einstein

The Quest
CHAPTER FIFTEEN
UNIFIED FIELD THEORIES
1923–1931
With Bohr at the 1930 Solvay Conference
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.” 6 Unfortunately, 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