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June 02, 2005

General Relativity Made Concise

John Baez writes:

Einstein's Equation: We promised to state Einstein's [general relativity] equation in plain English, but have not done so yet. Here it is:

Given a small ball of freely falling test particles initially at rest with respect to each other, the rate at which it begins to shrink is proportional to its volume times: the energy density at the center of the ball, plus the pressure in the x direction at that point, plus the pressure in the y direction, plus the pressure in the z direction.

In the final section of this article, we will prove that this sentence is equivalent to Einstein's equation. The reader who already knows general relativity may be somewhat skeptical of this claim. After all, Einstein's equation in its usual tensorial form is really a bunch of equations.... It is hard to believe that the single equation (2) captures all that information. It does, though, as long as we include one bit of fine print: in order to get the full content of the Einstein equation from equation (2), we must consider small balls with all possible initial velocities -- i.e., balls that begin at rest in all possible local inertial reference frames...

That is remarkably concise. Of course, the amount of auxiliary stuff you need to surround that equation with in order to calculate things with it is enormous...

And I wish somebody, sometime would tell me why Einstein's theory differs from Newton's in its prediction of the precession of the perihelion of Mercury...

Posted by DeLong at June 2, 2005 11:08 AM