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Unification in Higher Dimensions

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  • Unification in Higher Dimensions

    THE FABRIC of the COSMOS, Brian Greene, 2004
    ```(annotated and with added bold highlights by Epsilon=One)
    Chapter 12 - The World on a String
    Unification in Higher Dimensions
    In 1919, Einstein received a paper that could easily have been dismissed as the ravings of a crank. It was written by a little-known German mathematician named Theodor Kaluza, and in a few brief pages it laid out an approach for unifying the two forces known at the time, gravity and electromagnetism. To achieve this goal, Kaluza proposed a radical departure from something so basic, so completely taken for granted, that it seemed beyond questioning. He proposed that the universe does not have three space dimensions. Instead, Kaluza asked Einstein and the rest of the physics community to entertain the possibility that the universe has four space dimensions so that, together with time, it has a total of five spacetime dimensions.

    First off, what in the world does that mean? Well, when we say that there are three space dimensions we mean that there are three independent directions or axes along which you can move. From your current position you can delineate These as left/right, back/forth, and up/down; in a universe with three space dimensions, any motion you undertake is some combination of motion along these three directions. Equivalently, in a universe with three space dimensions you need precisely three pieces of information to specify a location. In a city, for example, you need a building's street, its cross street, and a floor number to specify the whereabouts of a dinner party. And if you want people to show up while the food is still hot, you also need to specify a fourth piece of data: a time. That's what we mean by spacetime's being four-dimensional.

    Kaluza proposed that in addition to left/right, back/forth, and up/down, the universe actually has one more spatial dimension that, for some reason, no one has ever seen. If correct, this would mean that there is another independent direction in which things can move, and therefore that we need to give four pieces of information to specify a precise location in space, and a total of five pieces of information if we also specify a time.

    Okay; that's what the paper Einstein received in April 1919 proposed. The question is, Why didn't Einstein throw it away? We don't see another space dimension — we never find ourselves wandering aimlessly because a street, a cross street, and a floor number are somehow insufficient to specify an address — so why contemplate such a bizarre idea? Well, here's why. Kaluza realized that the equations of Einstein's general theory of relativity could fairly easily be extended mathematically to a universe that had one more space dimension. Kaluza undertook this extension and found, naturally enough, that the higher-dimensional version of general relativity not only included Einstein's original gravity equations but, because of the extra space dimension, also had extra equations. When Kaluza studied these extra equations, he discovered something extraordinary: the extra equations were none other than the equations Maxwell had discovered in the nineteenth century for describing the electromagnetic field! By imagining a universe with one new space dimension, Kaluza had proposed a solution to what Einstein viewed as one of the most important problems in all of physics. Kaluza had found a framework.that combined Einstein's original equations of general relativity with those of Maxwell's equations of electromagnetism. That's why Einstein didn't throw Kaluza's paper away.

    Intuitively, you can think of Kaluza's proposal like this. In general relativity, Einstein awakened space and time. As they flexed and stretched, Einstein realized that he'd found the geometrical embodiment of the gravitational force. Kaluza's paper suggested that the geometrical reach of space and time was greater still. Whereas Einstein realized that gravitational fields can be described as warps and ripples in the usual three space and one time dimensions, Kaluza realized that in a universe with an additional space dimension there would be additional warps and ripples. And those warps and ripples, his analysis showed, would be just right to describe electromagnetic fields. In Kaluza's hands, Einstein's own geometrical approach to the universe proved powerful enough to unite gravity and electromagnetism.

    Of course, there was still a problem. Although the mathematics worked, there was — and still is — no evidence of a spatial dimension beyond the three we all know about. So was Kaluza's discovery a mere curiosity, or was it somehow relevant to our universe? Kaluza had a powerful trust in theory — he had, for example, learned to swim by studying a treatise on swimming and then diving into the sea — but the idea of an invisible space dimension, no matter how compelling the theory, still sounded outrageous. Then, in 1926, the Swedish physicist Oskar Klein injected a new twist into Kaluza's idea, one that suggested where the extra dimension might be hiding.
    Last edited by Reviewer; 09-28-2012, 07:21 PM.