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I have read that the night sky should have been bright because every spot should end up pointing to a star in the infinite universe but this is not the case because the universe is expanding. I am thinking if the universe cannot be expanding with speed faster than light then the dark night sky is also due to the universe is relatively young and when it gets older the night sky will eventually end up bright.

Is this correct or am I missing something? Will the speed of universe expansion will make the sky bright but the red shift make it invisible to our eyes ?

Also if it's correct, does this mean that cosmologists do detect new stars appearing from nowhere from time to time? Does this really happen?

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We obviously know too few things about the Universe at such a high scale. Your question is too specific. Ask it again in twenty years. –  Isaac Jun 12 '11 at 18:00

2 Answers 2

up vote 7 down vote accepted

UPDATE: As Zassounotsukushi correctly points out in the comments, my original answer was wrong. I said before that objects move out across our horizon, but they don't. Sorry about that. I hope I've fixed things now.

It's best to avoid phrases like "the Universe is expanding faster than the speed of light." In general relativity, notions like distances and speeds of faraway objects become hard to define precisely, with the result that sentences like that have no clear meaning.

But if we leave that terminological point aside, your questions are perfectly well-posed and physically meaningful.

It's true that we can only see out to a finite distance, due to the Universe's finite age, and that this is an explanation of Olbers's paradox, which is the name for the old puzzle of why the night sky is dark.

As the Universe expands, more objects pop into view, since that "horizon distance" is continually getting bigger, at least in principle. In fact, though, that's a very small effect and would not lead to the night sky becoming brighter in practice.

First, we should note that we wouldn't expect to see stars popping into view as our horizon expands. The reason is that objects right near the edge of the horizon are so far away that we would see them as they were long ago, around the time of the Big Bang. In practice, we can't see all the way back to $t=0$, because the early Universe was opaque, but still, we can see back in time to long before there were discrete objects like stars. When we look back near the horizon, we see a nearly-uniform plasma.

But there's a much more important point. The further away we try to look, the more redshifted the light from a given object is. Even if we could see an object near our horizon, the radiation from it would be shifted to extremely long wavelengths, which also means that it would carry extremely little energy. In practice, this just means that things near our horizon become unobservably faint. In a practical sense, our ability to see faraway objects actually decreases with time: although in principle our horizon grows, the redshift causes any given object to become unobservably faint much faster than the rate at which new stuff is brought in across the horizon.

Lawrence Krauss has written a bunch about this stuff. The details are in this paper, and he has a Scientific American article (paywalled). Dennis Overbye wrote about this stuff in the NY Times a while back too. (If you read the pop stuff, tread carefully. Some of it seems to be saying the incorrect thing I said before, namely that things that are currently inside our horizon move outside of it. The technical article is correct, but the nontechnical ones can be misleading. That's my excuse for messing things up in my original answer, but it's not a very good excuse, because I should've known better.)

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Thank you very much @Ted. I still have some points that are not clear to me in your answer. My knowledge in physics is basic so it will be very nice of you to clear them out to me. If we mean by "Horizon" the edge of our observable space, this implies that it expands with speed of light (I mean our horizon radius where we are the center gains 3*10^8 Km every second). How could the universe expansion beats that? Doesn't this contradicts theory of relativity? You mentioned in your first paragraph that this is have no clear meaning but I do not understand why. –  M.Sameer Jun 12 '11 at 21:16
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In the curved spacetime of general rlativity, different "reasonable" choices of coordinates give different answers to questions such as "how far away is that object?" and "how fast is that object moving?". Questions like that have well-defined answers only in the limit of very close distances. One consequence is that many familiar laws are only valid at short distances. In particular, the prohibition on going faster than the speed of light only holds locally in general relativity: it's impossible for something very near you to move faster than the speed of light, relative to you. –  Ted Bunn Jun 12 '11 at 21:56
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I think the horizon effect might actually be intutive in a simple minded Galleon(sp?) sort of way. Ignore relativity, simply assume an expanding universe. At a constant expansion, such as after a "big-bang" explosion, an object at some cutoff velocity will remain at the cutoff velocity. Whereas if this object is speeding up, it will soon be going faster than our arbitrary cutoff velocity and hence vanish. Similarly for a slowing expansion objects just a little too fast to be visible will soon be slow enough to be seen. So an intuitive if incorrect picture exists. –  Omega Centauri Jun 12 '11 at 23:34
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Either I don't understand something or I think something genuinely needs to be revised about the following statement: "objects right at the edge of our horizon are moving out, not in". I can make lots of arguments for this, but to keep it simple, wouldn't this imply that we see galaxy $x$ at time $t$ then at $t-dt$, seeing it go backward in time. I think all of your statements are consistent with an absolute horizon, but the question requires an answer relevant to apparent horizons, and not only that, but the actual light that arrives. All 3 are very different in GR. –  Alan Rominger Jun 13 '11 at 3:18
    
Uh-oh -- I think @Zassounotsukushi is right, and I've messed things up. How embarrassing. I'll work on fixing my answer later today. –  Ted Bunn Jun 13 '11 at 14:19

The way that you ask your question confuses the answer because you say "Will the speed of universe expansion will make the sky bright but the red shift make it invisible to our eyes", because the sky is already "bright" in certain wavelengths, particularly the centimeter cosmic background radiation (CMB).

Other than this revision, yes, the observation that the night sky is dark has been a clear argument against an infinitely old universe since long ago. The evidence for the big bang in the form of a consistently increasing red shift pretty much seals the deal for myself, regarding the fact that the universe has an age.

Furthermore, over time, you are entirely correct in the assertion that the number of observable objects will increase drastically, and quite possibly infinitely. Consider that we only see $x$ distance away which terminates at the CMB, thus limiting the number of galaxies we can see, with the furthest galaxies being the earliest evolutionary stage of galaxies. The number of "young" galaxies we can see will progressively increase as more of the veil from the CMB is pulled back through the arrival of the new light. The "young" galaxies we can see now will mature and the total number will increase. Whether or not this will increase forever is disputable since dark energy pulls space apart could prevent it but we can't claim to know exactly what the behavior of dark energy far in to the future will be.

Additions

I started thinking about the problem more and I wanted to formalize things a bit better. Take the most basic case, we'll deal with a flat Newtonian space for now. As before, take $x$ to be the distance to a certain galaxy we are current seeing. Take the present time (after the big bang) to be $t$ and that we're observing that galaxy at $t'$. It follows...

$$x=c (t-t')$$

Imagine the universe has a galaxy density of $\rho$ galaxies per unit volume. Then knowing that, we can actually write the rate $r$ at which galaxies older than $t'$ are appearing into our view. This is done knowing the surface of a sphere is $4\pi r^2$.

$$r=4 \rho c \pi x^2$$

It's fascinating to consider that in a line connecting every object in the night sky and us, there exists the entire history of the object encoded in the light waves making their way to us. One way to talk about the acceleration of the universe is to say that there is a slowdown in the rate at which we are receiving this information. We are watching the far off objects in slow motion.

If we make the obviously incorrect but useful assumption that all objects emit light at the same rate at all times, then the intensity we see will be proportional to $1/x^2$, and given some $S$ which is, say, the number of photons emitted total per unit time, then the intensity of light we receive from a given body would be $S/(4 \pi x^2)$. Multiplying this by the rate, we can get a very nice equation for $s(x)$ which is the contribution to the number of photons we receive from the differential "shell" of stars at $x$.

$$s(x) = S \rho c $$

This equation is important because it is cumulative from time at $t'$ to $t$, meaning that the objects that entered our field of vision from the "genesis" of that type of object are still contributing to the population of photons reaching us today. So the number of photons we are receiving could be said to be:

$$\int_{t'}^t S \rho c dt = S \rho c (t-t')$$

A more advanced view of the situation simply notes that the "movie" for each of these stars is being played in slow motion. We'll just define a factor for that and put it in the equation.

$$l(x) = \frac{\Delta t_{object}}{\Delta t_{Earth}}$$

I should preface this by saying that this isn't actually saying time is going slower for that object, and this isn't even the time dilation as defined by general relativity, this is the time dilation you would measure by watching a clock in a galaxy far away with a space telescope and comparing it to the local time. Yes, these two are different, and yes, I am avoiding advanced relativistic concepts by making it an accounting problem. Now the total # of photons we receive per unit time is the following.

$$\int_{t'}^t S \rho c l(x) dt$$

I won't use any calculus chain rules because there's no guarantee that $l(t)$ is any more helpful to you than $l(x)$! But I should also note that the final $x$ you get in this equation at $t$ will be meaningless. It is not the general relativity distance, it's some bastardization of that by using $c t$, which is clearly not how it actually works. Nonetheless, there is some usefulness in the above equation. We can even identify the radiative energy being received by considering the energy of the photon being proportional to it's frequency, with $E_e$ being the energy of the emitted photon and $E_o$ the observed photon.

$$\frac{E_e}{E_o} = l(x)$$

And the total energy would then be the following with $h$ the familiar plank constant.

$$E = \int_{t'}^t S h \rho c l(x)^2 dt$$

Anyway, my intent is for these to be instructive "kindergarten" equations for the subject. The bottom line is still clear from them - that the # of photons reaching us would increase linearly over time but it's less since $l(x)\le 1$. Similarly, the radiative energy reaching us would be less by even a smaller factor due to the redshift. I hope this is a clear picture.

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Well, an argument against an infinitely old universe which is infinite in size and has infinitely-many stars. Any one of those not being true could explain why the night sky is not bright. –  BlueRaja - Danny Pflughoeft Jun 12 '11 at 5:35
    
@Zasso: I'm afraid you're wrong. Due to accelerating expansion the cosmological horizon will get smaller, not larger. Light from the most distant stars will be increasingly red-shifted. Eventually their light will not reach us at all as the space between us and them will be expanding faster than light can travel. This does not violate special relativity since no information is being transfered whilst the space expands. In the remote future the Universe will be a very dark, cold place. That shouldn't stop us enjoying it for now though :-) –  qftme Jun 12 '11 at 12:13
    
@qftme I thought the universal acceleration will not cause the furthest regions of space to travel faster than the speed of light relative to us, instead light beyond a certain point just can't make it due to being outrun by the acceleration. I mentioned this possibility and there's a good case most physicists would say this is "most likely". –  Alan Rominger Jun 12 '11 at 14:17
    
@Zasso: Unless I'm just getting confused by your wording, you seem to have contradicted youself. I.e. "light beyond a certain point just can't make it due to being outrun by the acceleration" - exactly what I was getting at. But, you also said "over time, [sic] the number of observable objects will increase drastically, and quite possibly infinitely" - to me, this contradicts your comment above. Also, according to current models at least, it's incorrect. –  qftme Jun 12 '11 at 18:31
    
@qftme Do you mean to say that current models simply assume a positive cosmological constant? And yes, the number of observable objects will increase dramatically and the possibility of doing so infinitely also exists, which is a possibility that contradicts a constant acceleration. We don't yet confidently know the fate of the universe. –  Alan Rominger Jun 12 '11 at 19:30

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