Walter Isaacson - Einstein - His Life and Universe

Like Spinoza, Einstein did not believe in a personal God who interacted with man. But they both believed that a divine design was reflected in the elegant laws that governed the way the universe worked.

This was not merely some expression of faith. It was a principle that Einstein elevated (as he had the relativity principle) to the level of a postulate, one that guided him in his work. “When I am judging a theory,” he told his friend Banesh Hoffmann, “I ask myself whether, if I were God, I would have arranged the world in such a way.”

When he posed that question, there was one possibility that he simply could not believe: that the good Lord would have created beautiful and subtle rules that determined most of what happened in the universe, while leaving a few things completely to chance. It felt wrong. “If the Lord had wanted to do that, he would have done it thoroughly, and not kept to a pattern . . . He would have gone the whole hog. In that case, we wouldn’t have to look for laws at all.” 69

This led to one of Einstein’s most famous quotes, written to Max Born, the friend and physicist who would spar with him over three decades on this topic. “Quantum mechanics is certainly imposing,” Einstein said. “But an inner voice tells me that it is not yet the real thing. The theory says a lot, but it does not really bring us any closer to the secrets of the Old One. I, at any rate, am convinced that He does not play dice.” 70

Thus it was that Einstein ended up deciding that quantum mechanics, though it may not be wrong, was at least incomplete. There must be a fuller explanation of how the universe operates, one that would incorporate both relativity theory and quantum mechanics. In doing so, it would not leave things to chance.

CHAPTER FIFTEEN

UNIFIED FIELD THEORIES

1923–1931

With Bohr at the 1930 Solvay Conference

The Quest

While others continued to develop quantum mechanics, undaunted by the uncertainties at its core, Einstein persevered in his lonelier quest for a more complete explanation of the universe—a unified field theory that would tie together electricity and magnetism and gravity and quantum mechanics. In the past, his genius had been in finding missing links between different theories. The opening sentences of his 1905 general relativity and light quanta papers were such examples.*

He hoped to extend the gravitational field equations of general relativity so that they would describe the electromagnetic field as well. “The mind striving after unification cannot be satisfied that two fields should exist which, by their nature, are quite independent,” Einstein explained in his Nobel lecture. “We seek a mathematically unified field theory in which the gravitational field and the electromagnetic field are interpreted only as different components or manifestations of the same uniform field.” 1

Such a unified theory, he hoped, might make quantum mechanics compatible with relativity. He publicly enlisted Planck in this task with a toast at his mentor’s sixtieth birthday celebration in 1918: “May he succeed in uniting quantum theory with electrodynamics and mechanics in a single logical system.” 2

Einstein’s quest was primarily a procession of false steps, marked by increasing mathematical complexity, that began with his reacting to the false steps of others. The first was by the mathematical physicist Hermann Weyl, who in 1918 proposed a way to extend the geometry of general relativity that would, so it seemed, serve as a geometrization of the electromagnetic field as well.

Einstein was initially impressed. “It is a first-class stroke of genius,” he told Weyl. But he had one problem with it: “I have not been able to settle my measuring-rod objection yet.” 3

Under Weyl’s theory, measuring rods and clocks would vary depending on the path they took through space. But experimental observations showed no such phenomenon. In his next letter, after two more days of reflection, Einstein pricked his bubbles of praise with a wry putdown. “Your chain of reasoning is so wonderfully self-contained,” he wrote Weyl. “Except for agreeing with reality, it is certainly a grand intellectual achievement.” 4

Next came a proposal in 1919 by Theodor Kaluza, a mathematics professor in Königsberg, that a fifth dimension be added to the four dimensions of spacetime. Kaluza further posited that this added spatial dimension was circular, meaning that if you head in its direction you get back to where you started, just like walking around the circumference of a cylinder.

Kaluza did not try to describe the physical reality or location of this added spatial dimension. He was, after all, a mathematician, so he didn’t have to. Instead, he devised it as a mathematical device. The metric of Einstein’s four-dimensional spacetime required ten quantities to describe all the possible coordinate relationships for any point. Kaluza knew that fifteen such quantities are needed to specify the geometry for a five-dimensional realm. 5

When he played with the math of this complex construction, Kaluza found that four of the extra five quantities could be used to produce Maxwell’s electromagnetic equations. At least mathematically, this might be a way to produce a field theory unifying gravity and electromagnetism.

Once again, Einstein was both impressed and critical. “A five-dimensional cylinder world never dawned on me,” he wrote Kaluza. “At first glance I like your idea enormously.” 6Unfortunately, there was no reason to believe that most of this math actually had any basis in physical reality. With the luxury of being a pure mathematician, Kaluza admitted this and challenged the physicists to figure it out. “It is still hard to believe that all of these relations in their virtually unsurpassed formal unity should amount to the mere alluring play of a capricious accident,” he wrote. “Should more than an empty mathematical formalism be found to reside behind these presumed connections, we would then face a new triumph of Einstein’s general relativity.”

By then Einstein had become a convert to the faith in mathematical formalism, which had proven so useful in his final push toward general relativity. Once a few issues were sorted out, he helped Kaluza get his paper published in 1921, and followed up later with his own pieces.

The next contribution came from the physicist Oskar Klein, son of Sweden’s first rabbi and a student of Niels Bohr. Klein saw a unified field theory not only as a way to unite gravity and electromagnetism, but he also hoped it might explain some of the mysteries lurking in quantum mechanics. Perhaps it could even come up with a way to find “hidden variables” that could eliminate the uncertainty.

Klein was more a physicist than a mathematician, so he focused more than Kaluza had on what the physical reality of a fourth spatial dimension might be. His idea was that it might be coiled up in a circle, too tiny to detect, projecting out into a new dimension from every point in our observable three-dimensional space.

It was all quite ingenious, but it didn’t turn out to explain much about the weird but increasingly well-confirmed insights of quantum mechanics or the new advances in particle physics. The Kaluza-Klein theories were put aside, although Einstein over the years would return to some of the concepts. In fact, physicists still do today. Echoes of these ideas, particularly in the form of extra compact dimensions, exist in string theory.

Next into the fray came Arthur Eddington, the British astronomer and physicist responsible for the famous eclipse observations. He refined Weyl’s math by using a geometric concept known as an affine connection. Einstein read Eddington’s ideas while on his way to Japan, and he adopted them as the basis for a new theory of his own. “I believe I have finally understood the connection between electricity and gravitation,” he wrote Bohr excitedly. “Eddington has come closer to the truth than Weyl.” 7