Inflation and the false vacuum

[PeterDonis]

I was assuming that for ANY "vacuum" state the lowest energy is governed by ΔEΔt≥ħ/2.

No, this has nothing to do with zero point energy. Trying to think about ZPE in terms of the uncertainty principle doesn't work when you look at the underlying math, however much it gets described that way in pop science sources.

This paper describes a Generalized Uncertainty Principle, which might be interpreted as a changing ħ.

What in the paper leads you to this interpretation? I don't see anything at all that would justify it. The paper is using "natural" units, in which $\hbar$ does not even appear in the equations; the closest thing to it would be the Planck mass $M_p$, and everything I can see in the paper indicates that $M_p$ is assumed to be constant, which would correspond to $\hbar$ being constant.

Note also that equation (2) in the paper, which is the standard QFT expression for the vacuum energy of a scalar field, does not have anything in it corresponding to an uncertainty principle.

 

[friend]

No, this has nothing to do with zero point energy. Trying to think about ZPE in terms of the uncertainty principle doesn't work when you look at the underlying math, however much it gets described that way in pop science sources.

So are you saying that the standard deviation of a constant inflation energy is zero, right? There are no fluctuations so there is no ΔE, right?

What in the paper leads you to this interpretation? I don't see anything at all that would justify it. The paper is using "natural" units, in which $\hbar$ does not even appear in the equations; the closest thing to it would be the Planck mass $M_p$, and everything I can see in the paper indicates that $M_p$ is assumed to be constant, which would correspond to $\hbar$ being constant.

It does not directly say that ħ changes, although it puts an equation where ħ is normally placed. This strongly suggests that what we call ħ is changing.

Section 1, second sentence reads in part "through deforming the usual Heisenberg
uncertainty principle." I took the word deforming to mean to change.

Also, equation 1 has terms such as <p> and <p²>. I assumed those expectation values would change with given circumstances.

Note that in equation 3 they use a similar equation where ħ normally is in the commutation relation, again indicating what we normally would think is $\hbar$ is being replaced with an equation.

Besides, if the uncertainty principle did not change values for various situations, then what is the point of the paper?

 

[PeterDonis]

So are you saying that the standard deviation of a constant inflation energy is zero, right? There are no fluctuations so there is no ΔE, right?

No; I'm saying something much more general. $\Delta E$ in the uncertainty relation you gave refers to the standard deviation of measurements of $E$ at different times when a quantum system is in a given state. It does not refer to the standard deviation of "fluctuations" in the underlying quantum state; there are no such fluctuations. That's true of quantum states in general, not just states of the inflaton field.

it puts an equation where ħ is normally placed. This strongly suggests that what we call ħ is changing.

What equation?

"through deforming the usual Heisenberg
uncertainty principle." I took the word deforming to mean to change.

It means changing the equation that we call the "uncertainty principle". It does not mean changing $\hbar$.

equation 1 has terms such as <p> and <p2>. I assumed those expectation values would change with given circumstances.

What does that have to do with $\hbar$ changing? Expectation values can change without $\hbar$ changing, if we are taking expectation values of different operators or operators acting on different states.

in equation 3 they use a similar equation where ħ normally is in the commutation relation, again indicating what we normally would think is $\hbar$ is being replaced with an equation.

No, one equation is being replaced with another. The $i$ outside the parentheses on the RHS of equation (3) would be $i \hbar$ in conventional units. The $1$ inside the parentheses is all that would be there in the standard commutation relation. Adding the extra terms inside the parentheses changes the commutation relation, but it doesn't change $\hbar$.

if the uncertainty principle did not change values for various situations, then what is the point of the paper?

On their hypothesis, the uncertainty principle does change values. It just doesn't do so because of any change in $\hbar$. It does so because extra terms involving $M_p$ are added to the commutation relations.

 

[friend]

No; I'm saying something much more general. $\Delta E$ in the uncertainty relation you gave refers to the standard deviation of measurements of $E$ at different times when a quantum system is in a given state. It does not refer to the standard deviation of "fluctuations" in the underlying quantum state; there are no such fluctuations. That's true of quantum states in general, not just states of the inflaton field.

As I recall, there is some description where the whole universe itself came into being because of a quantum mechanical fluctuation. They say that the enormous energy of the big bang could come into existence for only a very brief moment of time, etc. So I wonder, how long did inflation take place? How much did the inflation field energy change from false vacuum to true vacuum energy? Is this comparable to the ħ we normally use?

 

[PeterDonis]

As I recall, there is some description where the whole universe itself came into being because of a quantum mechanical fluctuation.

This is another pop science description. Please, please, take some time to look at the actual theories. A significant portion of this thread has been you saying things based on misconceptions due to pop science, and me having to correct them.

how long did inflation take place?

The usual number quoted for the time of the end of inflation is something like $10^{-35}$ second, but that's not really correct because it's using the time coordinate from a notional FRW spacetime model in which inflation does not take place and there is an "initial singularity". But nobody actually uses that model.

In terms of actual inflation models, this question doesn't really have a well-defined meaning. In at least one family of such models, the "eternal inflation" models, the obvious answer is "for an infinite amount of time", but that isn't really correct; a better answer would be that there is no such thing as "time" in the usual sense in a region which is in a "false vacuum" state; "time" only has meaning in the bubbles of "true vacuum".

How much did the inflation field energy change from false vacuum to true vacuum energy?

I'd have to look up the figures for energy density just after "reheating", but it's a large number.

Is this comparable to the ħ we normally use?

$\hbar$ doesn't have units of energy or energy density. If you mean, what do we get if we multiply the energy density of the inflaton field by the time inflation lasted (and then multiply by some volume, such as the volume of the observable universe, to get something with the right units), I would expect that the answer is a number much, much larger than $\hbar$. But I'm not sure that calculation has any physical meaning. For one thing, any volume you could pick is arbitrary. For another, the time, as I said above, isn't really well-defined.

 

[friend]

This is another pop science description. Please, please, take some time to look at the actual theories. A significant portion of this thread has been you saying things based on misconceptions due to pop science, and me having to correct them.

You do realize, don't you, that these ideas are coming from experts in the field being interviewed in documentaries or in debates. Why would they mention something this specific if there were no truth to it? Although, to be fair, IIRC, they qualify their statements as "possibilities".

I guess the question is whether this change from false vacuum energy to true vacuum energy in such a brief amount of time qualifies as a "fluctuation" for which it is legitimate to ask what its standard deviation would be. Wouldn't that be the full range of the change of energy? And wouldn't the standard deviation of the time be the time it took for this change to occur? Or would the actual fluctuation be larger because the energy may have stayed level for a while before changing very much faster?

 

[PeterDonis]

You do realize, don't you, that these ideas are coming from experts in the field being interviewed in documentaries or in debates.

Sorry, pop science is still pop science. Scientists will say things in interviews, documentaries, and debates that they would never say in a peer-reviewed paper--because they know that in a peer-reviewed paper they would get called on it if they were vague or imprecise, or used ordinary language that was likely to cause misunderstandings, or used analogies that were of limited usefulness, or failed to distinguish properly between known facts, reasonable probabilities, plausible hypotheses, and way-out speculations. This is why we have rules about sources here at PF.

Why would they mention something this specific if there were no truth to it?

It's not a matter of "truth". It's that the actual physics and math that they are referring to when they say, in some pop science venue, that "the universe came into being because of a quantum mechanical fluctuation" is nothing like what those words suggest to the average lay person. Again, if they tried this in a peer-reviewed paper, they wouldn't get away with it.

I guess the question is whether this change from false vacuum energy to true vacuum energy in such a brief amount of time qualifies as a "fluctuation" for which it is legitimate to ask what its standard deviation would be.

Once again, the concept of "standard deviation" applies to a set of measurements of a quantum system in a particular state--more precisely, to a set of measurements on an ensemble of quantum systems all prepared in the same state. It doesn't even apply in the context we're discussing, because no measurements are involved, and we don't have an ensemble of universes anyway; we only have one. We just have a single quantum system undergoing a deterministic change of state from "false vacuum" to "true vacuum". So the answer to your question is no.

 

[friend]

Once again, the concept of "standard deviation" applies to a set of measurements of a quantum system in a particular state--more precisely, to a set of measurements on an ensemble of quantum systems all prepared in the same state. It doesn't even apply in the context we're discussing, because no measurements are involved, and we don't have an ensemble of universes anyway; we only have one. We just have a single quantum system undergoing a deterministic change of state from "false vacuum" to "true vacuum". So the answer to your question is no.

You seem to be implying that the whole notion of false vacuum is not subject to theoretical development because it is not measurable. I think that's being a bit too dismissive. I think it's better to say we don't have enough information to develop theory for it yet.

 

[PeterDonis]

You seem to be implying that the whole notion of false vacuum is not subject to theoretical development because it is not measurable.

I'm saying no such thing. I'm only saying that the state transition at the end of inflation, from false vacuum to true vacuum, does not involve any measurement; it's just a quantum state transition. But there are certainly observable consequences of that transition, at least according to the various inflation models. So there are ways to test the models; they just don't involve direct measurements of the state transition (which would obviously be problematic).

I think it's better to say we don't have enough information to develop theory for it yet.

We are developing theories for it--that's what the various inflation models are. And, as above, those models do make predictions about observable quantities, so they can be tested.

 

[friend]

Once again, the concept of "standard deviation" applies to a set of measurements of a quantum system in a particular state--more precisely, to a set of measurements on an ensemble of quantum systems all prepared in the same state. It doesn't even apply in the context we're discussing, because no measurements are involved, and we don't have an ensemble of universes anyway; we only have one. We just have a single quantum system undergoing a deterministic change of state from "false vacuum" to "true vacuum". So the answer to your question is no.

What is an inflaton? How does that relate to the Heisenberg Uncertainty Principle?

 

[PeterDonis]

What is an inflaton?

"Inflaton" is the term for the scalar quantum field that drives inflation while it is in the "false vacuum" state.

How does that relate to the Heisenberg Uncertainty Principle?

It doesn't.

 

[Paulibus]

Fields are mathematical constructs, useful in physics, that assign scalar, vector, tensor quantities to each and every point in spacetime. The convention has developed in quantum physics of ending the names of the quanta of fields with "-on"; for example photon, electron and so also inflaton. Not to be confused with names like mine... Paul Jackson!

 

[friend]

"Inflaton" is the term for the scalar quantum field that drives inflation while it is in the "false vacuum" state.

It doesn't.

Your replies make it sound as if the inflaton field has NOTHING to do with quantum theory. Where is the quantum nature of the inflaton field taken into account as suggested by the quanta called "inflaton"?

As I recall, the CMB is a result of quantum fluctuations in the inflaton field. And these fluctuations eventually resulted in galaxies. Were these same quantum fluctuations that formed the CMB also present in the inflaton field during inflation? Can we get some idea how large these fluctuation were at various stages of inflation from information in the CMB? Thanks.

 

[PeterDonis]

Your replies make it sound as if the inflaton field has NOTHING to do with quantum theory.

Um, you did see that I said it was a quantum field, didn't you?

You seem to think that "quantum theory" is identical with "uncertainty principle". It isn't. There is a lot in quantum theory, and particularly in quantum field theory, that has nothing whatever to do with the uncertainty principle.

Where is the quantum nature of the inflaton field taken into account as suggested by the quanta called "inflaton"?

"Inflaton" doesn't have to refer to a "quantum" (i.e., particle). Not all quantum field states have useful particle interpretations. The states of the inflaton field that are used in inflationary cosmology models don't.

As I recall, the CMB is a result of quantum fluctuations in the inflaton field.

No. The CMB itself is a result of a large number of photons being emitted when the matter of the universe "recombined" into atoms (where before it had been a plasma, with electrons and ions). The small fluctuations in the CMB (more precisely, some of them, not all) are thought to be due to tiny fluctuations in whatever existed before inflation, that led to tiny fluctuations in the inflaton field at the start of inflation, that were magnified by inflation to a point where they could leave an "imprint" in the distribution of matter and radiation during "reheating", at the end of inflation. That imprint in turn left an imprint in the CMB.

The fluctuations before and during inflation are referred to as "quantum fluctuations" because they are fluctuations in the state of a quantum field from one point in spacetime to another. But that terminology is somewhat ambiguous. The SM fields that received a large energy density at "reheating" are also quantum fields, and the fluctuations in those fields after reheating, which in turn led to fluctuations in the CMB, are also fluctuations in the state of quantum fields from one point in spacetime to another. But they aren't usually referred to as "quantum fluctuations". So you have to be careful when interpreting ordinary language descriptions of what is going on. The only way to be sure is to look at the underlying math.

Can we get some idea how large these fluctuation were at various stages of inflation from what they were in the CMB?

Inflation is supposed to have magnified them by many, many orders of magnitude. The fluctuations we currently observe in the CMB are on the order of 1 part in $10^{5}$ or less, so the fluctuations that existed before inflation would have been many, many orders of magnitude less than that. I don't have a handy quick source for an estimate of how many orders of magnitude, though.

 

[friend]

Is it possible to expand the inflaton field in terms of plane waves? What would be the amplitude of these waves? Would these plane wave count as fluctuations? What would then be ΔE and Δt?

 

[PeterDonis]

Is it possible to expand the inflaton field in terms of plane waves?

How much do you know about perturbation theory and its limitations? That is what "expanding in terms of plane waves" refers to.

 

[friend]

How much do you know about perturbation theory and its limitations? That is what "expanding in terms of plane waves" refers to.

I've read about it years ago, but I haven't had a need to use it. So my understanding would be superficial in that regard. If you would like to write a few words in summary and perhaps flag some issues with respect to my concerns here, that would very helpful. Thank you.

 

[PeterDonis]

my understanding would be superficial in that regard.

Then I strongly suggest taking some time to learn more about it.

If you would like to write a few words in summary and perhaps flag some issues with respect to my concerns here, that would very helpful.

I pointed out before that you appear to think that "quantum" equals "uncertainty principle". It doesn't. There are many quantum phenomena which have nothing to do with the uncertainty principle. The behavior of the inflaton field in inflationary cosmology is one of them.

You appear to have a similar misconception with regard to "expanding in plane waves", namely that any quantum state can be so expanded. That's not correct. There are many quantum systems whose states can't be expanded that way, and the inflaton field as it is used in inflationary cosmology is one of them.

Also, even for cases where the relevant quantum states can be expanded in plane waves--for example, in particle scattering experiments--the amplitudes of the waves are quantum probability amplitudes, i.e., complex numbers whose absolute squares give the probabilities of various measurement results; they aren't amplitudes of anything "real" that is fluctuating.

This is a subject in which pop science sources, even when written by experts in the fields, can be very misleading to non-scientists. IMO it's worth taking the time to actually work your way through a good textbook on quantum mechanics and quantum field theory. Some of the frequent posters in the Quantum Physics forum can probably give good recommendations.