# Are galaxies expanding away from us at more than the speed of light? [duplicate]

If you go to the following video, at this certain time:

https://youtu.be/Iy7NzjCmUf0?t=435

you will see that the narrator says:

"We simply don't know what else is out there because the light from these incredibly distant places has not yet had enough time in the universes history to reach us yet back on Earth. And the light from some places might never reach us at all. Because some parts of space, very far from Earth, are expanding away from us, faster then the speed of light, that means that the light from these places will never, in an infinite amount of time reach Earth"

Am I understanding this correctly? Some parts in the universe are expanding faster then the speed of light? Is it yet proven that there are definitely things faster then the speed of light?

I feel like I am misunderstanding the above statement.

P.S, try watching the entire video, it will be 10 minutes well spent.

• I think astronomy.stackexchange.com/questions/25954/… may answer your question, and might be a duplicate – James K Jun 26 '18 at 23:12
• Just to make it clear, some parts of space, very far from Earth, are expanding away from us, faster then the speed of light, but the light from these places will reach us, see arxiv.org/abs/astro-ph/0310808 by Tamara Davis and Charles Lineweaver: "We show that we can observe galaxies that have, and always have had, recession velocities greater than the speed of light". – John Duffield Jun 28 '18 at 13:09

## 2 Answers

You've been confused by a subtle error that seems always to be made when trying to express the speed of light limitation of Relativity in words.

What's fundamental is something called the Lorentz Symmetry AKA Lorentz Invariance which is the basis of Relativity. This symmetry is a local symmetry and it's a strong symmetry of of the physical universe. Basically, what it says is that the laws of physics are independent of velocity. A consequence of this symmetry is that two objects can't pass each other at a speed greater than that of light. (The reason why is not especially difficult, but best explained using mathematics rather than words.)

General Relativity is not a local theory -- it's a theory of the structure of spacetime -- but its local structure is that of Special Relativity, and hence it has Lorentz symmetry. One of the surprising (utterly surprising -- Einstein himself didn't believe it for many years) consequences of General Relativity is that spacetime isn't stable, but it must either expand or contract. This expansion is not the galaxies flying further and further into the void like the bits of an exploded hand grenade, but is spacetime itself expanding everywhere (there is no center of expansion) and the galaxies everywhere more-or-less sorta sitting still in the expanding spacetime and being carried along with it.

If you pick two points which are far enough apart, they can be receding from each other at a speed greater than that of light -- or, alternatively and just as correctly -- more than 300,000 km of new space can be created between them each second. Because nothing is moving past each other at FTL speeds, local Lorentz symmetry is preserved and Einstein is happy and his equations are satisfied and all's well with the universe.

Note that everything I've said is wrong, but I hope it's not misleadingly wrong. You really need to do the math to see what's actually happening.

But the upshot is that we can't fly to the Moon (or Mars or Alpha Centauri or wherever) and come back at a speed faster than light, but many distant galaxies -- which we will never see or hear from again -- have just passed c moving away from us, and more do so every year.

And indeed there is another error in the quoted statement, which is that the statement implies there is something significant about objects whose distance from us is increasing faster than the speed of light, as though the light from those objects would never reach us. This is incorrect, we routinely see galaxies that have always been separating from us at a rate larger than c-- they were separating faster than that when the light was emitted, and they have only been speeding up since then, yet we see them clearly because a model where space itself is expanding at that rate makes it possible. It's subtle but routine.

That said, it should also be mentioned that because the expansion is accelerating, light emitted now (meaning at this same cosmological age) from galaxies that are separating from us faster than c now will never be able to be seen. But again, there's nothing special about c-- light from galaxies separating from us at a rate less than c right now will also never be seen, it just depends on how fast the acceleration goes from here on.

• Actually, there is a (relatively) small shell of the Universe that does recede faster than $c$, but from which we may still, in the far future and if $w$ doesn't evolve, receive light emitted today, namely the shell consisting of region outside the Hubble sphere ($d\gtrsim14.4$ Glyr) and inside the event horizon ($d\lesssim16.5$ Glyr). – pela Jun 27 '18 at 7:19
• As you say, that assumes the acceleration is ruled by a cosmological constant, which we really don't know. Even so, I take your point, it's interesting that the horizon can still be faster than c anyway. – Ken G Jun 28 '18 at 2:41
• We can also go the other way and regard galaxies emitting light in the past: For instance, when GN-z11 at $z=11.1$ emitted the light we see today, it was receding at $v\sim4c$ — yet its light caught up with us some 13 billion years later. – pela Jul 4 '18 at 21:33