Einstein, the searcher

by Alexander Moszkowski

This square is to denote the cross-section of a closed box which we imagine to be situated somewhere in the universe. Inside it there lives a physicist who makes observations and draws inferences from them. In the course of time he perceives, what is familiar to all of us, that every body not supported and left to itself, for example, a stone that is released, drops to the floor with uniform acceleration, that is, with a steady increase of velocity in going downwards. There are two ways open to him to explain this phenomenon.

Firstly, he might suspect—and this suspicion would be most likely to occur to him—that his box was resting on some body in the heavens. For if indeed the box were a cave in some part of the world, the falling of the stone would suggest nothing unusual; it would be quite self-evident to every occupant, and quite explicable to the physicist according to Galilei's (or Newton's) Laws for Falling Bodies. He need not necessarily restrict himself to the Earth, for if the box happened to be on some other star, this phenomenon of falling would likewise occur, with greater or less speed, and the body would certainly fall with uniform acceleration. Thus the physicist could say: this is an effect of gravitation, exhibiting the property of weight which I explain to myself as usual, as due to the attraction of a heavenly body.

Secondly, another idea might strike him. For we stipulated nothing about the position of the box, and assumed only that it was to exist "somewhere in the universe." The physicist in the box might reason as follows:

Supposing I am separated by incalculable distances from every attracting heavenly body, and supposing gravitation existed neither for me nor for the stone which I release from my hand, then it would still be possible for me to give a complete explanation of the phenomena I observe. I should only have to assume that the body is moving with uniform acceleration "upwards." The motion previously interpreted by me as a falling "downwards" need not take place at all. The stone, as an inert body, could persist in its position (relative to the box or the observer), and would, in spite of this, show exactly the same behaviour when the box moves with acceleration upwards as if it were falling with increasing velocity downwards.

Now since our physicist has no system which might serve for reference and orientation, and since in his box which is shut off from the universe he has no means at his disposal of determining whether he is in the sphere of influence of an attracting heavenly body or not, both the above explanations are feasible for him and both are equally valid, and it is impossible for him to come to a decision in his choice. He can interpret the acceleration in either way, as being upwards or downwards, connected to one another by relativity; a fundamental reason for preferring one interpretation to the other cannot be furnished, since the phenomenon of falling is represented unchanged whether he assumes the stone to be falling and the box to be at rest, or vice versa. This may be generalized in these words:

At every point of the world the observed acceleration of a body left to itself may be interpreted either as a gravitational or as an inertial effect—that is, from the point of view of physics we may assert with equal right that the system (the box, the complex defining the orientation) from which I observe the event is accelerated, or that the event takes place in a gravitational field. The equal right to these two views is called the "Principle of Equivalence" by Einstein. It asserts the equivalence or the identity of inertial and gravitational mass. If we familiarize ourselves with this identity, an exceedingly important road to knowledge is opened up to our consciousness. We arrive at the inevitable conclusion that every inertial effect that we perceive in bodies, the most essential quality of it, itself so to speak in its persistent nature, is to be traced back to the influence to which it is subjected by other bodies. When this has become clear to us, we feel impelled to inquire how a ray of light would behave under the influence of gravitation. Hence we return to our physicist in the box, and we now know that as a consequence of the Principle of Equivalence we are free to assume either that an attracting heavenly body, such as the sun, is situated somewhere below the box, or to refer the phenomena to the box regarded as being accelerated upwards. In the box we distinguish the floor, the ceiling, four walls, and among these again, according to the position we take up, the wall on the left and its opposite one on the right.

We now imagine a marksman to be outside the box and having no connexion with us, being poised freely in space, and suppose him to fire out of a horizontal gun at the box so that the bullet pierces both the wall on the left and the wall on the right. Now, if everything else were to remain at rest, the holes in both walls would be equally distant from the floor, and the bullet would move in a straight line parallel to the floor and to the ceiling. But, as we have seen, all events happen as if the box itself moved with constant acceleration. The bullet that requires time to pass from one wall to the other thus finds that when it reaches the wall on the right the latter has advanced a little, so that the resulting hole is a little lower than that on the left wall. This means that the flight of the bullet, according to our observation in the interior of the box, is no longer rectilinear. In fact, if we trace the bullet from point to point, we should find that for us, situated in the box, it would describe a line bent downwards, with its concave side to the floor.

Exactly the same thing happens with a ray of light which is emitted by a source outside in a horizontal direction and which traverses the space between the walls (supposed transparent). Only the velocity would be different. In the course of its flight the ray would move like a projectile that is whizzing along at the rate of 180,000 miles per second. But provided sufficiently delicate means of measurement are applied, it should still be possible to prove the existence of an infinitesimal deflection from the rectilinear horizontal path, an insignificant concavity towards the floor.

Consequently this curvature of the light-ray (say, from a star) must also be perceptible in places where it is subject to the influence of a gravitational field. If we drop our imaginary picture of the box, the argument is in nowise altered. A ray from a star which passes close by the sun seems to our perception to be bent in towards the sun, and the order of this deflection can be determined if sufficiently delicate instruments be used. As above remarked, it is a question of detecting a difference of 1.7 seconds of arc, which is to be manifested as a distance on the photographic plate, and is actually found to be present.

The fact that scientists are able to detect this appears in itself a marvel of technical precision far in advance of "splitting hairs," for in comparison a single hair is, in this case, to be removed to a considerable distance if we are to use it to give an idea of the size of angle under consideration. Fortunately stellar photography has been developed so wonderfully that in every single case extraordinarily accurate results are got even from preliminary measurements.