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GR In Higher Dimensions Results In Electricity And More.

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Posted by Alexander on October 1, 2001 22:29:06 UTC

If you take GR equations and assume that space has not only 3 dimensions, but 4: 3 "big" ones and 1 small curled into small sphere (it should be small, othervise we would see it the same way we see "big" dimensions in everyday life), and if you also assume that the small curled dimension is symmetric in both "+" and "-" directions (left curl = right curl),then very interesting things happen.

The 4-dimensional GR equations split into two distinctive groups. Three "big" components are the same as the Einstein's equations of GR in 3 dimensions we all know about. But the one in 4-th curled dimension becomes the equation identical to the equation describing electric charge in QED (quantum electrodynamics)! Upon adding the relativistic Lorents transformations it becomes what we call know as Maxwell equations in regular "big" 3 dimensions. So, entire electromagnetism becomes a mathematical outcome of existence and symmetry of extra spatial dimension.

This is not very new idea - it is called "Kaluza-Klein formalism" in theoretical physics after original paper of these physicists showing how electricity may oroginate from gravity was published in 1920.

So, all variety of forces we know (well, there are only 3 so far: gravitational, electromagnetic and nuclear) seems to be just gravity plus extra degrees of freedom of allowed motion (curled spatial dimensions).

Current string theory is heavily based on this finding - it considers that not only all forces, but all particles and antiparticles - ALL STUFF WE KNOW AT ALL (that is why it is called TOE) could be explained as the result of motion of small massless loops (presumably "made" of space itself) in many dimensions: 3 familiar "big" spatial dimension and 7 small dimensions (plus 1-D time, which is not really a dimension at all, because it is not a degree of freedom - you can not move back and forth in time).

So, it may after all be, that our universe is just a geometry, and all objects and phenomena in it are just geometrical objects and geometrical phenomena.

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