The evolution of scientific thought from Newton to Einstein

by A. D'Abro

At this point we must guard against possible confusion. It might be argued: “There is nothing very new in this relativity of simultaneity and of the order of succession of our perceptions; for we encounter such examples even in classical science. For instance, if two explosions occur at different spots, by adjusting our position as observers it may be possible for us to perceive the two noises now simultaneously and now in succession.” But such arguments would indicate that the revolutionary notion of the relativity of simultaneity had not been grasped.

Thus, in the example of the two explosions happening in different places on the earth’s surface, while it is perfectly true that the order of succession in which we hear or see these explosions will depend on our position as observers, yet, on the other hand, if we take into consideration the time which sound or light waves require to cover the distances separating us from the two explosions, we can always decide without ambiguity whether the two explosions occurred simultaneously or in succession. It was never the order or the simultaneity of our perceptions which was considered absolute in classical science; it was solely the simultaneity or order in which these explosions or events had taken place in the outside world.

Now, according to the theory of relativity, not only is the simultaneity of our perceptions relative, but in addition, even when we take into consideration the speed with which the sound waves or light waves advance towards us, it is still impossible to decide whether the two events (regarded as existing in the outside world independently of any observer) are simultaneous or not; for our calculations would show that this simultaneity in the outside world would vary from one observer to another.

The relativity of simultaneity leads us to the kindred subject of the relativity of the order of succession of two events occurring in different places. Here it is impossible to lay down a rigid rule; for we shall see that the theory compels us to recognise that in certain cases the order of succession is indeterminate or relative to our motion, while in others it is absolute, remaining the same for all observers.

The problem is of sufficient importance to warrant a more detailed explanation. Our awareness of the passage of time constitutes one of the most fundamental facts of consciousness. Not only is time continuously passing, but it is ever flowing in the same direction. To this mystery of the uni-directional passage of time, the theory of relativity contributes no new information, so that we may discuss the problem from the standpoint of classical science. Suppose, then, that in a bottle we place two layers of powder, one white and one black. If we shake the mixture long enough, we know that the final result will be a uniform grey mixture. Now we might have anticipated this result without actually performing the experiment. For if we consider the various ways in which the particles of the powders could be distributed in the bottle, sufficient reason would urge us to assert that all distributions were equally probable. But it so happens that by far the greater number of these possible schemes of distribution would yield the appearance of a uniform grey mixture. Probability would suggest, therefore, that on shaking the bottle long enough, the uniform grey mixture would finally appear. When this homogeneous state had been obtained, only once in æons of time would the black and white separation reappear, and then but for an instant. We may express these facts by saying that the general tendency would be a passage from the heterogeneous (black and white layers) to the homogeneous (uniform grey mixture).

The example we have considered is one of extreme simplicity, but inasmuch as the arguments involved appear to be of universal validity, we may say that natural phenomena present a uni-directional sense of advance, passing from the states of lesser probability to those of greater probability. We may therefore identify the states of lesser probability with the past and those of greater probability with the future. The direction of time’s passage can thus be defined physically in terms of probability considerations, entailing a mere appeal to sufficient reason and to operations of counting.

This was the definition suggested by Boltzmann (the founder of the kinetic theory of gases). According to him the universe was passing from states of lesser probability to that of maximum probability, and the direction of this passage defined that of time. As can be gathered from the preceding explanations, a uni-directional passage in the course of phenomena is to be ascribed to the fact that phenomena are irreversible, i.e., that the various states are not equally probable.

It is true that there also exist types of phenomena for which all states present the same probability. In this case no privileged direction exists, and the phenomena are called reversible. An adiabatic transformation under ideal conditions, and the rotation of a body in the absence of friction, are illustrations of reversible processes; such phenomena would of course be incapable of defining the direction of time.

But by far the greater number of phenomena in nature are of the irreversible type; with these a definite direction of change is privileged. When we wish to force the phenomenon against its natural trend, work must be furnished. All phenomena entailing friction are of the irreversible sort, for whereas motion generates heat through friction, the heat cannot be used to regenerate the motion. The example of the two powders also presented us with an illustration of the irreversible type of phenomenon, since the natural evolution was from heterogeneity to homogeneity. To be sure, it would be possible to reverse the process, but only through the medium of some intelligent activity sorting out the particles and distributing them according to states of lesser probability. The action of a demon of this sort, Maxwell’s demon, would cause the direction of the irreversible phenomena to be reversed, so that the direction of time would appear to change. Needless to say, however, Maxwell’s demon is but a fiction.

In the illustration of the two powders we can readily understand the reason for the irreversibility, but it was not by this method that the principle involved was first discovered. We must go back to Carnot and to his investigations on the cycle of the steam engine in order to trace the origin of what was to become one of the most fundamental principles of science. Carnot’s celebrated principle relating to the efficiency of the steam engine was shown by Clausius to be a special case of a general physical principle which may be stated thus: “Heat cannot flow unaided from a colder to a hotter body, but tends invariably to seek lower levels of temperature.”