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Because the spaceship does not travel at a constant velocity, but instead must turn around, it’s the twin on the spaceship, not the one on earth, who would age more slowly.
The phenomenon of time dilation has been experimentally confirmed, even by using test clocks on commercial planes. 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 airline food.
His life was a constant quest for unifying theories.
Even as his fame increased exponentially, Einstein would retain a personal simplicity, an unaffected style, and at least a veneer of genial humility.
“I even seriously doubt that it will be possible to maintain the general validity of Maxwell’s equations.”44 (As it turned out, his love of Maxwell’s equations was well placed. They are among the few elements of theoretical physics to remain unchanged by both the relativity and quantum revolutions that Einstein helped launch.)
“Would it not be possible,” he asked, “to retain at least the equations for the propagation of radiation and conceive only the processes of emission and absorption differently?” But after comparing the behavior of light to the behavior of gas molecules, as he had done in his 1905 light quanta paper, Einstein concluded that, alas, this was not possible.
Einstein tried to persuade Adler to focus on science rather than be enticed into politics. “Be a little patient,” he said. “You will certainly be my successor in Zurich one day.” (Einstein was already assuming that he would move on to a more prestigious university.) But Adler ignored the advice and decided to become an editor at the Social Democratic Party newspaper. Loyalty to a party, Einstein felt, meant surrendering some independence of thought. Such conformity confounded him. “How an intelligent man can subscribe to a party I find a complete mystery,” Einstein later lamented about Adler.
“During the complicated development of his theme he had still found time to reflect upon the nature of that particular mathematical transformation.”
He was writing with his right hand and holding Eduard with his left. Hans Albert was playing with toy bricks and trying to get his attention. “Wait a minute, I’ve nearly finished,” Einstein said, as he handed Eduard to Tanner and kept scribbling his equations. “It gave me,” said Tanner, “a glimpse into his immense powers of concentration.”8
When Lorentz died in 1928, Einstein would say in his eulogy, “I stand at the grave of the greatest and noblest man of our times.” And in 1953, for the celebration of the hundredth anniversary of Lorentz’s birth, Einstein wrote an essay on his importance. “Whatever came from this supreme mind was as lucid and beautiful as a good work of art,” he wrote. “He meant more to me personally than anybody else I have met in my lifetime.”18
“These discontinuities, which we find so distasteful in Planck’s theory, seem really to exist in nature.”29 Really to exist in nature. It was, for Einstein, an odd phrase. To a pure proponent of Mach, or for that matter of Hume, the whole phrase “really to exist in nature” lacked clear meaning. In his special relativity theory, Einstein had avoided assuming the existence of such things as absolute time and absolute distance, because it seemed meaningless to say that they “really” existed in nature when they couldn’t be observed. But henceforth, during the more than four decades in which he
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The Swiss personality agreed with him. His wife had a Slav’s revulsion for all things Teutonic, and he had a similar distaste that had been ingrained in childhood. As a boy he had run away from Prussian-accented parades and Germanic rigidity.
In Euclidean geometry, a vector is a quantity (such as of velocity or force) that has both a magnitude and a direction and thus needs more than a 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 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.
His headsnapping insight was that gravity could be defined as the curvature of spacetime, and thus it could be represented by a metric tensor. For more than three years he would fitfully search for the right equations to accomplish his mission.15
after he finally returned to the mathematical strategy and it proved spectacularly successful, he would from then on proclaim the virtues—both scientific and philosophical—of mathematical formalism.
What worried Einstein most about the Entwurf, justifiably, was that its mathematical equations did not prove to be generally covariant, thus deflating his goal of assuring that the laws of nature were the same for an observer in accelerated or arbitrary motion as they were for an observer moving at a constant velocity.
they would have two minutes to make photographs that could be used to analyze whether the starlight was deflected by the sun’s gravity. All did not go well. Twenty days before the eclipse, Europe tumbled into World War I and Germany declared war on Russia. Freundlich and his German colleagues were captured by the Russian army, and their equipment was confiscated.
Yet the termination of the eclipse mission had a silver lining. Einstein’s Entwurf equations were not correct. The degree to which gravity would deflect light, according to Einstein’s theory at the time, was the same as that predicted by Newton’s emission theory of light. But, as Einstein would discover a year later, the correct prediction would end up being twice that. If Freundlich had succeeded in 1914, Einstein might have been publicly proven wrong.
The chain reaction that pushed Europe into war in August 1914 inflamed the patriotic pride of the Prussians and, in an equal and opposite reaction, the visceral pacifism of Einstein, a man so gentle and averse to conflict that he even disliked playing chess.
“Europe in its madness has now embarked on something incredibly preposterous,” he wrote Ehrenfest that month. “At such times one sees to what deplorable breed of brutes we belong.”40
But he had generally shunned public activism. World War I changed that. Einstein would never forsake physics, but he would henceforth be unabashedly public, for most of his life, in pushing his political and social ideals.
The irrationality of the war made Einstein believe that scientists in fact had a special duty to engage in public affairs.
As the physicist John Wheeler has put it, “Matter tells spacetime how to curve, and curved space tells matter how to move.”
Apparently, Hilbert made a correction in the revised version of his article to match Einstein’s version. His revisions, quite generously, also added the phrase “first introduced by Einstein” when he referred to the gravitational potentials.
Judging from Hilbert’s revisions to his own page proofs, Einstein seems to have published the final version of these equations first. And in the end, even Hilbert gave Einstein credit and priority.
“Without Einstein, the general relativistic laws of gravity might not have been discovered until several decades later.”
The general theory of relativity was not merely the interpretation of some experimental data or the discovery of a more accurate set of laws. It was a whole new way of regarding reality.
The curving and rippling fabric of spacetime explained gravity, its equivalence to acceleration, and, Einstein asserted, the general relativity of all forms of motion.92 In the opinion of Paul Dirac, the Nobel laureate pioneer of quantum mechanics, it was “probably the greatest scientific discovery ever made.” Another of the great giants of twentieth-century physics, Max Born, called it “the greatest feat of human thinking about nature, the most amazing combination of philosophical penetration, physical intuition and mathematical skill.”93
For the rest of his life Einstein would expound a democratic socialism that had a liberal, anti-authoritarian underpinning.
Basic to his political thinking was the recognition of the dignity of the individual and the protection of political and intellectual freedom.”50
his socialist sentiments did not make him sympathetic to Soviet-style controls.
a finite universe, but one without boundaries. The masses in the universe caused space to curve, and over the expanse of the universe they caused space (indeed, the whole four-dimensional fabric of spacetime) to curve completely in on itself. The system is closed and finite, but there is no end or edge to it.
“This suggestion of a finite but unbounded space is one of the greatest ideas about the nature of the world which has ever been conceived,” the physicist Max Born has declared.11
Now he had just completed a more prolonged creative slog, from the fall of 1915 to the spring of 1917, which Dennis Overbye has called “arguably the most prodigious effort of sustained brilliance on the part of one man in the history of physics.”
During this period he generalized relativity, found the field equations for gravity, found a physical explanation for light quanta, hinted at how the quanta involved probability rather than certainty,† and came up with a concept for the structure of the universe as a whole. From the smallest thing conceivable, the quantum, to the largest, the cosmos itself, Einstein had proven a master.
Einstein would have been, and later was, appalled at the conflation of relativity with relativism.
Moreover, he was not a relativist in his own morality or even in his taste. “The word relativity has been widely misinterpreted as relativism, the denial of, or doubt about, the objectivity of truth or moral values,” the philosopher Isaiah Berlin later lamented. “This was the opposite of what Einstein believed. He was a man of simple and absolute moral convictions, which were expressed in all he was and did.”49
There are historical moments when an alignment of forces causes a shift in human outlook. It happened to art and philosophy and science at the beginning of the Renaissance, and again at the beginning of the Enlightenment. Now, in the early twentieth century, modernism was born by the breaking of the old strictures and verities. A spontaneous combustion occurred that included the works of Einstein, Picasso, Matisse, Stravinsky, Schoenberg, Joyce, Eliot, Proust, Diaghilev, Freud, Wittgenstein, and dozens of other path-breakers who seemed to break the bonds of classical thinking.
Eventually, Einstein came around to the cause. “I am, as a human being, an opponent of nationalism,” he declared. “But as a Jew, I am from today a supporter of the Zionist effort.”
religious faith instead of tribal affiliation.”
“I am well aware that the two speakers are unworthy of reply by my pen,” he said, but then proceeded not to be restrained by that awareness.
“The value of a college education is not the learning of many facts but the training of the mind to think,”
In one of his most revealing remarks about himself, Einstein lamented, “To punish me for my contempt of authority, Fate has made me an authority myself.”20
Among other things, Mach’s idea that inertia is caused by the presence of all of the distant bodies in the universe implied that these bodies could instantly have an effect on an object, even though they were far apart. Einstein’s theory of relativity did not accept instant actions at a distance. Even gravity did not exert its force instantly, but only through changes in the gravitational field that obeyed the speed limit of light. “Inertial resistance to acceleration in relation to distant masses supposes action at a distance,” Einstein lectured. “Because the modern physicist does not accept
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In other words, the equations work only if each quantum of radiation is emitted in some particular direction. That was not necessarily a problem. But here was the rub: there was no way to determine which direction an emitted photon might go. In addition, there was no way to determine when it would happen. If an atom was in a state of higher energy, it was possible to calculate the probability that it would emit a photon at any specific moment. But it was not possible to determine the moment of emission precisely. Nor was it possible to determine the direction. No matter how much information
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For Einstein, and indeed for most classical physicists, the idea that there could be a fundamental randomness in the universe—that events could just happen without a cause—was not only a cause of discomfort, it undermined the entire program of physics. Indeed, he never would become reconciled to it.
More than just a friendship, their relationship became an intellectual entanglement that began with divergent views about quantum mechanics but then expanded into related issues of science, knowledge, and philosophy. “In all the history of human thought, there is no greater dialogue than that which took place over the years between Niels Bohr and Albert Einstein about the meaning of the quantum,” says the physicist John Wheeler, who studied under Bohr. The social philosopher C. P. Snow went further. “No more profound intellectual debate has ever been conducted,” he proclaimed.44 Their dispute
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In Bohr’s model of the atom, electrons could change their orbits (or, more precisely, their stable standing wave patterns) only by certain quantum leaps. De Broglie’s thesis helped explain this by conceiving of electrons not just as particles but also as waves. Those waves are strung out over the circular path around the nucleus. This works only if the circle accommodates a whole number—such as 2 or 3 or 4—of the particle’s wavelengths; it won’t neatly fit in the prescribed circle if there’s a fraction of a wavelength left over.
Einstein made his own contribution when he received in June of that year a paper in English from a young physicist from India named Satyendra Nath Bose. It derived Planck’s blackbody radiation law by treating radiation as if it were a cloud of gas and then applying a statistical method of analyzing it. But there was a twist: Bose said that any two photons that had the same energy state were absolutely indistinguishable, in theory as well as fact, and should not be treated separately in the statistical calculations.

