- One must stand stiller than still.
- Regarding reverse time travel Through Space and Time
The Mysterious Universe (1930)
- From the intrinsic evidence of his creation, the Great Architect of the Universe now begins to appear as a pure mathematician.
- p. 134, 1930 ed.
- Life exists in the universe only because the carbon atom possesses certain exceptional properties.
- p. 19, Pelican Books 1938 reprint of 1931 2nd ed.
- For, for aught we know, or for aught that the new science can say to the contrary, the gods which play the part of fate to the atoms of our brains may be our own minds. Through these atoms our minds may perchance affect the motions of our bodies and so the state of the world around us. To-day science can no longer shut the door on this possibility; she has no longer any unanswerable arguments to bring against our innate conviction of free-will. On the other hand, she gives no hint as to what absence of determinism or causation may mean. If we, and nature in general, do not respond in a unique way to external stimuli, what determines the course of events? If anything at all, we are thrown back on determinism and causation; if nothing at all, how can anything ever occur? As I see it, we are unlikely to reach any definite conclusions on these questions until we have a better understanding of the true nature of time.
- p. 29-30 of 1930 ed.
- Everything that has been said, and every conclusion that has been tentatively put forward, is quite frankly speculative and uncertain. We have tried to discuss whether present-day science has anything to say on certain difficult questions, which are perhaps set for ever beyond the reach of human understanding. We cannot claim to have discerned more than a very faint glimmer of light at the best; perhaps it was wholly illusory, for certainly we had to strain our eyes very hard to see anything at all. So that our main contention can hardly be that the science of to-day has a pronouncement to make, perhaps it ought rather to be that science should leave off making pronouncements: the river of knowledge has too often turned back on itself.
- The closing sentences of the book, on p. 188 of Pelican Books 1938 reprint of 1931 2nd ed.
The Stars in their Courses (1931)
- The motion of the stars over our heads is as much an illusion as that of the cows, trees and churches that flash past the windows of our train.
- p. 3.
- The human race, whose intelligence dates back only a single tick of the astronomical clock, could hardly hope to understand so soon what it all means.
- p. 153.
An Introduction to the Kinetic Theory of Gases (1940)
- If we assume that the last breath of, say, Julius Caesar has by now become thoroughly scattered through the atmosphere, then the chances are that each of us inhales one molecule of it with every breath we take.
Physics and Philosophy (1942)
- Superficially at least the forces of electricity and magnetism seem to present the same kind of problem as gravitation. Experiment shows that two electrically charged bodies attract one another (or repel if their charges are of the same kind) with a force which conforms to the same mathematical law as the force of gravitation - both forces fall off inversely as the inverse square of the distance. The same is true of the magnetic force also; two magnetic poles attract or repel one another with a force which again follows the law of the inverse square of the distance.
- Gravitational force is simple, and a thing by itself, as also are electric and magnetic forces as long as the electric and magnetic poles stand at rest. But as soon as motion comes into the picture, the whole situation is changed. Forces of new kinds come into play, for moving electric charges exert magnetic forces in addition to the electric forces they exert when at rest, while moving magnets exert electric forces in addition to the magnetic forces they exert while at rest. When the exact laws governing these intricate laws had been discovered by a great number of experimenters, Clerk Maxwell succeeded in expressing them in a mathematical form which was both simple and elegant.
- At this time, space was supposed to be filled with an ether, a substance which might well serve, among other functions, to transmit forces across space. So long as such an ether could be called on, the transmission of force to a distance was easy to understand; it was like ringing a distant bell by pulling a bell-rope.
- Faraday, Maxwell, Larmor and a great number of others tried to explain electromagnetic action on these lines, but all attempts failed, and it began to seem impossible that any properties of ether could explain the observed pattern of events.
- Then the theory of relativity came and explained the cause of the failure. Electric action requires time to travel from one point of space to another, the simplest instance of this being the finite speed of travel of light... Thus electromagnetic action may be said to travel through space and time jointly. But by filling space and space alone [excluding time] with an ether, the pictorial representations had all supposed a clear-cut distinction between space and time.
- ...when the experiment was attempted by Michelson and Morley it failed, thus showing that space and time assumed in the picture were not true to the facts of nature. ...the pattern of events was the same whether the world stood at rest in the supposed ether, or had an ether wind blowing through it at a million miles an hour. It began to look as though the supposed ether was not very important in the scheme of things... and so might as well be abandoned. But if the bell-rope is to be discarded, what is to ring the bell?
- As the pattern of events is unaltered by motion, the mechanism must be the same when the electron is in motion as when it is at rest. But experiment shows that an electron in motion exerts additional forces which are not the same for all directions in space; if we picture this electron as moving head-foremost through space, these forces surround it like a belt around its waist.
- if a shower of electrons is shot on to a zinc sulfide screen, a number of flashes are produced - one for each electron - and we may picture the electrons as bullet-like projectiles hitting a target. But if the same shower is made to pass near a suspended magnet, this is found to be deflected as the electrons go by. The electrons may now be pictured as octopus-like structures with tentacles or 'tubes of force' sticking out from it in every direction.
- It would, however, be wrong to think of an electron as a bullet-like structure with tentacles sticking out from its surface. We can calculate the mass of the bullet, and also the mass of the tentacles. The two masses are found to be identical, each agreeing with the known mass of the electron. Thus we cannot take the electron to be bullet plus tentacles... The two pictures do not depict two different parts of the electron, but two different aspects of the electron. They are not additive but alternative; as one comes into play, the other must disappear.
- Actually the situation is even more complicated, since a separate tentacle picture is needed for each speed of motion of the electron, the speed being measured relative to the suspended magnet or other object on which the moving electron is to act. ...When the electron is at rest, the tentacles stick out equally in all directions. But an electron which is at rest relative to one magnet may be in motion relative to another, and to discuss the action of the electron on this second magnet we must picture it as having a belt of tentacles round its waist. This shows that we must have a different picture for every speed of relative motion, so that the total number of pictures is infinite, and we cannot form the picture we need unless we know the speed of the electron relative to the object it is about to meet.
- ...experimental physics was particularly interested in the processes taking place inside the atom, and in this field the classical mechanics was failing conspicuously and completely. Perhaps its most spectacular failure was with the fundamental problem with the structure of the atom.
- Another conspicuous failure of classical mechanics was with one aspect of the problem of radiation. ...Imagine a crowd of steel balls rolling about on a steel floor. ...There must... be a steady leakage of energy from... causes, such as air resistance and the friction of the floor, so the balls will eventually lose energy, and, after no great length of time, will be found standing at rest on the floor. The energy of their motion seems to have been lost... most of it has been transformed into heat. The classical mechanics predicts that this must happen; it shows that all energy of motion, except possibly a minute fraction of the whole, must be transformed into heat whenever such a transformation is physically possible. It is because of this that perpetual-motion machines are a practical impossibility.
- Precisely similar ideas are applicable to the molecules that form the air in a room. ...The classical mechanics now predicts that the whole energy of motion will be changed into radiation [heat], so that the molecules will shortly be found lying at rest on the floor... In actual fact they continue to move with undiminished energy, forming a perpetual-motion machine in defiance of classical mechanics. ...We have passed from one to another of three worlds... from the man-sized world to the world of the electron.
- This fallacious result is not... a peculiarity of classical mechanics; it is given also by a very wide class of possible systems of mechanics. This being so, no minor modification of the classical mechanics can possibly put things right. Something far more drastic is needed; we are called upon to surrender either the  continuity or the  causality of classical mechanics, or else the possibility of  representing changes by motions in time and space.
- Now these three concepts form the foundation-stones of the philosophy of materialism and determinism to which the physics of the nineteenth century seemed to lead. Thus, as soon as any one of the three has to be rejected, the philosophical implications of physics undergo a great change; the mechanical age has passed, both in physics and philosophy, and materialism and determinism again become open questions...
- With the coming of the twentieth century, there came into being a new physics which was especially concerned with phenomenon on the atomic and sub-atomic scale. ...A preliminary glance over the vast territory of this new physics reveals three outstanding landmarks.
- First we notice an investigation which Prof. Plank of Berlin published in 1899. His aim was that it should fit the observed facts of radiation, and show why the energy of bodies was not wholly transformed into radiation. ...his investigation seemed to show that continuity had to be given up, suggesting that in the last resort changes in the universe do not consist of continuous motions in space and time, but in some way are discontinuous.
- An extension of Plank's ideas, due to Prof. Niels Bohr of Copenhagen, went on to suggest that... the ultimate particles of matter would be seen to move not like railway trains running smoothly on tracks, but like kangaroos hopping about in a field.
- A second conspicuous landmark... is the enunciation of the fundamental law of radioactive disintegration by Rutherford and Soddy in 1903. This law was in no sense a consequence or development of Plank's theories; indeed fourteen years were to elapse before any connection was noticed between the two. The new law asserted that the atoms of radioactive substances broke up spontaneously, and not because of any particular conditions or special happenings. This seemed to involve an even more startling break with classical theory than the new laws of Plank; radioactive break-up appeared to be an effect without a cause, and suggested that the ultimate laws of nature were not even causal.
- A theoretical investigation which Einstein published in 1917 provides a third conspicuous landmark. It connected up he two great landmarks already mentioned by showing that the disintegration of radioactive substances is governed by the same laws as the jumps of the kangaroo electrons in the theory of Bohr. In fact radioactive atoms were now seen merely to contain a special breed of kangaroos, much more energetic and ferocious than any that had hitherto been encountered.
- The laws which governed the spontaneous jumps of the kangaroos were shown to be of the simplest; out of any number of kangaroos a certain proportion always jumped within a specified time, and nothing seemed to be able to change this number. Also, before the jumps took place, there was nothing in the world of phenomena to distinguish those kangaroos that were about to jump from those that were not... to help fill the quota demanded by the statistical law. As discontinuity marched into the world of phenomena through one door, causality walked out through another.
- The classical mechanics had envisaged the world constructed of matter and radiation, the matter consisting of atoms and the radiation of waves. Plank's theory called for an atomicity of radiation similar to that which was so well established for matter. It supposed that radiation was not discharged from matter in a steady stream like water from a hose, but rather like lead from a machine-gun; it came off in separate chunks which Plank called quanta. This... carried tremendous philosophical consequences.
- Heisenberg finds that facts of observation lead uniquely and inevitably to the theoretical structure known as matrix mechanics. This shows that the total radiation in any region of empty space can change only by a single complete quantum at a time. Thus not only in the photo-electric phenomenon, but in all other transfers of energy through space, energy is always transferred by complete quanta; fractions of a quantum can never occur. This brings atomicity into our picture of radiation just as definitely as the discovery of the electron and its standard charge brought atomicity into our picture of matter and of electricity.
- Before the quantum theory appeared, the principle of the uniformity of nature - that like causes produce like effects - had been accepted as a universal and indisputable fact of science. As soon as the atomicity of radiation became established, this principle had to be discarded.
- In every previous application of the quantum law, Plank's law, that the energy is h [Plank's constant] times the frequency, had been used to deduce the energy of a quantum when the frequency of the radiation was already known. In the present case the formula was used the other way; the energy of the emitted photon was known to begin with, and the formula was utilized to deduce its frequency. The frequencies calculated in this way are found to agree completely and exactly with those of the spectrum of hydrogen.
- This spectrum is of the type known in spectroscopy as a line-spectrum. Its appearance is that of a group of bright lines on a dark background, indicating that the radiation divides itself between a number of clearly defined frequencies, and that there is no radiation in between. Before Bohr's explanation appeared, these frequencies had been supposed to belong to some sort of vibration taking place in the hydrogen atom - like frequencies of the musical note which is heard when a bell or piano wire is made to vibrate. It now became clear that they had an entirely different origin. The energy exhibited in the spectrum was not liberated by a vibration, or any kind of continuous motion, but by the sudden jump of an electron to an orbit of lower energy, and its frequency was determined by the compulsion put upon it to form a single quantum.
- In 1925 Heisenberg made a new attempt, on entirely novel lines, to obtain an explanation of atomic spectra. Working in collaboration with Bohr, he had come to the conclusion that the imperfections of Bohr's theory had been a consequence of assuming too simple a model for the atom. For Bohr had not only assumed that the atom consisted of particles moving through space and time, but also that the particles inside atoms were of the same kind as the electrons outside atoms.
- Bohr's investigation had typified what had become a standard procedure in problems of theoretical physics. The first step was to discover the mathematical laws governing certain groups of phenomena; the second was to devise hypothetical models or pictures to interpret these laws in terms of motion or mechanism; the third was to examine in what way these models would behave in other respects, and this would lead to prediction of other phenomena-predictions which might or might not be confirmed when put to the test of experiment. For instance, Newton had explained the phenomena of gravitation in terms of a force of gravitation; a later age had seen the luminiferous ether introduced to explain the propagation of light and, subsequently, the general phenomena of electricity and magnetism; finally Bohr had introduced electronic jumps in an attempt to explain atomic spectra. In each case the models had fulfilled their primary purpose, but had failed to predict further phenomena with accuracy.
- Heisenberg now approached the problem from a new philosophical angle. He discarded all models, pictures and parables, and made a clear distinction between sure knowledge we gain from observation of nature and the conjectural knowledge we introduce when we use models, pictures and parables. Sure knowledge... can only be numerical, so that Heisenberg's results were inevitably mathematical in form, and could not disclose anything about the true nature of physical properties or entities.
- Bohr had... discovered that the frequencies corresponding to very large integers could be calculated accurately from the classical mechanics; they were simply the number of times that an ordinary electron would complete the circuit of its orbit in one second when it was at a very great distance from the nucleus of the atom to which it belonged. This could only mean that when an electron receded to a great distance from the nucleus of its atom, it not only assumed the properties of an ordinary electron, but also behaved as directed by the classical mechanics. Yet the classical mechanics failed completely for the calculation of frequencies corresponding to small orbits.
- A similar situation occurred in astronomy, where the Newtonian law of gravitation had been found to predict the orbits of the outer planets with great accuracy, but had failed with the orbits of Mercury and Venus. The relativity theory of gravitation had provided the necessary modification of Newton's law, and in working out the details of the new theory, Einstein had utilized the fact that Newtonian law gave the right result at great distances from the sun. Heisenberg, confronted with a similar problem, was able to avail himself of the fact that the classical mechanics gave the right result at great distances from the atomic nucleus. Here, and here alone Heisenberg's theory made contact with the world of the older physics.
- In the interior of the atom, Bohr had tried the plan of retaining the particle-electron and modifying the classical mechanics. Heisenberg took the opposite course, his procedure amounting in effect to retaining the classical mechanics, at least in form, and modifying the electron. Actually, the electron dropped out all together, because it exists only as a matter of inference and not of direct observation. For the same reason, the new theory contains no mention of atoms, nuclei, protons, or of electricity in any shape or form. The existences of all these are matters of inference, and Heisenberg's purely mathematical theory could no more make contact with them than with the efficiency of a turbine or with the price of wheat.
- The main result reached by the new theory was that the classical mechanics can be made to account for the whole range of spectral phenomena, provided entirely new meanings are given to such symbols as p and q which had hitherto been taken to describe the position and motion of the electron. ...The most significant of the new properties is that the product pq is no longer the same as the product qp - in other words the order in which the two factors are multiplied together is no longer a matter of indifference. The difference between pq and qp is found to be always the same, being Plank's constant h multiplied by a numerical multiplier.
- We saw that radiation cannot suitably be pictured as particles when it is traveling through space. There is a corresponding property for electrons; these should not be pictured as waves so long as they are traveling through empty space.
- ...a detailed mathematical discussion shows that whatever kind of wave-packet we select to represent the electron, the product of the two uncertainties of position and momentum can never be less than h, which is precisely what Heisenberg found...
- The complete closed world consists of three parts-substratum, phenomenal world, and observer. By our experiments we drag up activities from the substratum into the phenomenal world of space and time, but there is no clear line of demarcation between subject and object, and by performing observations on the world, we alter it, much as a fisherman dragging up fish from the depths of the seas disturbs the waters and also damages the fish.
- When two hypotheses are possible, we provisionally choose that which our minds adjudge to be simpler, on the supposition that this is the more likely to lead in the direction of truth. It includes as a special case the principle of Occam's razor-entia non multiplicana praeter necessitatem.
- Physics and philosophy are at most a few thousand years old, but probably have lives of thousands of millions of years stretching away in front of them. They are only just beginning to get under way...
- It can hardly be a matter for surprise that our race has not succeeded in solving any large part of its most difficult problems in the first millionth part of its existence. Perhaps life would be a duller affair if it had. for to many it is not knowledge but the quest for knowledge that gives the greater interest to thought - to travel hopefully is better than to arrive.