Physicists From England

"The quest of the absolute leads into the four-dimensional world."

"There was just one alternative, the earth’s true velocity through space might happen to have been nil."

"In physics we have outgrown archer and apple-pie definitions of the fundamental symbols. To a request to explain what an electron really is supposed to be we can only answer, "It is part of the A B C of physics". The external world of physics has thus become a world of shadows. In removing our illusions we have removed the substance, for indeed we have seen that substance is one of the greatest of our illusions. Later perhaps we may inquire whether in our zeal to cut out all that is unreal we may not have used the knife too ruthlessly. Perhaps, indeed, reality is a child which cannot survive without its nurse illusion. But if so, that is of little concern to the scientist, who has good and sufficient reasons for pursuing his investigations in the world of shadows and is content to leave to the philosopher the determination of its exact status in regard to reality. In the world of physics we watch a shadowgraph performance of the drama of familiar life. The shadow of my elbow rests on the shadow table as the shadow ink flows over the shadow paper. It is all symbolic, and as a symbol the physicist leaves it. Then comes the alchemist Mind who transmutes the symbols. The sparsely spread nuclei of electric force become a tangible solid; their restless agitation becomes the warmth of summer; the octave of aethereal vibrations becomes a gorgeous rainbow. Nor does the alchemy stop here. In the transmuted world new significances arise which are scarcely to be traced in the world of symbols; so that it becomes a world of beauty and purpose — and, alas, suffering and evil. The frank realisation that physical science is concerned with a world of shadows is one of the most significant of recent advances."

"Science aims at constructing a world which shall be symbolic of the world of commonplace experience. It is not at all necessary that every individual symbol that is used should represent something in common experience or even something explicable in terms of common experience. The man in the street is always making this demand for concrete explanation of the things referred to in science; but of necessity he must be disappointed. It is like our experience in learning to read. That which is written in a book is symbolic of a story in real life. The whole intention of the book is that ultimately a reader will identify some symbol, say BREAD, with one of the conceptions of familiar life. But it is mischievous to attempt such identifications prematurely, before the letters are strung into words and the words into sentences. The symbol A is not the counterpart of anything in familiar life."

"The idealistic tinge in my conception of the physical world arose out of mathematical researches on the relativity theory. In so far as I had any earlier philosophical views, they were of an entirely different complexion. From the beginning I have been doubtful whether it was desirable for a scientist to venture so far into extra-scientific territory. The primary justification for such an expedition is that it may afford a better view of his own scientific domain."

"We have found a strange foot-print on the shores of the unknown. We have devised profound theories, one after another, to account for its origins. At last, we have succeeded in reconstructing the creature that made the footprint. And lo! It is our own."

"We can see that, the constant in the law of gravitation being fixed, there may be some upper limit to the amount of matter possible; as more and more matter is added in the distant parts, space curves round and ultimately closes; the process of adding more matter must stop, because there is no more space, and we can only return to the region already dealt with. But there seems nothing to prevent a defect of matter, leaving space unclosed. Some mechanism seems to be needed, whereby either gravitation creates matter, or all the matter in the universe conspires to define a law of gravitation."

"Spherical space is not very easy to imagine. We have to think of the properties of the surface of a sphere — the two-dimensional case — and try to conceive something similar applied to three-dimensional space. Stationing ourselves at a point let us draw a series of spheres of successively greater radii. The surface of a sphere of radius r should be proportional to r2; but in spherical space the areas of the more distant spheres begin to fall below the proper proportion. There is not so much room out there as we expected to find. Ultimately we reach a sphere of biggest possible area, and beyond it the areas begin to decrease. The last sphere of all shrinks to a point — our antipodes. Is there nothing beyond this? Is there a kind of boundary there? There is nothing beyond and yet there is no boundary. On the earth's surface there is nothing beyond our own antipodes but there is no boundary there."

"It is of interest to inquire what happens when the aviator's speed … approximates to the velocity of light. Lengths in the direction of flight become smaller and smaller, until for the speed of light they shrink to zero. The aviator and the objects accompanying him shrink to two dimensions. We are saved the difficulty of imagining how the processes of life can go on in two dimensions, because nothing goes on. Time is arrested altogether. This is the description according to the terrestrial observer. The aviator himself detects nothing unusual; he does not perceive that he has stopped moving. He is merely waiting for the next instant to come before making the next movement; and the mere fact that time is arrested means that he does not perceive that the next instant is a long time coming."

"It is the reciprocity of these appearances — that each party should think the other has contracted — that is so difficult to realise. Here is a paradox beyond even the imagination of Dean Swift. Gulliver regarded the Lilliputians as a race of dwarfs; and the Lilliputians regarded Gulliver as a giant. That is natural. If the Lilliputians had appeared dwarfs to Gulliver, and Gulliver had appeared a dwarf to the Lilliputians — but no! that is too absurd for fiction, and is an idea only to be found in the sober pages of science. … It is not only in space but in time that these strange variations occur. If we observed the aviator carefully we should infer that he was unusually slow in his movements; and events in the conveyance moving with him would be similarly retarded — as though time had forgotten to go on. His cigar lasts twice as long as one of ours. … But here again reciprocity comes in, because in the aviator's opinion it is we who are travelling at 161,000 miles a second past him; and when he has made all allowances, he finds that it is we who are sluggish. Our cigar lasts twice as long as his."

"Phys. I know that it is often a help to represent pressure and volume as height and width on paper; and so geometry may have applications to the theory of gases. But is it not going rather far to say that geometry can deal directly with these things and is not necessarily concerned with lengths in space? Math. No. Geometry is nowadays largely analytical, so that in form as well as in effect, it deals with variables of an unknown nature. … It is literally true that I do not want to know the significance of the variables x, y, z, t that I am discussing. … Phys. Yours is a strange subject. You told us at the beginning that you are not concerned as to whether your propositions are true, and now you tell us you do not even care to know what you are talking about. Math. That is an excellent description of Pure Mathematics, which has already been given by an eminent mathematician [Bertrand Russell]."

"[Experimental Physicist] Phys. I cannot imagine myself perceiving non-Euclidean space! Math. Look at the reflection of the room in a polished doorknob, and imagine yourself one of the actors in what you see going on there."

"[Relativist] Rel. There is a well-known proposition of Euclid which states that "Any two sides of a triangle are together greater than the third side." Can either of you tell me whether nowadays there is good reason to believe that this proposition is true? [Pure Mathematician] Math. For my part, I am quite unable to say whether the proposition is true or not. I can deduce it by trustworthy reasoning from certain other propositions or axioms, which are supposed to be still more elementary. If these axioms are true, the proposition is true; if the axioms are not true, the proposition is not true universally. Whether the axioms are true or not I cannot say, and it is outside my province to consider."

"The writings of Einstein, Minkowski, Hilbert, Lorentz, Weyl, Robb, and others, have provided the groundwork; in the give and take of debate with friends and correspondents, the extensive ramifications have gradually appeared."

"A non-mathematical presentation has necessary limitations; and the reader who wishes to learn how certain exact results follow from Einstein's, or even Newton's, law of gravitation is bound to seek the reasons in a mathematical treatise. ...[T]he geometry of relativity in its perfect harmony expresses a truth... which my bowdlerised version misses. But the mind is not content to leave scientific Truth in a dry husk of mathematical symbols, and demands that it shall be alloyed with familiar images."

"By his theory of relativity Albert Einstein has provoked a revolution of thought in physical science. ...Physical space and time are found to be closely bound... with... motion of the observer; and only an amorphous combination of the two is left... It is my aim to give an account of this work without introducing anything very technical in... mathematics, physics, or philosophy. ...[T]he task is one of interpreting a clear-cut theory... although perhaps not everyone would accept the author's views of its meaning."

"[P]erhaps there is something to be said for . The classic authorities tell us that he was only "doing a stunt," but I... think of him as a man who... brought to light a constructional defect in the flying-machines of his day. So too, in science, cautious Dædalus will apply his theories where he feels most confident... but by... excess caution their hidden weaknesses cannot be brought to light. Icarus will strain his theories to the breaking-point until the weak joints gape. ...But if he is not yet destined to reach the sun and solve for all time the riddle of its constitution, yet he may hope to learn from his journey some hints to build a better machine."

"Our model of Nature should not be like a building... for the populace to admire... until the edifice comes tumbling down. It should be like an engine with movable parts. ...[A]ny one lever ...is to be adjusted from time to time as the latest observations indicate. The aim of the theorist is to know the train of wheels which the lever sets in motion—that binding of the parts which is the soul of the engine."

"I suppose that the applied mathematician whose theory had just passed one still more stringent test by observation ought not to feel satisfaction, but rather disappointment—"Foiled again! This time I had hoped to find a discordance which would throw light on the points where my model could be improved." ...I own that I have never felt very keenly a disappointment of this kind."

"We have been pulling at the wrong end of the tangle, which has to be unravelled by a different approach. But after a general agreement with observation is established, and the tangle begins to loosen, we should always make ready for the next knot."

"There is no need for disappointment at the failure of the model to give perfect agreement with observation; it has served its purpose, for it has distinguished what are the features of the actual which require new conditions for their explanation."

"When the properties of an ideal model have been worked out by rigorous mathematics, all the underlying assumptions being clearly understood, then it becomes possible to say that such-and-such properties and laws lead precisely to such-and-such effects. If any other disregarded factors are present, they should now betray themselves when a comparison is made with Nature."

"If indeed, the subatomic energy is being freely used to maintain their great furnaces, it seems to bring a little nearer to fulfillment our dreams of controlling this latent power for the well being of the humans-or for its suicide."

"[T]he atoms of all elements are built of atoms bound together... the interior of a star seems as likely a place as any for the evolution to have occurred... a great amount of energy must have been set free; in a star a vast amount of energy is being set free which is hitherto unaccounted for. You may draw a conclusion if you like."

"I think that the suspicion has been generally entertained that the stars are the crucibles in which the lighter atoms which abound in the nebulæ are compounded into more complex elements. In the stars matter has its preliminary brewing to prepare the greater variety of elements which are needed for a world of life. The radio-active elements must have been formed at no very distant date; and their synthesis, unlike the generation of helium from hydrogen, is endothermic."

"What is the source of heat which the sun and the stars are continually squandering? The answer given is almost unanimous... the gravitational energy converted as the star steadily contracts. ...Lord Kelvin showed that this hypothesis, due to Helmholtz, necessarily dates the birth of the sun about 20,000,000 years ago; and he made strenuous efforts to induce geologists and biologists to accommodate... But... outrageous violations of this limit have prevailed. ...Sir 's theory of the earth-moon system, to the present Lord Raleigh's ...age of terrestrial rocks from occluded helium, and to all modern discussions of the statistical equilibrium of the stellar system. No one seems to have any hesitation... in carrying back the history of the earth long before the supposed date of formation of the solar system... in some cases... this appears... justified by experimental evidence... difficult to dispute. Lord Kelvin's date of the creation of the sun is treated with no more respect than Archbishop Ussher's."

"Probably the greatest need of stellar astronomy... in order to make sure that our theoretical deductions are starting on the right lines, is some means of measuring the apparent angular diameters of stars. At present we can calculate them approximately from theory, but there is no observational check. ...If the direct measurement ...could be made with any accuracy it would make a wonderfully rapid advance in our knowledge. The prospects... are now... hopeful. ...[W]ork is being carried out by interferometer methods with the 100-in. reflector at Mt. Wilson, and the results are promising. At present the method has been applied only to measuring the separation of close s... Although the great mirror is used for convenience, the interferometer method does not in principle require great apertures, but rather two small apertures widely separated, as in a range-finder."

"Our observational knowledge of the things here discussed is chiefly of a rather vague kind, and we can scarcely claim more than a general agreement of theory and observation. What we have been able to do in the way of tests is to offer the theory a considerable number of opportunities to "make a fool of itself," and so far it has not fallen into our traps. When the theory tells us that a star having the mass of the sun will at one stage in its career reach a maximum effective temperature of 9000° (the sun's effective temperature [of the ] being 6000°) we cannot do much in the way of checking it; but an erroneous theory might well have said that the maximum temperature was 20,000° (hotter than any known star), in which case we should have detected its error. If we cannot feel confident that the answers of the theory are true, it must be admitted that it has shown some discretion in lying without being found out."

"On the observational side we have fairly satisfactory knowledge of the masses and densities of the stars and of the total radiation emitted by them; this knowledge is partly individual and partly statistical. The theoretical analysis connects these observational data... with the physical properties of the material inside the star... We can thus find certain information as to the inner material, as though we had actually bored a hole. ...[W]e depend entirely on the well-tried principle of conservation of momentum and the second law of thermodynamics. If any element of speculation remains ...it is no more than is inseparable from every kind of theoretical advance."

"[T]heoretical researches of Einstein and Weyl make it probable that the space which remains beyond is not illimitable; not merely the material universe, but also space itself, is perhaps finite..."

"We used to think that if we knew one, we knew two, because one and one are two. We are finding that we must learn a great deal more about "and"."

"I am continually trying to find out why people find the procedure obscure. But I would point out that even Einstein was considered obscure, and hundreds of people have thought it necessary to explain him. I cannot seriously believe that I ever attain the obscurity that Dirac does. But in the case of Einstein and Dirac people have thought it worthwhile to penetrate the obscurity. I believe they will understand me all right when they realize they have got to do so--and when it becomes the fashion "to explain Eddington"."

"Observation and theory get on best when they are mixed together, both helping one another in the pursuit of truth. It is a good rule not to put overmuch confidence in a theory until it has been confirmed by observation. I hope I shall not shock the experimental physicists too much if I add that it is also a good rule not to put overmuch confidence in the observational results that are put forward until they have been confirmed by theory."

"It is impossible to trap modern physics into predicting anything with perfect determinism because it deals with probabilities from the outset."

"There once was a brainy baboon, Who always breathed down a bassoon, For he said, "It appears That in billions of years I shall certainly hit on a tune"."

"To the pure geometer the radius of curvature is an incidental characteristic — like the grin of the Cheshire cat. To the physicist it is an indispensable characteristic. It would be going too far to say that to the physicist the cat is merely incidental to the grin. Physics is concerned with interrelatedness such as the interrelatedness of cats and grins. In this case the "cat without a grin" and the "grin without a cat" are equally set aside as purely mathematical phantasies."

"I think that science would never have achieved much progress if it had always imagined unknown obstacles hidden round every corner. At least we may peer gingerly round the corner, and perhaps we shall find there is nothing very formidable after all."

"A star is drawing on some vast reservoir of energy by means unknown to us. This reservoir can scarcely be other than the sub-atomic energy which, it is known, exists abundantly in all matter; we sometimes dream that man will one day learn to release it and use it for his service. The store is well-nigh inexhaustible, if only it could be tapped."

"We do not argue with the critic who urges that the stars are not hot enough for this process; we tell him to go and find a hotter place."

"At terrestrial temperatures matter has complex properties which are likely to prove most difficult to unravel; but it is reasonable to hope that in the not too distant future we shall be competent to understand so simple a thing as a star."

"The present revolution of scientific thought follows in natural sequence on the great revolutions at earlier epochs in the history of science. Einstein's special theory of relativity, which explains the indeterminateness of the frame of space and time, crowns the work of Copernicus who first led us to give up our insistence on a geocentric outlook on nature; Einstein's general theory of relativity, which reveals the curvature or non-Euclidean geometry of space and time, carries forward the rudimentary thought of those earlier astronomers who first contemplated the possibility that their existence lay on something which was not flat. These earlier revolutions are still a source of perplexity in childhood, which we soon outgrow; and a time will come when Einstein's amazing revelations have likewise sunk into the commonplaces of educated thought."

"Physics has in the main contented itself with studying the abridged edition of the book of nature."

"If we are honest — and scientists have to be — we must admit that religion is a jumble of false assertions, with no basis in reality. The very idea of God is a product of the human imagination. It is quite understandable why primitive people, who were so much more exposed to the overpowering forces of nature than we are today, should have personified these forces in fear and trembling. But nowadays, when we understand so many natural processes, we have no need for such solutions. I can't for the life of me see how the postulate of an Almighty God helps us in any way. What I do see is that this assumption leads to such unproductive questions as why God allows so much misery and injustice, the exploitation of the poor by the rich and all the other horrors He might have prevented. If religion is still being taught, it is by no means because its ideas still convince us, but simply because some of us want to keep the lower classes quiet. Quiet people are much easier to govern than clamorous and dissatisfied ones. They are also much easier to exploit. Religion is a kind of opium that allows a nation to lull itself into wishful dreams and so forget the injustices that are being perpetrated against the people. Hence the close alliance between those two great political forces, the State and the Church. Both need the illusion that a kindly God rewards — in heaven if not on earth — all those who have not risen up against injustice, who have done their duty quietly and uncomplainingly. That is precisely why the honest assertion that God is a mere product of the human imagination is branded as the worst of all mortal sins."

"In the fight between you and the world, back the world."

"Dirac’s relationship with quantum electrodynamics was not an easy one. On the one hand, the theory owes to him much more than to anybody else, especially if one considers the years crucial for its emergence, the late 1920s and early 1930s, when practically all its main concepts, except for that of renormalization, were developed. After this period Dirac also wrote a number of important papers, specifically, on indefinite metrics and quantum dynamics with constraints. On the other hand, since the early 1930s he was an active critic of the theory and tried to develop alternative schemes. He did not become satisfied with the later method of renormalization and regarded it as a mathematical trick rather than a fundamental solution, and died unreconciled with what, to a large extent, was his own brainchild. …"

"Dirac has done more than anyone this century, with the exception of Einstein, to advance physics and change our picture of the universe. He is surely worthy of the memorial in Westminster Abbey. It is just a scandal that it has taken so long."

"Dirac, in his first paper, in contrast to what his “hole”-theory implied, had identified the positively charged particle corresponding to the electron also with the proton. However, after Weyl had pointed out that Dirac’s hole theory led to equal masses, he changed his mind and gave the new particle the same mass as the electron."

"Let me backtrack... to the 1920s when quantum mechanics was created. ...[O]ne of the things that the originators of quantum mechanics... were very unhappy about was that quantum mechanics was not compatible with the special theory of relativity. ...Attempts were made to create a theory of the electron that is consistent with relativity, and one person made such a theory, but it was inconsistent with the electron spin. Another person made a theory that was consistent with electron spin, but not consistent with relativity. Until finally... a then young man... Paul Dirac created the theory of an equation that correctly describes the electron, and is relativistic, and also includes the description of spin... [T]hat was the beginning of the marriage that would take place between quantum mechanics and relativity. ...He originally noticed that the equation had too many solutions... He thought the negatively charged solutions would be electrons and the positive charge solutions would be s... He realized that this made no sense and the two things had to have the same , and finally... realized that he was... predicting [the positively charged electron,] the , just shortly before the positron was... independently and serendipitously discovered."

"Here we find a man with an almost miraculous apprehension of the structure of the physical world, coupled with gentle incomprehension of that less logical, messier world, the world of other people."

"Before World War II there had been considerable theoretical effort directed towards the question of the self-energy of the electron. However, because of the war, interest had remained dormant. Now, the stimulus of results of Lamb and Retherford the latent interest developed into a major attack by theoretical physicists, and within a few years the problem was solved to the satisfaction of nearly everyone. (To the end of his life, however, Dirac maintained that any theory involving the subtraction of infinities was ugly, unsatisfactory and surely incomplete.)"