excited negative pole supplies the force majeure which entirely or partially changes into a rectilinear motion the irregular vibration in all directions ; and according to the extent to which this onward movement has replaced the irregular motions which constitute the essence of the gaseous condition, to that extent do I consider that the molecules have assumed the condition of radiant matter.

Various Crookes tubes in action. [Film by Alastair Wright, 30 sec]

Between the third and the fourth states there is no sharp line of demarcation, any more than there is between the solid and liquid states, or the liquid and gaseous states ; they each merge insensibly one into the other. In the fourth state properties of matter which exist even in the third state are shown directly, whereas in the state of gas they are only shown indirectly by viscosity and so forth.

The ordinary laws of gases are a simplification of the effects arising from the properties of matter in the fourth state ; such a simplification is only permissible when the mean length of path is small compared with the dimensions of the vessel. For simplicity's sake we make abstraction of the individual molecules, and feign to our imagination continuous matter of which the fundamental properties --- such as pressure varying as the density, and so forth --- are ascertained by experiment. A gas is nothing more than an assemblage of molecules contemplated from a simplified point of view. When we deal with phenomena in which we are obliged to contemplate the molecules individually, we must not speak of the assemblage as gas.

These considerations lead to another and curious speculation. The molecule --- intangible, invisible, and hard to be conceived --- is the only true matter, and that which we call matter is nothing more than the effect upon our senses of the movements of molecules, or, as John Stuart Mill expresses it, "a permanent possibility of sensation." The space covered by the motion of molecules has no more right to be called matter than the air traversed by a rifle bullet can be called lead.

From this point of view, then, matter is but a mode of motion ; at the absolute zero of temperature the inter-molecular movement would stop, and although something retaining the properties of inertia and weight would remain, matter, as we know it, would cease to exist.

Believe me,

Dear Professor Stokes,

Very sincerely yours,


Molecular-beam system at LAAS-CNRS, Toulouse. Photo: Guillaume Paumier, CC-BY.

This letter -- considered by historians to be one of Crookes's most important publications -- typifies both the strength of his thought and the insuperable obstacles he faced. He was England's foremost expert on electrical phenomena in near-vacuum, a subject that he studied all his life. The quality of his observations is beyond dispute. But how, in 1880, could they be interpreted? What were the mysterious "cathode rays" travelling down the tube? What caused the glow at the electrodes and sometimes elsewhere? And are there other kinds of radiation emerging from the tube unseen -- some kind of "X radiation", as it were?

Answering all these questions meant inventing "modern physics", a task at which Crookes obviously did not succeed. How could he have? Although, like Norman Lockyer and William Prout, he intuited the existence of the proton, without knowledge of the electron or neutron he could not avoid conflating it with the hydrogen atom itself and was unable to make the fundamental breakthrough to modern chemistry. (Perhaps if he or anyone else had paid attention to Richard Laming's disturbingly modern 1840s atomic model, the course of history would have been very different!) Even many years later, Crookes failed to understand that the cathode rays he studied so carefully were made of subatomic, not atomic, particles.

And yet! Here we see the first mentions of two concepts fundamental to Twentieth Century physics: the plasma state and the molecular beam. Crookes understood that the glow in his tubes was no mere gas, but an entirely new form of matter. His announcement of "radiant matter" in the paper above marks the birth of the entire plasma-physics discipline (and is so considered by plasma physicists themselves), even though Crookes in a way once again unavoidably misses the main point.

A plasma, from the modern point of view, is a pair of charged gases united into an electrically neutral whole; its unusual properties derive from the collective behaviour of the ions. Neither of these ideas (at least in 1880) seems to have figured at all in Crookes's thought: he supposed "radiant matter" to be gas not ionised but rarefied, to the point that its individual molecules, far from behaving collectively, no longer interacted at all.

And thus, by defining the newly-discovered plasma state in a way no modern physicist would accept, he was led to his other great innovation. He became one of the first to imagine a beam of molecules, all moving in the approximately the same direction and thus rarely colliding. Countless roads opened: to low temperatures, as Crookes seems to have realised; to epitaxy; to the Stern-Gerlach experiment and spin ...

But once again, a problem arises: Crookes thinks he has actually created a molecular beam, and that it is turning the windmill in one version of his tube (shown in video above). It was J. J. Thomson who proved this to be wrong.

Ubi Crux, Ibi Lux, but no light without a cross!

Twenty-three years later: Men of the Day No.879 --- Ubi Crookes, Ibi Lux by "Spy" (Leslie Ward) [Vanity Fair 1903 May 21]