Physics & Math / Einstein

The German astrophysicist Karl Schwarzschild spent the early years of World War I on the eastern front, calculating ballistics trajectories for artillery units. He used his spare time to vet old astronomical problems with the new metric of general relativity. One exercise considered what would happen if a star were radically compressed into an infinitesimal volume. Schwarzschild’s results showed that, at some critical density, the star’s gravity would become so strong that it would swallow everything—matter, light, even space and time—within a specific radius. Schwarzschild thus developed a mathematical description of black holes decades before they were observed or understood.

Einstein never took the idea seriously. “He thought they were an artifact, a sloppy application of the equations,” says Peebles. Mathematically, a black hole is a so-called singularity—a place where space and time become so distorted that the equations of general relativity yield infinities, rather than rational numbers, as solutions. To Einstein, infinity was no answer at all—it was a failure. He could believe in gravity waves and other unlikely predictions of general relativity because math supported them. Black holes defied math. He called Schwarzschild’s results “a true disaster.”

General relativity was Einstein’s favorite “free invention.” He was confident it could describe the behavior of every object in the universe. Thus he claimed, somewhat tautologically, that any instance in which his equations failed could not actually represent nature. “Einstein didn’t think that [Schwarzschild’s] solution corresponded to anything real,” says theoretical physicist Frank Wilczek of MIT.

Einstein had merely to step into another viewpoint to reconcile the apparent singularity with his philosophical beliefs, says Wilczek. Yet the man who knew the most about relativity failed to regard Schwarzschild’s solutions from a different vantage point. To an observer trapped within a black hole, the laws of general relativity still obtain. In fact, all the laws of physics would appear to function as usual. “We could be in a black hole right now and not know it,” Wilczek says.

That is an idea worthy of Einstein.

“The most beautiful experience we can have is the mysterious,” Einstein once wrote. Yet when his thinking revealed one of the most notorious paradoxes of the physical world, he ultimately shunned it. The mystery has to do with the nature of light. Experiments conducted at the start of the century had shown that light shining on a metal plate produced showers of electrons whose speed, or energy, was the same no matter how bright the light. Einstein explained the so-called photoelectric effect by asserting that light, which was known to flow in continuous waves, could also be regarded as sputtering along in discrete particles, or quanta. Each of these particles—every quantum of light at a given wavelength—carried the same amount of energy, he argued, and so dispatched a single electron with the same energetic kick. Thus did Einstein discover the photon. He lived to regret it.

The wave-particle duality was unsettling enough. But when Danish physicist Niels Bohr showed that the electrons in atoms, too, must behave as quanta to account for observations, Einstein made a conceptual leap that troubled him even more. In pondering the quantum interactions between matter and light, Einstein found he could calculate neither the timing nor the direction of the photons spontaneously emitted from atoms. The emissions were fundamentally random. Chance seemed to be an ineluctable element of the quantum world.

In fact, quantum theory suggests that random events are rampant at the subatomic level. There is no way to predict cause and effect on a case-by-case basis. The best that physicists can do is calculate probabilities, which do or do not prove out for a large number of events. To Einstein, a statistical probability was even less acceptable than the infinities of a singularity. A physics that could not predict individual events was no physics at all, he said. It was, at best, guesswork. And it certainly did not correspond to reality, which, like the universe, Einstein preferred to see as stable, orderly, and knowable to the most intimate detail. Apparently, he regarded mysteries as beautiful only if they offered some hope of solution.

“[T]hat he would choose to play dice with the world,” Einstein wrote [of God], “is something that I cannot believe for a single moment.” Bohr supposedly replied, “Stop telling God what to do.” But the aesthete in Einstein turned his back on quantum theory.

A new generation of physicists rushed to embrace it. In the 1920s quantum mechanics became the rage, and it advanced by leaps and bounds, thanks in large part to Einstein’s persistent efforts to discredit it. At the famous Solvay conferences in 1927 and 1930, Einstein challenged his friend Bohr, the chief proponent of quantum mechanics, with thought experiments meant to reveal logical contradictions in the theory. At first Bohr would be devastated, but he always managed to produce an answer to Einstein’s critique. By the 1930s quantum mechanics had become intellectually unassailable. The vast majority of physicists today believe that the subatomic realm really is, in some sense, unknowable.

Einstein eventually relaxed his vigilance, but he never accepted quantum mechanics as truth. “The more successes the quantum theory enjoys, the sillier it looks,” he said. With its wave-particle paradox, the theory offended his aesthetic sensibilities; with its irreducible randomness, it impugned his scientific potency; with its popularity among the younger crowd, it may have triggered some very human aversion in an aging icon.

“He had dominated fundamental physics from 1905 to 1915, with an extraordinary series of insights,” Wilczek says. “And then he continued to dominate for 10 years more. To be competing with young whippersnappers would not be a very appealing prospect for a scientist of his stature.”

Einstein seemed to agree. “Truly new things one finds only in one’s youth,” he once opined. “Later one becomes more experienced, more famous, and dumber.”

In the last decades of his life, Einstein chose to work far from the madding crowd of quantum enthusiasts. He followed the mathematics of general relativity toward what he hoped would be a theory subsuming the laws of gravity and subatomic particles. He would recognize this unified theory, he said, by its beauty or self-evident rightness. He never came close to finding it, but he never doubted that someone would. “I cannot base this conviction on logical reasons,” he said. “My only witness is the pricking of my little finger.”

Some might call his last, fruitless quest a mistake too. But it’s a mistake other physicists are more than willing to emulate. The theory of everything, the deeper truth that unites all the forces of nature, that pulls cosmology and quantum theory together, remains the most important quest of physics. No one has pursued Einstein’s peculiar approach, but before his efforts are dismissed, it may be instructive to consider the eventual fate of Einstein’s self-proclaimed greatest blunder, lambda.

Lambda, also known as the cosmological constant, has come in handy of late. In the last decade astronomers discovered the expanding universe is also accelerating—expanding faster and faster. That confounding scenario can be represented mathematically if general relativity includes a term, just like the cosmological constant, that imbues empty space with an unidentified force. “Making use of the cosmological constant is by now a venerable aspect of contemporary cosmology,” says Fred Goldhaber.

The day may come when all of Einstein’s blunders seem equally prescient.

Discuss this article in the Discover Forum