John’s post on light-induced sonic booms has set a bad precedent of actually answering questions. (And it’s been a big hit around the internets, so our server keeps overheating.) Sensing an opportunity, commenters hungry for knowledge have chimed in to ask all sorts of perfectly good questions about cosmology. To keep things on track, let’s divert those questions to this separate thread. So this is the chance to ask all of those questions about the universe you’ve always wondered about. For example:
Q: If I plug in Hubble’s law for the velocity of a galaxy in terms of its distance (v = Hd, where H is the Hubble constant), at large enough distances the velocity will be greater than the speed of light! Doesn’t that violate relativity?
A: Yes, it would be greater than the speed of light, but no, it doesn’t violate relativity. What relativity actually says is that two objects can’t pass by each other at a relative velocity greater than the speed of light. The relative velocity of two distant objects can be whatever it wants. In fact, to be more of a stickler, the relative velocity of two distant objects is completely ill-defined in general relativity; you can only compare velocity vectors of objects at the same point. The notion of “velocity” almost makes sense in cosmology, but you have to keep in mind that it’s only an approximate concept. What’s really going on is that the space between you and the distant galaxy is expanding, which redshifts the photons traveling from there to here, and that reminds you of the Doppler shift, so you (and Professor Hubble, so you’re in good company) interpret it as a velocity. But it’s not a Doppler shift; both you and the galaxy are essentially “stationary” (although that concept is also not precisely defined), it’s just that the space between you is expanding.