The evolution of scientific thought from Newton to Einstein

by A. D'Abro

It is not because a causal connection happens to exist between two events that the order is non-reversible; the non-reversibility is due entirely to the spatio-temporal separation of the events. As for the causal connection, it may or may not exist. The only reason we mention causal connections with reference to this problem is in order to show that there is nothing in the relativity theory to suggest a reversal of causality; hence, though Einstein’s theory entails the relativity of simultaneity and in certain cases that of temporal sequence, there is no danger of a cause appearing as an effect or vice versa. In particular, no relative motion of the observer could ever lead him to believe that the glass we had let fall had in reality leaped up from the floor into our hand. No danger of the black and white powders which we had shaken into a grey mixture, appearing to separate back into black and white, as a result of a change in our relative motion. In short, no danger of the principle of entropy being overthrown.

We may also add that whereas, in classical science, owing to the possible existence of influences transmitted with infinite velocity, any two events happening in space might have been conceived of as causally connected or at least as related, Einstein’s theory, by requiring the velocity of light to be unsurpassable, permits us to restrict the cases of possible causal relationships and thereby to gain a better understanding of the cross influences which may be active in the universe.

CHAPTER XXI
THE REALITY OF THE CONTRACTION OF LENGTHS AND OF THE LENGTHENING OF DURATIONS

LET us now pass to the question of lengths and durations. Consider a rigid rod placed on a table, and suppose that both table and rod are drawn away from us with constant speed along a straight line. The contraction of lengths implies that both rod and table will appear to us to be contracted, owing to their relative motion with respect to us.

Here we must emphasise the fact that this contraction has nothing to do with the motion of the rod through space or the ether. As we know, motion, or at least Galilean motion, through space has no meaning. It is purely a relative; so that exactly the same effects of contraction would ensue were we to conceive of the table and rod as at rest and of the observer as moving away from them. It follows that an observer attached to the rod would perceive no contraction, although his friend in motion with respect to him would assert that a contraction had taken place.

The nature of this contraction is obviously rather mysterious, and the question is to decide as to its reality. Here we are met with the difficulty of defining what we wish to convey by the word “reality”; in some respects the contraction of the rod is a physical reality, in others it is a fiction, but in no case is it an illusion.

Let us consider the problem of illusions. For instance, we experience an aggregate of visual impressions which we unhesitatingly ascribe to the presence of a table situated “there in the room.” Yet all we have any right to be positive about is that certain visual impressions have been experienced; our belief in the existence of the table situated “there” results from an inference, a judgment formulated in an attempt to ascribe a cause to our visual sensations. By an association of ideas and by recalling past experience, we feel justified in claiming the existence of the table “there” as we see it. In the majority of cases our judgment will be correct, but in a certain number of instances it will be erroneous. Such would be the case were we to be viewing the reflection of a table in the mirror. An illusion is therefore an error of judgment. And what prompts us to state that our belief in the object behind the mirror is an illusion? Obviously, the bare fact that on testing the matter out in a variety of different ways it appears impossible to credit the table with any existence at the spot where we claim to see it in the common objective world of science. In much the same way we see a mirage and interpret our sensations as connoting the presence of water. Yet were a meteor to fall into the water it would not appear to be extinguished by the waters of the lake. Kindred observations of an indirect order would finally compel us to recognise that our initial judgment was at fault, and that no water lay before us.

And now let us consider the FitzGerald contraction. Is it an illusion? To this question our reply must unhesitatingly be in the negative. Not only should we perceive the contraction were our eyes capable of yielding a snap-shot picture of a rapidly moving object, but in addition every conceivable physical experiment performed in our frame would indicate that the contraction was physically present. And yet we have said that the contraction differed essentially from the one contemplated by Lorentz, generated as was the latter by a real compression caused by the motion of the object through the stagnant ether. The explanation of the dilemma is as follows:

In Einstein’s theory, the rod is contracted, but we must add that this contraction holds only in the space of the frame with respect to which the rod is in motion. In the space of the frame accompanying the rod in its motion, no contraction would occur. We see, then, that as there exists no privileged space, only “my space,” “your space,” “his space,” there is no particular length to the rod, only a length “for me,” “for you” and “for him.” The contraction is thus embodied in a two-term relationship extending between the observer and the observed; it is a “relative.” But, once again, for a given observer it is as physically real as a chair or a table. Only when we consider the contraction from an impersonal standpoint, from that of space-time, without mentioning the conditions of observation, is the contraction not an illusion, but downright meaningless. It is, as we see, the concept of spatial magnitude, of primary qualities, which is at stake, in a form entirely different from anything science or philosophy had ever dreamed.

Now although length, size and duration are relatives, the theory of relativity has discovered absolutes which transcend the observer, remaining the same for all. They are to be found in the absolute world of space-time; and it is this thought that Minkowski desired to convey when he said: “Henceforth space and time by themselves are mere shadows.” In the absence of some specified observer, space and time become indeterminate, and with them length and duration; that which endures and transcends the observer is a something in space-time, and this is neither a length nor a duration. Or, again, lengths and durations are the projections of something in absolute space-time on to the space and time directions of the observer. These latter are indeterminate (until the frame of the observer is specified), since no one space and no one time exists above all others. Space and time being indeterminate, the same will apply to those projections which we call length and duration.