“Life is like riding a bicycle. To keep your balance you must keep moving.” ~Albert Einstein 1930
Einstein offered her a deal. He would win the Nobel prize someday, he said; if she gave him a divorce, he would give her the prize money. Because his theories were so radical, it was seventeen years after his miraculous outpouring from the patent office before he was awarded the prize and she collected.
Beneath all his theories, including relativity, was a quest for invariants, certainties, and absolutes. There was a harmonious reality underlying the laws of the universe, Einstein felt, and he goal of science was to discover it.
An appreciation for the methods of science is a useful asset for a responsible citizenry. What science teaches us, very significantly, is the correlation between factual evidence and general theories, something well illustrated in Einstein’s life.
A society’s competitive advantage will come not from how well its schools teach the multiplication and periodic tables, but from how well they stimulate imagination and creativity.
Einstein’s wisecracking, sarcastic exterior was a shell around a softer inner soul. “He was one of those split personalities who know how to protect, with a prickly exterior, the delicate realm of their intense personal life.
The thrust of his parents’ view—at least when applied to the situation of Mileva Mari rather than Marie Winteler—was that a wife was “a luxury” affordable only when a man was making a comfortable living. “I have a low opinion of that view of a relationship between a man and wife,” he told Mari, “because it makes the wife and the prostitute distinguishable only insofar as the former is able to secure a lifelong contract.”
“Blind respect for authority is the greatest enemy of truth.”
The baby brought out Einstein’s wry side. “She’s certainly able to cry already, but won’t know how to laugh until much later,” he said. “Therein lies a profound truth.”
Haller had a credo that was as useful for a creative and rebellious theorist as it was for a patent examiner: “You have to remain critically vigilant.” Question every premise, challenge conventional wisdom, and never accept the truth of something merely because everyone else views it as obvious.
Shut yourself up with some friend in the main cabin below decks on some large ship, and have with you there some flies, butterflies, and other small flying animals. Have a large bowl of water with some fish in it; hang up a bottle that empties drop by drop into a wide vessel beneath it. With the ship standing still, observe carefully how the little animals fly with equal speed to all sides of the cabin. The fish swim indifferently in all directions; the drops fall into the vessel beneath it; and, in throwing something to your friend, you need throw it no more strongly in one direction than another, the distances being equal; jumping with your feet together, you pass equal spaces in every direction. When you have observed all these things carefully, have the ship proceed with any speed you like, so long as the motion is uniform and not fluctuating this way and that. You will discover not the least change in all the effects named, nor could you tell from any of them whether the ship was moving or standing still.
“A new idea comes suddenly and in a rather intuitive way,” Einstein once said. “But,” he hastened to add, “intuition is nothing but the outcome of earlier intellectual experience.”
Some scientific theories depend primarily on induction: analyzing a lot of experimental findings and then finding theories that explain the empirical patterns. Others depend more on deduction: starting with elegant principles and postulates that are embraced as holy and then deducing the consequences from them. All scientists blend both approaches to differing degrees. Einstein had a good feel for experimental findings, and he used this knowledge to find certain fixed points upon which he could construct a theory. But his emphasis was primarily on the deductive approach.
Einstein rejected the emission theory in favor of postulating that the speed of a light beam was constant no matter how fast its source was moving. “I cam to the conviction that all light should be defined by frequency and intensity alone, completely independent of whether it comes from a moving or from a stationary light source.”
The key insight was that two events that appear to be simultaneous to one observer will not appear to be simultaneous to another observer who is moving rapidly. And there is now way to declare that one of the observers is really correct. In other words, there is no way to declare that the two events are truly simultaneous.
It means that there is no absolute time. Instead, all moving reference frames have their own relative time.
Einstein pointed out that time itself can be defined only by referring to simultaneous events, such as the small hand of a watch point to 7 as a train arrives. The obvious yet still astonishing conclusion: with no such thing as absolute simultaneity, there is not such thing as “real” or absolute time. As he later put it, “There is no audible tick-tock everywhere in the world that can be considered as time.”
This phenomenon, called time dilation, leads to what is known as the twin paradox. If a man stays on the platform while his twin sister takes off in a spaceship that travels long distances at nearly the speed of light, wen she returns she would be younger than he is. But because motion is relative, this seems to present a paradox. The sister on the spaceship might think it’s her brother on earth who is doing the fast traveling, and when they are rejoined she would expect to observe that it was he who did not age much.
The phenomenon of time dilation has been experimentally confirmed, even by using test clocks on commercial airplanes. But in our normal life, it has no real impact, because our motion relative to any other observer is never anything near the speed of light. In fact, if you spent almost your entire life on an airplane, you would have aged merely 0.00005 seconds or so less than your twin on earth when you returned, an effect that would likely be counteracted by a lifetime spent eating airplane food.
They would take walks together and be there for each other. Should she choose to offer even more, he would be grateful. But by not marrying they would be protecting themselves from lapsing into a “contented bourgeois” existence and preventing their relationship “from becoming banal and from growing pale.” To him, marriage was confining, which was a state he instinctively resisted. “I’m glad our delicate relationship does not have to founder on a provincial narrow-minded lifestyle.”
One consequence of this equivalence is that gravity, as Einstein had noted, should bend a light beam. That is easy to show using the chamber thought experiment. Imagine that the chamber is being accelerated upward. A laser beam comes in through a pinhole on one wall. By the time it reaches the opposite wall, it’s a little closer to the floor, because the chamber has shot upward. And if you could plot its trajectory across the chamber, it would be curved because of the upward acceleration. The equivalence principle says that this effect should be the same whether the chamber is accelerating upward or is instead resting still in a gravitational field.
If a light beam curves as it passes through regions of changing gravitational fields, how can a straight line be determined? One solution might be to liken the path of the light beam through a changing gravitational field so that of a line drawn on a sphere or on a surface that is warped. In such cases, the shortest line between two points is curved, a geodesic like a great arc or a great circle route on our globe. Perhaps the bending of light meant that the fabric of space, through which the light beam traveled, was curved by gravity.
To do so he used something called a tensor. In Euclidean geometry, a vector is a quantity (such as velocity or force) that has both a magnitude and a direction and thus needs more than s single simple number to describe it. In non-Euclidean geometry, where space is curved, we need something more generalized—sort of a vector on steroids—in order to incorporate, in a mathematically orderly way, more components. These are called tensors. A metric tensor is a mathematical tool that tells us how to calculate the distance between two points in a given space. For two-dimensional maps, a metric tensor has three components. For three-dimensional space, it has six independent components. And once you get to that glorious four-dimensional entity known as spacetime, the metric tensor needs ten independent components.
Since the 1840s, scientists have been worrying about a small but unexplained shift in the orbit of Mercury. The perihelion is the spot in a planet’s elliptical orbit when it is closest to the sun, and over the years this spot in Mercury’s orbit has slipped a tiny amount more—about 43 seconds of an arc each century—than what was explained by Newton’s laws. At first it was assumed that some undiscovered planet was tugging at it, similar to the reasoning that had earlier led to the discovery of Neptune. The Frenchman who discovered Mercury’s anomaly even calculated where such a planet would be and named it Vulcan. But it was not there.
Haber reorganized his institute to develop chemical weapons for Germany. He had already found a way to synthesize ammonia from nitrogen, which permitted the Germans to mass-produce explosives. He then turned his attention to making deadly chlorine gas, which, heavier than air, would flow down into the trenches and painfully asphyxiate soldiers by burning through their throats and lungs. In April 1915, modern chemical warfare was inaugurated when some five thousand French and Belgians met that deadly fate at Ypres, with Haber personally supervising the attack. (In an irony that may have been lost on the inventor of dynamite, who endowed the prize, Haber won the 1918 Nobel prize in chemistry for his process of synthesizing ammonia.)
Einstein published a three-page essay titled “My Opinion of the War” that skirted the border of what was permissible, even for a great scientist, to say in Germany. He speculated that there existed “a biologically determined feature of the male character,” that was one of the causes of wars. When the article was published by the Goethe League that month, a few passages were deleted for safety’s sake, including an attack on patriotism as potentially containing “the moral requisites of bestial hatred and mass murder.”
The left side of the equation starts with the term Rmn, which is the Ricci tensor he had embraced earlier. The term gmn is the all-important metric tensor, and the term R is the trace of the Ricci tensor called the Ricci scalar. Together, this left side of the equation—which is now known as the Einstein tensor and can be written simply as Gmn—compresses together all of the information about how geometry of spacetime is warped and curved by objects. The right side describes the movement of matter in the gravitational field. The interplay between the two sides shows how objects curve spacetime and how, in turn, this curvature affects the motion of objects. As the physicist John Wheeler has put it, “Matter tells space-time how to curve, and curved space tells matter how to move.”
Then he added an amazing new inducement. He was convinced, with good reason, that he would someday win the Nobel prize. Even though the scientific community had not yet fully come to grips with special relativity, much less his new and unproven theory of general relativity, eventually it would. Or his groundbreaking insights into light quanta and the photoelectric effect would be recognized. And so he made a striking offer to Mari: “The Nobel Prize—in the event of the divorce and the event that it is bestowed upon me—would be ceded to you in full.”