# Expansion of the Universe, will light from some galaxies never reach us?

Is it true that the light from some galaxies will never reach us?

The explanation for that is that the Universe expanding faster than the speed of light. But, if the speed of light is constant in all reference frames, then in the reference frame of a galaxy, light must move at the speed of light and thus it must reach us (?).

Could you also explain how is it possible that the Universe is expanding faster than the speed of light if an object can never be observed to move faster than light? (without Doppler effects).

• Related: physics.stackexchange.com/q/26549/2451 and links therein. – Qmechanic Aug 8 '14 at 9:29
• Not a dupe, I fixed the title, should be clear at this point. – Aaron Hall Aug 8 '14 at 15:54
• Agreed that this is not a dupe at least of the indicated question (late-time acceleration vs. early-time inflation, for one). – user10851 Aug 8 '14 at 17:26

Let me present a slightly different perspective to Luboš, though I'm saying basically the same thing. From our current location we can define an area of space called the future light cone. This is the region of spacetime that is connected to us by motion at less than or equal to the speed of light. If we draw a spacetime diagram then the lightcone looks like:

Anything that is within our future light cone will always stay within our future light cone. As an aside, this is why nothing can ever fall into a black hole in our coordinates because crossing the event horizon would take it outside our light cone. Instead we see the object freeze at the event horizon.

But back to the universe: your argument that:

an object can never be observed to move faster than light

is true for everything in our future light cone, but the bits of the universe that are moving faster than light relative to us, and that we will never see, were never in our (past) light cone. This basically because the Big Bang wasn't an explosion outwards from a single point (as misleadingly shown in most TV documentaries).

However, as Luboš says, if we wait long enough even the most distant galaxies will eventually enter our light cone. Well, probably. This is always true for a decelerating expansion, and is even true for accelerated expansion provided $\dot{a}$ increases more slowly than $a$. See the paper Expanding Confusion for the gory details.

• Where in the paper "Expanding confusion" was it said that even the most distant galaxies will enter our past light cone if $\dot{a}$ increases more slowly than $a$? As I mentioned to bobie, fig. 1 says "Our event horizon is our past light cone at the end of time, $t=\infty$ in this case", so anything outside that cone will never be seen, and p. 4 says "Most observationally viable cosmological models have event horizons", so even if your statement is correct that would suggest that models where $\dot{a}$ increases more slowly than $a$ are mostly not "observationally viable". – Hypnosifl Dec 11 '14 at 3:58
• In fact, Davis & Lineweaver explicitly write that we are currently routinely observing galaxies that have always been receding from us faster than light. – Thriveth Dec 11 '14 at 11:37

I am aware that my answer can sound surprising, too simple to be true, but please take a deep breath before downvoting.The answer has little to do with relativity.

• In SR it is the moving object that gets shorter , but space is stable. In such a universe, even if a body is receding at 2,3,30 c, its light will reach us sometime, and the time is short as it is simply D/C. That is because once the photon is discharged, what the sources does is absolutely irrelevant.

• In a universe where space is not stable but is stretching (FLRW) the situation is different because D is increasing. It might seem obvious then that light, on certain conditions, might never reach us. It is not so:

It is counter-intuitive, but no matter how fast D is stretching, light will always reach us, and you find a good math explanation here, of course in some cases it will take a very looooong time. This is not the case here, as the fastest acknowledged rate is about $\pi$ C.

This is what lubos Motl is conceding , only as a codicil:

One should perhaps also point out that in some distant future, any galaxy (or the place where it lived before it ran out of energy) is ultimately going to be visible from Earth.

For an obscure reason, cosmologist adore to make simple things look complicated

• There are FLRW cosmologies where light from sufficiently distant parts of the universe will literally never reach us, and the current ΛCDM concordance model is one of them. See my comment on Luboš Motl's answer. – benrg Aug 9 '14 at 20:21
• This is incorrect. You link to the "ant on a rope" to justify your claim, but as explained by julian fernandez in an update here, that puzzle assumes distance increases linearly with time, whereas with the expansion of space it should increase exponentially. There is in fact a cosmic event horizon, where light emitted from beyond that distance will never reach us in infinite time, see fig. 1 here which says "Our event horizon is our past light cone at the end of time, $t = \infty$ in this case" – Hypnosifl Dec 10 '14 at 23:32
• Claiming that @Hypnosifl 's source has "no authority" is the joke here. Davis and Lineweaver are some of the world's finest capacities on this subject. – Thriveth Dec 11 '14 at 11:28
• Also see my answer here for some quotes from another peer-reviewed paper by a number of physicists, which talks about the "future visibility limit" and says "Stars and galaxies that lie beyond this co-moving future visibility limit are forever hidden from our view". And as I pointed out in the answer, both this paper and Fig. 1 in the Davis/Lineweaver paper put this ultimate limit at a little over 60 billion light years away. – Hypnosifl Dec 11 '14 at 15:34
• @bobie - I don't think the argument based on the ant-on-a-rope would have been correct in any era of cosmology, unless there was ever a mainstream model that involved the distance between galaxies increasing at a constant rate. It's true that in the flat FLRW model with no cosmological constant you would eventually see every galaxy, but this has to do with the slowing of the expansion with time, so the ant-on-a-rope scenario where the distance between points increases at a constant rate still doesn't give a correct picture of why you will see every galaxy in this cosmological model. – Hypnosifl Dec 12 '14 at 16:45

I am sorry to say that I can not agree with previous answers. We believe, but do not know for sure, that light from some galaxies will never reach us. This has nothing to do with the fact that they are moving away from us at more than the speed of light. Rather, it is assumed that these galaxies, like us, are not moving relative to the special frame in the universe: the one in which large clusters of galaxies are stationary. They seem to be moving away from us because the universe is expanding. And, if there is "dark energy" (as we currently think) and that dark energy persists for long enough, then the expansion of the universe will accelerate more and more with the passage of time. It is this acceleration of the expansion of the universe that implies that light from sufficiently distant galaxies will never reach us.

And, actually, it is not known that light from sufficiently distant galaxies will never reach us. There are (at least) two possible reasons for this: a) we are wrong about details of dark energy b) the universe is not infinite but really is finite: something like (say) the surface of a sphere or donut, closed in on itself. If this is the case, it maybe we will see all the galaxies. We will just not see all the repeat images of each galaxy, as you keep going around the donut.

The relative speed between two objects is only restricted within the special theory of relativity. These restrictions are only guaranteed to apply in general relativity – the theory of curved space that you need for the Big Bang theory – if the space surrounding the objects is the flat Minkowski spacetime, or at least can be approximated by the flat Minkowski spacetime.

In practice, it means that special relativity is guaranteed to hold locally, in very small regions of spacetime which are always nearly flat if they are small enough. That's why the relative speed of two objects that are just passing by one another can't exceed $c$. Special relativity would also (approximately) apply in much larger regions of the spacetime if those were (nearly) flat – if the Riemann curvature were zero (or small) everywhere.

But if you consider the distant galaxies that are receding very quickly – comparably to the speed of light or faster – away from us due to the expansion of the whole Universe, then the condition of the flatness of the spacetime in between the two galaxies, our and theirs, is explicitly violated. That's why the restriction from special relativity no longer holds.

One should perhaps also point out that in some distant future, any galaxy (or the place where it lived before it ran out of energy) is ultimately going to be visible from Earth. That's because the Universe is getting older and we can therefore see further.

• There is one caveat... This is true if the expansion of the Universe is done at a fixed rate. If the expansion is accelerating, this might not be true... Second problem : the Earth will be no more in any case ;-) – Martigan Aug 8 '14 at 7:22
• Sorry, you're confused. The question wasn't whether we can already observe all "types" of galaxies, or galaxies of all ages. Of course that at each moment, we can observe pretty much everything if telescopes are good enough, as you say. The question was whether there are some particular galaxies whose position guarantees that we can't see them today, with arbitrarily good telescopes, and be sure that there are galaxies that we can't see today but we will be able to see in 1 billion years if we're here. – Luboš Motl Aug 9 '14 at 16:08
• "in some distant future, any galaxy [...] is ultimately going to be visible from Earth" is incorrect in ΛCDM cosmology. The most distant CMBR light we will ever see is at $\tfrac{1}{z_*} \int_{t_*}^\infty c\,dt/a(t)$. In many FLRW cosmologies this is infinite, but in ΛCDM it is finite and equal to about 57 Mly in decoupling-time comoving distance (the distance we can currently see is about 42 Mly). Any galaxies that condense from matter beyond that point will never be visible to us, unless ΛCDM is wrong. – benrg Aug 9 '14 at 20:19
• @Bobie, apologies, it's surely not clear. Demonstrably getting light from a star is a special type of detection, and we are both getting light from and detecting the Methuselah star, so your comments contradict one another. It's just 190 light years away from us - why do you talk about it at all? Its cosmological behavior with respect to us is as unmysterious as the Sun's. – Luboš Motl Aug 10 '14 at 4:35
• Did you misspell UDFy-38135539 as Methuselah? Quite a typo! ;-) Otherwise we seem to agree, don't we? – Luboš Motl Aug 10 '14 at 7:53