George Musser sent me and David Hogg an email with some questions about the paper Hogg and I wrote about the interpretation of the redshift (which I’ve written about before). The discussion may help to clarify a bit what Hogg and I are and are not claiming, so here it is (with Musser and Hogg’s permission, of course).
Musser’s original question:
I’m still absorbing your paper from a couple of years ago on the cosmological redshift, being one of those people who has made the distinction with Doppler shift and, more generally, between “expansion of space” of “motion through space”.
If these are equivalent and, in fact, the latter is preferred, then should I think of the big bang as spraying out galaxies through space like a conventional explosion — i.e. the very picture cosmologists have been telling us is wrong all these years? If the rubber-sheet model of space is so problematic, then what picture should I keep in my head?
Also, if the photon only ever sees locally flat spacetime, is that why the cosmological redshift does not entail a loss of energy?
The only cosmologist saying that that the “explosion” picture is wrong is Harrison (who himself is very wrong), although others think it is uncomfortable, like Sean Carroll (who is not wrong). Empirically, there is no difference; what is definitely wrong is the idea that the space is “rubber” or has dynamics of its own. There is no absolute space–the investigator has coordinate freedom, and the empty space has no dynamics, so this rubber sheet picture is very misleading. And no, the photon does not “lose energy” in any sense. It is just has different energies for different observers, and we are all different observers on different galaxies.
That is helpful, but I am still confused. An explosion goes off at a certain position in space and matter shoots outward in every direction. Is that really a valid picture of the big bang? What do I make of the presence of horizons?
And finally me:
It’s still true that there is no spatial center to the expansion. That is, there is no point in space that is “really” at rest with everything moving away from it. Space is homogeneous, which means that whatever point you pick looks as much like the center as any other point.
One thing that can be said for the expanding-rubber-sheet picture: at least in its form as an expanding balloon, it conveys this idea of homogeneity tolerably well. (Well, except that it’s hard for people to remember that only the surface of the balloon counts as “space” in this metaphor. People always want to think of the center of the balloon’s volume as “where” the Big Bang happened.)
So I’d rather you not think of the Big Bang as an explosion “at a certain position in space”. It’s still true that it happened everywhere rather than somewhere. There’s no preexisting space into which stuff expands. For instance, if we imagine a closed Universe (i.e., one that has a finite volume today), its volume was smaller in the past, approaching zero as you get closer to the Big Bang. So in that sense space really is expanding.
[A bit of fine print: All of the above is true as applied to the standard model of the Universe, in which homogeneity is assumed. Whether it’s true of our actual Universe is of course an empirical question. The answer is yes, as far as we can tell so far. But there’s no way to tell — and there probably never will be any way to tell — what space is like outside of our horizon. But anyway, this point is independent of the question of interpretation that we’re discussing at the moment. So it’s safe to ignore this point for the present discussion.]
As Hogg says, the main thing we object to is the idea that the rubber sheet has its own dynamics and interacts with the stuff in the Universe — that is, that the stretching of the rubber sheet tends to pull things apart, or that it “stretches” the wavelengths of light. As far as I’m concerned, the main reason for objecting to this language is not because it gives the wrong idea about cosmology, but because it gives the wrong idea about relativity. The most important point about relativity is that space doesn’t have any such powers and abilities. If you’re a small particle whizzing through space, at every moment space looks to you just like ordinary, gravity-free, non-expanding space.
So if you’re going to abandon the heresy of the rubber sheet, what should you replace it with? I don’t have anything as catchy as the rubber sheet, unfortunately. What I visualize when I visualize the expanding Universe is just a bunch of small neighborhoods, each one of which is completely ordinary gravity-free space, but each of which is moving away from its neighbors.
In this picture, the redshift is easy to understand. If a guy in one neighborhood tosses a ball to his neighbor, the speed of the ball as measured by the catcher will be less than the speed as measured by the thrower. That is, the two measure different energies for the ball, not because there’s some phenomenon taking energy away, but just because they’re in different reference frames. If the catcher then turns around and throws again to his neighbor, the same thing happens again, and so on. That’s all the redshift is. It’s not some mysterious “stretching.”