The evolution of scientific thought from Newton to Einstein

by A. D'Abro

, and the proof of the statement we made in a previous chapter is given thereby.[101]

It now remains to be seen how this curvature of time may be detected directly. Here we must recall that the curvature of time is expressive of the repartition of the temporal metrical field obtained by splitting up the metrical field of space-time into one of space and one of time. The repartition of this temporal metrical field in the space and time separation we are discussing shows that its curvature will increase as we consider regions of space nearer and nearer the sun, indicating thereby a slowing down of time as we approach the sun. Now it is this temporal metrical field which controls the rate of evolution of any isolated periodic phenomenon from place to place, hence which defines practical time-congruence as given by perfect clocks. In the present case, therefore, the action of this field would be to slow down the temporal evolution of all phenomena when these have their spatial locus nearer and nearer the sun. This effect was anticipated by Einstein and is known as the Einstein shift-effect.

Of course, if we, as conscious beings, were to be situated at any particular point of the sun’s gravitational field, we should never appreciate this slowing down of time and of the evolution of all things in our immediate neighbourhood; for our consciousness would participate in the same slowing down that was active around us. It would only be when we viewed distant phenomena occurring in other parts of the field of gravitation that discrepancies in their speeds of evolution would become apparent. Thus, although we should not be directly conscious of aging at various rates in the different parts of a gravitational field, we should discover eventually, either by direct vision or by meeting again, that our friend who had lived in the proximity of the sun had aged less than ourselves, who had lived farther away from its mass. Gravitation would thus preserve youth, and, more generally, two men living on two different stars of unequal mass would not age at the same rate.

It is to be noted that it is not the force of gravitation itself which is responsible for this slowing down of time as we near the sun. It is rather the decrease in the value of the potential; and in the present case we have seen that the only potential which enters into account is

, or the Newtonian potential.

All these phenomena predicted by Einstein were entirely new to science, and it was most important to verify their correctness before accepting Einstein’s theory. The method suggested was that of exploring a field of gravitation with vibrating atoms, these being assumed to behave like perfect clocks marking correct time. For instance, if Einstein’s law of space-time curvature was correct, atoms of sodium placed in different parts of the solar field would appear to be vibrating faster or slower than the atom in our immediate neighbourhood, according to whether they were farther removed from or nearer the sun than we happened to be situated. These variations in the rates of vibrations of the atoms would be betrayed physically by variations in the colour of the light they emitted or absorbed. It would follow that while the atom of sodium by our side would always emit a yellow light in our estimation, those atoms nearer the sun would appear redder, and those farther away from the sun would appear greener. In particular, an atom of sodium situated in the sun’s atmosphere would beat more slowly and appear to us redder than an identical atom examined in our laboratory (the earth’s gravitational field being insignificant compared with that of the sun).[102]

For a number of years it was questionable whether this effect really existed, because the difficulty in detecting so minute a displacement of the spectral lines was very great. Quite recently, however, the phenomenon has been observed on a star of enormous density, the companion of Sirius.[103] This is perhaps the most beautiful of all the verifications of Einstein’s theory, since the effect contemplated was totally unsuspected by classical science—even more so than the bending of light in a gravitational field.

Now the postulate of equivalence, by assimilating gravitational fields to fields of inertia, requires that similar phenomena should occur in an accelerated enclosure (allowing, of course, for the slight discrepancies in the actual field-distribution when produced by matter or by acceleration). Thus, consider a train pursuing a Galilean motion, and two identical sodium atoms or clocks placed on the engine and rear car, respectively. So long as the motion of the train remains Galilean, an observer at rest in any point of the train would detect no difference in the rates of vibration of the atoms,[104] hence in the colours which they emitted. On the other hand, were the train to be accelerated, moving faster and faster, a field of inertial force directed from engine to rear car would now be present; and as a result the atom on the rear car would appear to the train observer to be vibrating more slowly than the atom on the engine.

We must realise, therefore, that whereas in the special theory a slowing down of time was always due to relative motion, in the present case, the slowing down of time takes place in spite of the absence of relative motion between the atoms and the train observer. In the same way, there was no relative motion in the example of the Einstein shift-effect in the sun’s gravitational field, and yet we had to accept a slowing down of time. So we see that acceleration, even when unaccompanied by relative motion, will produce a variation in the flow of time; and the same variations would also ensue in the case of distance.