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Is there perfect vacuum about some 10,000 billion light years away? With perfect vacuum, I mean that there are no particles, not even virtual photons!

I had this idea by assuming that all particle filled space was created by the big bang and the max speed of light combined with the age of the universe.

Although probably impossible to measure, I wonder what the consensus is (if any) and what the theory says about it (if there is a theory about perfect vacuum at all)?

By the way, I'm aware of the Cosmological constant problem, but that's not what I require as an answer.

I haven't heard much about vacuum during education is that normal?

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Related: physics.stackexchange.com/q/25378/2451 and links therein. –  Qmechanic Oct 23 '12 at 16:43
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You should have asked "is there a perfect vacuum 13.7 billion light years away", since this is the speed of light times the age of the universe. The answer is no, there is nothing past 13.7 billion light years away (appropriately measured) because that's the wall at the end of the universe, the cosmological horizon. –  Ron Maimon Oct 23 '12 at 18:50
    
I consider nothing as a potential form of vacuum. One could argue about space and time not existing , but for perfect vacuum I cannot give a meaning to space and time unless there is a nonconstant force acting there. –  mick Oct 23 '12 at 20:24
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mick, Ron is stating a position which fortunately is not yet official dogma among physicists, and will never be, among people who actually study anything galaxy-sized or smaller. He has two motivations. The first is the philosophically extreme position that if you can't measure it, it isn't real. Galaxies in the expanding universe become undetectable once they cross the horizon, so in Ron's philosophy, they no longer exist at that point. No-one who actually studies stars or galaxies is going to believe that they stop existing because we can't see them, of course. –  Mitchell Porter Oct 23 '12 at 20:31
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The second reason is harder to convey, but it has to do with the holographic principle and the existence of a "dual description" of a theory with quantum gravity, on the boundary of its space. The main counterargument here is simply that there is no working example of holographic duality in which the cosmological horizon is the boundary. He's just guessing how the duality works for an expanding universe, and the illogic of the answer suggests he is guessing wrongly. –  Mitchell Porter Oct 23 '12 at 20:37
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The big bang in relativity is not what you are imagining--- it isn't a localized explosion. You don't have stuff rushing out from a point, you have everything getting denser in the past in a homogenous way.

This is complicated a little by the fact that a Newtonian big bang has things rushing out from a single point. But even in a Newtonian bang everything is homogenous, all points look the same as all other points after a translation and a Galilean boost. The particles have a speed which is proportional to their distance, and this goes all the way to infinite speed in the Newtonian version.

But we don't live in a Newtonian universe, and when you have a relativistic big bang, the way it works is that all points are the same as all other points after a translation and a relativistic boost. At the point where the boost boosts you at the speed of light, so at the limit of the sphere you are imagining, you have a cosmological horizon. So it isn't that there is "perfect vacuum" beyond this sphere, there is a visibility boundary which marks the end of the universe as we can ever see it, and for a positivist (i.e. for a physicist) this makes it the boundary of the universe, period.

The sphere you are imagining is then not a boundary between stuff and vaccum, but it is the boundary of the entire universe, and there is nothing, not even vacuum, outside this sphere.

This is complicated a little by the fact that you can extend the solutions of General Relativity past horizons, so that you can imagine that there is extra space beyond the horizon, at least classically. In the extended model, the universe goes on beyond the horizon, and in a big-bang model, in a homogenous way, so that if you call "time" local time since the big bang, all places look the same at the same time. In an inflation model, you can have most of the external volume still inflating, so that the banging is at different "time" at different places, and in most places, counted by extended volume, the bang never happens. This point of view is called eternal inflation.

All these extended scenarios are just-so stories, since they either make no predictions for the observable universe (since by definition, we can't see the stuff outside the horizon), or they make statistical predictions based on saying that we live in a typical volume of the extended universe, and these statistical predictions are ridiculously wrong (they predict that inflation lasts as long as possible conditioned on us being here to observe what we observe, and this is false). These points of view attribute more information to the external universe than what can be encoded on the cosmological horizon, they are not compatible with causal patch complementarity and the holographic principle, and they should be considered dead.

The other answers to this question misinterpret your question. You are asking about a point explosion not having time to fill all of space, and this is just not how the big-bang works. The best way to talk about the relativistic big bang is to say that it happens everywhere, not at a point. The only caveat is that the Newtonian big-bang isn't like that, but ignore that for day-to-day intuition.

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Well I consider the big bang as a curvature change that happened everywhere at once. But the mass came from one point , and is limited to light speed. How can it be everywhere at once if there is a boundary and there are not particles everywhere ? Setting a boundary seems like admitting it has a center , that seems mathematicly unavoidable. –  mick Oct 23 '12 at 20:31
    
It seems a bit like your using the cosmological constant problem as an answer to my question , but that is considered unsolved physics I note. –  mick Oct 23 '12 at 20:33
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@mick: Having a boundary does not mean it has a center, because the boundary is symmetric at any observation point. This is counterintuitive but true--- the space constant time slices have a translation symmetry, they look the same at every point. If you are seeing galaxy X, and it's halfway to the cosmological horizon sphere from your point of view, you are seeing it in the past, and an inhabitant on galaxy X will see a cosmological horizon which is half as big, and won't see your past at all. This is how it works in past-light cones. The boundary business is difficult to see outside of GR. –  Ron Maimon Oct 23 '12 at 20:48
    
Your example is just a logical consequence of the fact that light takes time to travel. How can a boundary be symmetric at any point ? Consider a point very near the boundary ? If you do not accept the concept of nearness , how do you have space ? –  mick Oct 23 '12 at 20:59
    
@mick: The sphere is the end of a past light cone. The point near the boundary has a shorter light cone, and is just very close to the big-bang that's all (looking out is looking back in time). This is a symmetric boundary to space, something Aristotle couldn't imagine. –  Ron Maimon Oct 24 '12 at 0:13
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You say:

With perfect vacuum I mean that there are no particles, not even virtual photons

but the quantum mechanical vacuum is a complicated place. For example see the Wikipedia article on the QCD vacuum. If you count virtual particles then there is nowhere in the universe that is a perfect vacuum in sense that there are no virtual particles present.

Re your question:

I havent heard much about vacuum during education is that normal?

Yes that's normal. You wouldn't usually cover this stuff until post graduate level.

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This has nothing to do with the question--- he is imagining that the big bang is at a point, and that there is nothing beyond the place where the big bang can reach, and this is just false. –  Ron Maimon Oct 23 '12 at 18:39
    
Oops yes, I missed that in his question. –  John Rennie Oct 24 '12 at 5:49
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It seems like your idea of "perfect vacuum" is something like "nothingness", which you definitely cannot find anywhere in our universe.

Firstly, if we travel 10000 light years away, we would still be well within the Milky Way galaxy. Interstellar space, while mostly empty, still contains a good amount of hydrogen and other debris.

Even if we travel a million light years away, to intergalactic space, we would still encounter one or two protons per cubic meter.

Edited to reflect your updated question: If we travel 10000 billion light years away, we would be in a different Hubble volume (beyond our cosmological horizon). However, based on our current assumptions, we can expect space to look similarly to what it looks like in our observable area of the universe (with the same particle density).

And finally, even if we find a region of space devoid of all matter, it would still be permeated by electromagnetic and gravitational fields, whose virtual particles are inescapable.

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You can't trave 10,000 billion light years away and get there "now", you would get there 10,000 billion light years in the future, which, ignoring the CC, means that the universe Hubble volume would have expanded to include where you are. With a CC, you would fall past our cosmological horizon, but this is why CC universes are strange--- they have a thermal mixing time, and there is only so long you can travel before you are thermalized or run out of fuel. –  Ron Maimon Oct 24 '12 at 17:05
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A quick go at this from another angle:

As a look at wikipedia can tell you, the observable universe (that is, the parts of the universe near enough to us to have had time to communicate some signal to us since the Big Bang) is about 45.7 billion light years away. This is about 200 times smaller than the distance you propose (10,000 billion light years).

Now, there isn't really a physical boundary at the edge of the observable (to us) universe, and for most current theories to hold up there needs to be quite a bit more of "universe" past that distance, probably by some orders of magnitude (10$^{23}$ in some theories).

That aside, it is important to keep in mind that there is very little one can say about places outside of the observable universe, and even less that can be verified with any sort of direct or indirect evidence. This is particularly important when piling zeros on top of numbers to make them look more impressive, since then one runs the danger of referring to absurdly unphysical quantities. It is just as easy to say "a billion years!" as to say "a hundred trillion!", but while the first is about a tenth of the age of the universe, the second would hold ten thousand ages-of-the-universe, and is therefore not a timescale that physics can meaningfully talk about.

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In the classical expansion from the Big Bang outside the expanding universe there is "vacuum", in the sense of nothing there outside the universe. So if your numbers are to mean a size of the universe not yet reached, a mathematical coordinate system, I think the answer classically is perfect vacuum.

I am not sure how this "vacuum" will be treated in string theory. I would expect that it would be the same, nothing, not even virtual pair creation until the expansion is large enough to reach your 10000billion light years. On the other hand this is at the frontier of research and will probably not be settled for a long time.

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Is that actually the case? I thought that the universe isn't really expanding "into" anything, and that space itself is expanding. There's no distance (even "10000 billion light years"), at which the universe hasn't "expanded into" yet. (is there?) –  Dmitry Brant Oct 23 '12 at 17:48
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Mathematically there can be. One has to separate coordinate system space from the General Relativity space. It is the GR space that is expanding. 10000billion light years is a coordinate system length since the universe has not reached these dimensions. If one wants to mathematically imagine it, it is empty by construction, of everything, because everything fields et al must be within the universe.imo ofcourse –  anna v Oct 23 '12 at 18:08
    
This is not right. –  Ron Maimon Oct 23 '12 at 18:39
    
@RonMaimon I am open to learning, but you do not state what is correct. When the big bang started and the universe was one second old, i.e. one light year length , everything was in the universe, but the coordinates to describe the universe are there, even though unphysical. One can draw 10 light years in imagination, an x,y,z system as a mathematical system. –  anna v Oct 23 '12 at 18:48
    
@RonMaimon Just read your answer, with which I agree. –  anna v Oct 23 '12 at 18:55
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