Ether and Motion

by
ALBERT EINSTEIN AND LEOPOLD INFELD
The Evolution of Physics. New York: Simon and Schuster, 1961, pp. 164-187
Ye Gods! annihilate but space and time,! And make two lovers happy.
-ALEXANDER POPE, The Art of Sinking in Poetry, 11
Science has, as its whole purpose, the rendering of the physical world understandable and beautiful. Without this you only have fables and statistics. The measure of our success is our ability to live with this knowledge effectively, actively and with delight. If we succeed we will be able to cope with our knowledge and not create despair. But this also means appreciation of the plurality of knowledge. Order is not monolithic, it is plural.
-J. ROBERT OPPENHEIMER
However successful the theory of a four-dimensional world may be, it is difficult to ignore a voice inside us which whispers: At the back of your mind, you know that a fourth dimension is all nonsense.". . . Let us not be beguiled by this voice. It is discredited. . . .
-ARTHUR STANLEY EDDINGTON

THE GALILEAN RELATIVITY principle is valid for mechanical phenomena. The same laws of mechanics apply to all inertial systems moving relative to each other. Is this principle also valid for nonmechanical phenomena, especially for those for which the field concepts proved so very important? All problems concentrated around this question immediately bring us to the starting point of the relativity theory.

We remember that the velocity of light in vacuo, or in other words, in ether, is 186,000 miles per second and that light is an electromagnetic wave spreading through the ether. The electromagnetic field carries energy which, once emitted from its source, leads an independent existence. For the time being, we shall continue to believe that the ether is a medium through which electromagnetic waves, and thus also light waves, are propagated, even though we are fully aware of the many difficulties connected with its mechanical structure.

We are sitting in a closed room so isolated from the external world that no air can enter or escape. If we sit still and talk we are, from the physical point of view, creating sound waves, which spread from their resting source with the velocity of sound in air. If there were no air or other material medium between the mouth and the ear, we could not detect a sound. Experiment has shown that the velocity of sound in air is the same in all directions, if there is no wind and the air is at rest in the chosen Coordinate System (CS).

Let us now imagine that our room moves uniformly through space. A man outside sees, through the glass walls of the moving room (or train if you prefer) everything which is going on inside. From the measurements of the inside observer he can deduce the velocity of sound relative to his CS connected with his surroundings, relative to which the room moves. Here again is the old, much discussed, problem of determining the velocity in one CS if it is already known in another.

The observer in the room claims: the velocity of sound is, for me, the same in all directions.

The outside observer claims: the velocity of sound, spreading in the moving room and determined in my CS, is not the same in all directions. It is greater than the standard velocity of sound in the direction of the motion of the room and smaller in the opposite direction.

These conclusions are drawn from the classical transformation and can be confirmed by experiment. The room carries within it the material medium, the air through which sound waves are propagated, and the velocities of sound will, therefore, be different for the inside and outside observer.

We can draw some further conclusions from the theory of sound as a wave propagated through a material medium. One way, though by no means the simplest, of not hearing what someone is saying, is to run, with a velocity greater than that of sound, relative to the air surrounding the speaker. The sound waves produced will then never be able to reach our ears. On the other hand, if we missed an important word which will never be repeated, we must run with a speed greater than that of sound to reach the produced wave and to catch the word. There is nothing irrational in either of these examples except that in both cases we should have to run with a speed of about four hundred yards per second, and we can very well imagine that further technical development will make such speeds possible. A bullet fired from a gun actually moves with a speed greater than that of sound and a man placed on such a bullet would never hear the sound of the shot.

All these examples are of a purely mechanical character and we can now formulate the important questions: could we repeat what has just been said of a sound wave, in the case of a light wave? Do the Galilean relativity principle and the classical transformation apply to mechanical as well as to optical and electrical phenomena? It would be risky to answer these questions by a simple "yes" or "no" without going more deeply into their meaning.

In the case of the sound wave in the room moving uniformly, relative to the outside observer, the following intermediate steps are very essential for our conclusion:

The moving room carries the air in which the sound wave is propagated. The velocities observed in two CS moving uniformly, relative to each other, are connected by the classical transformation.

The corresponding problem for light must be formulated a little differently. The observers in the room are no longer talking, but are sending light signals, or light waves in every direction. Let us further assume that the sources emitting the light signals are permanently resting in the room. The light waves move through the ether just as the sound waves moved through the air.

Is the ether carried with the room as the air was? Since we have no mechanical picture of the ether it is extremely difficult to answer this question. If the room is closed, the air inside is forced to move with it. There is obviously no sense in thinking of ether in this way, since all matter is immersed in it and it penetrates everywhere. No doors are closed to ether. The "moving room," now means only a moving CS to which the source of light is rigidly connected. It is, however, not beyond us to imagine that the room moving with its light source carries the ether along with it just as the sound source and air were carried along in the closed room. But we can equally well imagine the opposite: that the room travels through the ether as a ship through a perfectly smooth sea, not carrying any part of the medium along but moving through it. In our first picture, the room moving with its light source carries the ether. An analogy with a sound wave is possible and quite similar conclusions can be drawn. In the second, the room moving with its light source does not carry the ether. No analogy with a sound wave is possible and the conclusions drawn in the case of the sound wave do not hold for a light wave. These are the two limiting possibilities. We could imagine the still more complicated possibility that the ether is only partially carried by the room moving with its light source. But there is no reason to discuss the more complicated assumptions before finding out which of the two simpler limiting cases experiment favors.

We shall begin with our first picture and assume, for the present: the ether is carried along by the room moving with its rigidly-connected light source. If we believe in the simple transformation principle for the velocities of sound waves, we can now apply our conclusions to light waves as well. There is no reason for doubting the simple mechanical transformation law which only states that the velocities have to be added in certain cases and subtracted in others. For the moment, therefore, we shall assume both the carrying of the ether by the room moving with its light source and the classical transformation.

If I turn on the light and its source is rigidly connected with my room, then the velocity of the light signal has the well-known experimental value 186,000 miles per second. But the outside observer will notice the motion of the room, and, therefore, that of the source and, since the ether is carried along, his conclusion must be: the velocity of light in my outside CS is different in different directions. It is greater than the standard velocity of light in the direction of the motion of the room and smaller in the opposite direction. Our conclusion is: if ether is carried with the room moving with its light source and if the mechanical laws are valid, then the velocity of light must depend on the velocity of the light source. Light reaching our eyes from a moving light source would have a greater velocity if the motion is toward us and smaller if it is away from us.

If our speed were greater than that of light we should be able to run away from a light signal. We could see occurrences from the past by reaching previously sent light waves. We should catch them in a reverse order to that in which they were sent, and the train of happenings on our earth would appear like a film shown backward, beginning with a happy ending. These conclusions all follow from the assumption that the moving CS carries along the ether and the mechanical transformation laws are valid. If this is so, the analogy between light and sound is perfect.

But there is no indication as to the truth of these conclusions. On the contrary, they are contradicted by all observations made with the intention of proving them. There is not the slightest doubt as to the clarity of this verdict, although it is obtained through rather indirect experiments in view of the great technical difficulties caused by the enormous value of the velocity of light. The velocity of light is always the same in all CS independent of whether or not the emitting source moves, or how it moves.

We shall not go into detailed description of the many experiments from which this important conclusion can be drawn. We can, however, use some very simple arguments which, though they do not prove that the velocity of light is independent of the motion of the source, nevertheless make this fact convincing and understandable.

In our planetary system the earth and other planets move around the sun. We do not know of the existence of other planetary systems, similar to ours. There are, however, very many double-star systems, consisting of two stars moving around a point, called their center of gravity. Observation of the motion of these double stars reveals the validity of Newton's gravitational law. Now suppose that the speed of light depends on the velocity of the emitting body. Then the message, that is, the light ray from the star, will travel more quickly or more slowly, according to the velocity of the star at the moment the ray is emitted. In this case the whole motion would be muddled and it would be impossible to confirm, in the case of distant double stars, the validity of the same gravitational law which rules over our planetary system.

Let us consider another experiment based upon a very simple idea. Imagine a wheel rotating very quickly. According to our assumption, the ether is carried by the motion and takes a part in it. A light wave passing near the wheel would have a different speed when the wheel is at rest than when it is in motion. The velocity of light in ether at rest should differ from that in ether which is being quickly dragged round by the motion of the wheel, just as the velocity of a sound wave varies on calm and windy days. But no such difference is detected! No matter from which angle we approach the subject, or what crucial experiment we may devise, the verdict is always against the assumption of the ether carried by motion. Thus, the result of our considerations, supported by more detailed and technical argument, is:

The velocity of light does not depend on the motion of the emitting source.

It must not be assumed that the moving body carries the surrounding ether along.

We must, therefore, give up the analogy between sound and light waves and turn to the second possibility: that all matter moves through the ether, which takes no part whatever in the motion. This means that we assume the existence of a sea of ether with all CS resting in it, or moving relative to it. Suppose we leave, for a while, the question as to whether experiment proved or disproved this theory. It will be better to become more familiar with the meaning of this new assumption and with the conclusions which can be drawn from it.

There exists a CS resting relative to the ether-sea. In mechanics, not one of the many CS moving uniformly, relative to each other, could be distinguished. All such CS were equally "good" or "bad." If we have two CS moving uniformly, relative to each other, it is meaningless, in mechanics, to ask which of them is in motion and which at rest. Only relative uniform motion can be observed. We cannot talk about absolute uniform motion because of the Galilean relativity principle. What is meant by the statement that absolute and not only relative uniform motion exists? Simply that there exists one CS in which some of the laws of nature are different from those in all others. Also that every observer can detect whether his CS is at rest or in motion by comparing the laws valid in it with those valid in the only one which has the absolute monopoly of serving as the standard CS. Here is a different state of affairs from classical mechanics, where absolute uniform motion is quite meaningless because of Galileo's law of inertia.

What conclusions can be drawn in the domain of field phenomena if motion through ether is assumed? This would mean that there exists one CS distinct from all others, at rest relative to the ether-sea. It is quite clear that some of the laws of nature must be different in this CS, otherwise the phrase, "motion through ether," would be meaningless. If the Galilean relativity principle is valid then motion through ether makes no sense at all. It is impossible to reconcile these two ideas. If, however, there exists one special CS fixed by the ether, then to speak of "absolute motion" or "absolute rest," has a definite meaning.

We really have no choice. We tried to save the Galilean relativity principle by assuming that systems carry the ether along in their motion, but this led to a contradiction with experiment. The only way out is to abandon the Galilean relativity principle and try out the assumption that all bodies move through the calm ether-sea.

The next step is to consider some conclusions contradicting the Galilean relativity principle and supporting the view of motion through ether, and to put them to the test of an experiment. Such experiments are easy enough to imagine, but very difficult to perform. As we are concerned here only with ideas, we need not bother with technical difficulties.

Again we return to our moving room with two observers, one inside and one outside. The outside observer will represent the standard es, designated by the ether-sea. It is the distinguished es in which the velocity of light always has the same standard value. All light sources, whether moving or at rest in the calm ether-sea, propagate light with the same velocity. The room and its observer move through the ether. Imagine that a light in the center of the room is flashed on and off and, furthermore, that the walls of the room are transparent so that the observers, both inside and outside, can measure the velocity of the light. If we ask the two observers what results they expect to obtain, their answers would run something like this:

The outside observer: My es is designated by the ether-sea. Light in my es always has the standard value. I need not care whether or not the source of light or other bodies are moving, for they never carry my ethersea with them. My es is distinguished from all others and the velocity of light must have its standard value in this es, independent ofthe direction of the light beam or the motion of its source.

The inside observer: My room moves through the ether-sea. One of the walls runs away from the light and the other approaches it. If my room traveled, relative to the ether-sea, with the velocity of light, then the light emitted from the center of the room would never reach the wall running away with the velocity of light. If the room traveled with a velocity smaller than that of light, then a wave sent from the center of the room would reach one of the walls before the other. The wall moving toward the light wave would be reached before the one retreating from the light wave. Therefore, although the source of light is rigidly connected with my es, the velocity of light will not be the same in all directions. It will be smaller in the direction of the motion relative to the ether-sea as the wall runs away, and greater in the opposite direction as the wall moves toward the wave and tries to meet it sooner.

Thus, only in the one es distinguished by the ether-sea should the velocity of light be equal in all directions. For other es moving relatively to the ether-sea it should depend on the direction in which we are measuring.

The crucial experiment just considered enables us to test the theory of motion through the ether-sea. Nature, in fact, places at our disposal a system moving with a fairly high velocity: the earth in its yearly motion around the sun. If our assumption is correct, then the velocity of light in the direction of the motion of the earth should differ from the velocity of light in an opposite direction. The differences can be calculated and a suitable experimental test devised. In view of the small time-differences following from the theory, very ingenious experimental arrangements have to be thought out. This was done in the famous Michelson-Morley experiment. The result was a verdict of "death" to the theory of a calm ether-sea through which all matter moves. No dependence of the speed of light upon direction could be found. Not only the speed of light, but also other field phenomena would show a dependence on the direction in the moving es, if the theory of the ether-sea were assumed. Every experiment has given the same negative result as the Michelson-Morley one, and never revealed any dependence upon the direction of the motion of the earth.

The situation grows more and more serious. Two assumptions have been tried. The first, that moving bodies carry ether along. The fact that the velocity of light does not depend on the motion of the source contradicts this assumption. The second, that there exists one distinguished es and that moving bodies do not carry the ether but travel through an ever calm ether- sea. If this is so, then the Galilean relativity principle is not valid and the speed of light cannot be the same in every es. Again we are in contradiction with experiment.

More artificial theories have been tried out, assuming that the real truth lies somewhere between these two limiting cases: that the ether is only partially carried by the moving bodies. But they all failed! Every attempt to explain the electromagnetic phenomena in moving es with the help of the motion of the ether, motion through the ether, or both these motions, proved unsuccessful.

Thus arose one of the most dramatic situations in the history of science. All assumptions concerning ether led nowhere! The experimental verdict was always negative. Looking back over the development of physics we see that the ether, soon after its birth, became the "enfant terrible" of the family of physical substances. First, the construction of a simple mechanical picture of the ether proved to be impossible and was discarded. This caused, to a great extent, the breakdown of the mechanical point of view. Second, we had to give up hope that through the presence of the ether-sea one CS would be distinguished and lead to the recognition of absolute, and not only relative, motion. This would have been the only way, besides carrying the waves, in which ether could mark and justify its existence. All our attempts to make ether real failed. It revealed neither its mechanical construction nor absolute motion. Nothing remained of all the properties of the ether except that for which it was invented, i.e., its ability to transmit electromagnetic waves. Our attempts to discover the properties of the ether led to difficulties and contradictions. After such bad experiences, this is the moment to forget the ether completely and to try never to mention its name. We shall say: our space has the physical property of transmitting waves, and so omit the use of a word we have decided to avoid.

The omission of a word from our vocabulary is, of course, no remedy. Our troubles are indeed much too profound to be solved in this way!

Let us now write down the facts which have been sufficiently confirmed by experiment without bothering any more about the "e-r" problem.
1. The velocity of light in empty space always has its standard value, independent of the motion of the source or receiver of light.
2. In two CS moving uniformly, relative to each other, all laws of nature are exactly identical and there is no way of distinguishing absolute uniform motion.

There are many experiments to confirm these two statements and not a single one to contradict either of them. The first statement expresses the constant character of the velocity of light, the second generalizes the Galilean relativity principle, formulated for mechanical phenomena, to all happenings in nature.

In mechanics, we have seen: If the velocity of a material point is so and so, relative to one CS, then it will be different in another CS moving uniformly, relative to the first. This follows from the simple mechanical transformation principles. They are immediately given by our intuition (man moving relative to ship and shore) and apparently nothing can be wrong here! But this transformation law is in contradiction to the constant character of the velocity of light. Or, in other words, we add a third principle:

3. Positions and velocities are transformed from one inertial system to another according to the classical transformation. The contradiction is then evident. We cannot combine (1), (2), and (3).

The classical transformation seems too obvious and simple for any at tempt to change it. We have already tried to change (1) and (2) and came to a disagreement with experiment. All theories concerning the motion of "e-r" required an alteration of (1) and (2). This was no good. Once more we realize the serious character of our difficulties. A new clue is needed. It is supplied by accepting the fundamental assumptions (1) and (2), and, strange though it seems, giving up (3). The new clue starts from an analysis of the most fundamental and primitive concepts; we shall show how this analysis forces us to change our old views and removes all our difficulties. Our new assumptions are:

1. The velocity of light in vacuo is the same in all CS moving uniformly, relative to each other.

2. All laws of nature are the same in all CS moving uniformly, relative to each other.

The relativity theory begins with these two assumptions. From now on we shall not use the classical transformation because we know that it contradicts our assumptions.

It is essential here, as always in science, to rid ourselves of deep-rooted, often uncritically repeated, prejudices. Since we have seen that changes in (1) and (2) lead to contradiction with experiment, we must have the courage to state their validity clearly and to attack the one possibly weak point, the way in which positions and velocities are transformed from one CS to another. It is our intention to draw conclusions from (1) and (2), see where and how these assumptions contradict the classical transformation, and find the physical meaning of the results obtained.

Once more, the example of the moving room with outside and inside observers will be used. Again a light signal is emitted from the center of the room and again we ask the two men what they expect to observe, assuming only our two principles and forgetting what was previously said concerning the medium through which the light travels. We quote their answers:

The inside observer: The light signal traveling from the center of the room will reach the walls simultaneously, since all the walls are equally distant from the light source and the velocity of light is the same in all directions.

The outside observer: In my system, the velocity of light is exactly the same as in that of the observer moving with the room. It does not matter to me whether or not the light source moves in my CS since its motion does not influence the velocity of light. What I see is a light signal traveling with a standard speed, the same in all directions. One of the walls is trying to escape from and the opposite wall to approach the light signal. Therefore, the escaping wall will be met by the signal a little later than the approaching one. Although the difference will be very slight if the velocity of the room is small compared with that of light, the light signal will nevertheless not meet these two opposite walls, which are perpendicular to the direction of the motion, quite simultaneously.

Comparing the predictions of our two observers we find a most astonishing result which flatly contradicts the apparently well-founded concepts of classical physics. Two events, i.e., the two light beams reaching the two walls, are simultaneous for the observer on the inside, but not for the observer on the outside. In classical physics, we had one clock, one time flow, for all observers in all es. Time, and therefore such words as "simultaneously," "sooner," "later," had an absolute meaning independent of any es. Two events happening at the same time in one es happened necessarily simultaneously in all other es.

Assumptions (1) and (2), i.e., the relativity theory, force us to give up this view. We have described two events happening at the same time in one es, but at different times in another es. Our task is to understand this consequence, to understand the meaning of the sentence: "Two events which are simultaneous in one es, may not be simultaneous in another es."

What do we mean by "two simultaneous events in one es"? Intuitively everyone seems to know the meaning of this sentence. But let us make up our minds to be cautious and try to give rigorous definitions, as we know how dangerous it is to overestimate intuition. Let us first answer a simple question. What is. a clock?

The primitive subjective feeling of time flow enables us to order our impressions, to judge that one event takes place earlier, another later. But to show that the time interval between two events is 10 seconds, a clock is needed. By the use of a clock the time concept becomes objective. Any physical phenomenon may be used as a clock, provided it can be exactly repeated as many times as desired. Taking the interval between the beginning and the end of such an event as one unit of time, arbitrary time intervals may be measured by repetition of this physical process. All clocks, from the simple hourglass to the most refined instruments, are based on this idea. With the hourglass the unit of time is the interval the sand takes to flow from the upper to the lower glass. The same physical process can be repeated by inverting the glass.

At two distant points we have two perfect clocks, showing exactly the same time. This statement should be true regardless of the care with which we verify it. But what does it really mean? How can we make sure that distant clocks always show exactly the same time? One possible method would be to use television. It should be understood that television is used only as an example and is not essential to our argument. I could stand near one of the clocks and look at a televised picture of the other. I could then judge whether or not they showed the same time simultaneously. But this would not be a good proof. The televised picture is transmitted through electromagnetic waves and thus travels with the speed of light. Through television I see a picture which was sent some very short time before, whereas on the real clock I see what is taking place at the present moment. This difficulty can easily be avoided. I must take television pictures of the two clocks at a point equally distant from each of them and observe them from this center point. Then, if the signals are sent out simultaneously, they will all reach me at the same instant. If two good clocks observed from the mid-point of the distance between them always show the same time, then they are well suited for designating the time of events at two distant points.

In mechanics we used only one clock. But this was not very convenient, because we had to take all measurements in the vicinity of this one clock. Looking at the clock from a distance, for example by television, we have always to remember that what we see now really happened earlier, just as we receive light from the sun eight minutes after it was emitted. We should have to make corrections, according to our distance from the clock, in all our time readings.

It is, therefore, inconvenient to have only one clock. Now, however, as we know how to judge whether two, or more, clocks show the same time simultaneously and run in the same way, we can very well imagine as many clocks as we like in a given CS. Each of them will help us to determine the time of the events happening in its immediate vicinity. The clocks are all at rest relative to the CS. They are "good" clocks and are synchronized, which means that they show the same time simultaneously.

There is nothing especially striking or strange about the arrangements of our clocks. We are now using many synchronized clocks instead of only one and can, therefore, easily judge whether or not two distant events are simultaneous in a given CS. They are if the synchronized clocks in their vicinity show the same time at the instant the events happen. To say that one of the distant events happens before the other has now a definite meaning. All this can be judged by the help of the synchronized clocks at rest in our CS.

This is in agreement with classical physics, and not one contradiction to the classical transformation has yet appeared.

For the definition of simultaneous events, the clocks are synchronized by the help of signals. It is essential in our arrangement that these signals travel with the velocity of light, the velocity which plays such a fundamental role in the theory of relativity.

Since we wish to deal with the important problem oftwo CS moving uniformly, relative to each other, we must consider two rods, each provided with clocks. The observer in each of the two ts moving relative to each other now has his own rod with his own set of clocks rigidly attached.

When discussing measurements in classical mechanics we used one clock for all CS. Here we have many clocks in each CS. This difference is unimportant. One clock was sufficient, but nobody could object to the use of many, so long as they behave as decent synchronized clocks should.

Now we are approaching the essential point showing where the classical transformation contradicts the theory of relativity. What happens when two sets of clocks are moving uniformly, relative to each other? The classical physicist would answer: Nothing; they still have the same rhythm, and we can use moving as well as resting clocks to indicate time. According to classical physics, two events simultaneous in one CS will also be simultaneous in any other CS.

But this is not the only possible answer. We can equally well imagine a moving clock having a different rhythm from one at rest. Let us now discuss this possibility without deciding, for the moment, whether or not clocks really change their rhythm in motion. What is meant by the statement that a moving clock changes its rhythm? Let us assume, for the sake of simplicity, that we have only one clock in the upper CS and many in the lower. All the clocks have the same mechanism, and the lower ones are synchronized, that is, they show the same time simultaneously. We have drawn three subsequent positions of the two CS moving relative to each other. In the first drawing the positions of the hands of the upper and lower clocks are, by convention, the same because we arranged them so. All the clocks show the same time. In the second drawing, we see the relative positions of the two CS some time later. All the clocks in the lower CS show the same time, but the clock in the upper CS is out of rhythm. The rhythm is changed and the time differs because the clock is moving relative to the lower CS. In the third drawing we see the difference in the positions of the hands increased with time.

An observer at rest in the lower CS would find that a moving clock changes its rhythm. Certainly the same result could be found if the clock moved relative to an observer at rest in the upper CS; in this case there would have to be many clocks in the upper CS and only one in the lower. The laws of nature must be the same in both CS moving relative to each other.

In classical mechanics it was tacitly assumed that a moving clock does not change its rhythm. This seemed so obvious that it was hardly worth mentioning. But nothing should be too obvious; if we wish to be really careful, we should analyze the assumptions, so far taken for granted, in physics.

An assumption should not be regarded as unreasonable simply because it differs from that of classical physics. We can well imagine that a moving clock changes its rhythm, so long as the law of this change is the same for all inertial CS.

Yet another example. Take a yardstick; this means that a stick is a yard in length as long as it is at rest in a CS. Now it moves uniformly, sliding along the rod representing the CS. Will its length still appear to be one yard? We must know beforehand how to determine its length. As long as the stick was at rest its ends coincided with markings one yard apart on the CS. From this we concluded: the length of the resting stick is one yard. How are we to measure this stick during motion? It could be done as follows. At a given moment two observers simultaneously take snapshots, one of the origin of the stick and the other of the end. Since the pictures are taken simultaneously we can compare the marks on the CS rod with which the origin and the end of the moving stick coincide. In this way we determine its length. There must be two observers to take note of simultaneous events in different parts of the given CS. There is no reason to believe that the result of such measurements will be the same as in the case of a stick at rest. Since the photographs had to be taken simultaneously, which is, as we already know, a relative concept depending on the CS, it seems quite possible that the results of this measurement will be different in different CS moving relative to each other.

We can well imagine that not only does the moving clock change its rhythm, but also that a moving stick changes its length, so long as the laws of the changes are the same for all inertial CS.

We have only been discussing some new possibilities without giving any justification for assuming them.

We remember: the velocity of light is the same in all inertial CS. It is impossible to reconcile this fact with the classical transformation. The circle must be broken somewhere. Can it not be done just here? Can we not assume such changes in the rhythm of the moving clock and in the length of the moving rod that the constancy of the velocity of light will follow directly from these assumptions? Indeed we can! Here is the first instance in which the relativity theory and classical physics differ radically. Our argument can b~ reversed: if the velocity of light is the same in all CS, then moving rods must change their length, moving clocks must change their rhythm, and the laws governing these changes are rigorously determined.

There is nothing mysterious or unreasonable in all this. In classical physics it was always assumed that clocks in motion and at rest have the same rhythm, that rods in motion and at rest have the same length. If the velocity of light is the same in all CS, if the relativity theory is valid, then we must sacrifice this assumption. It is difficult to get rid of deep-rooted prejudices, but there is no other way. From the point of view of the relativity theory the old concepts seem arbitrary. Why believe, as we did some pages ago, in absolute time flowing in the same way for all observers in all CS? Why believe in unchangeable distance? Time is determined by clocks, space co-ordinates by rods, and the result of their determination may depend on the behavior of these clocks and rods when in motion. There is no reason to believe that they will behave in the way we should like them to. Observation shows, indirectly, through the phenomena of electromagnetic fields, that a moving clock changes its rhythm, a rod its length, whereas on the basis of mechanical phenomena we did not think this happened. We must accept the concept of relative time in every CS, because it is the best way out of our difficulties. Further scientific advance, developing from the theory of relativity, shows that this new aspect should not be regarded as a malum necessarium, for the merits of the theory are much too marked.