Never interested in solving this small physics problem here, or that larger one over there (although he did a bit of that, too), Einstein was concerned with the big picture. The really big picture.
“I want to know how God created this world. I’m not interested in this or that phenomenon, in the spectrum of this or that element. I want to know His thoughts; the rest are just details.”
Most people understand Einstein’s concept of a “unified field theory” as a joining of the theories of the gravitational and electromagnetic forces. But it was far deeper than that.
Isaac Newton had introduced the idea of mass—a property we assign to bits of matter called particles—exerting forces on one another, and thereby changing one another’s motion. This is easy to understand when particles collide—think of pool balls on a table. But how could the Earth’s gravitational force, acting across a quarter million miles of empty space, influence the distant Moon’s motion, and, as Newton showed, thereby “keep the Moon in her orb”? How could this “action-at-a-distance” be?
Newton simply accepted it as fact and admitted that he could offer no explanation. “Hypotheses non fingo.” I frame no hypotheses. The solution would have to wait another century and a half.
Sometime in the 1830s autodidact British physicist Michael Faraday, while investigating magnetism, performed an experiment we all have seen in elementary school, and began to take it quite seriously. He investigated the magnetic “lines of force” which may be traced out by iron filings sprinkled on a sheet of paper resting on a bar magnet. Faraday came to believe—as we still believe today—that the entire space around a magnet was filled with an actual physical substance. The space was not empty. That substance he called the magnetic field. Fields (today we know of four—gravitational, electromagnetic, weak nuclear and strong nuclear) interact with particles, changing their motion. Particles are the sources of—they produce—the fields.
A beautiful description of how things are. But not beautiful enough for Einstein. Why should there be two quite different kinds of things, particles and fields, comprising the world? Wouldn’t it be a much simpler and more beautiful universe if it were constructed of just one?
For Einstein, that would be fields. And Einstein’s fields do more—much more—than just describe the electromagnetic and gravitational forces that are felt at any point in space. They are geometrical—they determine the “interval,” the geometric distance in space and time, between any two events. They define the geometry of spacetime.
So, here’s Einstein’s unified field theory. There are fields, and field equations, which determine how the fields change from place-to-place and from time-to-time. That’s it. No particles. Certain solutions of the field equations—certain configurations of the fields—are “localized.” They exist in a very small region of space and vanish everywhere else. These are what we are used to calling particles. And since the field equations determine time evolution, they also determine how these “particles” change in time—how they move. What Newton called “the equations of motion” are contained in the field equations, and no longer have to be added to the theory.
In the two letters that follow, Einstein considers a particular solution to his field equations—a particular metric—presented by Silberstein, and in doing so he describes in some detail this problem of expressing matter and its motion in terms of fields.
Silberstein claimed that this static, axisymmetric, metric described the spacetime around two point-masses at rest. But with neither kinetic energy, nor any other structure to hold them apart, the masses should fall together. No such solution to Einstein’s equations should exist. General Relativity must be flawed.
Unconvinced by Einstein’s arguments here (and perhaps in letters which followed), Silberstein published his metric in 1935, and also brought his cause before the popular press. On March 7, 1936 the Evening Telegram of Toronto published an article titled “Fatal blow to relativity issued here.”
Einstein, of course, was correct. Mathematician Hermann Weyl later showed that Silberstein’s metric contains singular structures that are responsible for holding the masses static against the attractive force of gravity.