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TimS comments on The Fabric of Real Things - Less Wrong
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Ok, I've thought about it, and I'm still confused about the terminology.
Suppose Alice and Bob agree to try to escape each other's lightcone - so they start traveling away from each other at .5c (relative to the resting frame they started in). I'm a lawyer and can't do the transformations, but I know that the speed Alice perceives Bob traveling at is less than c - let's call that speed X.
If Alice breaks the agreement, turns around, and starts traveling towards Bob at a speed greater than X (relative to the mutual starting frame), she'll eventually catch up with Bob.
Given that, either (a) I've made a mistake about how relativity works, or (b) it seems impossible for Bob to get outside of Alice's lightcone. Please help.
You forgot that space itself is expanding. In theory, it's possible for Alice and Bob to travel far enough apart that the space between them expands faster than light, meaning the distance between them continues to increase even if they travel toward each other at the speed of light.
Isn't that violating the lightspeed limit? As you describe it, there's a frame of reference in which Alice and Bob are moving away from each other faster than the photons they are traveling near.
The lightspeed limit is a local notion. Something whizzing by you cannot be clocked to travel at or faster than light, but there is no clear definition of the relative velocity of two spatially separated objects in a curved spacetime.
I don't suppose you have a link to a reasonably accessible explanation of this point?
Maybe this will help... It's not overly accurate, but seems to be accessible enough.
Putting this here to help passers-by. My basic confusion appears to have been caused by not realizing that the universe is stretching. Thus, we aren't in an inertial frame with respect to other galaxies.
Inertial frame is a local notion, as well, so "inertial frame with respect to other galaxies" is not a meaningful statement. In GR inertial frame is generalized to a geodesic. There is also the concept of comoving frame, that in which the expansion rate looks the same in all directions.
I'm afraid the links I've seen are all actually less accessible than shminux's explanation.
It's not so much 'violating' the lightspeed limit as laughing in its face because it isn't constrained by it. Stuff within space travels at or less than the speed of light, space itself can do as it pleases (as determined by weirder stuff than just special relativity).
I'm not sure on the appropriate terminology here. Do they call it "moving away from" when neither thing has moved but have simply become further away from due to space changing?