# B The "true" vacuum

Tags:
1. Dec 13, 2016

### Delta²

First of all I want to say that I am a *scrub* in relativity so when people say things like that the universe expands and/or inflates I still don't get the full grasp of it.

Here is my question.

When we refer to a vacuum I would expect it to be a region of space that has absolutely no particles (fermions like the electron or bosons like the photon). But what about the gravitational field and its particle the gravitron, is it possible to make a region of space that has absolutely zero gravitational field? Since we cant shield the gravitational field there is no way to construct the perfect "true" vacuum as I say in the title of the thread.

Is the perfect true vacuum in the "hypothetical" region of space that the universe hasn't expanded yet there. Like if we imagine universe is a sphere with a diameter of 100bilion light years (just saying I don't have accurate info on what are the estimates for the diameter of the universe), is the perfect true vacuum somewhere in a region outside that sphere, in a radius say of 101 billion light years?

Also if someone can recommend me a good book on the Universe Evolution ( birth (matter and antimatter), growth (formation of dust clouds, stars/planets/comets, galaxies cluster of galaxies e.t.c) and possible death of the Universe).

2. Dec 13, 2016

### Staff: Mentor

This is fine as long as you remember that "no particles" does not mean "nothing", at least not in the usual layman's sense of that word. There are still quantum fields, and there is still spacetime. A more rigorous definition of "vacuum" is "ground state", i.e., "the state of minimum possible energy". See below.

"Gravitational field" is actually not a very good term since it can mean any of several different things. What you probably want to ask is if it's possible to have a region of space (more properly spacetime) that has absolutely zero spacetime curvature. Mathematically, yes, this is possible, but physically it's not so clear. To have absolutely zero spacetime curvature, you need to have absolutely zero stress-energy tensor (and absolutely zero cosmological constant, but we'll treat that as just part of the stress-energy tensor). Nobody knows whether an absolutely zero stress-energy tensor is physically possible; I would suspect it isn't because, even if all quantum fields are in their ground states (in some hypothetical universe, not ours, where this is very far from being true), that doesn't mean they all have absolutely zero energy (more precisely, zero expectation value for energy).

No. There is no such place; the universe is expanding everywhere.

First, as best we can tell, your assumption here is false: the universe is spatially infinite.

Second, even if your assumption were true, there would be no "outside" of the universe. The universe, at least in our best current models, is a self-contained spacetime.

3. Dec 13, 2016

### Delta²

I will skip the second paragraph of your reply since it seems that it requires for me to have a certain background in Relativity to comprehend it. Just want to ask something about the 1st paragraph. Can there be fields inside a region even if their respective particle count is zero. For example can we have electromagnetic field inside a region, even if the photons(real and virtual) in the region are zero (at all times, ok well now comes in my mind an article I read here about vacuum fluctuations, not sure if it fits here). Similarly can we have the electron field there, even if there are absolutely no electrons inside the region?
Let me describe it how I have it in my mind. We have $R^4$ . The spacetime in our universe is like a bounded subset $A$ of $R^4$ that has a diameter (I ve read multiple times that our universe has a diameter (and hence its not infinite), what do they mean by that?). What exists in $R^4-A$ is the true vacuum. Is this picture that I have in my mind totally wrong?

4. Dec 14, 2016

### Staff: Mentor

Since you marked this thread as "I", you should have that background. If you don't, this thread should probably be a "B" thread (and it will be difficult to discuss the topic much further at that level).

Yes. This is also something that is part of the background that "I" level threads usually assume. Note also that even the very concept of "particle count" does not apply to all states of quantum fields. Only a very limited set of the possible field states have a useful particle interpretation.

No, our observable universe is a bounded subset with a diameter. Our observable universe is not the entire universe.

Yes. See above. (This is also something that is usually assumed as part of the "I" level background.)

5. Dec 14, 2016

### Delta²

Well sorry for the lack of background knowledge, I am not a physicist I am actually a mathematician with a master in logic (fixed my personal info here) during my undergraduate course I took some courses in classical electromagnetism and quantum mechanics and that's all I know about physics.

Ok so the only thing left to discuss is whether the total universe (sorry again if the word total is not appropriate) (observable + non observable) is finite or infinite.
In the case it is finite wouldn't still have a diameter (though we cant measure exactly or with error estimates the diameter of something we cannot observe) or the diameter is definable only for the observable universe?

6. Dec 14, 2016

### Chalnoth

This is unanswerable at present. We only know that it is significantly larger than the observable universe. How much larger is likely to be impossible to determine.

It'd only have a diameter if the universe was a hypersphere. It might be, but this is by no means clear. Either way, it's likely to be impossible to determine whether or not this is the case.

7. Dec 14, 2016

### houlahound

In relation to the vacuum the word needs defining. If you mean a place where no thing exists then there is no vacuum in physics. In fact the concept of no thing ie nothing existing somewhere is illogical.

8. Dec 14, 2016

### Delta²

yes that's exactly what I had in mind.
I am not sure about this I ll have to think about it .

9. Dec 14, 2016

### houlahound

Should be semantically obvious without bothering to physics.

10. Dec 14, 2016

### Delta²

Not so obvious. No thing has no physical existence but has conceptual existence, that is it is a concept or an idea like every other concept.

11. Dec 14, 2016

### houlahound

What region of space do concepts occupy?

12. Dec 14, 2016

### Delta²

Well I really don't know :D , this goes back to the space of ideas and idealism, but you are right concepts do not occupy a region of the physical 3D space or 4D space-time.
So, well, if the universe is finite outside of it exists just the concept of a subset of $R^4$ no thing particle or field can exist there.

13. Dec 14, 2016

### houlahound

I dont know what you mean by "outside" of the universe??? That's a logical contradiction.

14. Dec 14, 2016

### Delta²

In the physical interpretation it is a contradiction but seeing things purely mathematically, and seeing the finite universe (if the universe is finite) as a bounded subset of $R^4$ , outside of this subset exists the rest of $R^4$.

15. Dec 14, 2016

### Staff: Mentor

That's not a problem, it's just helpful to set the thread level appropriately so we know your general knowledge level. I have changed this thread to a "B".

As I said in post #2, as best we can tell, our universe is spatially infinite.

If it were spatially finite, then it would have the spatial geometry of a 3-sphere (at least in the simplest model), so it would have a diameter, yes. The data we have tells us that if this is the case (possible given the error bars in the data but most cosmologists consider it very unlikely), the diameter of the whole universe would be much, much larger than the diameter of the observable universe.

16. Dec 14, 2016

### Staff: Mentor

If the universe is finite and has the spatial geometry of a 3-sphere, then the overall topology is $S^3 \times R$. This is not a bounded subset of $R^4$.

The word "exists" is a very vague word, and we should not get sidetracked over all the possible arguments about whether and in what sense mathematical concepts "exist" if they are not physically realized. This is a physics forum, and as far as physics is concerned, the universe, whatever its geometry and topology might be, is what "exists"; an abstract mathematical object in which the geometry and topology could, mathematically, be embedded does not "exist" as far as physics is concerned.

17. Dec 14, 2016

### Delta²

One thing is a set or subset and another thing is its topology. A finite universe could be like $S^3$ which is a bounded subset of $R^4$ I am not sure why you give it a topology of $S^3xR$. I ll take a guess you probably want to say that the universe can be infinitely inflated?
Though I have my views on what conceptually exists,what physically exists, and what really exists, and that these three are not necessarily the same thing, I agree that this forum is not the place to discuss it.

18. Dec 14, 2016

### Staff: Mentor

A topology requires an underlying set, so by asking if the spacetime of the universe is a bounded subset of $R^4$ you are implicitly asking about its topology, or at least the underlying set of its topology.

No, it can't, because you are leaving out the time dimension.

Because you have to include the time dimension; the full spacetime is an $R$'s worth of $S^3$ hypersurfaces. And it's the full spacetime you have to look at if you are trying to determine whether or not it is a bounded subset of $R^4$; if you were just looking at "space", not spacetime, you would have to ask whether $S^3$ is a bounded subset of $R^3$, not $R^4$. (Which it isn't.)

19. Dec 14, 2016

### Delta²

What definition for $S^3$ physicists use in relativity? The one I know $S^3$ is by definition bounded subset of R^4.

Anyway you seem to imply that the time dimension is infinite?

20. Dec 14, 2016

### Staff: Mentor

This is one way of defining $S^3$, yes, but it's not the only way. You can define $S^3$ purely in terms of its intrinsic properties, without reference to it being a subset of anything else. The latter is the definition physicists use in relativity. An example of such a definition is that $S^3$ is the manifold obtained by "gluing" two 3-balls together by identifying their boundaries, as described here:

https://en.wikipedia.org/wiki/3-sphere#Gluing

(Note that the "fourth dimension" mentioned in this Wikipedia article is not necessary to the construction; it's just an aid to visualization.)