GR: Why does space HAVE to contract in a gravitational well?

[dsoodak]

I've been playing with the idea of seeing how far I can get with general relativity without resorting to the learning of tensor calculus (at one point I decided I wouldn't believe SR until I derived it myself. I did (didn't need much more than 8th grade algebra), came up with the same results, and then made a simple simulator to understand the "paradoxes").

I've already thought of an example for predicting & calculating time dilation in a gravitational well:

If you assume that E=mc^2 and E=hv (both experimentally verified many times over), then photons have to lose a precise amount of energy (and thus frequency since E=hv) when going up out of a gravitational well or conservation of energy would be violated if you were to convert them into regular matter (since E=mc^2 and mass has more potential energy if higher up). Since the frequency of radio waves is related directly to the speed of the clocks in the circuit that generates them, time must move slower by the same amount.

Can anyone think of (or know of) a similarly intuitive example for why space has to contract in a gravitational field?

The only headway I've made so far is that the case where one of the observers is floating in a spherical shell (instead of standing on a planet's surface) makes it clear that the contraction would have to be equal in all directions (as opposed to SR where it is just in the direction of travel) and wouldn't be related to gravitational or tidal "forces" on the observer's atomic or molecular structure.

Thanks!

Dustin Soodak

 

[pervect]

Well, you might start off by thinking more about time dilation. Do you have the idea that there is some sort of "absolute time" that time dilates relative to? Or do you have something else in mind,,.