Once again, Einstein was at the forefront of discovering an aspect of quantum theory that would cause him discomfort in the future. And once again, younger colleagues would embrace his ideas more readily than he would—just as he had once embraced the implications of the ideas of Planck, Poincaré, and Lorentz more readily than they had.53
An additional step was taken by another unlikely player, Erwin Schrödinger, an Austrian theoretical physicist who despaired of discovering anything significant and thus decided to concentrate on being a philosopher instead. But the world apparently already had enough Austrian philosophers, and he couldn’t find work in that field. So he stuck with physics and, inspired by Einstein’s praise of de Broglie, came up with a theory called “wave mechanics.” It led to a set of equations that governed de Broglie’s wavelike behavior of electrons, which Schrödinger (giving half credit where he thought it was due) called “Einstein–de Broglie waves.”54
Einstein expressed enthusiasm at first, but he soon became troubled by some of the ramifications of Schrödinger’s waves, most notably that over time they can spread over an enormous area. An electron could not, in reality, be waving thus, Einstein thought. So what, in the real world, did the wave equation really represent?
The person who helped answer that question was Max Born, Einstein’s close friend and (along with his wife, Hedwig) frequent correspondent, who was then teaching at Göttingen. Born proposed that the wave did not describe the behavior of the particle. Instead, he said that it described the probability of its location at any moment.55 It was an approach that revealed quantum mechanics as being, even more than previously thought, fundamentally based on chance rather than causal certainties, and it made Einstein even more squeamish.56
Meanwhile, another approach to quantum mechanics had been developed in the summer of 1925 by a bright-faced 23-year-old hiking enthusiast, Werner Heisenberg, who was a student of Niels Bohr in Copenhagen and then of Max Born in Göttingen. As Einstein had done in his more radical youth, Heisenberg started by embracing Ernst Mach’s dictum that theories should avoid any concepts that cannot be observed, measured, or verified. For Heisenberg this meant avoiding the concept of electron orbits, which could not be observed.
He relied instead on a mathematical approach that would account for something that could be observed: the wavelengths of the spectral lines of the radiation from these electrons as they lost energy. The result was so complex that Heisenberg gave his paper to Born and left on a camping trip with fellow members of his youth group, hoping that his mentor could figure it out. Born did. The math involved what are known as matrices, and Born sorted it all out and got the paper published.57 In collaboration with Born and others in Göttingen, Heisenberg went on to perfect a matrix mechanics that was later shown to be equivalent to Schrödinger’s wave mechanics.
Einstein politely wrote Born’s wife, Hedwig, “The Heisenberg-Born concepts leave us breathless.” Those carefully couched words can be read in a variety of ways. Writing to Ehrenfest in Leiden, Einstein was more blunt. “Heisenberg has laid a big quantum egg,” he wrote. “In Göttingen they believe in it. I don’t.”58
Heisenberg’s more famous and disruptive contribution came two years later, in 1927. It is, to the general public, one of the best known and most baffling aspects of quantum physics: the uncertainty principle.
It is impossible to know, Heisenberg declared, the precise position of a particle, such as a moving electron, and its precise momentum (its velocity times its mass) at the same instant. The more precisely the position of the particle is measured, the less precisely it is possible to measure its momentum. And the formula that describes the trade-off involves (no surprise) Planck’s constant.
The very act of observing something—of allowing photons or electrons or any other particles or waves of energy to strike the object—affects the observation. But Heisenberg’s theory went beyond that. An electron does not have a definite position or path until we observe it. This is a feature of our universe, he said, not merely some defect in our observing or measuring abilities.
The uncertainty principle, so simple and yet so startling, was a stake in the heart of classical physics. It asserts that there is no objective reality—not even an objective position of a particle—outside of our observations. In addition, Heisenberg’s principle and other aspects of quantum mechanics undermine the notion that the universe obeys strict causal laws. Chance, indeterminacy, and probability took the place of certainty. When Einstein wrote him a note objecting to these features, Heisenberg replied bluntly, “I believe that indeterminism, that is, the nonvalidity of rigorous causality, is necessary.”59
When Heisenberg came to give a lecture in Berlin in 1926, he met Einstein for the first time. Einstein invited him over to his house one evening, and there they engaged in a friendly argument. It was the mirror of the type of argument Einstein might have had in 1905 with conservatives who resisted his dismissal of the ether.
“We cannot observe electron orbits inside the atom,” Heisenberg said.“A good theory must be based on directly observable magnitudes.”
“But you don’t seriously believe,” Einstein protested, “that none but observable magnitudes must go into a physical theory?”
“Isn’t that precisely what you have done with relativity?” Heisenberg asked with some surprise.
“Possibly I did use this kind of reasoning,” Einstein admitted, “but it is nonsense all the same.”60
In other words, Einstein’s approach had evolved.
Einstein had a similar conversation with his friend in Prague, Philipp Frank. “A new fashion has arisen in physics,” Einstein complained, which declares that certain things cannot be observed and therefore should not be ascribed reality.
“But the fashion you speak of,” Frank protested, “was invented by you in 1905!”
Replied Einstein: “A good joke should not be repeated too often.”61
The theoretical advances that occurred in the mid-1920s were shaped by Niels Bohr and his colleagues, including Heisenberg, into what became known as the Copenhagen interpretation of quantum mechanics. A property of an object can be discussed only in the context of how that property is observed or measured, and these observations are not simply aspects of a single picture but are complementary to one another.
In other words, there is no single underlying reality that is independent of our observations. “It is wrong to think that the task of physics is to find out how nature is,” Bohr declared. “Physics concerns what we can say about nature.”62
This inability to know a so-called “underlying reality” meant that there was no strict determinism in the classical sense. “When one wishes to calculate ‘the future’ from ‘the present’ one can only get statistical results,” Heisenberg said, “since one can never discover every detail of the present.”63
As this revolution climaxed in the spring of 1927, Einstein used the 200th anniversary of Newton’s death to defend the classical system of mechanics based on causality and certainty. Two decades earlier, Einstein had, with youthful insouciance, toppled many of the pillars of Newton’s universe, including absolute space and time. But now he was a defender of the established order, and of Newton.
In the new quantum mechanics, he said, strict causality seemed to disappear. “But the last word has not been said,” Einstein argued. “May the spirit of Newton’s method give us the power to restore union between physical reality and the profoundest characteristic of Newton’s teaching—strict causality.”64
Einstein never fully came around, even as experiments repeatedly showed quantum mechanics to be valid. He remained a realist, one who made it his creed to believe in an objective reality, rooted in certainty, that existed whether or not we could observe it.
“He does not play dice”
So what made Einstein cede the revolutionary road to younger radicals and spin into a defensive crouch?
As a young empiricist, excited by his readings of Ernst Mach, Einst
ein had been willing to reject any concepts that could not be observed, such as the ether and absolute time and space and simultaneity. But the success of his general theory convinced him that Mach’s skepticism, even though it might be useful for weeding out superfluous concepts, did not provide much help in constructing new theories.
“He rides Mach’s poor horse to exhaustion,” Einstein complained to Michele Besso about a paper written by a mutual friend.
“We should not insult Mach’s poor horse,” Besso replied. “Didn’t it make possible the tortuous journey through the relativities? And who knows, in the case of the nasty quanta, it may also carry Don Quixote de la Einsteina through it all!”
“You know what I think about Mach’s little horse,” Einstein wrote Besso in return. “It cannot give birth to anything living. It can only exterminate harmful vermin.”65
In his maturity, Einstein more firmly believed that there was an objective “reality” that existed whether or not we could observe it. The belief in an external world independent of the person observing it, he repeatedly said, was the basis of all science.66
In addition, Einstein resisted quantum mechanics because it abandoned strict causality and instead defined reality in terms of indeterminacy, uncertainty, and probability. A true disciple of Hume would not have been troubled by this. There is no real reason—other than either a metaphysical faith or a habit ingrained in the mind—to believe that nature must operate with absolute certainty. It is just as reasonable, though perhaps less satisfying, to believe that some things simply happen by chance. Certainly, there was mounting evidence that on the subatomic level this was the case.
But for Einstein, this simply did not smell true. The ultimate goal of physics, he repeatedly said, was to discover the laws that strictly determine causes and effects. “I am very, very reluctant to give up complete causality,” he told Max Born.67
His faith in determinism and causality reflected that of his favorite religious philosopher, Baruch Spinoza. “He was utterly convinced,” Einstein wrote of Spinoza, “of the causal dependence of all phenomena, at a time when the success of efforts to achieve a knowledge of the causal relationship of natural phenomena was still quite modest.”68 It was a sentence that Einstein could have written about himself, emphasizing the temporariness implied by the word “still,” after the advent of quantum mechanics.
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.”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 mathematic
al 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
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