Non-Perturbative QFT without Virtual Particles

[rogerl]

I think everyone is agreed that the maths does not change, neither does what the theory predicts about any experimental outcome. The disagreement is only on how to name the maths.

If the maths do not change supposed virtual particles were really there versus they were not. Then it is possible to assume they exist?? So if the math is the same, We may as well say it is possible that virtual particles were really there in the vacuum appearing thanks to Heisenberg Uncertainty Principle where they can borrow the energy from the vacuum and appear in short time?? But then some folks say Lattice QFT that doesn't use perturbation theory don't require the multivariage integrals. Here supposed the virtual particles were really there, how do you integrate it into Lattice QFT math??

 

[atyy]

If the maths do not change supposed virtual particles were really there versus they were not. Then it is possible to assume they exist?? So if the math is the same, We may as well say it is possible that virtual particles were really there in the vacuum appearing thanks to Heisenberg Uncertainty Principle where they can borrow the energy from the vacuum and appear in short time?? But then some folks say Lattice QFT that doesn't use perturbation theory don't require the multivariage integrals. Here supposed the virtual particles were really there, how do you integrate it into Lattice QFT math??

There are many ways of calculating the same thing.

 

[rogerl]

There are many ways of calculating the same thing.

So how do you use Lattice QFT without perturbation to describe virtual particles (supposed for the sake of arguments these were real in that they could borrow the energy from the vacuum and appear in short time thanks to Heisenberg Uncertainty Principle).

 

[atyy]

So how do you use Lattice QFT without perturbation to describe virtual particles (supposed for the sake of arguments these were real in that they could borrow the energy from the vacuum and appear in short time thanks to Heisenberg Uncertainty Principle).

The point is that there is an underlying theory.

Lattice methods and virtual particles are two different ways of calculating what experimental predictions the underlying theory makes.

As long as both methods proceed correctly from the underlying theory, they will make the same experimental predictions.

 

[rogerl]

The point is that there is an underlying theory.

Lattice methods and virtual particles are two different ways of calculating what experimental predictions the underlying theory makes.

As long as both methods proceed correctly from the underlying theory, they will make the same experimental predictions.

Does this underlying theory involves virtual particles?
If you meant lattice methods don't involve virtual particles and it's true virtual particles are just side effect of our perturbation method. How come they have to propose Supersymmetry to solve the Hierarchy Problem. In Hierarchy Problem, the Higgs can have Planck mass because of quantum contributions. So what they do is propose that the virtual particles of Supersymmetric particles can cancel the very large quantum contributions in the Hierarchy Problem. Why do they have to take drastic measure and radical idea just to get rid of the large contribution if virtual particles are just multivariate integrals. Why didn't they just go to lattice methods to solve it?

 

[Vanadium 50]

But Arnold Neimaier who is the top Particle Physicist in the world

Don't be snotty.

It's clear you have a lot to learn. It would behoove you to be nicer to the people who are spending their time trying to teach you.

 

[rogerl]

Don't be snotty.

It's clear you have a lot to learn. It would behoove you to be nicer to the people who are spending their time trying to teach you.

What. But I really think A. Neumaier is one of the top physicists in the world. Just look at his website with very complex mathematics and he is writing a book. So I'm just admiring him and consider his opinion important because of his multidisciplinary background in mathematics and physics. That's why I'm basing the facts about virtual particles on what he has to say and whether he admit they may still be real in spite of being just multivariate integrals because he is an expert in his department. My latest question on him is how physics have to take radical ideas like Supersymmetry just to deal with the virtual particles problems and why not just propose lattice QFT.

 

[atyy]

Does this underlying theory involves virtual particles?
If you meant lattice methods don't involve virtual particles and it's true virtual particles are just side effect of our perturbation method. How come they have to propose Supersymmetry to solve the Hierarchy Problem. In Hierarchy Problem, the Higgs can have Planck mass because of quantum contributions. So what they do is propose that the virtual particles of Supersymmetric particles can cancel the very large quantum contributions in the Hierarchy Problem. Why do they have to take drastic measure and radical idea just to get rid of the large contribution if virtual particles are just multivariate integrals. Why didn't they just go to lattice methods to solve it?

That's an interesting question. I don't know. My understanding is that the underlying theory is given by special relativity, quantum mechanics, Wilsonian renormalization, and the standard model Lagrangian. I would guess that the fine tuning problem is a heuristic argument based on Wilsonian renormalization, so it should have a counterpart in a lattice language.

Also, is there such a thing as non-perturbative QED? Unless a QFT is asymptotically free or safe, isn't it by definition only perturbatively defined? According to http://www.sciencedirect.com/science?_ob=ArticleURL&_udi=B6TVC-47319XP-1C5&_user=108429&_coverDate=03%2F09%2F1992&_rdoc=1&_fmt=high&_orig=gateway&_origin=gateway&_sort=d&_docanchor=&view=c&_acct=C000059713&_version=1&_urlVersion=0&_userid=108429&md5=02d57ae15e181b9774e884147a99780a&searchtype=a , QED is likely not asymptotically safe. The only question then is how we choose to name the terms in a particular perturbation expansion.

 

[A. Neumaier]

Also, is there such a thing as non-perturbative QED? Unless a QFT is asymptotically free or safe, isn't it by definition only perturbatively defined? According to http://www.sciencedirect.com/science?_ob=ArticleURL&_udi=B6TVC-47319XP-1C5&_user=108429&_coverDate=03%2F09%2F1992&_rdoc=1&_fmt=high&_orig=gateway&_origin=gateway&_sort=d&_docanchor=&view=c&_acct=C000059713&_version=1&_urlVersion=0&_userid=108429&md5=02d57ae15e181b9774e884147a99780a&searchtype=a , QED is likely not asymptotically safe.

This problem is completely open, and the opinion of the physics community on this is divided. Most theorist think that QED does not exist as a nonperturbative theory, but they have no hard arguments - the renormalization group argument leading to the Landau pole and the lack of nontrivial fixed points is itself of a perturbative nature.

To settle the case, one would either need a nonperturbative construction for QED, or better foundations for QFT so that one can make the notion of ''some theory not existing'' more precise.

 

[A. Neumaier]

What. But I really think A. Neumaier is one of the top physicists in the world. Just look at his website with very complex mathematics and he is writing a book. So I'm just admiring him and consider his opinion important because of his multidisciplinary background in mathematics and physics.

My multidisciplinary background in mathematics and physics doesn't make me a top physicist. Only 10% of my publications are in physics, and none is in quantum field theory. moreover, all my highly cited papers are in mathematics, not in physics.

 

[rogerl]

This problem is completely open, and the opinion of the physics community on this is divided. Most theorist think that QED does not exist as a nonperturbative theory, but they have no hard arguments - the renormalization group argument leading to the Landau pole and the lack of nontrivial fixed points is itself of a perturbative nature.

To settle the case, one would either need a nonperturbative construction for QED, or better foundations for QFT so that one can make the notion of ''some theory not existing'' more precise.

If you say lattice methods don't involve virtual particles and it's true virtual particles are just side effect of our perturbation method. How come they have to propose Supersymmetry to solve the Hierarchy Problem?? In Hierarchy Problem, the Higgs can have Planck mass because of quantum contributions. So what they do is propose that the virtual particles of Supersymmetric particles can cancel the very large quantum contributions in the Hierarchy Problem. Why do they have to take drastic measure and radical idea just to get rid of the large contribution if virtual particles are just multivariate integrals. Why didn't they just go to lattice methods to solve it?

Unless it's possible virtual particles were really fundamental entities in the vacuum.

 

[A. Neumaier]

If you say lattice methods don't involve virtual particles and it's true virtual particles are just side effect of our perturbation method. How come they have to propose Supersymmetry to solve the Hierarchy Problem?? .

The hierarchy problem is not linked to virtual particles. It is the problem of how to avoid fine-tuning in the coupling constants in order to reproduce vastly different scales observed phenomenologically. http://en.wikipedia.org/wiki/Hierarchy_problem

As everywhere, virtual particles enter the picture only when discussing the problem in perturbation theory, looking at particular diagrams.

 

[rogerl]

The hierarchy problem is not linked to virtual particles. It is the problem of how to avoid fine-tuning in the coupling constants in order to reproduce vastly different scales observed phenomenologically. http://en.wikipedia.org/wiki/Hierarchy_problem

As everywhere, virtual particles enter the picture only when discussing the problem in perturbation theory, looking at particular diagrams.

But Lisa Randall said it has everything to do with virtual particles. Page 252 of Warped Passages states:

"The problem for the hierarchy is that the contribution to the Higgs particle's mass from virtual particles with extremely high mass will be about as big as the Planck scale mass, which is ten million billion times greater than the Higgs particle mass we want - the one that will give the right weak scale mass and elementary particle masses"

page 265:

"In a supersymmetric theory, the virtual Standard Model particles aren't the only virtual particles that contributes to the Higgs particle's mass. Virtual superpartners do, too. And because of the remarkable properties of supersymmetry, the two kinds of contributions always add up to zero. The quantum contributions of virtual fermions and bosons to the Higgs particle's mass are related so precisely that the large contributions made by either bosons or fermions individually are guaranteed to cancel each other out. The value of the fermion's contribution is negative and exactly cancels the bosons' contribution."

You see. Randall said virtual particles have everything to do with it.

Virtual particles is the heart and soul of particle physicists. Are you 100% certain they don't really exist? By exist is meant they could borrow the energy from the vacuum and appear in very short time thanks to Heisenberg Uncertainty Principle.. this distinguishes it from pure mathematic artifacts.

 

[A. Neumaier]

You see. Randall said virtual particles have everything to do with it.

Virtual particles is the heart and soul of particle physicists.

Only in as far as perturbation theory (including individual Feynman diagrams) is taken for reality. I have higher standards for existence. Figurative talk does not yet make things real.

Are you 100% certain they don't really exist? By exist is meant they could borrow the energy from the vacuum and appear in very short time thanks to Heisenberg Uncertainty Principle.. this distinguishes it from pure mathematic artifacts.

These properties are wishful thinking, associated to virtual particle to make them sound intelligible.

But nobody ever has written down equations for how a virtual particle could borrow energy from the vacuum, and in which sense it exists for a short time. This would require to have a dynamical entity associated with virtual particles that changes in time according to some evolution equation such as Schroedinger's.

The existence of virtual particles is therefore no more than virtual. Real particles have a state and a dynamical law that virtual particles lack.

 

[alxm]

But Lisa Randall said it has everything to do with virtual particles. Page 252 of Warped Passages states:

That's a popular-scientific book. There are many popular-scientific books which describe virtual particles as if they're real things. I don't know if they're necessarily taking an ontological position with it. It can also be just a more interesting way of visualizing or describing a perturbation calculation. Saying you're adding up a bunch of terms doesn't sound as fun as interpreting those terms as virtual particle contributions and so on. But nothing you quoted there actually said virtual particles were "real" or spoke of them as if they were more than mathematical abstractions. It talks about "virtual particle contributions", which means the contribution from that term in the perturbation series.

Nobody's disputing you can describe those terms as virtual particle contributions. But that in-itself doesn't make them real. Since I just mentioned it in another thread, you have Goldstone and Hugenholtz diagrams in many-body perturbation theory. In those diagrams the vertices are graphical representations of the contributions to the perturbation series from various electron-pair interactions. But as far as I know, nobody's yet decided to interpret that as meaning electrons actually interact two-at-a-time.

 

[Lapidus]

Lisa Randall has more to say about 'virtual' particles in her book

Virtual particles, a consequence of quantum mechanics, are strange, ghostly twins of actual particles. They pop in and out of existence, lasting only the barest moment. Virtual particles have the same interactions and the same charges as physical particles, but they have energies that look wrong. For example, a particle moving very fast clearly carries a lot of energy. A virtual particle, on the other hand, can have enormous speed but no energy. In fact, virtual particles can have any energy that is different from the energy carried by the corresponding true physical particle. If it had the same energy, it would be a real particle, not a virtual one.

Virtual particles are a strange feature of quantum field theory that you have to include to make the right predictions.

So how can these apparently impossible particles exist? A virtual particle with its borrowed energy could not exist were it not for the uncertainty principle, which allows particles to have the wrong energy so long as they do so for such a short time that it would never be measured.

The uncertainty principle tells us that it would take infinitely long to measure energy (or mass) with infinite precision, and that the longer a particle lasts, the more accurate our measurement of its energy can be. But if the particle is short-lived and its energy cannot possibly be determined with infinite precision, the energy can temporarily deviate from that of a true long-lived particle. In fact, because of the uncertainty principle, particles will do whatever they can get away with for as long as they can. Virtual particles have no scruples and misbehave whenever no one is watching.

You can think of the vacuum as a reservoir of energy—virtual particles are particles that emerge from the vacuum, temporarily borrowing some of its energy. They exist only fleetingly and then disappear back into the vacuum, taking with them the energy they borrowed. That energy might return to its place of origin, or it might be transferred to
particles in some other location.

The quantum mechanical vacuum is a busy place. Even though the vacuum is by definition empty, quantum effects give rise to a teeming sea of virtual particles and antiparticles that appear and disappear— even though no stable, long-lasting particles are present. All particle-antiparticle pairs can in principle be produced, albeit only for very short visits, too short to be seen directly. But however brief their existence, we care about virtual particles because
they nonetheless leave their imprint on the interactions of long-lived particles.

Virtual particles have measurable consequences because they influence the interactions of the real physical particles that enter and leave an interaction region. During its brief span of its existence, a virtual particle can travel between real particles before disappearing and repaying its energy debt to the vacuum. Virtual particles thereby act as intermediaries that influence the interactions of long-lived stable particles.

 

[alxm]

Well, I suppose that settles whether or not she considers them 'real' or not.
Nevertheless, it's still an opinion/interpretation rather than hard physical fact. I'm also doubtful it represents popular opinion among physicists.
(not that I think Randall is speaking for anyone other than herself, although I haven't read the book, so.. )

 

[Lapidus]

Nevertheless, it's still an opinion/interpretation rather than hard physical fact. I'm also doubtful it represents popular opinion among physicists.

Not sure about the popular opinion among physicists on this. Maybe we should take a poll!

 

[A. Neumaier]

Virtual particles, a consequence of quantum mechanics, are strange, ghostly twins of actual particles. They pop in and out of existence, lasting only the barest moment. Virtual particles have the same interactions and the same charges as physical particles, but they have energies that look wrong. For example, a particle moving very fast clearly carries a lot of energy. A virtual particle, on the other hand, can have enormous speed but no energy.

You can think of the vacuum as a reservoir of energy—virtual particles are particles that emerge from the vacuum, temporarily borrowing some of its energy. They exist only fleetingly and then disappear back into the vacuum, taking with them the energy they borrowed. That energy might return to its place of origin, or it might be transferred to
particles in some other location.

The quantum mechanical vacuum is a busy place. Even though the vacuum is by definition empty, quantum effects give rise to a teeming sea of virtual particles and antiparticles that appear and disappear

Look in the literature at a proof of any of these statements, or even a more precise description of what is meant with them, and you won't find anything. This sort of discourse is good for story-telling, but for nothing else.

 

[Vanadium 50]

I think one needs to distinguish between a popularization and a textbook.

 

[rogerl]

Look in the literature at a proof of any of these statements, or even a more precise description of what is meant with them, and you won't find anything. This sort of discourse is good for story-telling, but for nothing else.

Let's say Virtual Particles are only used for story telling and really just mathematical artifacts of perturbation theory. How about quantum fluctuations? It is said that "Quantum fluctuations may have been very important in the origin of the structure of the universe: according to the model of inflation the ones that existed when inflation began were amplified and formed the seed of all current observed structure". But quantum fluctuations are related to virtual particles. If quantum fluctuations are also mathematical artifacts of perturbation theory. How come they have observable effect in that they form the seeds of galaxies, nebalae, etc.?!

Without quantum fluctuations (and maybe virtual particles). We may not even exist. So we owe them our lives and must regard them to the highest degrees.

 

[Demystifier]

How about quantum fluctuations?

They are real, or at least much more real than virtual particles.

But quantum fluctuations are related to virtual particles.

Not directly. In principle, and sometimes even in practice, you can calculate the fluctuations without using virtual particles.

If quantum fluctuations are also mathematical artifacts of perturbation theory.

Quantum fluctuations are NOT mathematical artifacts of perturbation theory.

 

[A. Neumaier]

Let's say Virtual Particles are only used for story telling and really just mathematical artifacts of perturbation theory. How about quantum fluctuations?

Fluctuations have a much better ontological status than virtual particles. Their properties are indeed computable nonperturbatively, hence are properties of the system under study and (unlike virtual particles) not of the approximation method used.

But they are not what conventional story-telling claims they are: They are not changes in time. Instead, quantum fluctuations describe uncertainties about what one gets when one tries to measure something. It's the fluctuations in the measurements when one repeats them under identical conditions - not fluctuations in what is measured.

Thus quantum fluctuations reflect something about the limits of measurement processes, not something about rapid changes in time.

It is said that "Quantum fluctuations may have been very important in the origin of the structure of the universe: according to the model of inflation the ones that existed when inflation began were amplified and formed the seed of all current observed structure". But quantum fluctuations are related to virtual particles. If quantum fluctuations are also mathematical artifacts of perturbation theory. How come they have observable effect in that they form the seeds of galaxies, nebalae, etc.?!

They don't form a seed in any dynamical sense (as a real seed - that changes in due time into a real plant).

More in the entry ''Does the vacuum fluctuate?'' in Chapter A7 of my theoretical physics FAQ at http://arnold-neumaier.at/physfaq/physics-faq.html#vacfluc

 

[dm4b]

But they are not what conventional story-telling claims they are: They are not changes in time. Instead, quantum fluctuations describe uncertainties about what one gets when one tries to measure something. It's the fluctuations in the measurements when one repeats them under identical conditions - not fluctuations in what is measured.

Thus quantum fluctuations reflect something about the limits of measurement processes, not something about rapid changes in time.

This way of explaining quantum fluctuations seems to make them dependent upon someone measuring them.

Do quantum fluctuations exist, if nobody makes a measurement?

 

[A. Neumaier]

This way of explaining quantum fluctuations seems to make them dependent upon someone measuring them.

Do quantum fluctuations exist, if nobody makes a measurement?

They are properties of the system, whether or not somebody measures it. In this sense ithey exist independent of measurement, like a tree exists no matter whether someone looks at it.

But the meaning of the quantum fluctuation of a quantity Q is not the value of a measurement of Q but the intrinsic uncertainty of the measurement result in any attempt to measure Q. (There may be additional uncertainty due to limitations of the particular equipment used - but this is not a property of the system but of the equipment.)

 

[dm4b]

They are properties of the system, whether or not somebody measures it. In this sense ithey exist independent of measurement, like a tree exists no matter whether someone looks at it.

But the meaning of the quantum fluctuation of a quantity Q is not the value of a measurement of Q but the intrinsic uncertainty of the measurement result in any attempt to measure Q. (There may be additional uncertainty due to limitations of the particular equipment used - but this is not a property of the system but of the equipment.)

Is this different than say measuring the position of the electron in a hydrogen atom? We'll get a different position each time we measure but, after many repeated measurements, on identically prepared systems, we'll notice that we obtain the probability distribution predicted by the Schrodinger Equation.

Is this essentially what's going on with quantum fluctuations?

Or, is it something more akin to the HUP? At small scales in size, the energy will fluctuate rapidly.

I guess, put simply, what the heck is a quantum fluctuation, exactly? ;-)

I guess I always took it as more of the latter. And, since in SR E=m, those fluctuations in energy can give rise to particles (the dreaded virtual particles mentioned above)?

 

[A. Neumaier]

Is this different than say measuring the position of the electron in a hydrogen atom? We'll get a different position each time we measure but, after many repeated measurements, on identically prepared systems, we'll notice that we obtain the probability distribution predicted by the Schrodinger Equation.

Is this essentially what's going on with quantum fluctuations?

Yes, precisely. Please read the FAQ entry mentioned in posting #93

Or, is it something more akin to the HUP? At small scales in size, the energy will fluctuate rapidly.

I guess, put simply, what the heck is a quantum fluctuation, exactly? ;-)

I guess I always took it as more of the latter.

It is _not_ the latter.
Fluctuations are neither objects nor energy but system properties, and have _nothing_ to do with changes in time.

What a quantum fluctuation is, exactly, is spelled out in the FAQ. The FAQ exists because I don't want to explain the same thing over and over again. So please read it before asking further questions.

 

[dm4b]

Hi A. Neumaier,

I read your FAQ and overall it seemed like a good description. I specifically liked your analogy with the 1D Harmonic Oscillator., which was helpful. I've read several areas of your FAQ, even the parts on Christianity/Religion, much of which I found interesting - thanks.

But, I am still having the following problems with the vacuum fluctutations.

(1) I'm not sure that everybody out there agrees with the description in your FAQ. It seems some say the HUP goes beyond just an observer measurement. That a particle cannot come to rest, because then you would have a perfectly defined position AND momentum, and that cannot be, whether somebody measures it or not. Hence, this gives rise to a ground state, or a Zero-Point Energy (ZPE). (I guess another way to look at it, is that the entity in question is not just a particle, but also partly a wave, which can never be assigned to a particular point in space). This seems to also be the common explanation of why you can never reach absolute zero. Do you feel this viewpoint is incorrect? If so, how?

(2) A non-trivial zero-point energy is established, as mentioned in your FAQ. Since E=m, what stops the creation of particles from this ZPE - whether real or virtual? And, if vacuum fluctuations are not a process in time, then wouldn't the ZPE have a constant value over space and time?

(3) I'm having a hard time picturing vacuum fluctuations having a physical effect on anything. Specifically, under inflation, aren't they supposed to provide the "seeds" for galaxy formations. How can something inherit to a measurement process, which presumably should include an observer, be able to kick off galaxy formation, when presumably no observers were around? Also, if the above is correct, and the ZPE is a constant value in all space, how can it "seed" anything within a particular spot in space?

Thanks for any feedback you can give on this.

 

[A. Neumaier]

(1) I'm not sure that everybody out there agrees with the description in your FAQ.

I am sure that not everybody out there agrees with the description in your FAQ. The FAQ is there to correct poor opinion. if everyone agreed, there were no need to discuss many of these questions.

It seems some say the HUP goes beyond just an observer measurement.

The Heisenberg uncertainty principle (HUP) just states that the product of the variances of p and q is bounded below by a small number. It doesn't say what the variances represent.

The general consensus is that the variance represents an ensemble average - i.e., the result of a statistics over many independent measurements on identically prepared systems.

In order to take the variance as a time average one needs to invoke an ergodic theorem stating that the time average equals the ensemble average. However such an ergodic theorem makes sense only semiclassically, and is valid only for very simple systems. Most systems are far from ergodic.

That a particle cannot come to rest, because then you would have a perfectly defined position AND momentum, and that cannot be, whether somebody measures it or not.

Here you assume a semiclassical picture. One cannot measure whether a microscopic particle is at rest - and apart from such a measurement the statement about the rest of a particle is meaningless.

Hence, this gives rise to a ground state, or a Zero-Point Energy (ZPE).

Only energy differences matter; the zero-point energy is completely spurious.

(I guess another way to look at it, is that the entity in question is not just a particle, but also partly a wave, which can never be assigned to a particular point in space).

This is another way to say that talking of rest is meaningless. When is a wave at rest?
But waves have real energy, not an unobservable ZPE.

This seems to also be the common explanation of why you can never reach absolute zero. Do you feel this viewpoint is incorrect? If so, how?

This is the explanation in classical mechanics. In quantum mechanics, zero absolute temperature is equivalent to being in the ground state, and this is very well possible for a single hydrogen atom, but impossible for a macroscopic body.

(2) A non-trivial zero-point energy is established, as mentioned in your FAQ.

Where did I mention this?

Since E=m, what stops the creation of particles from this ZPE - whether real or virtual?

Only energy differences can be exploited for the creation of anything.

(3) I'm having a hard time picturing vacuum fluctuations having a physical effect on anything.

Vacuum fluctuations cause nothing, hence have no effect. Their presence in the equations has some observable consequences.

Specifically, under inflation, aren't they supposed to provide the "seeds" for galaxy formations.

To discuss this, please provide a reference that says more specifically how vacuum fluctuations provide the "seeds" for galaxy formation. (In the present vagueness this is just another instance of modern mystic story telling.)

 

[dm4b]

Only energy differences matter; the zero-point energy is completely spurious.

I'm not sure this is true in GR, is it? The presence of energy alone has potential gravitational effects, does it not? Isn't that the whole cosmological constant problem?

Where did I mention this?

Here:

"On the other hand, the fact that sigma^2 resp. sigma^2(x) and similar
expectations do not vanish shows in nontrivial physics, for example,
a nontrivial zero-point energy."

Only energy differences can be exploited for the creation of anything.

okay, that makes sense.

Vacuum fluctuations cause nothing, hence have no effect. Their presence in the equations has some observable consequences.

How can something that causes nothing and has no effect, have observable consequences? That makes no sense to me.

To discuss this, please provide a reference that says more specifically how vacuum fluctuations provide the "seeds" for galaxy formation. (In the present vagueness this is just another instance of modern mystic story telling.)

C'mon, a reference? This is so commonly stated you must have heard it before.

If you think it's a myth, please provide details on the real mechanism on how this really works. Otherwise, folks have no reason to not believe in the "myth".

 

[A. Neumaier]

I'm not sure this is true in GR, is it? The presence of energy alone has potential gravitational effects, does it not? Isn't that the whole cosmological constant problem?

A zero-point energy is not energy present. The cosmological constant problem has a different origin.
It is a nontrivial term in the action.

Here:

"On the other hand, the fact that sigma^2 resp. sigma^2(x) and similar
expectations do not vanish shows in nontrivial physics, for example,
a nontrivial zero-point energy."

Yes. The context is that one compares the energy with another energy in perturbation theory, and since the reference energy also makes physical sense one has an energy difference. Nevertheless, since only one of the two systems is realized, this energy difference is not physically utilizable.

How can something that causes nothing and has no effect, have observable consequences? That makes no sense to me.

Immediately after the above quote, I wrote:
''The zero-point energy can often, but
not always be neglected. It can be utilized for the derivation of
observable consequences. One of them is the Casimir effect.
But the Casimir effect can also be derived without reference to
the zero-point energy.''
The last sentence shows why the zero-point energy cannot be regarded as a cause, though one can use it to derive the effect.

C'mon, a reference? This is so commonly stated you must have heard it before.

I want to have an online reference as a clear staring point for a discussion.

 

[dm4b]

A zero-point energy is not energy present. The cosmological constant problem has a different origin.
It is a nontrivial term in the action.

Well, Sean Carrol would seem to disagree with this. The nontrivial term in the action, which contains the Cosmological Constant, can be related to a vacuum energy density. In fact, see page 172, of his GR text, where he does this by decomposing the energy-momentum tensor into a matter piece and a vacuum peice. The action is then defined and he goes on to claim the terms "Cosmological Constant" and "Vacuum Energy" are essentially interchangeable.

Also, to parapharse other parts of the text on page 171:

"A characteristic feature of general relativity is that the source for the gravitational field is the entire energy-momentum tensor. In nongravitational physics only changes in energy from one state to another are measurable ... In gravitation, however, the actual value of the energy matters, not just the differences between states".

Is there any reason to expect the vacuum energy is zero? Quantum fluctuations change the zero-point energy from our classical expectation.

More on all this below.

Immediately after the above quote, I wrote:
''The zero-point energy can often, but not always be neglected. It can be utilized for the derivation of observable consequences. One of them is the Casimir effect. But the Casimir effect can also be derived without reference to the zero-point energy.''

Ah, okay, I see where you're coming from now. I agree up to this extent - that is, for the Casimir Effect.

However, as mentioned in the paper (http://lanl.arxiv.org/abs/hep-th/0503158) by R. L. Jaffe, "The object of this paper is to point out that the Casimir effect gives no more (or less) support for the “reality” of the vacuum energy of fluctuating quantum fields than any other one-loop effect in quantum electrodynamics ... ".

In other words, the analysis on the Casimir effect, to date, does not definitively determine whether the vacuum energy is real or not. It only shows that the ZPE has been incorrectly claimed as the cause of the Casimir Effect, when in actuality it is the Van Der Waals force between the plates.

The last sentence shows why the zero-point energy cannot be regarded as a cause, though one can use it to derive the effect.

Although apparently true for the Casmir effect, we don't know if this is true, in general.

Once again, as stated by R. L. Jaffe in his conclusion: "The deeper question remains: Do the zero point energies of quantum fields contribute to the energy density of the vacuum and ... to the cosmological constant?" Also, see Carroll above.

The jury is still out on this one, I believe. It seems to me, it may be a thornier one to deal with than the Casimir Effect, as well.

I want to have an online reference as a clear staring point for a discussion

Well, how about we just go back to Carrol again, which has the most sophisticated treatment on this topic that I have read, which sure isn't saying much. Indeed, Carrol says it is beyond the scope of his GR book, which is no surprise. Admittedly, I never fully understood what he was talking about anyhow.

On page 371, he mentions that that there are fluctuations in the inflation field phi, corresponding to a Gibbons-Hawking temperature, which is the tempature of a vacuum state of an accelerating Universe. Paraphrasing Carrol again: "Since the potential is by hypothesis nearly flat, the fluctuations in phi lead to small fluctuations in energy density ... Inflation therefore produces density perturbations ... which may be the origin of the CMB temperature anistropies and the large-scale sturcture in galaxies we observe today."

These fluctuations sure sound like they have a dynamical effect, but I sure don't understand the details. So, what am I missing?

 

[A. Neumaier]

Well, Sean Carrol would seem to disagree with this. The nontrivial term in the action, which contains the Cosmological Constant, can be related to a vacuum energy density. In fact, see page 172, of his GR text, where he does this by decomposing the energy-momentum tensor into a matter piece and a vacuum peice. The action is then defined and he goes on to claim the terms "Cosmological Constant" and "Vacuum Energy" are essentially interchangeable.

Also, to parapharse other parts of the text on page 171:

"A characteristic feature of general relativity is that the source for the gravitational field is the entire energy-momentum tensor. In nongravitational physics only changes in energy from one state to another are measurable ... In gravitation, however, the actual value of the energy matters, not just the differences between states".

Is there any reason to expect the vacuum energy is zero? Quantum fluctuations change the zero-point energy from our classical expectation.
[...]
Once again, as stated by R. L. Jaffe in his conclusion: "The deeper question remains: Do the zero point energies of quantum fields contribute to the energy density of the vacuum and ... to the cosmological constant?" Also, see Carroll above.
[...]
Well, how about we just go back to Carrol again, which has the most sophisticated treatment on this topic that I have read, which sure isn't saying much. Indeed, Carrol says it is beyond the scope of his GR book, which is no surprise. Admittedly, I never fully understood what he was talking about anyhow.

On page 371, he mentions that that there are fluctuations in the inflation field phi, corresponding to a Gibbons-Hawking temperature, which is the tempature of a vacuum state of an accelerating Universe. Paraphrasing Carrol again: "Since the potential is by hypothesis nearly flat, the fluctuations in phi lead to small fluctuations in energy density ... Inflation therefore produces density perturbations ... which may be the origin of the CMB temperature anistropies and the large-scale sturcture in galaxies we observe today."

These fluctuations sure sound like they have a dynamical effect, but I sure don't understand the details. So, what am I missing?

I am not an expert in quantum gravity, so maybe I am missing something. In any case, what I said is true for all observationally verified QM and QFT, including the the standard model.

I believe that in case of QG, the resolution of the problem is in the renormalization procedure. There is a difference between the energy-momentum tensor and the Hamiltonian. The latter is _formally_ the integral of the e/m tensor over all space. But if the e/m tensor contains an additive constant then this contribute infinity to the Hamiltonian. This infinity is removed by renormalization, where normal ordering moves the zero point energy to exactly zero.

I don't have the book by Carrol, and I need formulas, not mere words, to discuss the issue further. So if you are interested in my analysis of the situation, please provide a public online source that we can take as a formal starting point.

 

[dm4b]

I don't have the book by Carrol, and I need formulas, not mere words, to discuss the issue further. So if you are interested in my analysis of the situation, please provide a public online source that we can take as a formal starting point.

Yes, I would be interested. I believe Carroll's notes are online. I'll see if I can't find them later (or some other source) and will post back if I do.