Relativity Simply Explained

Relativity Simply Explained is a book written by Martin Gardner to explain Einstein's special theory of relativity and general theory of relativity to a popular audience. It was first published in 1962.

Chapter 1 Absolute or Relative

 * Jules Henry Poincaré... who anticipated many aspects of relativity theory, once put it this way... Suppose... everything in the universe became a thousand times larger than before. ...would you be able to tell that anything had changed? Is there an experiment you could perform that would prove you had altered in size? No, said Poincaré... "Larger" means larger in relation to something else. ...Size, then, is relative. There is no absolute way to measure an object.

Chapter 2 The Michelson-Morley Experiment

 * G. J. Whitrow points out in his book The Structure and Evolution of the Universe, a very simple explanation [for the Michelson–Morley experiment] would immediately occurred to everyone: the earth doesn't move!


 * The strangest explanation [for the Michelson–Morley experiment] was put forth by an Irish physicist, George Francis Fitzgerald. Perhaps, he said, the ether wind puts pressure on a moving object, causing it to shrink a bit in the direction of motion. To determine the length of a moving object, its length at rest must be multiplied by the following simple formula, in which $$ \scriptstyle v^2$$ is the velocity of the object multiplied by itself, $$ \scriptstyle c^2$$ is the velocity of light multiplied by itself: $$ \scriptstyle \sqrt{1-\frac{v^2}{c^2}}$$.


 * The speed of light in an unobtainable limit; when this is reached the formula becomes $$ \scriptstyle \sqrt{1-\frac{c^2}{c^2}}$$ which reduces to 0. ...In other words, if an object could obtain the speed of light, it would have no length at all in the direction of its motion!


 * FitzGerald's theory was put into elegant mathematical form by the Dutch physicist Hendrick Antoon Lorentz, who had independently thought of the same explanation. ...The theory came to be known as the Lorentz-FitzGerald contraction theory.


 * Lorentz made an important addition to his original theory. He introduced changes in time. Clocks, he said, would be slowed down by the ether wind, and in just such a way as to make the velocity of light always measure 299,800 meters per second.

Chapter 3 The Special Theory of Relativity, Part I

 * There were many other experiments that had created a highly unsatisfactory state of affairs with respect to theory about electromagnetic phenomenoa. If the Michelson-Morley test had never been made, the special theory would still have been formulated.


 * Einstein, following the steps of Ernst Mach, took a bolder view. The reason Michelson and Morley were unable to detect an ether wind, Einstein said, is simple: There is no ether wind. He did not say that there was no ether; only... [that the ether] is of no value in measuring uniform motion.


 * Classical physics—the physics of Isaac Newton—made clear that if you are on a uniformly [non-accelerating] moving object, say a train car that is closed on all sides so you cannot see the scenery as you go by, there is no mechanical experiment by which you can prove that you are moving. ...If you toss a ball straight up in the air, it comes straight down again. This is exactly what would happen if you standing still.


 * The special theory of relativity carries the classical relativity of Newton forward another step. It says that in addition to being unable to detect the train's motion by a mechanical experiment, it is also impossible to detect its motion by an optical experiment.


 * Imagine two spaceships, A and B. There is nothing in the cosmos except these two ships. They move toward each other at uniform speed. ...To speak of an absolute motion of either ship is to say something that has no meaning. There is only one reality: a relative motion that brings the ships together at uniform speed.


 * It is not possible to measure uniform motion in any absolute way.


 * In the special theory of relativity, the speed of light becomes... a new absolute. ...Regardless of the motion of its source, light always moves through space with the same constant speed.


 * There is no absolute time throughout the universe by which absolute simultaneity can be measured. Absolute simultaneity of distant events is a meaningless concept.


 * If an astronaut traveled as fast as light his clock would stop completely.


 * If two spaceships are in relative motion, an observer on each ship will measure the other ship as contracted slightly in the direction of its motion. ...The theory does not say that each ship is shorter than the other; it says that astronauts on each ship measure the other ship as shorter.


 * Two ships are passing each other with uniform speed close to that of light. As they pass, a beam of light on the other ship is sent from the ceiling to the floor. There it strikes a mirror and is reflected back to the ceiling again. You will see the path of this light as a V [shape]. If you had sufficiently accurate instruments (of course no such instrument exists), you could clock the time it takes this light beam to traverse the V-shaped path. By dividing the length of the path by the time, you obtain the speed of light. ...an astronaut inside the other ship is doing the same thing [measuring his light beam's speed]. From his point of view... the light simply goes down and up along the same line, obviously a shorter distance than along the V that you observed. ...he also obtains the speed of light. ...But his light path is shorter. ...There is only one possible explanation: his clock is slower. Of course, the situation is perfectly symmetrical. If you send a beam down and up inside your ship, he will see its path as V-shaped. He will deduce that your clock is slower.

Chapter 4 The Special Theory of Relativity, Part II

 * All three variables—length, time, mass—are covered by the same Lorentz contraction [ $$ \scriptstyle \sqrt{1-\frac{v^2}{c^2}}$$ ]... Length and the rate of clocks vary in the same direct proportion, so the formula is the same for each. Mass... varies in the inverse proportion... $$ \scriptstyle \frac{1} {\sqrt{1-\frac{v^2}{c^2}}}$$.


 * If the ships could attain a relative speed equal to that of light, observers on each ship would think the other ship had shrunk to zero in length, acquired an infinite mass, and that time on the other ship had slowed to a full stop! If inertial mass did not vary in this way, then the steady application of force, such as the force supplied by rocket motors, could keep increasing a ship's velocity until it passed the speed of light. ...When the ship has contracted to one-tenth its rest length, its relativistic mass has become ten times as great. ...ten times as much force is required to produce the same increase in speed.


 * The speed of light can never be reached. If it were reached, the outside observer would find that the ship had shrunk to zero length, had acquired an infinite mass, and was exerting an infinite force with its rocket motors. Astronauts inside the ship would observe no changes in themselves, but they would find the cosmos hurtling backward with the speed of light, cosmic time at a standstill, every star flattened to a disk and infinitely massive.