# A Neighborhood of Infinity

## Friday, January 06, 2006

### General Relativity for Dummies

No, really, for complete dummies. John Baez has just posted a description of Einstein's field equations that just about anyone can understand. So simple, even, that it can be described in words. And yet the formulation is equivalent to the field equations. It goes like this:

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.

More information is here. He also has a derivation of Newton's law of gravition here.

As Baez points out - at first it looks implausible because the Einstein field equation is a tensor equation and this looks like a scalar equation. But the statement must hold true for any set of test particles that are at rest relative to each other. So at any point it doesn't just give one constraint.

This is pretty neat stuff and it ought to go into all GR textbooks...