LITMIR.BIZ

      He reminded his listeners that space is denoted by three orthogonal coordinates, x, y, z, for length, breadth, and thickness. Let t denote time. With a piece of chalk, he said, he could draw four axes on the blackboard: “the somewhat greater abstraction associated with the number 4 does not hurt the mathematician.” And so on. He was excited. This was “a new conception of space and time,” he declared; “the first of all laws of nature.” He called this conception the “principle of the absolute world.”

      Four numbers, x, y, z, t, define a “world point.” Together, all the world points that trace an object’s existence from birth to death form a “world line.” And what shall we call the whole shebang?

      The multiplicity of all thinkable x, y, z, t systems of values we will christen the world.

      Die Welt! Good name. But we just call it spacetime now. (The continuum.) If we resist (“Because I know that time is always time/And place is always and only place,” said T. S. Eliot), we do so in vain.

      It was a bit of misdirection for Minkowski to begin by saying his lecture was grounded in experimental physics. His true subject was the power of abstract mathematics to reshape our understanding of the universe. He was a geometer above all. The physicist and historian Peter Galison puts it this way: “Where Einstein manipulated clocks, rods, light beams, and trains, Minkowski played with grids, surfaces, curves, and projections.” He thought in terms of the most profound visual abstraction.

      “Mere shadows,” Minkowski said. That was not mere poetry. He meant it almost literally. Our perceived reality is a projection, like the shadows projected by the fire in Plato’s cave. If the world—the absolute world—is a four-dimensional continuum, then all that we perceive at any instant is a slice of the whole. Our sense of time: an illusion. Nothing passes; nothing changes. The universe—the real universe, hidden from our blinkered sight—comprises the totality of these timeless, eternal world lines. “I would fain anticipate myself,” said Minkowski in Cologne, “by saying that in my opinion physical laws might find their most perfect expression as reciprocal relations between these world lines.” Three months later he was dead of a ruptured appendix.

      Thus the idea of time as a fourth dimension crept forward. It did not happen all at once. In 1908 Scientific American “simply explained” the fourth dimension as a hypothetical space analogous to the first three: “For passing into the fourth dimension, we should pass out of our present world.” The next year the magazine sponsored an essay contest on the topic “The Fourth Dimension,” and not one of the winners or runners-up considered it to be time—notwithstanding the German physicists and the English writer of fantastic fiction. The space-time continuum was radical indeed. Max Wien, an experimental physicist, described his initial reaction as “a slight brain-shiver—now space and time appear conglomerated together in a gray, miserable chaos.”^fn5 It offends common sense. “The texture of Space is not that of Time,” cries Vladimir Nabokov, “and the piebald four-dimensional sport bred by relativists is a quadruped with one leg replaced by the ghost of a leg.” If these critics sound Filbyish, even Einstein did not immediately embrace Minkowski’s vision: “überflüssige Gelehrsamkeit,” he called it—superfluous learnedness. But Einstein came around. When his friend Besso died in 1955, Einstein consoled his family with words that have been quoted many times:

      Now he has departed from this strange world a little ahead of me. That means nothing. People like us, who believe in physics, know that the distinction between past, present, and future is only a stubbornly persistent illusion.

      Einstein died three weeks later.

      FUNNY IRONY, though.

      A century after Einstein discovered that perfect simultaneity is a chimera, the technology of our interconnected world relies on simultaneity as never before. When telephone-network switches get out of sync, they drop calls. While no physicist “believes in” absolute time, humanity has established a collective official timescale, preached by a choir of atomic clocks maintained at a temperature near absolute zero in vaults at the United States Naval Observatory in Washington, the Bureau International des Poids et Mesures near Paris, and elsewhere. They bounce their networked light-speed signals to one another, make the necessary relativistic corrections, and thus the world sets its myriad clocks. Confusion about past and future cannot be tolerated.

      To Newton this would make perfect sense. International atomic time has the effect of codifying the absolute time that he created, and for the same reason: it lets the equations work out and the trains run on time. A century before Einstein, this technical achievement in simultaneity would have been almost impossible to conceive. The very notion of simultaneity scarcely existed. It was a rare philosopher who considered the question of what time it might be in a faraway place. One could hardly even hope to know, said the doctor and philosopher Thomas Browne in 1646,

      It being no ordinary or Almanack business, but a probleme Mathematical, to finde out the difference of hours in different places; nor do the wisest exactly satisfy themselves

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