What is the true vacuum and does it exist in our expanding universe?

[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 can't 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).

 

[PeterDonis]

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).

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.

is it possible to make a region of space that has absolutely zero gravitational field?

"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).

Is the perfect true vacuum in the "hypothetical" region of space that the universe hasn't expanded yet there.

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

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?

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.

 

[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?

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.

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?

 

[PeterDonis]

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.

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).

Can there be fields inside a region even if their respective particle count is zero.

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.

The spacetime in our universe is like a bounded subset $A$ of $R^4$ that has a diameter

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

Is this picture that I have in my mind totally wrong?

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

 

[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 can't measure exactly or with error estimates the diameter of something we cannot observe) or the diameter is definable only for the observable universe?

 

[Chalnoth]

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.

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.

In the case it is finite wouldn't still have a diameter (though we can't measure exactly or with error estimates the diameter of something we cannot observe) or the diameter is definable only for the observable universe?

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.

 

[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.

 

[Delta2]

If you mean a place where no thing exists then there is no vacuum in physics

yes that's exactly what I had in mind.

In fact the concept of no thing ie nothing existing somewhere is illogical.

I am not sure about this I ll have to think about it .

 

[houlahound]

Should be semantically obvious without bothering to physics.

 

[Delta2]

Should be semantically obvious without bothering to physics.

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.

 

[houlahound]

When we refer to a vacuum I would expect it to be a region of space

What region of space do concepts occupy?

 

[Delta2]

What region of space do concepts occupy?

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.

 

[houlahound]

I don't know what you mean by "outside" of the universe? That's a logical contradiction.

 

[Delta2]

I don't know what you mean by "outside" of the universe? That's a logical contradiction.

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 $R^4$.

 

[PeterDonis]

sorry for the lack of background knowledge

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".

whether the total universe (sorry again if the word total is not appropriate) (observable + non observable) is finite or infinite.

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

In the case it is finite wouldn't still have a diameter

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.

 

[PeterDonis]

seeing the finite universe (if the universe is finite) as a bounded subset of $R^4$

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 $R^4$.

outside of this subset exists the rest

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.

 

[Delta2]

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 $R^4$.

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?

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.

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.

 

[PeterDonis]

One thing is a set or subset and another thing is its topology.

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.

A finite universe could be like $S^3$

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

I am not sure why you give it a topology of $S^3 \times R$.

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.)

 

[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?

 

[PeterDonis]

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

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.)

 

[Chronos]

In set theoretic terms the question can be phased - is set A [nothing] a member of set B [all things]? The answer, unequivocally, is $$\mu$$

 

[houlahound]

Can you expand for us non set theorists, what the hell is mu? Sorry can't write symbols.

 

[Chronos]

It was intended in the Zen sense, where mu means nothingness, or lack of ponderable properties. In this context, the answer is undefined.

 

[Chalnoth]

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 can't shield the gravitational field there is no way to construct the perfect "true" vacuum as I say in the title of the thread.

In quantum mechanics, the vacuum is the state where all quantum fields are in their ground state.

In General Relativity, the vacuum is any region of space-time where the stress-energy tensor is zero. That space-time may still be curved by masses elsewhere, a cosmological constant, or gravitational waves.

These two descriptions are similar, but we don't yet know the correct model of quantum gravity. General Relativity has no component of gravity which contributes to the vacuum state (only matter contributes), and quantum mechanics doesn't (yet) know how to describe gravity at all, so gravity isn't a part of this either.

One possible description is that a quantum theory of gravity might have the "vacuum" being a region of space-time where there is no stress-energy tensor and also no gravity waves (as the gravity waves would be excitations of the graviton field). But without a theory of quantum graivty, it's hard to say what the best way to define the vacuum would be in that case.

 

[Mohd Abdullah]

Is space devoid of anything (including quantum fields, etc.) equal to absolute nothing?

 

[Drakkith]

Is space devoid of anything (including quantum fields, etc.) equal to absolute nothing?

If that's what you define "absolute nothing" to be, then yes. Unfortunately there is no universally accepted answer that I can give you.

 

[Delta2]

Is space devoid of anything (including quantum fields, etc.) equal to absolute nothing?

If I have understand correctly what it has been written here, then we can't deprive space-time completely of the fields, the best we can get is the fields to be in the so called "ground" state.

So I was wondering what it can exist "outside" the space-time of our universe. The only scientifically accepted answer to this is https://en.wikipedia.org/wiki/Multiverse I am afraid.

 

[PeterDonis]

I was wondering what it can exist "outside" the space-time of our universe.

All of the serious attempts at modeling a multiverse have quantum fields or the equivalent in the part that is "outside" our universe. So taking the multiverse into account doesn't change the fundamental answer to the question being posed in this thread.

 

[Mohd Abdullah]

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.

Sorry, what do you mean exactly by self-contained spacetime? Do you mean Universe, including beyond the observable Universe, is indeed finite and limited?

I think what people mean by finite but unbounded Universe is the Universe is indeed finite and has a shape of a sphere. This kind of Universe is not actually unbounded or infinite, it just means that if an imaginary object keep moving straight, actually it doesn't move straight instead it is moving around a sphere like an ant moving incessantly on a ball. Finite but unbounded Universe seems only possible in math but I'm not sure if it applies to reality.

If the Universe is spatially infinite, then it is not finite but unbounded.

 

[PeterDonis]

what do you mean exactly by self-contained spacetime?

I mean that you don't need to postulate anything else in order to have the model be consistent and complete.

Do you mean Universe, including beyond the observable Universe, is indeed finite and limited?

No. An FRW spacetime that was spatially infinite would also be a self-contained spacetime, because you wouldn't need to postulate anything outside it for it to be a consistent and complete model.

I think what people mean by finite but unbounded Universe is the Universe is indeed finite and has a shape of a sphere.

Spatially it has the shape of a 3-sphere, yes. This is often called a "closed universe" in the literature. Each spatial slice has a finite volume, but there is no boundary (just as the surface of the Earth has a finite area, but has no boundary).

Finite but unbounded Universe seems only possible in math but I'm not sure if it applies to reality.

Such a model is still possible given our current measurements, but it is considered highly unlikely.

If the Universe is spatially infinite, then it is not finite but unbounded.

Correct.

 

[Mohd Abdullah]

I think, only the observable Universe can be said as finite but unbounded. So, infinite Universe (that's it, if an imaginary object keep moving straight forever it will never return to its starting point) is more likely than the finite yet unbounded Universe.

Sometimes, if I want to show that space is indeed "something" rather than "nothing", I will make an assumption by imagining a lone object without anything else. So, hypothetically this lone object would be fully static because motion is relative. But as these terms, "static" and "motion" are both relational concepts, then in reality we can't really say that this hypothetical lone object is static. But nevermind, for the sake of this imaginary assumption, the lone object would be static. This is sometimes begging the question, why makes this lone object to remains stationary in its position?

 

[PeterDonis]

I think, only the observable Universe can be said as finite but unbounded.

This is not correct. Our observable universe is finite because the age of the universe is finite, so light has only had a finite time to get to us from distant parts of the universe. But it is not "unbounded" in the sense in which that term is normally used--it is not a 3-sphere. It's an ordinary 3-volume that is part of something larger--we just don't know whether the something larger is an infinite space or a finite but unbounded space like a 3-sphere.

infinite Universe (that's it, if an imaginary object keep moving straight forever it will never return to its starting point) is more likely than the finite yet unbounded Universe.

This is true, but not for the reason you give. It's true because the model in which the universe is spatially infinite (and spatially flat) is the best fit to the data we have.

The rest of your post is personal speculation.

 

[PeterDonis]

This topic has been sufficiently discussed. Thread closed.