- #1

msumm21

- 218

- 16

- TL;DR Summary
- I'm trying to learn general relativity, but misunderstanding how the metric implies that time appears to pass slower for something near a heavy mass, as viewed from something far away

Using an example of 1 space dimension and 1 time dimension, consider the metric ##d\tau^2 = a dt^2 - dx^2## near a heavy mass (##a>1##).

From what I've read a clock ticks slower near a heavy mass, as viewed from an observer far away. A clock tick would be representative of ##d\tau## right (not ##dt##)? If so, then my confused understanding is below.

If ##a## is large, then small ##dt## results in large ##d\tau##. If the far away observer's ##d\tau## is approximately ##dt##, then his clock tick, say ##dt=1## corresponds to ##d\tau >> 1## near the mass. My interpretation of this is that the clock near the mass ticks ##d\tau >> dt## ticks (it ticks more than the clock far from the mass), and hence the clock near the mass moves faster. I realize this is wrong, but not clear what part is wrong.

From what I've read a clock ticks slower near a heavy mass, as viewed from an observer far away. A clock tick would be representative of ##d\tau## right (not ##dt##)? If so, then my confused understanding is below.

If ##a## is large, then small ##dt## results in large ##d\tau##. If the far away observer's ##d\tau## is approximately ##dt##, then his clock tick, say ##dt=1## corresponds to ##d\tau >> 1## near the mass. My interpretation of this is that the clock near the mass ticks ##d\tau >> dt## ticks (it ticks more than the clock far from the mass), and hence the clock near the mass moves faster. I realize this is wrong, but not clear what part is wrong.