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Address to Nobel Prizewinners
by Frederick Soddy
(Published by New World Publications, St.Stephens House Westminster, S.W.1, 1954)
In this address one of the greatest scientists of the 20th Century shares his concerns over the state of science to a group of outstanding fellow scientists .
I believe that if every professional scientist and every author of science textbooks were to read this address every Monday morning before starting their week’s work a major change would occur - a much needed change. If every Christian took the trouble to study this address. I believe there would be fewer prepared to compromise their faith for the wisdom of this world. Almost every paragraph of Part II deserves a commentary, but I leave it to the reader to reflect on the pearls presented to us by this great scientist. PRS.
THE WIDER ASPECTS OF THE
DISCOVERY OF ATOMIC DISINTEGRATION CONTRASTING THE EXPERIMENTAL FACTS WITH THE
M.A., L.L.D., F.R.S.
An Address to the fourth Conference of Nobel Prizewinners at Lindau (Bodensee), S. Germany, 30.VI.1954
PART I: THE FACTS
It has taken the full half-century since the discovery of atomic disintegration for the picture to become clear of the fogs and irrelevancies which developed around it and tended to obscure from the perception of the layman the grandeur and uniqueness of that discovery. However, everyone now can appreciate that science then entered an absolutely virgin and hitherto un-penetrated domain.
Under our very eyes was going on what from the early dawn of civilization men had in vain attempted, lured on by the hope of pecuniary gain beyond the dreams of avarice, the transmutation of the elements - not it is true of the base into the noble metals but of the two elements with the heaviest atoms then known, uranium and thorium, though at rates almost inconceivably slow even on the scale of geological time. However, this last - which at first made radioactivity seem merely of academic interest, if not indeed no more than another scientific curiosity - was only the reverse side of an infinitely greater obverse than the ancient alchemist’s dream. For such slow changes to be perceptible at all implied a store of energy in the atom beyond the uttermost reach of previous imaginings. With not the slightest help from, or anticipation by, any theory whatever, this discovery extended in a single bound a million-fold our former horizons concerning matter and energy. Without exception the whole vast domain of new phenomena which radioactivity soon disclosed was completely accounted for by one single straightforward and rational conception. In each unit of time a constant proportion - though for the parent elements uranium and thorium an almost inconceivably small proportion- of their atoms suddenly and explosively disintegrate. Each bursts into two parts, a heavy and a light. The light one is either a light atom, known as the alpha particle, or a negative electron, known as the beta-particle. They are expelled like bullets from a gun as radiant particles at a velocity an appreciable fraction of, and sometimes for the negative electron, almost with, the velocity of light. The residual heavy atom recoils according to the law of the conservation of momentum. True ! there was one feature about this simple atomic disintegration not appreciated at first which still defies rational explanation and this will be referred to later.
This disintegration process, once started, then repeated itself over and over again. As the broad general trend for uranium and thorium, the next few disintegrations occurred at an ever increasing rate, resulting in a succession of new radioactive elements being produced of which Mme Curie’s polonium was the first to be recognized, to be quickly followed by the discovery also of radium and actinium, all in the uranium minerals. Such complications as there were arose out of the great number of these successive disintegrations, producing almost half as many new unstable radioactive elements as the number of ordinary inactive elements. They are of all degrees of instability and average life, for the two parent elements from many times longer than the age of the earth - as now measured directly by radioactive methods, which vastly extended all former estimates to the enormous period of some two thousand million years - down to times estimated as less than a millionth of a second. With this decrease of stability goes a corresponding decrease of quantity. Thus of Mme Curie’s new elements, radium, the average life of which is now known to be 2,300 years, is the only one existing in quantity capable of detection even by spectroscope, the average life and relative quantity of polonium being thousands of times less. Nevertheless this minuteness of quantity is in itself no obstacle to their study by radioactive methods, as it is exactly compensated for by the rapidity at which they break up and evolve their energy, and it is the energy not the mass upon which the methods depend.
From being a theory this quickly passed into the realm of well established and even directly observable fact. I can well remember the amazement of a world-renowned German microscopist, Quincke, at one of our British Association meetings in the first decade of the century, whose life had been spent on the borderland between the visible and the invisible - even so never able to study aggregates of atoms less than thousands of times greater than the number of the whole world’s inhabitants - when he first learned that, in these atomic disintegrations the disintegration of a single atom could be seen by the scintillation which is produced by the radiant particle expelled on a phosphorescent zinc sulphide screen. He became lost to the world repeating to himself in a variety of intonations:
"A single atom of matter ! A single atom of matter !"
This theory of atomic disintegration was founded on chemical, not physical evidence, the first direct evidence that a transmutation was taking place was for thorium, one of the products of which, discovered by Rutherford, is an argon gas, which he termed the "thorium emanation" but which is now more briefly referred to as "thoron". Similar "emanations" are given by radium and actinium, called radon and actinon, all three being quite different in their periods of life and in those of the products now called "the active deposits", to which they give rise by their disintegrations. The discovery - that these three emanations were argon gases - in turn led indirectly to the prediction that helium, the lightest argon gas, is a product of atomic disintegration. Indeed the radiant particle known as the alpha-particle, which is produced by all the alpha-rays alike, is in fact an atom of helium, carrying a positive charge double that of the negative charge of the electron which constitutes the beta-particle.
The atomic disintegration theory owed nothing to the fallacious electrical theory of matter then in vogue among physicists, or to the mathematicians. The equations of Einstein connecting energy and matter was not put forward till after the magnitude of the energy of atomic disintegration - as a million times that of the most energetic chemical changes - had been experimentally measured in 1903 by Ramsay and myself. Before that we had established directly with the spectroscope the predicted production of helium from radium. Rutherford who received the Nobel Prize for the discovery of atomic disintegration in 1908 was awarded the prize in Chemistry not in Physics.
Contrary to popular opinion this discovery of natural transmutation confirmed rather than upset the established basis of chemistry. True it was unexpected but so too was radioactivity itself which at first seemed to upset the law of the conservation of energy. Also it was, and remained for long, unpopular with the then high priests of the subject, as witness Dr. Hahn who recalls in his recent book "New Atoms" being called "an anglicized Berliner" as late as 1907 for indiscreetly advocation the new doctrine ! It was, indeed, because chemists during the nineteenth century had threshed our the difference between the atom and the molecule - and that is tantamount to understanding the difference between a transmutational and an ordinary chemical change - that the true character of radioactive changes was instantly recognized. It was due to the fact that the physicists then did not know the difference between the atom and the molecule that they went astray. They regarded the existence of the electron, the atom of negative electricity - a particle only one two-thousandth the mass of the hydrogen atom which is a normal constituent of matter in the electrically neutral state - as implying a transmutation, and so got wrong ideas about matter being built up out of electric charges.
But now I pass on to something which, though not upsetting any chemical doctrine, was certainly chastening to the proud presumption of the chemist that chemical analysis was the ultimate analysis of matter into homogeneous chemical elements, the atoms of each of which had been definitely postulated by Dalton to be all exactly alike and different in mass from the atoms of all the other elements. I refer to what, after the totally unexpected and unforseen discovery of the colossal internal energy of the atom, was the equally unexpected and unforeseen discovery of isotopes, whereby one of Nature’s most closely guarded secrets of the internal composition of matter was laid bare. That this was an inevitable consequence of the prior discovery of atomic disintegration followed from the work of Hahn with Ramsay, first, and then with Rutherford, resulting in the discovery in thorium materials of two comparatively long lived members, called mesothorium, and radiothorium, in the thorium disintegration series, in 1905-6, though this was not understood till some years later.
In the original work by Rutherford and myself, the suspicion that thorium was transmuting itself spontaneously into an argon gas had been enormously strengthened when we found that this was not the direct product of thorium but of an intermediate member of the disintegration series which we named thorium X, and which, we had found, regrew from the thorium as fast as the radioactivity of that which had been removed decayed. But we had entirely missed the intervening members, which Hahn later discovered between thorium and thorium X, because the mesothorium had been removed in the preliminary purification of the thorium and is too long lived appreciably to reform during the experiments, and because - as McCoy and Ross had the hardihood categorically to affirm as early as 1907 - the radiothorium is chemically inseparable from thorium, that is as we now say the two are isotopes.
The earliest example of such chemical identities, in this case between a radioactive and a common element, lead, had been what is called radiolead. This is a member of the uranium disintegration series emitting the penetrating beta-type of radiation, consisting of negative electrons, in contradistinction to the alpha-type, which is but very feebly penetrating and is constituted of doubly positively charged helium atoms. As we now know, lead being the ultimate stable product both of thorium and uranium, lead must be a constant constituent of all uranium and thorium minerals. Indeed it is upon the ratio between the quantities of lead and uranium or thorium in the mineral that its age in millions of years may be directly evaluated.
Radiolead is of historical interest also because it was the first of what are now called isotopes to be used as a "tracer" element, by Hevesy and Paneth in 1913, after they had confirmed by exhaustive trials its complete chemical non-separability from common lead. But the work of McCoy and Ross had established for thorium and radiothorium this complete chemical non-separability six years earlier.
The climax occurred in 1911-3 after I had found that Hahn’s mesothorium is isotopic with radium, and with the aid of my late wife, had attempted in vain to alter the ratio between the two elements by Mme Curie’s method of separating radium from barium by the systematic fractional crystallization of their chlorides. It was this that absolutely convinced me, as early as 1910, that this isotopy was an entirely new and fundamental property of matter, the chemical non-separability of isotopes being in a totally different category to the great difficulty, for example, that chemistry has in separating the dozen or so so-called "rare-earth" elements from one another.
The first step of what is now called the Displacement Law was taken in 1911. It was that the expulsion of the doubly positively charged helium atom as an alpha-particle causes the element expelling it to shift to a place in the Periodic Table two places nearer the beginning than the place occupied by the parent element. This was followed in 1913 by the second step after Alexander Fleck, then the Demonstrator in my department at Glasgow University, had spent two years determining the chemical character of the more ephemeral beta-rayers. This he did with absolute correctness, and it resulted in the second step completing that Law, that the emission of the single negatively charged beta-particle sends the element one place forward in the Periodic Table.
This complete Displacement Law instantly cleared up the whole subject and first showed that the successive places in the periodic Table differ by unit charge in the atomic constitution, and that it is the integral number of these charges, now called the Atomic Number, not the mass of the atom, that determines its chemical character. The isotopes are varieties of the same chemical element with different atomic masses and / or different stabilities, but with identical chemical character. Some of these radioactive isotopes differed by as much as the mass of three alpha-particles, i.e. by 12 units.
Now just as there was no vestige of a hint in all the earlier literature of the colossal magnitude of the internal energy of the atom, so there was none whatever of the existence of isotopes. After the First World War, Aston extended the discovery throughout the whole Periodic Table by the same physical method as had enabled J.J.Thomson, his teacher, to evaluate the mass of the negative electron in 1897. From the vantage point of the radio-elements, in 1913 we had to think back, as it were, and ask ourselves, if the common elements were simple mixtures of different isotopes of different atomic weights, what evidence would we have of it. The surprising answer was that we should not have any evidence of the fact at all, and that the belief that chemical analysis was the ultimate analysis of matter into homogeneous elements might be an illusion.
This Aston established. He showed that only a few, mainly of the lighter elements with integral atomic weights of the Oxygen - 16 basis, are homogeneous. The forty even atomic numbered elements are all mixtures, having between them some 220 isotopes. The extreme example is the element tin with ten isotopes having atomic weights varying by units over the range 112-124. Whereas the odd-atomic-numbered elements are either homogeneous or a mixture of two isotopes, the atomic weights of which are usually two consecutive odd-numbers. His discovery that the atomic weight of the individual isotopes is for all, approximately integral foreshadowed the discovery of the neutron by Boethe and Becker in 1930, whilst his even more important discovery that the small departures from exact integral values are regular and are, on Einstein’s generalization, a measure of the difference of their internal energy, may prove to be one of the most important and far-reaching generalizations ever made.
PART II: THE THEORIES
Further to hide its real origins, and to make it appear to have originated in the corkscrew brains of the mathematical physicists, its very name "radioactivity" has been changed to "nuclear physics"! Whereas, as already indicated, if any new name were required, which it was not, it should have been nuclear chemistry. Some Cambridge wag once called chemistry "only the messier part of physics" which suggests the retort that nuclear physics is only the guessier part of nuclear chemistry.
I have entitled my Address "The Wider Aspects of Atomic Disintegration" but if I too for the moment claim the prerogative of the pedant of beginning at the end, and start with the widest aspect of all, it is this. We can see clearly from what has happened in radio-activity within a single lifetime what has been happening to all knowledge from the beginning. Since the day of the first Academy in Greece, centuries before the birth of Christ, knowledge has been perverted to bolster up some preconceived grandiloquent idea or philosophy, though the original Greek philosophers, before the triumvirate of Socrates, Plato and Aristotle, seem to have been genuine scientists in pursuing knowledge for its own sake.
About one-half of the population seem only interested in new knowledge if it can be made practically useful and the other half as a basis for speculations and theories to try to account for it, not to mention the gentlemen Faraday satirized as hoping to be able to tax it. Really scientific minds like Robert Boyle, who wrote "The Sceptical Chemist", are still rare freaks by comparison. I remember F.W.Aston, who was trained as a chemist, remarking offhandedly to me one day that chemistry has now become a branch of technology dependent on physics for her theoretical basis. At any rate that is more honest than the current dope that chemistry and physics are now one science, which has been used as an excuse to rob chemistry of its endowments, such as the Fullerian Professorship of Chemistry at the Royal Institution, an institution, by the way, founded by Count Rumford for the benefit of the layman. Indeed, on the same pretext, at Oxford, my own Chair, the Dr.Lees’s Professorship, of which I was the first occupant, has now been appropriated by an upstart so-called "Physical Chemistry", and the vast subject of inorganic chemistry, the original chemistry, just when it was becoming vitally important in connection with the growth of nuclear chemistry, has been reduced to a subordinate position no longer represented by a chair. Had I known this would happen I certainly would not have resigned it !
Now, again as in the day of Robert Boyle, antagonism, rather than co-operation, has developed between theory and experiment and it is again necessary for Chemistry to put theory into its proper place as the servant rather than the purpose and goal of science. For these precious theories, which the chemist is asked to swallow blindfold from the physicist and mathematician, convey not the slightest hint of the commonest properties of matter, such as that bromine is a red stench and iron an invaluable ferrous metal. There are still some 92 natural chemical elements, each a law unto itself, the properties of which have to be learnt before the theory is even remotely intelligible. Such theories as there are, are nothing but a boring repetition of the facts. The Bohr theory of the elements is a relic of the day when the physicist supposed that the spectrum was the key to atomic structure, whereas it is only of chemical importance as a valuable means of identifying elements in the minutest quantity. Bohr all the time was using chemistry to interpret spectra, not vice versa as put about. In the case of the simplest element, hydrogen, as the theory of the origin of spectra, it was a very great advance and contribution, But for the most part chemistry is still too complicated a science for the theories to be a substitute for the facts as any real theory should be.
You have still to learn the facts even before understanding the theory supposed to account for them. So why burden the beginner with the theory at all? To take a topical example, the use of isotopes in medicine. It is entirely redundant and superfluous to have to learn the number of protons, neutrons and negatrons in the various isotopes employed. What is required is to know which common element the one used is an isotope of, and how their complete chemical identity enables, for example, the movement of the common elements taking part in metabolism to be studied by external means, which involve no interference with the normal functioning of the living body, much as X-rays enable the surgeon to diagnose an injury prior to operating. There was no theory whatever involved in the discovery of the Displacement Law, which as a matter of fact Bohr had prior knowledge of, as he cited it in his very first paper on spectra.
To turn now to the theoretical, or more strictly, the mathematical side, to me one of the greatest dangers of the age is the pathetic belief that mathematics cannot lie, for, if misunderstood, mathematics can be the arch.-deceiver. To begin at the root, consider the use of negative quantities introduced first by the Hindu mathematicians and justified on the ground of their analogy to debts. This has now converted political economy, which, if political, should be a science of wealth, into a science of debt, politically disastrous and suicidal, and to which the frustration of the beneficial effects of science on humanity can be directly traced.
Normally, negative quantities are mere mathematical operators to facilitate counting, and are only of physical meaning when the existence of equal or greater positive quantities is first taken for granted. For no man can apprehend a minus pig and even the tax gatherer, reputed able to extract blood from a stone, cannot subtract three from your two pounds and leave you minus one pound. As the Hindus, at any rate, understood, you can only owe him it.
Next take the imaginary operator the square-root of minus one, usually written i, which multiplied by any real number produces what used to be called an imaginary number, though now the mathematicians call it a complex number to hide its imaginary character. Certainly imaginary is not a good name, as the point is that, like space of more than three dimensions, it cannot be imagined. A better term would be irrational, except that that term seems already appropriated in other senses. The use of i arose of course out of the solution of the quadratic, or any other equation of even order, which involves the square root of a number, which for a certain range of coefficients is negative. Whereas for the cubic, or any odd order, equation, one can sling down any coefficients at random and the equation must have a real root. The mundane reason for this is that these imaginary numbers can so arise only as + and - pairs, which when added or multiplied become real numbers. Also the cube, or other odd, root of minus one is minus one, a real number.
So far as I know, the first attempt to attach a physical meaning to a mathematical solution, from which the operator i had not first been eliminated from the final result, was in the theory of relativity. This started the pretentious humbug that theory has been saddled with, and which I think it is time to characterize as a backward step into the realm of fantasy and mysticism, tending, if indeed not so intended, to bring science into contempt with the layman, and a source of satisfaction only to the traditional enemies of science - dogma, charlatanry, and obscurantism.
I refer to Minkowski’s four-dimensional continuum, in which time multiplied by the square root of minus one and by c, the velocity of light, is the fourth dimension, mathematically completely on a par with the three real dimensions of space. [Since a velocity is, dimensionally, a length divided by a time, multiplying imaginary time by a real velocity gives, not unnaturally an imaginary length!] In 1916, Einstein wrote a little book for laymen, "Relativity" translated by R.W.Lawson (Methuen & Co. 1920), which today reads, to say the least, somewhat curiously. For, in Section VIII, p.23, we find, in an attempt at a fool proof definition of "simultaneity", the invariance of the velocity of light stated to be "in reality neither a supposition nor a hypothesis about the physical nature of light, but a stipulation which I can make of my own freewill in order to arrive at a definition of simultaneity". The experimental proof by Michelson and Morley in 1877, of the invariance of light-velocity, is not mentioned until p.53. and, as the book now reads, it is impossible to tie down its author to any definite argument at all.
After saying (p.55) that the non-mathematician shudders at the "four-dimensional" as awakening thoughts of the occult, he goes on to say "yet there is no more commonplace statement than that the world we live in is a four-dimensional space-time continuum". There followed the oracular utterances of Jeans, who remarked condescendingly that God must have been a mathematician, and of Eddington in Britain, whose writings became "best-sellers" to the lasting disgrace, in my opinion, of my countrymen for their lack of common sense.
The matter was summed up by the late Susan Stebbings, Professor of Philosophy in the University of London, who, with the age-long experience of her sex of the posturing male, remarked acidly about such writings, "All of this means just nothing at all". A quarter of a century ago (Interpretation of the Atom, 1932, p.203) I had accused the mathematicians "of trying to account for everything by varying the nature of nothingness". But since then a subtler and more deadly criticism in the same vein has been made by Viscount Samuel (Essay in Physics, 1951). Accepting Whitehead’s "The event is the unit of things real" and remarking that every phenomenon may be analysed into events - en event being anything that happens - he says that is as well to remember that you cannot have something happening to nothing. He likens Einstein’s mode of argument to the grin of the Cheshire Cat in Alice in Wonderland which remains behind after the Cat had vanished !
My thesis is primarily that there is really no a priori reason why the facts of the inanimate world should be capable of explanation or interpretation by the human mind, and that, anyhow, an inexplicable fact is infinitely preferable to an unintelligible explanation of it. Whilst there is no objection urged against mathematicians doing whatever seems good to them in their own sphere, quite definitely they should be stopped from presenting their whims as science, let alone pretending that in the last analysis they are the real scientists.
Personally I find no difficulty in accepting as a fact the invariance of the velocity of light in vacuo, irrespective of the relative velocity of the transmitter and receiver, which started the theory of relativity - particularly nowadays when the photon has put into the melting pot all our former ideas as to light itself. Nor as a chemist do I feel any urge to solve the riddle. Exactly the same is true as to the Quantum theory which postulates the atomicity of Action, which at first appeared even stranger, but for which a satisfactory physical reason has now been found. These two theories are strangely contrasted in their history, and, as I shall try to explain, now they seem largely to cancel one another out. Certainly they cannot both be true.
The Quantum Theory of Max von Planck dates from 1900, as a brilliant mathematical inspiration, then totally beyond physical accounting. It was that the old dynamical quantity, Action - usually regarded dimensionally as energy multiplied by time or momentum multiplied by length [The commonest and most easily apprehended example of Action, is angular momentum, such as the product of the mass, velocity and radius of orbit of a planet moving round a central sun.] - was atomic, like the electron in electricity.
That is to say, Planck’s Quantum of Action is indivisible and is the smallest quantity of Action capable of existence. But very soon the theory was found to be the key to a small host of anomalies encountered in such mundane spheres of physics as the specific heat, photo-electricity and then spectra. It was only later under Heisenberg, with his Principle of Uncertainty, Schrodinger with his Wave-Mechanics, and Lindemann (Lord Cherwell) with his attempt to derive it from the essential nature of space and time rather than Action, that it entered the realm of metaphysics.
The history of relativity was almost the opposite, both in that there are very few means of testing it and that some of its later deduced consequences had been predicted from the electromagnetic theory of light. Notably it was predicted from the electric charge, if sufficiently concentrated, must possess inertial mass like matter, and that this mass must increase, ultimately to infinity, as its speed approaches and ultimately reaches the speed of light. This was verified experimentally as early as 1903, for the beta-particles of radium, some of which travel at speed indefinitely close to that of light. But at the time this was merely regarded as a proof that the whole mass or inertia of the electron was of electromagnetic origin, in contradistinction to material. It was Einstein’s later 1905 theory of relativity which, completely independently of the electromagnetic theory, and based solely on the Michelson and Morley proof of the invariance of the light-velocity in 1887, extended this necessity to all mass, material as well as electromagnetic in origin. So that the discovery of the neutron as the unit of pure matter without electric charge, in 1930 by Boethe and Becker, left the invariance of light-velocity without any connection with the rest of physics at all.
Whereas the Quantum Theory, at first devoid of any physical interpretation, received a very elegant and satisfying possible one at the hands of Prince Louis de Broglie in 1924 who suggested that every moving particle had the nature of a wave. The "stationary states" of the Bohr theory of spectra of increasing radii corresponding to 1,2,3, ... quanta of Action would arise through interference, if the revolving electron were replaced by a standing wave, for in any other orbits the two ends of the circular wave would cancel rather than reinforce each other, much as in the ordinary optical theory of interference.
Also the simple exponential law of radioactive change, though at first this was not appreciated, is probably the simplest and best example of the Heisenberg Principle of Uncertainty. It is no theory but a fact easily proved experimentally that the average future life of an atom is completely unaltered by the time it has already lived. There is no certainty at all as to when it will disintegrate, but the probability of its disintegration remains unchanged however long it has already lived. This is an example of the Heisenberg Uncertainly Principle, but otherwise quite inexplicable.
What one complains about in the Quantum Theory, and still more in the theory of Relativity, is that the objections are never frankly met. The weak points are disguised by a torrent of word-spinning. For example, there is the clearest experimental difference between the particle and wave forms of radiation. The former - cathode-rays, beta-rays, and alpha-rays - can be observed as radiant particles whether in the Wilson cloud-chamber or by the scintillations they produce on phosphorescent substances. But the wave-form - light, X-rays, and the gamma-rays - cannot, and it is nonsense to pretend that there is no difference between wave and particle forms of radiation.
There is a more fundamental objection that, strangely enough, never seems to have been raised. The designers of interferometers take it as an accepted principle that to obtain interference is impossible with two distinct sources of light, and that the same source of light must be somehow split or subdivided for this phenomenon to be observed. But the Quantum Theory of the nature of light substitutes for the single beam, as a spreading spherical wave with a definite phase, a practically infinite number of individual photons carrying waves the phases of which can be in no way related ! In other words the new theory absolutely fails to explain the very phenomenon, interference, upon which the wave theory of light was originally based.
But the Theory of Relativity is much more vulnerable and open to criticism than the Quantum Theory.
Let us now return to the earlier history of the attempts of the mathematicians to account for the invariance of light-velocity on which, solely, the later theory of relativity was based. Lorentz in Germany and Fitzgerald in Ireland brazenly cooked the units of mass, length, and time to make it so. For this the cooking factor is the square root of (1-v2) where v is the relative velocity of receiver and transmitter in terms of the velocity of light as unity. The units of length are shrunk, and those of mass and time stretched by multiplying and dividing them respectively by this factor, which is necessarily always less than unity.
Now if any schoolboy were to commit such a cardinal crime in maths as to cook his figures to get the answer right he would be held up to obloquy to the whole school and probably spanked. But apparently the mathematicians themselves have no sense of shame in doing things like this, which sufficiently justifies my earlier warning that the really dangerous liars in the world today are the mathematicians if you are fool enough to believe them. But it was not Lorentz and Fitzgerald who are chiefly to blame. No doubt they were merely exploring purely mathematical ways of expressing the inconsistency. A genuine scientist would have said of this result - "It is as though the three fundamental physical dimensions, length on the one hand and mass and time on the other, suffered a change in the magnitude of their units, that of length being shrunk, and those of mass and time being stretched, by multiplying and dividing respectively by a factor less than unity, in such a way as to make the velocity of light independent of the relative motion of the transmitter and receiver. Whereas it has been made the occasion for an orgy of amateurish metaphysics, all tending to represent the mathematician - a mere calculator apart from experimental knowledge - into a heaven-sent-magician able to make length and time physically equivalent !
The real culprit was Einstein. Any condemnation on my part is unnecessary. It is only necessary to quote de Broglie:
The Lorentz transformation and
the Fitzgerald contraction appeared to be artifices permitting one to account
for certain aspects of the electromagnetic field without disclosing their
profound significance." [Whatever that may mean. F.S.]
As regards the Lorentz transformation itself, surely it is a perfect example of the old adage that by mathematical reasoning you can only get out what you have already, consciously or not, put into the enunciation. But note that this cannot be said of Einstein’s really great further deduction that the internal energy of matter is 9.1020 ergs per gram. But of course his equation could not have been so interpreted but for the prior knowledge of the magnitude of the energy released in transmutation. In fact it was not so interpreted by Einstein at all. It seems to have been given this interpretation first by J.J.Thomson in 1914.
No doubt Einstein himself would regard this fundamental generalization - of the general accuracy of which as well as of its cardinal importance it is no longer possible to doubt - as justifying his mode of approach and his regarding the necessary change of the units of measurement as physically real.
I, myself, regard as still in doubt, whether it connotes a colossal piece of luck, still, by the way, to be rigorously tested, or a totally new departure in the history of human reasoning. This only time will decide.
However that may be, the modern view that light is propagated not as a spreading spherical wave-front, but as individual particles called photons carrying a wave along with them, seems to blow sky high most of the arguments on which the theory of relativity was based, as well as much, if not all, of modern cosmological speculation. For today we have not the vaguest idea of why light moves at all, let alone why its speed (in vacuo) is invariant. This is straining at a gnat but swallowing a camel, the invariance being the gnat and the velocity the camel. Together, the theory of relativity, as modified by the modern quantum theory, seems an excellent example of progress in the merely mathematical sphere signifying motion as much in the backward as in the forward direction. Why ! we do not even know whether light will go where there is nothing to go to. The assumption, that it could, derives from the old spreading-spherical-pulse-in-the-luminiferous-ether theory. This still underlies almost all mathematical and speculative cosmogony, in which field speculation can run riot without much fear of its ever being put to the test. The modern school of theoretical physicists in contrast with the sceptical chemist, appear positively credulous.
Lastly this photon is in point blank contradiction to the Einstein relation, E=mc2, for its velocity c being the velocity of light, m its mass, must be zero otherwise it would be infinite, and E must be zero or infinity also. Whereas nothing is more certain I suppose in theoretical physics than the magnitude of energy of the photon, as half the energy gained in the "fall" of the electron from any outer to any inner of the possible integral-quanta orbits of the atom. One may leave it to the mathematical physicists to try to wriggle out of this dilemma. Possibly the Einstein relation is a one-way relation only between mass and energy not between energy and mass, or even more probably, it may not be strictly true at all, as mathematical infinities do not occur in Nature.
At last year’s Conference, in connexion with Powell’s address on cosmical rays, I pointed out how modern cosmogony was encountering unanswerable contradictions. For the cosmical ray physicists claim to have found radiant cosmical particles with energy a thousand times greater than would be given by the total annihilation into energy of the heaviest atoms known. The idea that these result by the purely chance interaction of stellar electric and magnetic fields, with double stars acting as a sort of astral cyclotron, seems to me as fanciful as the sorting demon of Maxwell that could upset the 2nd law of Thermodynamics. Maxwell imagined a tiny trap door between two closed compartments containing a gas, small enough only to admit a molecule at a time, and controlled by a very agile demon, able when he spotted a molecule making for it at greater than average speed to open the door in time to let it through, and when a molecule approached of less than average speed to slam it in its face. This would upset the Second Law. So, too, it is not the existence of double stars or of astral electric and magnetic fields - able to act as a cyclotron in accelerating a charged particle until its velocity-mass reaches that of 1,000 uranium atoms, that is involved in the cosmical-ray phenomena at all, but the timing to produce any such result. For the cyclotron, in contradistinction to Maxwell’s simple trap-door, is one of the most ingenious and cunning instruments ever conceived by the human brain.
Finally, since modern ideas conceive the photon as a packet of energy of definite amount, the rest-mass of which is zero, what becomes of the prediction that a ray of light passing the limb of the sun at eclipse must be bent? For, owing to its being energy and therefore, according to Einstein, mass, it would be subject to deflection by the sun’s gravitational field. Incidentally the attempt to verify this during a recent solar eclipse, provided the world with the most disgusting spectacle perhaps ever witnessed of the lengths to which a preconceived notion can bias what was supposed to be an impartial scientific inquiry. For Eddington, who was one of the party, and ought to have been excluded as an ardent supporter of the theory that was under examination, in his description spoke of the feeling of dismay which ran through the expedition when it appeared at one time that Einstein might be wrong!
Remembering that in this particular astronomical investigation, the corrections for the normal errors of observation - due to diffraction, temperature changes, and the like - exceeded by many times the magnitude of the predicted deflection of the star’s ray being looked for, one wonders exactly what this sort of "science" is really worth.