The evolution of scientific thought from Newton to Einstein

by A. D'Abro

So far we have considered the cancellation of a field of gravitation, but we may also consider the creation of a field of force in empty space far from matter. Thus, if a hollow chest be subjected to a variable acceleration through empty space, a variable field of force (inertial force) will be experienced by an observer in the chest’s interior. If now we consider a second chest at rest in a varying gravitational field distributed throughout the chest in exactly the same way as were the forces of inertia and with the same intensity, the equality of the two masses proves that mechanical experiments conducted in either of the two enclosures would yield exactly the same results, and hence that bodies would fall towards the floor of the enclosure in exactly the same way. And so it would be impossible, on the basis of mechanical experiments conducted in the interior of the enclosure, to decide whether we were in a field of inertial force generated by acceleration or in a field of gravitational force generated by matter. These are the conclusions which the equality of the two masses urges upon us. Inasmuch as the equality of the two types of masses constitutes a fact established by experiment, we may also regard as established empirically the inability of mechanical experiments to differentiate between a field of inertia and one of gravitation.[81]

Now, up to this point, all the facts we have mentioned were perfectly well known to classical science. It is solely in the interpretation of these facts that Einstein suggests highly original views. Let us first examine what classical science had to say. Its arguments ran somewhat as follows: Our inability to differentiate between a field of inertial forces generated by acceleration and one of gravitation generated by matter is due solely to a miraculous coincidence, that of the equality of the two masses. Again, when, in the elevator falling in the earth’s gravitational field, we experience no feeling of weight, it is not that the gravitational field has vanished; it is solely that the field of gravity has been counteracted by an equal and opposite field of inertia generated by the elevator’s accelerated motion. The equality in the intensities of these two opposing fields is due once more to the equality of the two masses. Thus, according to classical science, there existed a very decided difference between the two types of fields of force, and it was always assumed that this difference would be detected when we performed non-mechanical experiments such as optical or electromagnetic ones.

It is this classical interpretation which Einstein challenges. He maintains that the field of force generated in an enclosure is of exactly the same nature regardless of whether it has been generated by acceleration or by gravitation. Also, in the case of the falling elevator, we should not say that the field of gravitation had been counteracted; we should say that it had vanished. Thus interpreted, the miraculous equality of the two types of masses is no miracle at all. There are no two types of masses which react to two types of forces. Since there is but one type of force, there is but one type of mass, to which classical science had erroneously given two different names, and then marvelled at the fact that whatever name was given, its value remained the same. In this way Einstein succeeded in accounting for a miraculous equality which had baffled classical science.

But, of course, Einstein’s idea was susceptible of experimental proof or disproof. For if we assume that the two types of fields of force are all one, we must assume that not alone mechanical experiments, but also all manner of experiments, will fail to detect the slightest difference. This is indeed Einstein’s attitude, and he upholds it in the postulate of equivalence.

This postulate states that there can exist no difference in the conditions prevailing in the interior of an enclosure, regardless of whether the field of force experienced be generated by acceleration or by gravitation.

Now, when all is said and done, it might appear that when Einstein stated his postulate of equivalence he was taking a leap in the dark. The equality of the two masses proved that so far as mechanical experiments were concerned, conditions existing in a falling elevator would be identical with those enduring in an enclosure floating in free space far from matter. These anticipations were based on experience. But what justification was there for generalising these results and extending them without hesitation to all manner of non-mechanical experiments? At first sight the generalisation might appear somewhat hasty, and most certainly such generalisations should not be encouraged at the hands of those who do not possess any profound scientific knowledge. But with Einstein the case is different. On this occasion, as on many others, his generalisations are those of a man who seems to be able to read the secrets of nature as no one else has ever done before. It is not his knowledge of mathematics or of physics that causes admiration; it is his insight into the philosophy of nature, which is stupendous. As a matter of fact, a similar generalisation on his part was encountered in the special theory. There he generalised from electrodynamics to mechanics; here it is the reverse. But, in either case, a desire to find unity in nature appears to have been his guiding motive.

There is a great analogy between Einstein’s interpretation of the problem we are discussing and his explanation of Michelson’s experiment. In the latter, we remember that Galilean motion through the ether appeared to generate no ether drift. Lorentz explained this absence of an ether drift by assuming that a physical drift was really present, but that it was automatically cancelled in a miraculous way by the trickiness of nature working through the compensating influences of a real physical contraction of bodies moving through the ether and of a real physical slowing down of the duration of events. Einstein, as we have seen, preferred to assume that if no ether drift could be detected, it was because no ether drift was present. Classical science demanded the ether drift and attempted to explain why in spite of its expectations none could be detected. Einstein, by refusing to patch up classical science so as to explain the miraculous, was led to declare that classical science was wrong in attaching any credence to the existence of an ether drift, and that its belief in this ether drift was attributable to mistaken premises.

If we now pass to the problem of gravitation we see that the situation is very similar. Gravitational force vanishes in a falling elevator; this is the physical fact. Classical science took the stand that the force did not really vanish, but that it was compensated. Einstein prefers to assume that if the gravitational force appears to vanish, it is because it really does vanish.

With these new views, the force of gravitation acting at a point loses its attributes of absoluteness. Just like a force of inertia, a force of gravitation betrays a relationship existing between the frame of reference selected and the surrounding conditions of the world. Just as a force of inertia can be annulled by changing the motion of our frame, so now can a force of gravitation be annulled. This does not mean that a force of gravitation is unreal. It is perfectly real, since it can be detected and measured. But it is no longer an absolute; it is a relative, like a force of inertia, for its value varies with our choice of a frame of reference. Henceforth no intrinsic difference exists between a force of gravitation and a force of inertia; these forces are of the same essence. When, therefore, we are in the presence of a force acting on mass, we may refer to it as a force without specifying whether it has been generated by the acceleration of our frame (field of inertia) or by the proximity of matter (field of gravitation).[82]

Einstein maintains the appellation of a gravitational field of force. But he applies it indifferently to fields which classical science would have considered due to the acceleration of the frame, and to the fields which classical science would have recognised as generated by the proximity of matter. By classing both types of fields as gravitational, his object is to differentiate these identical types of fields from fields of other types, such as fields of electric, magnetic or electromagnetic forces.