Einstein: His Life and Universe

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 Schrodinger 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