The logic of modern physics

by P. W. Bridgman

This discussion of the concept of time will doubtless be felt by some to be superficial in that it makes no mention of the properties of the physical time to which the concept is designed to apply. For instance, we do not discuss the one dimensional flow of time, or the irrevocability of the past. Such a discussion, however, is beyond our present purpose, and would take us deeper than I feel competent to go, and perhaps beyond the verge of meaning itself. Our discussion here is from the point of view of operations: we assume the operations to be given, and do not attempt to ask why precisely these operations were chosen, or whether others might not be more suitable. Such properties of time as its irrevocability are implicitly contained in the operations themselves, and the physical essence of time is buried in that long physical experience that taught us what operations are adapted to describing and correlating nature. We may digress, however, to consider one question. It is quite common to talk about a reversal of the direction of flow of time. Particularly, for example, in discussing the equations of mechanics, it is shown that if the direction of flow of time is reversed, the whole history of the system is retraced. The statement is sometimes added that such a reversal is actually impossible, because it is one of the properties of physical time to flow always forward. If this last statement is subjected to an operational analysis, I believe that it will be found not to be a statement about nature at all, but merely a statement about operations. It is meaningless to talk about time moving backward: by definition, forward is the direction in which time flows.

THE CAUSALITY CONCEPT

The causality concept is unquestionably one of the most fundamental, perhaps as fundamental as that of space and time, and therefore at least equally entitled to a first place in the discussion. But as ordinarily understood, there are certain spatial and temporal implications in the causality concept, so that it can best be discussed in this order after our examination of space and time.

There is an aspect of the causality concept that in many respects is closely related to the question of "explanation", for to find the causes of an event usually involves at the same time finding its explanation. But there are nevertheless sufficient differences to warrant a separate discussion.

It seems fairly evident that there was originally in the causality concept an animistic element much like that in the concept of force to be discussed later. The physical essence of the concept as we now have it, freed as much as possible from the animistic element, seems to be somewhat as follows. We assume in the first place an isolated system on which we can perform unlimited identical experiments, that is, the system may be started over again from a definite initial condition as often as desired.[9]

[9]We must include in general in the concept of "initial condition" the past history of the system. In order not to make this condition so broad as to defeat itself, we have to add the observation that actually identity of past history is necessary over only a comparatively short interval of time. Logical precision seems unattainable here—the physical concepts themselves have not the necessary precision.

We assume further that when so started, the system always runs through exactly the same sequence of events in all its parts. This contains the assumption that the course of events runs independent of the absolute time at which they occur—there is no change with time of the properties of the universe.[10] It is a result of experience that systems with these properties actually exist. An alternative way of stating our fundamental hypothesis is that two or more isolated similar systems started from the same initial condition run through the same future course of events. Upon the system given in this way, which by itself runs a definite course of events, we assume that we can superpose from the outside certain changes, which have no connection with the previous history of the system, and are completely arbitrary. Now of course in nature, as we observe it, there is no such thing as an arbitrary change, without connection with past history, so that strictly our assumption is a pure fiction. It is here that the animistic element still seems to persist, although perhaps not necessarily.

[10]As so often in physics, we appear to be doing two things at once here. It is doubtful whether we can give a meaning to "definite initial condition" apart from the future behavior of the system, so that we have no real right to infer from uniform future behavior both a constancy of the laws of nature, independent of time, and a constancy of initial condition. I very much question whether a thoroughgoing operational analysis would show that there are really two independent concepts here, and whether the use of two formally quite different concepts is anything more than a convenience in expression. It seems to me that it may be just as meaningless to ask whether the laws of nature are independent of time as it was to ask with Clifford whether the absolute scale of magnitude may not be changing as the solar system travels through space.

We regard our acts as not determined by the external world, so that changes produced in the external world by acts of our wills are, to a certain degree of approximation, arbitrary. The system, then, on which we are experimenting, is one capable of isolation from us in that we may regard ourselves as outside the system, and having no connection with it. The system, furthermore, is capable of isolation from the rest of the physical universe, in that events taking place outside the system have no connection with those taking place inside.[11] Experience gives the justification for assuming that physical isolation of this sort is possible. Actually, of course, isolation is never complete, but only partial, up to presumably any desired degree of approximation.

[11]Here again, the concept of "isolation" or "connection" is defined only in terms of the behavior of the system, and it is not clear whether this is really an operationally independent concept or not.