The ABC of Relativity

„What is demanded is a change in our imaginative picture of the world—a picture which has been handed down from remote, perhaps pre-human, ancestors, and has been learned by each one of us in early childhood. A change in our imagination is always difficult, especially when we are no longer young. The same sort of change was demanded by Copernicus, when he taught that the earth is not stationary and the heavens do not revolve about it once a day. To us now there is no difficulty in this idea, because we learned it before our mental habits had become fixed. Einstein’s ideas, similarly, will seem easy to a generation which has grown up with them; but for our generation a certain effort of imaginative reconstruction is unavoidable.”

„We gradually learn to judge distances roughly by the eye, but we rely upon touch for accuracy. Moreover it is touch that gives us our sense of “reality.”

„When you travel from place to place on the earth, you say the train moves and not the stations, because the stations preserve their topographical relations to each other and the surrounding country.”

„A certain type of superior person is fond of asserting that “everything is relative.”

„just as you can estimate a man’s fortune in different currencies without altering its relations to the fortunes of other men, so you can estimate a body’s motion by means of different reference bodies without altering its relations to other motions.”

„Physics is intended to give information about what really occurs in the physical world, and not only about the private perceptions of separate observers. Physics must, therefore, be concerned with those features which a physical process has in common for all observers, since such features alone can be regarded as belonging to the physical occurrence itself. This requires that the laws of phenomena should be the same whether the phenomena are described as they appear to one observer or as they appear to another. This single principle is the generating motive of the whole theory of relativity.”

„If there were no reality in the physical world, but only a number of dreams dreamed by different people, we should not expect to find any laws connecting the dreams of one man with the dreams of another. It is the close connection between the perceptions of one man and the (roughly) simultaneous perceptions of another that makes us believe in a common external origin of the different related perceptions. Physics accounts both for the likenesses and for the differences between different people’s perceptions of what we call the “same”

„…if a light signal is sent out from a body, that body will remain at the center of the waves as they travel outwards, no matter how it may be moving—at least, that will be the view of observers moving with the body. This was the plain and natural meaning of the experiments, and Einstein succeeded in inventing a theory which accepted it. But at first it was thought logically impossible to accept this plain and natural meaning.”

„Dr. A. A. Robb, in his Theory of Time and Space, suggests a point of view which may or may not be philosophically fundamental, but is at any rate a help in understanding the state of affairs we have been describing. He maintains that one event can only be said to be definitely before another if it can influence that other in some way. Now influences spread from a center at varying rates. Newspapers exercise an influence emanating from London at an average rate of about twenty miles an hour—rather more for long distances. Anything a man does because of what he reads in the newspaper is clearly subsequent to the printing of the newspaper. Sounds travel much faster: it would be possible to arrange a series of loud speakers along the main roads, and have newspapers shouted from each to the next. But telegraphing is quicker, and wireless telegraphy travels with the velocity of light, so that nothing quicker can ever be hoped for.”

„When two bodies are moving relatively to each other, lengths on either appear shorter to the other than to themselves. This is the Fitzgerald contraction, which was first invented to account for the result of the Michelson- Morley experiment. But it now emerges naturally from the fact that the two observers do not make the same judgment of simultaneity.”

„We call a motion “accelerated”

„Pythagoras, like many of the greatest characters in history, perhaps never existed: he is a semi-mythical character, who combined mathematics and priestcraft in uncertain proportions.”

„Measurements of distances and times do not directly reveal properties of the things measured, but relations of the things to the measurer. What observation can tell us about the physical world is therefore more abstract than we have hitherto believed.”

„geodesic on a surface is the shortest line that can be drawn on the surface from one point to another;”

„bodies left to themselves do their journeys as slowly as they can; it is a sort of law of cosmic laziness. Its mathematical expression is that they travel in geodesics, in which the total interval between any two events on the journey is greater than by any alternative route. (The fact that it is greater, not less, is due to the fact that the sort of interval we are considering is more analogous to time than to distance.) For example, if a person could leave the earth and travel about for a time and then return, the time between his departure and return would be less by his clocks than by those on the earth: the earth, in its journey round the sun, chooses the route which makes the time of any bit of its course by its clocks longer than the time as judged by clocks which move by a different route.”

„the electrons and protons in the neighborhood of your feet exert a repulsion on your feet which is just enough to overcome the earth’s gravitation. This is what prevents you from falling through the earth, which, solid as it looks, is mostly empty space.”

„All the laws of dynamics have been put together into one principle, called “The Principle of Least Action.”

„We have been dealing hitherto with matters that must be regarded as acquired scientific results—not that they will never be found to need improvement, but that further progress must be built upon them, as Einstein is built upon Newton. Science does not aim at establishing immutable truths and eternal dogmas: its aim is to approach truth by successive approximations, without claiming that at any stage final and complete accuracy has been achieved. There is a difference, however, between results which are pretty certainly in the line of advance, and speculations which may or may not prove to be well founded.”

„We all have a tendency to think that the world must conform to our prejudices. The opposite view involves some effort of thought, and most people would die sooner than think—in fact, they do so. But the fact that a spherical universe seems odd to people who have been brought up on Euclidean prejudices is no evidence that it is impossible. There is no law of nature to the effect that what is taught at school must be true. We cannot therefore dismiss the hypothesis of a spherical universe as in any degree less worthy of examination than any other. We have to ask ourselves the same two questions as we should in any other case, namely: (1) Are the facts consistent with this hypothesis? (2) Is this hypothesis the only one with which the facts are consistent?”

„One of the most difficult matters in all controversy is to distinguish disputes about words from disputes about facts: it ought not to be difficult, but in practice it is.”

„Our own perceptions and feelings must be part of the crude material of events which physics arranges into a pattern—or rather, which physics finds to be arranged in a pattern. As regards events which do not form part of our own lives, physics tells us the pattern of them, but is quite unable to tell us what they are like in themselves. Nor does it seem possible that this should be discovered by any other method.”

„past experience enables us to foresee more or less what is going to happen without the need of mathematical calculations.”

„Since intervals can be compared by experimental methods, he ought soon to discover that his (formula for the interval) cannot be reconciled with observational results, and so realize his mistake. But the mind does not so readily get rid of an obsession. It is more likely that our observer will continue in his opinion, and attribute the discrepancy of the observations to some influence which is present and affects the behavior of his test-bodies. He will, so to speak, introduce a supernatural agency which he can blame for the consequences of his mistake....”

„It has been customary for people to draw arguments from the laws of nature as to what we ought to do. Such arguments seem to me a mistake: to imitate nature may be merely slavish. But if nature, as portrayed by Einstein, is to be our model, it would seem that the anarchists will have the best of the argument. The physical universe is orderly, not because there is a central government, but because every body minds its own business. No two particles of matter ever come into contact; when they get too close, they both move off. If a man were had up for knocking another man down, he would be scientifically correct in pleading that he had never touched him. What happened was that there was a hill in space-time in the region of the other man’s nose, and it fell down the hill.”

„Most of the events in the world are not isolated occurrences, but members of groups of more or less similar events, which are such that each group is connected in an assignable manner with a certain small region of space-time.”

„Suppose you let loose a tiger in the middle of a Bank Holiday crowd: they would all move, and the tiger would be the center of their various movements. A person who could see the people but not the tiger would infer that there was something repulsive at that point. We say in this case that the tiger has an effect upon the people, and we might describe the tiger’s action upon them as of the nature of a repulsive force. We know, however, that they fly because of something which happens to them, not merely because the tiger is where he is. They fly because they can see and hear him, that is to say, because certain waves reach their eyes and ears. If these waves could be made to reach them without there being any tiger, they would fly just as fast, because the neighborhood would seem to them just as unpleasant.”

„All that we have a right to say is that certain groups of occurrences happen together, that is to say, in neighboring parts of space-time. A given observer will regard one member of the group as earlier than the other, but another observer may judge the time order differently. And even when the time order is the same for all observers, all that we really have is a connection between the two events, which works equally backwards and forwards. It is not true that the past determines the future in some sense other than that in which the future determines the past: the apparent difference is only due to our ignorance, because we know less about the future than about the past. This is a mere accident: there might be beings who would remember the future and have to infer the past. The feelings of such beings in these matters would be the exact opposite of our own, but no more fallacious.”

„The world which the theory of relativity presents to our imagination is not so much a world of “things” in “motion”

„geodesic,” and it is the route which a body will choose if left to itself.”

„Propositions which used to be proved by reasoning have now become either conventions, or merely approximate truths verified by observation. It is a curious fact—of which relativity is not the only illustration—that, as reasoning improves, its claims to the power of proving facts grow less and less. Logic used to be thought to teach us how to draw inferences; now, it teaches us rather how not to draw inferences. Animals and children are terribly prone to inference: a horse is surprised beyond measure if you take an unusual turning. When men began to reason, they tried to justify the inferences that they had drawn unthinkingly in earlier days. A great deal of bad philosophy and bad science resulted from this propensity. “Great principles,”

„uniformity of nature,” the “law of universal causation,”

„I suggest that an emotion which can be destroyed by a little mathematics is neither very genuine nor very valuable.”

„We naturally interpret the world pictorially; that is to say, we imagine that what goes on is more or less like what we see. But in fact this likeness can only extend to certain formal logical properties expressing structure, so that all we can know is certain general characteristics of its changes.”

„A financier, whose dealings with the world are more abstract than those of any other “practical”

„bodies left to themselves do their journeys as slowly as they can; it is a sort of law of cosmic laziness. Its mathematical expression is that they travel in geodesics, in which the total interval between any two events on the journey is greater than by any alternative route. (The fact that it is greater, not less, is due to the fact that the sort of interval we are considering is more analogous to time than to distance.) For example, if a person could “the electrons and protons in the neighborhood of your feet exert a repulsion on your feet which is just enough to overcome the earth’s gravitation. This is what prevents you from falling through the earth, which, solid as it looks, is mostly empty space.”

„Suppose you let loose a tiger in the middle of a Bank Holiday crowd: they would all move, and the tiger would be the center of their various movements. A person who could see the people but not the tiger might be beings who would remember the future and have to infer the past. The feelings of such beings in these matters would be the exact opposite of our own, but no more fallacious.”

„geodesic,” and it is the route which a body willchoose if left toitself.”