MoonDragn said:
But according to some recent articles I've read, doesn't gravity directly affect the speed of light? To use that as a measurement would certainly be distorted.
No. Gravity directly affects the
velocity of light, but not the
speed. Velocity is a vector quantity; speed is a scalar quantity.
I'm not picking nits here. The difference between scalar and vector quantities, while it might be glossed over in everyday use, is
crucial to understanding relativity. Back to the zen, like Mount Fuji, there are many different views of relativity, all correct. One of those views is that relativity is a geometry of spacetime that allows observers to differ in their measurements of some vector quantities but requires them to agree on some scalar quantities derived from the vectors.
These scalar quantities include the speed of light, the absolute value of the Minkowskian 4-vector spacetime interval (which can also be expressed as a quaternion), and the absolute value of the momentum/energy 4-vector (or quaternion).
This leads to an interesting heuristic that you yourself can apply. Of course, people sometimes scree up, so in informal conversation and quasi-conversation (such as email, or this forum), somebody might confuse "speed" and "velocity." However, publications have editing and peer review to get rid of stuff like this.
So if you ever see a paper that conflates velocity and speed or talks about whether the "velocity of light" is a constant, it's a pretty safe bet that the author either 1) doesn't really know what he's talking about, or 2) is trying to pull a mathematical fast one.
Anyway, back to clocks. Gravity or acceleration does, of course, change the rate of clocks, as has already been described.
However, this isn't a problem, because you can make the light clock as small as you like. Except for what's called a "singularity," spacetime, even though it may be curved, is locally Euclidean.
It's also worth mentioning that every clock really is a light clock deep down. A quartz clock, a grandfather clock, everything you can imagine. They're made of parts, gears and springs and vibrating crystals, and they're made of atoms, and the atoms influence each other by virtual photons, in other words, light. Everything that happens to the light in the light clock is going to happen to this light as well. So you can't get rid of the light.
So an idealized light clock is the best you can get, because what it has, all other clocks have anyway, and it gets rid of stuff (like the pendulum on a grandfather clock) that is far more obviously affected by gravity.
Under Special Relativity, we can argue that all clocks have to go at the same rate, because if they didn't, then we'd be able to tell how fast we were going just by looking at our clocks, and if the Principle of Relativity is correct, that's impossible.
Under acceleration or gravity, we can't argue that. We know that the grandfather clock is going to go faster. But that's OK, because acceleration isn't relative in the same sense that velocity is relative (and yes, I meant to say "velocity," not "speed," though in some degenerate cases, speeds other than the speed of light are also relative). We can already measure that we are accelerating without looking outside. Everything is flying to the stern of the spaceship, or we feel the chair on our butts, or our faces go all wiggly and floppy on the acceleration couch, or something.
But an idealized, arbitrarily small light clock is still the best clock we can get, because the only things that are in it that matter are the only things we can't possibly get rid of: a distance (ruler), and light.
