To use an analogy, the sculptured head of Shakespeare on my table may appear to have hollow cheeks when I admit light from the east window only, or to have sunken eyes with light from the skylight in the roof, but the true shape of the head remains the same in all lights.
Hence, if with reference to two consecutive dots in our block of film a mathematical quantity can be found which will not change no matter how we changes our axes of coordinates, that quantity must be an expression of the true law of motion of the fly between the two points of the paper and the two times represented by these two dots. Einstein has worked out such a quantity remaining constant for all changes of coordinates of the four dimensional world of space-time.
In passing we may notice a feature of Einstein’s world of space-time which we shall doubtless find it difficult to conceive, namely, that there is no essential difference between a time and a distance in space. Since one set of coordinates is as good as another, we can transform time into space and space into time according as we choose our axes. For example if we change OX, OT, the axes of x and time in [Fig. 2], into OX′, OT′ by a simple rotation, the new time represented by OT′ consists partly of OA in the old time and partly of OB in the old x direction. Referring to our block of movie film again, it means that although I might separate the block into space and time by slicing it into the original pictures, I can just as readily slice it in any direction I choose and still get individual pictures representing the motion of the fly but with, of course, new time and space. So whilst I may be believe that a liner has travelled 3,000 miles in 4 days, an observer on a star who knows nothing of my particular axes in space-time may say, with equal truth, that it went 2,000 miles in 7 days. Thus, time and space are not two separate identities in Einstein’s view; there only exists a world of four dimensions which we can split up into time and space as we choose.
Let us see now how Einstein explains gravitation. When a body is not acted on by any forces (except gravitation) the quantity which remains constant for all changes of coordinates implies that the body will follow that path in the space of an outside observer which takes the least time. It is an observed fact that one body attracts another by gravitation; that is, the path of one body is bent from its course by the presence of another. Now we can bend the path of the fly in our block of film by straining the block in some way. Suppose, therefore, that I strain the world so as to bend the path of a body exactly as the gravitation due to some other body bends it; i.e., by a change of coordinates I have obtained the same effect as that produced by gravitation. Einstein’s theory, therefore, explains gravitation as a distortion of the world of space-time due to the presence of matter. Suppose first that a body is moving with no other bodies near; according to Einstein it will take the path in space which requires the least time, i.e., a straight line as agrees with our experience. If now the world be strained by the presence of another body or by a change of coordinates it will still pursue the path of least time, but this path is now distorted from the straight line, just as in a similar way the path on a globe requiring the least time to travel follows a great circle. So, on Einstein’s view of gravitation, the earth moves in an elliptical path around the sun not because a force is acting on it, but because the world of space-time is so distorted by the presence of the sun that the path of least time through space is the elliptical path observed. There is, therefore, no need to introduce any idea of “force” of gravitation. Einstein’s theory explains gravitation only in the sense that he has explained it away as a force of nature and makes it a property of space-time, namely, a distortion not different from an appropriate change of coordinates. He does not, however, explain how or why a body can distort space-time. It is noteworthy that whilst the law of gravitation and the law of uniform motion in a straight line when no force is acting were separate and independent laws under Newton, Einstein finds one explanation for both under the principle of relativity.[1]
[1] The balance of Dr. Royds’ essay is given to a discussion of the phenomena of Mercury’s perihelial advance, the deflection of light under the gravitational field of the sun, and the shift in spectral lines, in connection with which alone Einstein’s theory makes predictions which are sufficiently at variance with those of Newtonian science to be of value in checking up the theory observationally. In the interest of space conservation and in the presence of Dr. Pickering’s very complete discussion of these matters we omit Dr. Royds’ statement.—Editor. [↑]
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EINSTEIN’S THEORY OF GRAVITATION
The Discussion of the General Theory and Its Most Important Application, from the Essay by