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The Mind of God
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The discoveries were not front-page news, even though the one-column headline on page 17 of the New York Times (November 19, 1919) might suggest an event signaling the end of the world: “LIGHTS ALL ASKEW IN THE HEAVENS.” The story hastened to assure readers that “nobody need worry,” because the discoveries did not “affect anything on this earth” and “do not personally concern ordinary human beings; only astronomers are affected.” The article reported on the results of recent scientific expeditions to Brazil and to the West African island of Principe, where astronomers observed starlight passing near the sun during a solar eclipse. The astronomers were able to determine that light from these stars did not travel in a straight line but bent around a massive object like the sun, thus confirming Einstein’s general theory of relativity.
Contrary to the article’s suggestion, the finding that light bent to gravity was not new. Isaac Newton, who formulated the laws of gravity, had already stated as much in 1704. However, Newton wrongly assumed light had mass and therefore would be affected by gravity the same as ordinary matter. According to calculations based on Newton’s theories, the degree to which light would be deflected by gravity was roughly half what it turned out to be when Einstein’s field equations were applied. Photographs taken of the solar eclipses found that the position of stars near the sun had been altered by 1.7 arc-seconds, exactly as Einstein had predicted.
Although the Times article went out of its way to assure readers they had nothing to fear from Einstein’s theory, the world as we once knew it had indeed come to an end. Sir Arthur Eddington, the Cambridge astronomer who organized the expeditions to Brazil and West Africa, had tried to build interest in the undertaking by billing it as a contest between the competing theories of Newton and Einstein. The article was correct in stating that the difference between the two was “infinitesimal in a popular sense” — only 1.7 arc-seconds, which worked out to 1/60th of a millimeter on a photographic plate of starlight from 93 million miles away. For most practical purposes, Newton’s laws of gravity still applied. But Newton’s fixed universe of time and three-dimensional space had been replaced by a four-dimensional time-space continuum in which time was infinitely elastic and space was curved.
Eddington was one of the few astronomers with the mathematical skills to fully understand relativity, and he became an early champion. He later said the truth of Einstein’s theory was so self-evident it almost didn’t need to be proved. When asked if it was true he was one of only three people in the world who actually understood it, he demurred. When pressed, he paused and then said, “I’m trying to think of the third.” In fact, the Einstein’s field equations were formidably difficult. Einstein himself was only a middling mathematician, and often relied on colleagues to perform the computations for his work. In this case, the first exact solution of the equations to the theory were worked out independently by a German physicist named Karl Schwarzschild. Einstein himself had previously managed only approximate solutions.
Middling mathematician or not, Einstein was no less certain of the outcome of Eddington’s twin expeditions as the astronomer himself. When asked what he would do if his theory had been proved wrong, Einstein famously replied, "Then I would feel sorry for the good Lord. The theory is correct.” His response is sometimes mistaken for arrogance. It should be noted, however, that he made it after the results were already known, and after he had previously determined that his theory had correctly accounted for an anomaly in the planet Mercury’s orbit around the sun. He was also known to have an impish sense of humor.
How is it that a physicist who relied on others to do his math homework was able to come up with a theory of such formidable mathematical complexity? As it happens, its key component, known as the principle of equivalence, did not originate with any equation but with a thought experiment. Einstein realized that the effects of acceleration on an observer ascending in an elevator in the weightlessness of space would be equivalent to the force of gravity acting on an observer in a stationary elevator on earth.· Einstein later called the inspiration for his principle of equivalence “the happiest thought of my life.”
It is curious that the theory of general relativity and many other great scientific discoveries were inspired not by careful observation and measurement of natural phenomena but by pure acts of imagination. The forerunners of modern science in the 17th century — such “natural philosophers” as Galileo, Descartes, Newton, and Leibniz — all made use of thought experiments to propel their discoveries. Einstein’s first great breakthrough, the special theory of relativity, came about as the result of a thought experiment at age 16, when he tried to imagine chasing a light beam through space. He reasoned that if he were traveling at the speed of light, the beam would appear frozen.
The granddaddy of all thought experiments was Plato’s allegory of prisoners in a cave whose only knowledge of the world was shadows thrown up on a wall by firelight. By analogy, the world we see by the light of day is itself merely the shadow of a higher reality. This higher realm of perfect forms exists outside of space and time and is not subject to the vagaries of messy everyday reality. Many mathematicians regard themselves as Platonists, believing numbers exist in their own realm, independent of human thought. Some physicists are also in this camp; indeed, it can be argued that physics itself is based in a Platonic understanding of reality.
Was Einstein a Platonist? Here it might be useful to revisit Einstein’s quip that he’d feel sorry for the good Lord if the evidence didn’t support his theory, because the theory was correct. No doubt he was gratified that Eddington’s observations did confirm his theory. But, joking or not, Einstein also seemed to be saying that the evidence didn’t ultimately matter because the theory was true regardless. How so? Did he think his thought experiment had given him a glimpse of some higher reality? Einstein once remarked, “I hold it to be true that pure thought can grasp reality, as the Ancients dreamed.” On another occasion he asked, “How can it be that mathematics, being after all a product of human thought, independent of experience, is so admirably appropriate to the objects of reality?” Einstein left his question unanswered, but many of his colleagues were not shy about taking things to the next step. Many believed the numbers that so exactly describe the workings of the physical world exist independently of human thought; in other words, physicists and mathematicians don’t invent them, they discover them.
Science is supposed to be grounded in the real world, while talk of higher realms is normally associated with religion. Is Platonism just religion by another name? Einstein did not believe in a personal God as such, although he did once say his ambition was to know the mind of God. Similarly, the physicist Paul Dirac, an outspoken atheist, conceded that the God he didn’t believe in was “a mathematician of a very high order.” Neither meant to be taken literally. And neither presumably would go so far as to say numbers were gods, as Pythagoras and his disciples in ancient Greek maintained.
Dirac, a Nobel laureate, was co-founder of a branch of physics known as quantum mechanics, which governs the often bizarre behavior of subatomic particles. As a young scientist, he was frankly unsettled by Einstein’s frequent references to God — literal or not — even though he was sometimes guilty of doing the same thing himself. Dirac grumbled, ”If we are honest—and scientists have to be—we must admit that religion is a jumble of false assertions, with no basis in reality. The very idea of God is a product of the human imagination.”
The idea of God is indisputably a product of the imagination, since here is nothing in the physical world that can be called God as such. But to say that God is a product of the imagination does not necessarily mean he is imaginary, any more than quantum mechanics or relativity were when Dirac and Einstein first imaged them. “Imagination is everything,” Einstein once said, deeming it to be more important than knowledge. Another quantum physicist and Nobel laureate, Richard Feynman, concurred, saying, “Our imagination is stretched to the utmost, not, as in fiction, to imagine things which are not really there, but just to comprehend those things which are there.”
When the Book of Genesis stated that humankind is made in the image and likeness of God, imagination may be the quality that we most hold in common with our Maker. Rabbi Moses ben Naḥman, a medieval Spanish scholar, pointed out that, the Hebrew root of the word “likeness” in the Genesis story is dimyon, meaning “imagination.” It is in the realm of the imagination that we can know the mind of God. Indeed, we might think of it as a meeting of the minds — or perhaps I should say, a meeting of the Mind.
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