In the Dark Future

In a recent episode of The Infinite Monkey Cage, The End of the Universe, one of the panel (Brian Greene) made a comment about a future state in which no other galaxies would be visible.  He suggested that, at that time, it would not be possible to work out that the universe is expanding.

I think that he’s wrong about this.

Prior to the work of Hubble, we did not know about other galaxies, for all we knew, the universe consisted only of the Milky Way Galaxy.  If there was nothing to be seen outside of our galaxy, the background would just be a tiny bit darker than it is already and it would be entirely possible to naïvely think that the universe consisted of nothing more that we can see.  Amateur astronomers and galaxologists could argue about whether space outside the Milky Way extended infinitely or if there were some sort of closed border that our spaceships would eventually bump into if we were so bold as to travel outside the galaxy (the only observable galaxy, hence the term galaxologist, rather than cosmologist).

I say amateur here because I believe that there are at least two ways that professional physicists could work out that the universe is not limited to galaxy, that it is expanding and that there is no border that extra-galactic spaceships would bump into (and that the universe is not necessarily infinitely large).

Hubble not only discovered galaxies outside our own, he also worked out that the further a galaxy was away from us, the more red-shifted it was.  There is consistent relationship between the distance of a galaxy and its rate of recession, expressed in the Hubble constant, H_o.  From this observation, it can be worked out that the universe is expanding.

In the far future, all other galaxies will be so far from us that they will be receding at greater than the speed of light and no more light from them will ever reach us.

Note that distant galaxies will not be travelling away from us at greater than the speed of light – that is not physically possible.  All that will be happening is that the totality of space between them and us will be expanding greater than the speed of light.  It is conjectured that there is already a part of the universe that is receding from us at greater than the speed of light – which would be the case if the radius of the observable universe is greater than 13.7 billion light years.  An object that is 13.7 billion light years away from us would be receding at the speed of light, so anything further way than that would be receding at a greater rate.

Note that the observable universe is estimated to have a (comoving) radius about three times greater than 13.7 billion light years.

How can we see objects that are receding at greater than the speed of light?  It gets a bit tangled here due to the notion of simultaneity, and the question of whether it is possible to point to a universal “now”.  Generally, physicists are reluctant to suggest that there is a meaningful “now” that links us here on Earth and observers in a location that is more than 13.7 billion light years away, but if we are fast and loose with the facts and pretend that there is such a meaningful "now", then we could say that no light emitted from those distant observers “now” will ever reach us and no light emitted by us will ever reach them.  (We could more accurately say that we are outside of each other’s light cone and nothing either group does will affect the other – so we are not currently, and cannot ever in the future be, causally linked.)

That said, light emitted from such distant locations in the past can reach us, and it does.  It’s very much red-shifted, from the visible spectrum into microwave spectrum, in which we can see the cosmic microwave background – remnants of the big bang (although it’s not really from the big bang per se, but rather from about 370,000 years later, just after the photon epoch, at the beginning of the somewhat counterintuitively named “dark ages”).

Note that a location that was, at the time, 370,000 light years away from us, “now” looks as if it were 13.7 billion light years away from us (on the erroneous assumption of a static universe).  It’s just that the expansion of the universe has meant that it took about 13.7 billion years for the radiation to reach us.

In the dark future, when our galaxy is the only thing visible to the naked eye, there will still be a cosmic background of some sort (although precisely which spectrum it is in will have changed).  If physicists think to check, there will be evidence of something out there beyond the galaxy, and the fact that we can’t see what caused it now may well give them enough evidence to postulate that the universe used to be smaller and motivate them to work out that the universe is still expanding.

If Hubble had not already provided an explanatory framework, the existence of a cosmic microwave background, whenever it was discovered, would have required some explanation.

There was also Einstein’s “greatest blunder”.  He was convinced that the universe was static, despite the fact that his equations were telling him that the universe was unstable and would either expand or contract.  This led him to introduce a cosmological constant that balanced the books and made the universe static.

Einstein conceded that this was an error when Hubble showed that the universe was expanding, but the point is that there is evidence of the universe expanding in the equations and some fiddling is required to make the universe appear static.  A future analogue of Einstein may not be so wedded to a static universe or a later tinkerer may question the introduction of an arbitrary cosmological constant and voila, you have evidence of expansion.

Finally, once it is understood that light is speed limited, it is possible to go through the process of amending the Galilean transforms and reach Special Relativity that way.  Once you have that, it becomes clear that space and time are mutable and someone like myself can reach the conclusion that the universe might be expanding (like I did quite a long time ago) and not be persuaded to abandon that line of thinking (like I was for a while) because of the odd notion of a universe expanding the way it does. 

Mathematics tells us that the universe is expanding and while observation makes universal expansion simpler to comprehend, that first-hand observation isn’t strictly necessary.