Quantum fluctuations of the metastable false vacuum

[momo666]

I have been trying so hard to get some answers to a few questions I have in regard to this paper: https://arxiv.org/abs/1404.1207
I think those questions can best be summarized this way:

1) A metastable false vacuum is a field and fields are just the changing value of a parameter in spacetime.The field and the fluctuations are the same thing. The fluctuations are described by field equations. The field is the changing values of those parameters throughout space and time. Those values fluctuate, and these are the quantum fluctuations, which are in turn the field. They're all one and the same thing. The fluctuations don't occur IN the field, they ARE the field. All activity in those fields is nothing more nor less than the changing values of parameters.
2) Absent space, there is no vacuum.
2.1) Absent space, there is no metastable false vacuum
3)The above mentioned paper claims that space and time are created by quantum fluctuations of the metastable false vacuum.

This is all I've been able to gather on the matter from someone who is educated on this subject. But my main point of confusion is how can the quantum fluctuations of the metastable false vacuum create space and time if a vacuum can not exist if there is no space.

The only answers I have been able to think of are:
1)A metastable false vacuum is something drastically different than a quantum vacuum; as such it does not require space to exist.
2)When the paper says these fluctuations create space and time; that is just word play. They get a "kind" of space from another kind of space. Similar to when physicists say "the Universe came from nothing" they in fact mean something.

 

[PeterDonis]

my main point of confusion is how can the quantum fluctuations of the metastable false vacuum create space and time if a vacuum can not exist if there is no space.

The transition from metastable false vacuum to true vacuum (driven by quantum fluctuations in the underlying field) does not create all of spacetime. It creates a "bubble" of spacetime which is in the true vacuum state, inside a larger region of spacetime which is in the metastable false vacuum state.

 

[momo666]

The transition from metastable false vacuum to true vacuum (driven by quantum fluctuations in the underlying field) does not create all of spacetime. It creates a "bubble" of spacetime which is in the true vacuum state, inside a larger region of spacetime which is in the metastable false vacuum state.

Are these spacetime's the same or do they differ ? If I understood it correctly; a "bubble" of spacetime is created inside a region of spacetime that is in a state of metastable false vacuum. But that spacetime that is in a state of metastable false vacuum is the same "kind" of spacetime that we are accustomed to ? Is it infinite and does it expand ?

 

[PeterDonis]

Are these spacetime's the same or do they differ ?

What do you mean by "the same"?

If I understood it correctly; a "bubble" of spacetime is created inside a region of spacetime that is in a state of metastable false vacuum.

More precisely, a bubble of spacetime containing quantum fields in a state of true vacuum is created inside a region of spacetime containing quantum fields in a state of metastable false vacuum.

that spacetime that is in a state of metastable false vacuum is the same "kind" of spacetime that we are accustomed to ? Is it infinite and does it expand ?

In most models (including, as far as I can see, the one in the paper you linked to), the metastable false vacuum region of spacetime is infinite and is inflating, i.e., expanding exponentially. But that doesn't mean it's anything like the "kind of spacetime we are accustomed to", since a metastable false vacuum quantum field is something we have no direct experience of.

 

[momo666]

What do you mean by "the same"?

The same properties. More precisely, do we have reasons to think one is more theoretical and unsupported than the other ?

More precisely, a bubble of spacetime containing quantum fields in a state of true vacuum is created inside a region of spacetime containing quantum fields in a state of metastable false vacuum.

So they do start from space after all. I think that is where my confusion came from. I assumed the paper started from no space and no time and ended with space and time.

In most models (including, as far as I can see, the one in the paper you linked to), the metastable false vacuum region of spacetime is infinite and is inflating, i.e., expanding exponentially. But that doesn't mean it's anything like the "kind of spacetime we are accustomed to", since a metastable false vacuum quantum field is something we have no direct experience of.

Doesn't that mean there was a beginning of that expansion ? The B.G.V. theorem comes to mind.

 

[PeterDonis]

do we have reasons to think one is more theoretical and unsupported than the other ?

Only the fact that we can't directly observe the metastable false vacuum. So any model that includes it must rely on indirect evidence to be tested.

Doesn't that mean there was a beginning of that expansion ?

Not necessarily. There are models of exponentially expanding spacetimes that have no initial singularity. (de Sitter spacetime is the simplest example.)

 

[momo666]

Only the fact that we can't directly observe the metastable false vacuum. So any model that includes it must rely on indirect evidence to be tested.

If it's not too much, what indirect evidence do the said models rely on ?

Not necessarily. There are models of exponentially expanding spacetimes that have no initial singularity. (de Sitter spacetime is the simplest example.)

Do you know why they used an expanding spacetime for this paper ? I mean, aren't they back to the same question they tried to answer ? Is there a subtler difference that I am missing ?
Also, does the paper rely on a particular model of spacetime or can the de Sitter spacetime be used with the same result ?

And I think I missed one basic point. You said that as far as you can see, the metastable false vacuum spacetime is infinite and is inflating. But if it is infinite, doesn't that mean that it had no beginning ? Isn't the B.G.V. theorem only about finite spacetimes that expand ?

Apologizes for the barrage of questions.

 

[PeterDonis]

what indirect evidence do the said models rely on ?

Not much right now, they are all speculative at this point. Looking for possible ways to test these and many other models of what might have happened before the Big Bang is an active area of research.

Do you know why they used an expanding spacetime for this paper ?

I'm not sure. I'm not even sure that their model of the metastable false vacuum is as simple as a single "expanding spacetime". They are using a fundamentally quantum model, where you don't have a single spacetime geometry, but a quantum superposition of many different spacetime geometries. (Even that is only a heuristic description. Look up the Wheeler-deWitt equation if you want more background. There is a lot of literature on this general technique of modeling, and it's still an open area of research.)

if it is infinite, doesn't that mean that it had no beginning ?

Not necessarily. By "infinite" I meant spatially infinite; there are possible spatially infinite models that have initial singularities.

 

[momo666]

Not necessarily. By "infinite" I meant spatially infinite; there are possible spatially infinite models that have initial singularities.

I feel like I am again missing an obvious point. Doesn't spatially infinite mean a space that is infinite in extent ? How can something that is spatially infinite have an initial singularity. Running back the clock of a spatially infinite space should never get you to a starting point right ?

 

[PeterDonis]

Doesn't spatially infinite mean a space that is infinite in extent ?

It means infinite in three dimensions. But spacetime has four dimensions. Spatially infinite says nothing about extent in the fourth dimension.

How can something that is spatially infinite have an initial singularity.

Because it is not infinite in the fourth dimension, only in three.

 

[momo666]

It means infinite in three dimensions. But spacetime has four dimensions. Spatially infinite says nothing about extent in the fourth dimension.

Because it is not infinite in the fourth dimension, only in three.

That is kind of mind boggling. Can you by any chance help me a bit on this ? I can't wrap my head around it. So you can have a space that is infinite in three dimensions but not infinite in time. I still can't conceptualize a way for the said space to end in a singularity. Wouldn't the said space ending in a singularity mean that "when" the singularity expanded; it instantly expanded into an infinite space ? It sounds crazy but that is what I think of when I hear you describe it. After all, if the singularity expanded into a finite space, since the forth dimension is finite, it would mean that the space should be finite as well since a finite amount of time can be clocked back along with the initial finite space.

Does that make sense ? I think it doesn't.

 

[PeterDonis]

I still can't conceptualize a way for the said space to end in a singularity.

The singularity isn't actually part of the spacetime; it's a limit point that isn't an actual event. Think of an open half-plane--"open" meaning it doesn't contain the line that is the boundary of the half-plane. The boundary line is the singularity, which isn't part of the open half-plane, it's just a limit. Add two more space dimensions and you have the model of the universe I am describing.

The only somewhat subtle point here is that the singularity is said to have "zero size". But that's a sloppy way of putting it. The correct way of putting is that, along any timelike worldline, the limiting value of the scale factor as the singularity is approached is zero. But that, in itself, does not tell you whether or not the limits taken along different timelike worldlines all end up at "the same point". It's perfectly consistent to have a model in which they don't, topologically speaking, and that's the model I described above. (Note that this is actually true even in the case of a spatially finite universe.)

Wouldn't the said space ending in a singularity mean that "when" the singularity expanded; it instantly expanded into an infinite space ?

No. The singularity didn't "expand" into anything. We are talking about a 4-dimensional spacetime geometry; it just has a particular "shape". It doesn't "change with time"--"time" is just one of the four dimensions of the geometry. And "expanding" has to do with the scale factor, which is only one aspect of the "shape".

 

[momo666]

Thank you for the answers so far, they have been very enlightening. I have two more if it's not too much to ask.

1) You said that as far as you can see the spacetime is infinite and is inflating in the paper I've shown. Can you tell if it also has an initial singularity ?
2) Is a singularity an actual "thing" ? Or is it just a mathematical artifact that tells us we can't look "beyond" the singularity ? It is not that clear to me how should I look at it.

 

[PeterDonis]

You said that as far as you can see the spacetime is infinite and is inflating in the paper I've shown. Can you tell if it also has an initial singularity ?

I don't think so, but the paper doesn't appear to have a definite statement one way or the other.

Is a singularity an actual "thing" ? Or is it just a mathematical artifact that tells us we can't look "beyond" the singularity ?

It's a property that certain models have. Whether that property corresponds to something "real" in the reality that the models are modeling, or is just a model artifact that has no "real" counterpart, is an open question.

 

[momo666]

I just thought of something that is related to this topic. Is there anything in physics about spaceless/timeless things ? I know for example that Hawking proposed a model that converts one spatial dimension into time but he still has space.
I've asked someone who is educated on this subject once and he told me that the closest we can get to that is a "simple mechanism" via Heisenberg uncertainty principle. But if Heisenberg uncertainty principle describes fields and fields cannot exist if there is no space, then it would seem this does not answer my question.

 

[PeterDonis]

Is there anything in physics about spaceless/timeless things ?

You might take a look at loop quantum gravity. It's an attempt to build a model that doesn't have space and time in it as a fundamental thing; in this model, what we call "spacetime" is an emergent property.

 

[nikkkom]

1) A metastable false vacuum is a field and fields are just the changing value of a parameter in spacetime. The field and the fluctuations are the same thing.

Actually, no. A (false or true) vacuum is a configuration of fields which is at a local minimum of potential. This condition requires that fields are not fluctuating, they are constant. They are not necessarily zero, but they are constant.

(Not any configuration of constant fields is a vacuum, though. If there would be a volume of space where Higgs field is set to constant zero instead of constant 246 GeV, this would not be a vacuum - it is not at a local minimum of energy, it will immediately "decay" into a very large number of Higgs bosons which in turn would decay into more typical particles).

The fluctuations are described by field equations. The field is the changing values of those parameters throughout space and time. Those values fluctuate, and these are the quantum fluctuations, which are in turn the field.

Same mistake. Field equations describe all configurations of fields allowed by a theory, fluctuating as well as non-fluctuating.

The fluctuations don't occur IN the field, they ARE the field.

No. Fluctuations are in the field. For example, an electron is a small fluctuation of electron field. A photon is a small fluctuation of the photon field. Etc.

 

[momo666]

It's a property that certain models have. Whether that property corresponds to something "real" in the reality that the models are modeling, or is just a model artifact that has no "real" counterpart, is an open question.

I just thought of a question regarding this. If indeed the scenario where the singularity corresponds to something real is the correct one, would then my claim that the singularity expands still fail ?

And two more questions on the main subject if I may.
1)Am I correct in thinking that bubble B of spacetime that forms in spacetime A has its own timeline ? That is to say, if spacetime A is infinite and eternal, it still makes sense to say that bubble B of spacetime had a first moment of time.
2)Are there any reasons why light from spacetime A would not enter spacetime bubble B ?

Actually, no. A (false or true) vacuum is a configuration of fields which is at a local minimum of potential. This condition requires that fields are not fluctuating, they are constant. They are not necessarily zero, but they are constant.

Quick question regarding this subject. Does the Heisenberg uncertainty principle allow for a field to stay constant at a certain value, including zero ?

 

[PeterDonis]

If indeed the scenario where the singularity corresponds to something real is the correct one, would then my claim that the singularity expands still fail ?

Yes. If the singularity is real, it is a particular event or set of events in spacetime. It doesn't expand for the same reason that any set of events in spacetime doesn't expand; because spacetime is a 4-dimensional geometry that doesn't change, it just is.

if spacetime A is infinite and eternal, it still makes sense to say that bubble B of spacetime had a first moment of time.

It might or it might not. It depends on the model.

Are there any reasons why light from spacetime A would not enter spacetime bubble B ?

Yes--because the boundary of spacetime bubble B is expanding too fast for even light headed into bubble B to cross it. More precisely, the boundary of bubble B, at least in the models I have seen, is a causal boundary--a horizon similar to the event horizon of a black hole, with spacetime A corresponding to the "interior" of the horizon (the side from which escape is impossible).

 

[momo666]

Yes. If the singularity is real, it is a particular event or set of events in spacetime. It doesn't expand for the same reason that any set of events in spacetime doesn't expand; because spacetime is a 4-dimensional geometry that doesn't change, it just is.

I always thought that by the time the model gets to the singularity, space and time already cease to exist. I think that is a fundamental misunderstanding I have. I thought the singularity, in the case that it corresponds to something real, is a timeless/spaceless thing which upon "expanding" gives rise to space and time. Something like an egg cracking and "letting spacetime out".

I have one additional question in regard to different timelines. Suppose I instantly teleported from bubble B of spacetime into spacetime A and I stayed there 1 billion years. If I then teleport back into spacetime B, how much time would have passed if any ?

 

[PeterDonis]

I thought the singularity, in the case that it corresponds to something real, is a timeless/spaceless thing which upon "expanding" gives rise to space and time. Something like an egg cracking and "letting spacetime out".

As you have probably gathered, this is not a good way to think of the singularity.

Suppose I instantly teleported from bubble B of spacetime into spacetime A

This is not physically possible.

 

[momo666]

This is not physically possible.

Is it possible to ignore that though ? I knew that is not possible but I was interested in the thought experiment. I need an answer to that so I can have a better visualization on the matter at hand. I don't know how should I look at this whole issue and these type of thought experiments might give me the answer.

 

[PeterDonis]

I knew that is not possible but I was interested in the thought experiment.

A thought experiment is meaningless if it is based on impossible premises.

 

[momo666]

A thought experiment is meaningless if it is based on impossible premises.

What about creating a wormhole from the bubble of spacetime B to somewhere in spacetime A ? Could that work as a possible premise for my thought experiment ?

 

[PeterDonis]

What about creating a wormhole from the bubble of spacetime B to somewhere in spacetime A ?

Nobody knows how to create a wormhole, but there are known spacetime geometries that describe wormholes--see for example here:

https://en.wikipedia.org/wiki/Wormhole#Metrics

But how time would "hook up" through the wormhole between B and A would depend on where you chose to "put" the wormhole mouths in the two spacetimes; there is no way to extract a unique prediction for that from the laws of physics. So a thought experiment based on this premise would not tell you anything you didn't put into it in the first place.

The more general answer to the question I think you are asking is that there is no well-defined relationship between "time" in the two spacetimes A and B.

 

[momo666]

Not necessarily. There are models of exponentially expanding spacetimes that have no initial singularity. (de Sitter spacetime is the simplest example.)

Yes--because the boundary of spacetime bubble B is expanding too fast for even light headed into bubble B to cross it. More precisely, the boundary of bubble B, at least in the models I have seen, is a causal boundary--a horizon similar to the event horizon of a black hole, with spacetime A corresponding to the "interior" of the horizon (the side from which escape is impossible).

I come back to this point for a clarification. I failed to raise this obvious point earlier. What about spacetimes that are not exponentially expanding ? In such a case, are there any reasons why light from spacetime A would not enter spacetime bubble B ?
And one further clarification on the application of the B.G.V. theorem. If memory serves, Alexander Vilenkin said that if quantum fluctuations are not wild enough to invalidate classical spacetime, the theorem still holds. This makes it sound like the theorem applies to pretty much any expanding spacetime. Someone pointed out to me though that the theorem does not imply a beginning of spacetime, merely that inflationary physics is not enough to provide us with a full picture of the Universe.

Also, what does "classical spacetime" mean ? I ask this because Alexander Vilenkin says that invalidating this kind of spacetime might have implications on our very notions of causality.

 

[PeterDonis]

What about spacetimes that are not exponentially expanding ?

In that case there is no such thing as the "bubble" we have been discussing.

In such a case, are there any reasons why light from spacetime A would not enter spacetime bubble B ?

Yes, because there are no "bubbles" in this case. See above.

the application of the B.G.V. theorem...the theorem does not imply a beginning of spacetime, merely that inflationary physics is not enough to provide us with a full picture of the Universe

That's my understanding; but AFAIK the applicability of the theorem to whatever model actually ends up describing our actual universe is still an open question.

what does "classical spacetime" mean ?

It means spacetime as modeled by GR, as a 4-dimensional manifold with a locally Lorentzian metric. When he talks about quantum fluctuations and whether or not they make classical spacetime "invalid", he is talking about whether spacetime modeled as a 4-dimensional manifold is exact or only an approximation, and if the latter, at what point does the approximation break down. This is also an open question--it is one of the key questions that the various proposed theories of quantum gravity are trying to address.

Alexander Vilenkin says that invalidating this kind of spacetime might have implications on our very notions of causality.

Whether this will end up being an issue is also an open question.

 

[momo666]

In that case there is no such thing as the "bubble" we have been discussing.

Is it possible for an infinite and non-expanding spacetime to start expanding ? Is it reasonable for me to assume that if it can do that, only regions of the said spacetime will start expanding and not the "whole" thing ? What mechanisms have been proposed to facilitate this expansion ? I assume the de-Sitter space is an example of an infinite spacetime that stars expanding for some reason and produces these bubbles ?

 

[PeterDonis]

Is it possible for an infinite and non-expanding spacetime to start expanding ?

The question doesn't make sense. Spacetime doesn't change; it is a 4-dimensional geometric object that already contains everything that happens in the entire history of the universe. So it can't "start" doing something.

What mechanisms have been proposed to facilitate this expansion ?

Expansion by itself doesn't need a "mechanism"; it's just inertia--things were moving apart in the past so they keep moving apart.

Accelerated expansion, the kind that is seen in de Sitter spacetime, is due to the presence of a positive cosmological constant. There is no other "mechanism".

I assume the de-Sitter space is an example of an infinite spacetime that stars expanding for some reason and produces these bubbles ?

No; de Sitter spacetime extends infinitely into the past and the future, and is "expanding" everywhere (when that term is properly defined--see below). The "bubbles" are not produced by spacetime itself, but by some kind of field in the spacetime that undergoes a transition.

To clarify the term "expanding": what this actually means, in technical terms, is that we can find a family of timelike geodesics whose expansion scalar is positive. Since this is an "A" level thread, you should know what that means; but if you don't, see here for a start:

https://en.wikipedia.org/wiki/Congr...atical_decomposition_of_a_timelike_congruence

 

[momo666]

I forgot to ask but is the Universe created in this paper a zero-energy one ? And do we know if our Universe is a zero-energy one or is that question still unanswered ?

 

[PeterDonis]

I forgot to ask but is the Universe created in this paper a zero-energy one ? And do we know if our Universe is a zero-energy one or is that question still unanswered ?

The concept of "the total energy of the universe" is not well-defined, so these questions are unanswerable.

 

[momo666]

The concept of "the total energy of the universe" is not well-defined, so these questions are unanswerable.

Does the paper rely on such concepts though ? Event if it is not well-defined, it could be clear if it does indeed invoke it right ?

 

[PeterDonis]

Does the paper rely on such concepts though ?

No, because the paper's authors know that the concept is not well-defined. You are the only one bringing up the concept.

 

[Thuring]

Within the theory of Eternal Inflation, it is said that a quantum fluctuation of some sort at some "point in the meta-stable false vacuum space" caused the false vacuum to decay out to a lower vacuum energy and form bubbles with matter and photons. Though each bubble may have different constants and parameters (like G, h, and c), the implication is that each false vacuum (including the so called meta-space) has at least some common physics such as quantum fluctuations, expansion (perhaps), space, vacuum energy, time, and apparently the uncertainty principle.

Is this right? Are there "intrinsic laws" ?

Also, I don't recall anything in the lectures I've seen considers any space "infinite"; just sometimes growing really fast and really big, but not infinite. I doubt infinity actually exists in nature, only as a concept. But, I'm often wrong. (

 

[Thuring]

I saw just yesterday an interview with Lawrence Krauss, the cosmologist, say that he considers the universe to have overall zero energy. His reasoning was that the expansion does work. Also, as vacuum energy is added, so is gravity added which is a negative energy. Not sure I fully understand.