Theory of relativity

"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 aviators 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."

"Einsteins famous theory of relativity states that while phenomena appear different to someone close to a black hole, traveling close to the speed of light, or in a falling elevator here on earth, scientists in profoundly different environments will nevertheless always discover the same underlying laws of nature."

"By the widening of the transformation group in general relativity the idea of distinguished inertial coordinate systems could also be eliminated by Einstein as inconsistent with the group-theoretical properties of the theory. Without this general critical attitude, which abandoned naive visualizations in favour of a conceptual analysis of the correspondence between observational data and the mathematical quantities in a theoretical formalism, the establishment of the modern form of quantum theory would not have been possible."

"There is a point of view according to which relativity theory is the end-point of "classical physics", which means physics in the style of Newton-Faraday-Maxwell, governed by the "deterministic" form of causality in space and time, while afterwards the new quantum-mechanical style of the laws of Nature came into play. This point of view seems to me only partly true, and does not sufficiently do justice to the great influence of Einstein, the creator of the theory of relativity, on the general way of thinking of the physicists of today. By its epistemological analysis of the consequences of the finiteness of the velocity of light (and with it, of all signal-velocities), the theory of special relativity was the first step away from naive visualization. The concept of the state of motion ,of the "luminiferous aether", as the hypothetical medium was called earlier, had to be given up, not only because it turned out to be unobservable, but because it became superfluous as an element of a mathematical formalism, the group-theoretical properties of which would only be disturbed by it."

"One clock stayed on the ground; its double flew. / And it ran slow. So, then. The mad things true."

"It was the space doctor who figured out the answer. He said that if our ideas about light were right, then our ideas about distance and seconds must be wrong. He said that time doesn’t pass the same for everyone. When you go fast, he said, the world around you changes shape, and time outside starts moving slower. The doctor came up with some numbers for how time and space must change to make the numbers for light work. With his idea, everyone would see light moving the right distance every second. This idea is what we call his special idea. The special idea is really, really strange, and understanding it can take a lot of work. Lots of people thought it must be wrong because it’s so strange, but it turned out to be right. We know because we’ve tried it out. If you go really fast, time goes slower. If you’re in a car, you see watches outside the car go slower. They only go a little slower, so you wouldn’t notice it in your normal life; it takes the best watches in the world to even tell that it’s happening. But it really does happen."

"Consider two observers, one... moving uniformly along a straight line, the other [stationary] on the embankment. At the precise instant these two observers pass each other at a point P, a flash of light is produced at the point P. The light wave produced by the instantaneous flash will present the shape of an expanding sphere. Since the invariant velocity of light holds equally for either observer, we must assume that either observer will find himself at all times situated at the centre of the expanding sphere. Our first reaction might be to say: "What nonsense! How can different people, travelling apart, all be at the centre of the same sphere?" Our objection, however, would be unjustified."

"Another topic deserving discussion is Einstein’s modification of Newton’s law of gravitation. In spite of all the excitement it created, Newton’s law of gravitation is not correct! It was modified by Einstein to take into account the theory of relativity. According to Newton, the gravitational effect is instantaneous, that is, if we were to move a mass, we would at once feel a new force because of the new position of that mass; by such means we could send signals at infinite speed. Einstein advanced arguments which suggest that we cannot send signals faster than the speed of light, so the law of gravitation must be wrong. By correcting it to take the delays into account, we have a new law, called Einstein’s law of gravitation. One feature of this new law which is quite easy to understand is this: In the Einstein relativity theory, anything which has energy has mass—mass in the sense that it is attracted gravitationally. Even light, which has an energy, has a “mass.” When a light beam, which has energy in it, comes past the sun there is an attraction on it by the sun. Thus the light does not go straight, but is deflected. During the eclipse of the sun, for example, the stars which are around the sun should appear displaced from where they would be if the sun were not there, and this has been observed."

"No mathematician can give any meaning to the language about matter, force, inertia used in current text-books of mechanics."

"What makes writing relativity so tricky is this: Built into ordinary language — in its use of tenses, for example — are many implicit assumptions about the nature of temporal relations that we now know to be false. Most importantly, we have known since 1905 that when you say that two events in different places happen at the same time you are not referring to anything inherent in the events themselves. You are merely adopting a conventional way of locating them that can differ from other equally valid conventional assignments of temporal order which do not have the events happening at the same time."

"After the doctor figured out the special idea, he started thinking about weight. Things with weight pull on each other. Earth pulls things down toward it, which is why you can’t jump to space. Earth also pulls on the moon, keeping it near us, and the sun pulls on Earth in the same way. It turns out that light gets pulled by weight, too. (People weren’t sure about this for a while, because it moves so fast that it only gets pulled a little.) Someone very careful might notice that this gives us a new problem: How can light turn? The numbers that explain how light moves also say that it can only go forward. It can’t change direction in empty space. That’s just what the numbers for light say—the same numbers that say it always moves a certain distance every second. If a light wave is pulled down, it has to turn to point down, since it can’t travel to the side. To turn, the bottom part of the wave has to go slower than the top part, since it’s going a shorter distance in the same time. But that can’t be right, because the numbers say that light can’t go faster or slower. We’re in trouble again. And, once again, the space doctor has an answer. The space doctor figured out that to explain how weight pulls things like light, we have to play around with time again. He showed that if time itself goes slower near heavy things, then the side of the light near the heavy thing won’t go as far every second. This lets the light turn toward the heavy thing. The doctor’s idea was that weight slows down time, and it explained how light could bend. But to figure out how much light bends, we need to look at the other part of the doctor’s big idea. To talk about that part, let’s forget about light and instead visit another world."

"The best presentation of the general theory [of relativity] is still Eddingtons book of 1923, The Mathematical Theory of Relativity. For the planetary motion and the motion of the moon, see: de Sitter, "On Einsteins theory of gravitation and and its astronomical consequences," Monthly Notices, R. Astr. Soc. London, 76:699; 77:155. The mathematical foundation, the calculus of tensors, is given very completely in Eddingtons book. For an exhaustive treatment see: Levi-Cevita, The Absolute Differential Calculus, translated by Dr. E. Perisco (1927)."