But he wasn’t. By 1928, a consensus had formed that quantum mechanics was correct, and de Broglie relented and adopted that view. “Einstein, however, stuck to his guns and continued to insist that the purely statistical interpretation of wave mechanics could not possibly be complete,” de Broglie recalled, with some reverence, years later.33
Indeed, Einstein remained the stubborn contrarian. “I admire to the highest degree the achievements of the younger generation of physicists that goes by the name quantum mechanics, and I believe in the deep level of truth of that theory,” he said in 1929 when accepting the Planck medal from Planck himself. “But”—and there was always a but in any statement of support Einstein gave to quantum theory—“I believe that the restriction to statistical laws will be a passing one.”34
The stage was thus set for an even more dramatic Solvay showdown between Einstein and Bohr, this one at the conference of October 1930. Theoretical physics has rarely seen such an interesting engagement.
This time, in his effort to stump the Bohr-Heisenberg group and restore certainty to mechanics, Einstein devised a more clever thought experiment. One aspect of the uncertainty principle, previously mentioned, is that there is a trade-off between measuring precisely the momentum of a particle and its position. In addition, the principle says that a similar uncertainty is inherent in measuring the energy involved in a process and the time duration of that process.
Einstein’s thought experiment involved a box with a shutter that could open and shut so rapidly that it would allow only one photon to escape at a time. The shutter is controlled by a precise clock. The box is weighed exactly. Then, at a certain specified moment, the shutter opens and a photon escapes. The box is now weighed again. The relationship between energy and mass (remember, E=mc2) permitted a precise determination of the energy of the particle. And we know, from the clock, its exact time of departing the system. So there!
Of course, physical limitations would make it impossible to actually do such an experiment. But in theory, did it refute the uncertainty principle?
Bohr was shaken by the challenge. “He walked from one person to another, trying to persuade them all that this could not be true, that it would mean the end of physics if Einstein was right,” a participant recorded. “But he could think of no refutation. I will never forget the sight of the two opponents leaving the university club. Einstein, a majestic figure, walking calmly with a faint ironic smile, and Bohr trotting along by his side, extremely upset.”35 (See picture, page 336.)
It was one of the great ironies of scientific debate that, after a sleepless night, Bohr was able to hoist Einstein by his own petard. The thought experiment had not taken into account Einstein’s own beautiful discovery, the theory of relativity. According to that theory, clocks in stronger gravitational fields run more slowly than those in weaker gravity. Einstein forgot this, but Bohr remembered. During the release of the photon, the mass of the box decreases. Because the box is on a spring scale (in order to be weighed), the box will rise a small amount in the earth’s gravity. That small amount is precisely the amount needed to restore the energy-time uncertainty relation.
“It was essential to take into account the relationship between the rate of a clock and its position in a gravitational field,” Bohr recalled. He gave Einstein credit for graciously helping to perform the calculations that, in the end, won the day for the uncertainty principle. But Einstein was never fully convinced. Even a year later, he was still churning out variations of such thought experiments.36
Quantum mechanics ended up proving to be a successful theory, and Einstein subsequently edged into what could be called his own version of uncertainty. He no longer denounced quantum mechanics as incorrect, only as incomplete. In 1931, he nominated Heisenberg and Schrödinger for the Nobel Prize. (They won in 1932 and 1933, along with Dirac.) “I am convinced that this theory undoubtedly contains a part of the ultimate truth,” Einstein wrote in his nominating letter.
Part of the ultimate truth. There was still, Einstein felt, more to reality than was accounted for in the Copenhagen interpretation of quantum mechanics.
Its shortcoming was that it “makes no claim to describe physical reality itself, but only the probabilities of the occurrence of a physical reality that we view,” he wrote that year in a tribute to James Clerk Maxwell, the master of his beloved field theory approach to physics. His piece concluded with a resounding realist credo—a direct denial of Bohr’s declaration that physics concerns not what nature is but merely “what we can say about nature”—that would have raised the eyebrows of Hume, Mach, and possibly even a younger Einstein. He declared, “Belief in an external world independent of the perceiving subject is the basis of all natural science.”37
Wresting Principles from Nature
In his more radical salad days, Einstein did not emphasize this credo. He had instead cast himself as an empiricist or positivist. In other words, he had accepted the works of Hume and Mach as sacred texts, which led him to shun concepts, like the ether or absolute time, that were not knowable through direct observations.
Now, as his opposition to the concept of an ether became more subtle and his discomfort with quantum mechanics grew, he edged away from this orthodoxy. “What I dislike in this kind of argumentation,” the older Einstein reflected, “is the basic positivistic attitude, which from my point of view is untenable, and which seems to me to come to the same thing as Berkeley’s principle, Esse est percipi.”*38
There was a lot of continuity in Einstein’s philosophy of science, so it would be wrong to insist that there was a clean shift from empiricism to realism in his thinking.39 Nonetheless, it is fair to say that as he struggled against quantum mechanics during the 1920s, he became less faithful to the dogma of Mach and more of a realist, someone who believed, as he said in his tribute to Maxwell, in an underlying reality that exists independently of our observations.
That was reflected in a lecture that Einstein gave at Oxford in June 1933, called “On the Method of Theoretical Physics,” which sketched out his philosophy of science.40 It began with a caveat. To truly understand the methods and philosophy of physicists, he said, “don’t listen to their words, fix your attention on their deeds.”
If we look at what Einstein did rather than what he was saying, it is clear that he believed (as any true scientist would) that the end product of any theory must be conclusions that can be confirmed by experience and empirical tests. He was famous for ending his papers with calls for these types of suggested experiments.
But how did he come up with the starting blocks for his theoretical thinking—the principles and postulates that would launch his logical deductions? As we’ve seen, he did not usually start with a set of experimental data that needed some explanation. “No collection of empirical facts, however comprehensive, can ever lead to the formulation of such complicated equations,” he said in describing how he had come up with the general theory of relativity.41 In many of his famous papers, he made a point of insisting that he had not relied much on any specific experimental data—on Brownian motion, or attempts to detect the ether, or the photoelectric effect—to induce his new theories.
Instead, he generally began with postulates that he had abstracted from his understanding of the physical world, such as the equivalence of gravity and acceleration. That equivalence was not something he came up with by studying empirical data. Einstein’s great strength as a theorist was that he had a keener ability than other scientists to come up with what he called “the general postulates and principles which serve as the starting point.”
It was a process that mixed intuition with a feel for the patterns to be found in experimental data. “The scientist has to worm these general principles out of nature by discerning, when looking at complexes of empirical facts, certain general features.”42 When he was struggling to find a foothold for a unified theory, he captured the essence of this process in a letter to Hermann Weyl: “I believe that, in order to make any real
progress, one would again have to find a general principle wrested from Nature.”43
Once he had wrested a principle from nature, he relied on a byplay of physical intuition and mathematical formalism to march toward some testable conclusions. In his younger days, he sometimes disparaged the role that pure math could play. But during his final push toward a general theory of relativity, it was the mathematical approach that ended up putting him across the goal line.
From then on, he became increasingly dependent on mathematical formalism in his pursuit of a unified field theory. “The development of the general theory of relativity introduced Einstein to the power of abstract mathematical formalisms, notably that of tensor calculus,” writes the astrophysicist John Barrow. “A deep physical insight orchestrated the mathematics of general relativity, but in the years that followed the balance tipped the other way. Einstein’s search for a unified theory was characterized by a fascination with the abstract formalisms themselves.”44
In his Oxford lecture, Einstein began with a nod to empiricism: “All knowledge of reality starts from experience and ends in it.” But he immediately proceeded to emphasize the role that “pure reason” and logical deductions play. He conceded, without apology, that his success using tensor calculus to come up with the equations of general relativity had converted him to a faith in a mathematical approach, one that emphasized the simplicity and elegance of equations more than the role of experience.
The fact that this method paid off in general relativity, he said, “justifies us in believing that nature is the realization of the simplest conceivable mathematical ideas.”45 That is an elegant—and also astonishingly interesting—creed. It captured the essence of Einstein’s thought during the decades when mathematical “simplicity” guided him in his search for a unified field theory. And it echoed the great Isaac Newton’s declaration in book 3 of the Principia: “Nature is pleased with simplicity.”
But Einstein offered no proof of this creed, one that seems belied by modern particle physics.46 Nor did he ever fully explain what, exactly, he meant by mathematical simplicity. Instead, he merely asserted his deep intuition that this is the way God would make the universe. “I am convinced that we can discover by means of purely mathematical constructions the concepts and the laws connecting them with each other,” he claimed.
It was a belief—indeed, a faith—that he had expressed during his previous visit to Oxford, when in May 1931 he had been awarded an honorary doctorate there. In his lecture on that occasion, Einstein explained that his ongoing quest for a unified field theory was propelled by the lure of mathematical elegance, rather than the push of experimental data. “I have been guided not by the pressure from behind of experimental facts, but by the attraction in front from mathematical simplicity,” he said. “It can only be hoped that experiments will follow the mathematical flag.”47
Einstein likewise concluded his 1933 Oxford lecture by saying that he had come to believe that the mathematical equations of field theories were the best way to grasp “reality.” So far, he admitted, this had not worked at the subatomic level, which seemed ruled by chance and probabilities. But he told his audience that he clung to the belief that this was not the final word. “I still believe in the possibility of a model of reality—that is to say, of a theory that represents things themselves and not merely the probability of their occurrence.”48
His Greatest Blunder?
Back in 1917, when Einstein had analyzed the “cosmological considerations” arising from his general theory of relativity, most astronomers thought that the universe consisted only of our Milky Way, floating with its 100 billion or so stars in a void of empty space. Moreover, it seemed a rather stable universe, with stars meandering around but not expanding outward or collapsing inward in a noticeable way.
All of this led Einstein to add to his field equations a cosmological constant that represented a “repulsive” force (see page 254). It was invented to counteract the gravitational attraction that would, if the stars were not flying away from one another with enough momentum, pull all of them together.
Then came a series of wondrous discoveries, beginning in 1924, by Edwin Hubble, a colorful and engaging astronomer working with the 100-inch reflector telescope at the Mount Wilson Observatory in the mountains above Pasadena, California. The first was that the blur known as the Andromeda nebula was actually another galaxy, about the size of our own, close to a million light years away (we now know it’s more than twice that far). Soon he was able to find at least two dozen even more distant galaxies (we now believe that there are more than 100 billion of them).
Hubble then made an even more amazing discovery. By measuring the red shift of the stars’ spectra (which is the light wave counterpart to the Doppler effect for sound waves), he realized that the galaxies were moving away from us. There were at least two possible explanations for the fact that distant stars in all directions seemed to be flying away from us: (1) because we are the center of the universe, something that since the time of Copernicus only our teenage children believe; (2) because the entire metric of the universe was expanding, which meant that everything was stretching out in all directions so that all galaxies were getting farther away from one another.
It became clear that the second explanation was the case when Hubble confirmed that, in general, the galaxies were moving away from us at a speed that was proportional to their distance from us. Those twice as far moved away twice as fast, and those three times as far moved away three times as fast.
One way to understand this is to imagine a grid of dots that are each spaced an inch apart on the elastic surface of a balloon. Then assume that the balloon is inflated so that the surface expands to twice its original dimensions. The dots are now two inches away from each other. So during the expansion, a dot that was originally one inch away moved another one inch away. And during that same time period, a dot that was originally two inches away moved another two inches away, one that was three inches away moved another three inches away, and one that was ten inches away moved another ten inches away. The farther away each dot was originally, the faster it receded from our dot. And that would be true from the vantage point of each and every dot on the balloon.
All of which is a simple way to say that the galaxies are not merely flying away from us, but instead, the entire metric of space, or the fabric of the cosmos, is expanding. To envision this in 3-D, imagine that the dots are raisins in a cake that is baking and expanding in all directions.
On his second visit to America in January 1931, Einstein decided to go to Mount Wilson (conveniently up the road from Caltech, where he was visiting) to see for himself. He and Edwin Hubble rode in a sleek Pierce-Arrow touring car up the winding road. There at the top to meet him was the aging and ailing Albert Michelson, of ether-drift experiment fame.
It was a sunny day, and Einstein merrily played with the telescope’s dials and instruments. Elsa came along as well, and it was explained to her that the equipment was used to determine the scope and shape of the universe. She reportedly replied, “Well, my husband does that on the back of an old envelope.”49
The evidence that the universe was expanding was presented in the popular press as a challenge to Einstein’s theories. It was a scientific drama that captured the public imagination. “Great stellar systems,” an Associated Press story began, “rushing away from the earth at 7,300 miles a second, offer a problem to Dr. Albert Einstein.”50
But Einstein welcomed the news. “The people at the Mt. Wilson observatory are outstanding,” he wrote Besso. “They have recently found that the spiral nebulae are distributed approximately uniformly in space, and they show a strong Doppler effect, proportional to their distances, that one can readily deduce from general relativity theory without the ‘cosmological’ term.”
In other words, the cosmological constant, which he had reluctantly concocted to account for a static universe, was apparently not necessary, for the universe was in fact expanding.* “The
situation is truly exciting,” he exulted to Besso.51
Of course, it would have been even more exciting if Einstein had trusted his original equations and simply announced that his general theory of relativity predicted that the universe is expanding. If he had done that, then Hubble’s confirmation of the expansion more than a decade later would have had as great an impact as when Eddington confirmed his prediction of how the sun’s gravity would bend rays of light. The Big Bang might have been named the Einstein Bang, and it would have gone down in history, as well as in the popular imagination, as one of the most fascinating theoretical discoveries of modern physics.52
As it was, Einstein merely had the pleasure of renouncing the cosmological constant, which he had never liked.53 In a new edition of his popular book on relativity published in 1931, he added an appendix explaining why the term he had pasted into his field equations was, thankfully, no longer necessary.54 “When I was discussing cosmological problems with Einstein,” George Gamow later recalled, “he remarked that the introduction of the cosmological term was the biggest blunder he ever made in his life.”55
In fact, Einstein’s blunders were more fascinating and complex than even the triumphs of lesser scientists. It was hard simply to banish the term from the field equations. “Unfortunately,” says Nobel laureate Steven Weinberg, “it was not so easy just to drop the cosmological constant, because anything that contributes to the energy density of the vacuum acts just like a cosmological constant.”56
It turns out that the cosmological constant not only was difficult to banish but is still needed by cosmologists, who use it today to explain the accelerating expansion of the universe.57 The mysterious dark energy that seems to cause this expansion behaves as if it were a manifestation of Einstein’s constant. As a result, two or three times each year fresh observations produce reports that lead with sentences along the lines of this one from November 2005: “The genius of Albert Einstein, who added a ‘cosmological constant’ to his equation for the expansion of the universe but then retracted it, may be vindicated by new research.”58
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