Einstein's Equation of Separation

Swami Vivekananda, toward the end of the last century, tried to square Advaita Vedanta with what he referred to as "modern science." What we now refer to as modern science, or rather, modern physics, is something very different. What we, in this century, refer to as modern physics was not born until 1905, three years after Swamiji had passed away. One of the most crucial measurements which pointed up the necessity for changing our point of view was made by Michelson and Morley in lP89, only three years after Sri Ramakrishna had passed away, but the explanation of the difficulty waited for Einstein in 1905. Michelson and his friend Morley wanted to measure the speed of the earth through space — through what was then called the "luminiferous ether." Light was thought to be a wave motion and required a medium through which the waves might be conveyed. Sound waves travel through the air. Water waves travel through the water. Likewise, it was thought, light waves travel through the "ether." If canoes are moving through the waters of a still lake, it is simple to measure the motion of the canoes with respect to each other, but how do we measure the motion of the canoes with respect to the waters of the lake? We drop pebbles into the lake and measure the speed of the canoes with respect to the circles of ripples left on the surface of the water by the impact of the pebbles. "Likewise," thought Michelson, "we'll drop a light wave into the ether and measure the motion of the earth with respect to the wave." It was an ingenious device, but the measurements always showed that the "waves" move along with the earth as if the earth were standing still with respect to the medium through which the waves were propagated. It is as though the circles of ripples left by our pebbles on the lake move along with our canoe. It is as though the occupants of all the canoes saw the circles of ripples moving along with their own canoes; not only the circles from the dropping of their own pebbles, but the circles left by the dropping of the other pebbles as well. Einstein said, "There is no lake! We have misunderstood the relation of space to time!" Einstein pointed out that we live in a four-dimensional universe, not a three- dimensional one. A three-dimensional universe is not objective. If we are to see the universe as objective, we must see it in four dimensions — we must put the equation of separation in four dimensions, that is, we must put time into the equation. We turn, then, for a closer look at the fascinating four-dimensional geometry of modern physics and its most unexpected consequence.