Since we realise that the definitions of time-congruence we ultimately adopt are governed by our desire to obtain the maximum of simplicity in the co-ordination of some particular group of phenomena, considerable divergences in our definitions might be expected when we considered in turn phenomena of a different nature. Why, indeed, should a determination arrived at in terms of the vibrations of atoms agree in any way with the astronomical definition issuing from the earth’s rotation? Even when restricting our attention to the vibrations of the atoms of the same element, it might have been feared that different atoms of cadmium would have beaten out time at different rates, since, after all, even though identical in many respects, yet their life-histories must have differed greatly. Instead of this we find that all the methods of time-congruence mentioned lead to exactly the same determinations so far as experiment can detect. It would appear as though a common understanding existed between the rates of evolution of the various phenomena mentioned. The situation is similar to that presented in the problem of space. There we saw that rods, whether of platinum or of wood, whether situated here or there, appeared to yield the same geometrical results (provided they were maintained at constant temperature and pressure). Again, it seemed as though some common understanding existed among the various rods.
Just as this same mysterious situation in the case of space suggested that the uniformity of our spatial measurements was due to the presence of an all-embracing physical reality, the metrical field of space, regulating the behaviour of material bodies and light rays, so now, as we shall see in later chapters, the general theory of relativity will compel us to extend the same ideas to time. We shall find that there exists a space-time metrical field which splits up into a temporal and a spatial field. The temporal metrical field will then be responsible for that apparent understanding which seems to exist among the various spatially separated phenomena.
These new ideas modify the position of the problem of time-congruence. While it is still correct to state that pure duration as a mathematical continuum is amorphous and possesses no intrinsic metrics, yet from the standpoint of the physicist we must concede a certain physical reality to this temporal metrical field which controls the processes of all isolated phenomena.
We may summarise the preceding statements by saying that we define time-congruence so as to introduce the maximum of simplicity in our co-ordinations of physical phenomena, regardless of the particular type of phenomenon we may be considering. That a unique definition of time-congruence should be possible, one holding for mechanics, optics, electromagnetics and astronomy, is a fact that could scarcely have been anticipated a priori; hence we must recognise its undeniable existence as establishing the presence of unity in nature.
And here we may mention a type of objection which is often encountered in people who do not trouble to differentiate between physical time and psychological duration. It has been claimed, for instance, that it is absurd to maintain that our sense of time was originated from a desire to retain harmony between the planetary motions and the requirements of Newton’s law, since men possessed an intuitive understanding of equal durations long before Newton’s law or any other natural law was discovered. We trust that those who have taken the trouble to follow the course of this analysis will realise that the criticism is quite beside the mark. No scientist has ever contended that we have derived our sense of time from astronomical observations, for we know that even savages are not lacking in a sense of rhythm. All that is claimed is that the accurate determination of time-congruence must be based on physical processes or laws, since our crude time-sense is too vague to be of any use in the precise problems with which science is concerned. The fact that our crude appreciation of time agrees in a more or less approximate way with the more refined methods of scientific determination offers no great mystery, for, after all, the laws which govern material processes in the outside world would in all probability also govern that which is material in our organisms. Regardless of our ultimate views as to matter and mind, we cannot banish matter from our anatomy.
At any rate, once the existence of a universal type of time-congruence is conceded, the problem is to select some particular phenomenon which can be studied with a minimum of contingency and a maximum of certainty. Now, when we consider the astronomical definition in terms of the earth’s rotation, we realise that were it not for the fact that we had started by assuming the absolute accuracy of Newton’s law, the corrections we made in order to account for the peculiarities of the lunar motion would have to be discarded or replaced by others. If, therefore, any doubt were to be cast on the accuracy of Newton’s law or on those of mechanics, corresponding modifications would ensue for our definition of time-congruence. But it is obvious that we have no right to assume that Newton’s law or those of mechanics are above all suspicion. The laws of physical science present no a priori inevitableness; and our sole reason for accepting them is because they appear to be borne out to a high degree of approximation when we compare their rational consequences with the results of observation. Approximation is thus all we can aspire to in physical science; and even classical scientists recognised the possibility that more precise observation might prove Newton’s law and those of mechanics to stand in need of correction. All that could be asserted was that the corrections would certainly be very slight, far too slight to entail any perceptible change in our understanding of time-congruence when applied to the processes of commonplace observation.
We now come to Einstein’s definition. As we shall see, it does not differ in spirit from the definitions of classical science; its sole advantage is that it entails a minimum of assumptions, and is susceptible of being realised in a concrete way permitting a high degree of accuracy in our measurements. Einstein’s definition is, then, as follows: If we consider a ray of light passing through a Galilean frame, its velocity in the frame will be the same regardless of the relative motion of the luminous source and frame, and regardless of the direction of the ray. It follows that a definition of equal durations in the frame will be given by measuring equal spatial stretches along the path of the ray, and asserting that the wave front will describe these equal stretches in equal times.
As can be seen, the definition is simple enough, but the major question is to decide on its legitimacy. Classical science would have rejected the definition. Why? Because it would have maintained that Einstein’s definition was equivalent to defining time in terms of a rigid body rotating round an axis, but submitted to frictional forces. It would have claimed that the velocity of the frame through the stagnant ether would have introduced complications entailing anisotropy, that is to say, a variation of the speed of light according to direction. It would then be necessary to take this perturbating effect into account just as it was necessary to take into consideration the frictional effect of the tides on the earth’s angular rate of rotation.
But when it was found that contrary to the anticipations of classical science not the slightest trace of anisotropy could be detected even by ultra-precise experiment, the objections which classical science might have presented against Einstein’s definition lost all force. Henceforth it was not necessary to take into consideration the velocity of the frame through the stagnant ether, since this ether drift appeared to exert no influence one way or the other.
Now, it may not be easy to understand how isotropic conditions could be demonstrated by experiment, for isotropy signifies that the velocity of light is the same in all directions. And how can we ascertain the equality of a velocity in all directions when we do not yet know how to measure time? Experimenters solved the difficulty by appealing to the observation of coincidences.