From Newton to Einstein: Changing Conceptions of the Universe

by Benjamin Harrow

How Einstein’s Conception of Time and Space Led to a New View of Gravitation. In our conventional language we speak of the sun as exerting a “force” on the earth. We have seen, however, that this force brings about a “distortion” or “strain” in world-lines; or, what amounts to the same thing, a “distortion” or “strain” of time and space. The sun’s “force,” the “force” of any body in space, is the “force” due to gravity; and these “forces” may now be treated in terms of the laws of time and space. “The earth,” Prof. Eddington tells us, “moves in a curved orbit, not because the sun exerts any direct pull, but because the earth is trying to find the shortest way through a space and time which have been tangled up by an influence radiating from the sun.”[8]

At this point Newton’s conceptions fail, for his views and his laws do not include “strains” in space. Newton’s law of gravitation must be supplanted by one which does include such distortions. It is Einstein’s great glory to have supplied us with this new law.

Einstein’s Law of Gravitation. This appears to be the only law which meets all requirements. It includes Newton’s law, and cannot be distinguished from it if our experiments are confined to the earth and deal with relatively small velocities. But when we betake ourselves to some orbits in space, with a gravitational pull much greater than the earth’s, and when we deal with velocities comparable to that of light, the differences become marked.

Einstein’s Theory Scores Its First Great Victory. In the beginning of this chapter we referred to the elaborate eclipse expedition sent by the British to test the validity of Einstein’s new theory of gravitation. The British scientists would hardly have expended so much time and energy on this theory of Einstein’s but for the fact that Einstein had already scored one great victory. What was it?

Imagine but a single planet revolving about the sun. According to Newton’s law of gravitation, the planet’s path would be that of an ellipse—that is, oval—and the planet would travel indefinitely along this path. According to Einstein the path would also be elliptical, but before a revolution would be quite completed, the planet would start along a slightly advanced line, forming a new ellipse slightly in advance of the first. The elliptic orbit slowly turns in the direction in which the planet is moving. After many years—centuries—the orbit will be in a different direction.

The rapidity of the orbit’s change of direction depends on the velocity of the planet. Mercury moving at the rate of 30 miles a second is the fastest among the planets. It has the further advantage over Venus or the earth in that its orbit, as we have said, is an ellipse, whereas the orbits of Venus and the earth are nearly circular; and how are you going to tell in which direction a circle is pointing?

Observation tells us that the orbit of Mercury is advancing at the rate of 574 seconds (of arc) per century. We can calculate how much of this is due to the gravitational influence of other planets. It amounts to 532 seconds per century. What of the remaining 42 seconds?

You might be inclined to attribute this shortcoming to experimental error. But when all such possibilities are allowed for our mathematicians assure us that the discrepancy is 30 times greater than any possible experimental error.

This discrepancy between theory and observation remained one of the great puzzles in astronomy until Einstein cleared up the mystery. According to Einstein’s theory the mathematics of the situation is simply this: in one revolution of the planet the orbit will advance by a fraction of a revolution equal to three times the square of the ratio of the velocity of the planet to the velocity of light. When we allow mathematicians to work this out we get the figure 43, which is certainly close enough to 42 to be called identical with it.

Still Another Victory? Einstein’s third prediction—the shifting of spectral lines toward the red end of the spectrum in the case of light coming to us from the stars of appreciable mass—seems to have been confirmed recently (March, 1920). “The young physicists in Bonn,” writes Prof. Einstein to a friend, “have now as good as certainty (so gut wie sicher) proved the red displacement of the spectral lines and have cleared up the grounds of a previous disappointment.”