Quantum fluctuation and quantum mysticism

[vanhees71]

The whole course does nothing except show how vacuum fluctuations get excited by acceleration and produces particles. In the second or third video he gets out a string with a weight and shows how parametric excitations (excited modes) can be produced by shortening the string in mid-oscillation. This is meant to show how the fluctuations of the vacuum state can be excited to produce particles.

I think this discussion goes in circles. As I've already stated, the term "vacuum fluctuations" is a pretty empty phrase if not clearly defined. I think it's best described as the (perturbative) corrections due to the quantization of the electromagnetic field beyond the approximation to treat the field as classical. You cannot observe them without having a detector and thus matter (i.e., particles). So it's not really the vacuum you test.

As we also stated more than once, the Casimir effect is about the interaction of charged particles through the electromagnetic field and the quantum fluctuations of both these charges and fields (see the paper by Jaffe, I've cited). Another example, not yet observed, is the Schwinger pair production, i.e., the creation of electron-positron pairs at presence of strong electromagnetic fields. Again, there's matter and an electric field present making the observation of the quantum effects possible. Thus, I'd rather simply speak about quantum effects or quantum fluctuations rather than vacuum fluctuations.

A formal statement is utmost simple: A quantum system in its ground state let alone must stay in its ground state. There's no additional energy to make an excitation from the ground state possible, and the ground state of QFT is called "vacuum", because it's the state where no real particles and fields are present.

 

[friend]

What is said about virtual particles is that they are produced in pairs, they exists for a moment and then they recombine. And what is also said is that real particles can come about if something prevents their recombination such as acceleration due to cosmic inflation and black hole horizons, etc. If this is a fair description of the underlying math, then the most immediate consequence would be a bare particle would recombine with one of the virtual pairs created in the vacuum nearby the bare particle, leaving the virtual partner real until it recombines with one of some other virtual pair produced nearby. In this view of things, the actual real particle is continually being traded among the nearby virtual pairs being produced in the vacuum. So the position of the particle can never be specified with precision and the singularity of a point particle is avoided. None of this is speculative. It's just a restatement that virtual pairs separate and come back together with their partners or with something identical with their partners. Is this a quantum field theoretical description of the quantum mechanical wave function?

 

[A. Neumaier]

If this is a fair description of the underlying math

It is impossible to describe what you say in underlying math.

None of this is speculative.

All of this is speculative.

How do you represent the time-dependence of the virtual particle in a dynamical mathematical view of what you talk about? It is impossible. Thus your talk is empty.

 

[friend]

It is impossible to describe what you say in underlying math.
All of this is speculative.
How do you represent the time-dependence of the virtual particle in a dynamical mathematical view of what you talk about? It is impossible. Thus your talk is empty.

It seems every video lecture I've watched on graduate level QFT that shows the details of the math, the professors always end up using the virtual particle analogy. I think the ball is in your court to supply a reference to a university professor denouncing virtual particles as never appropriate to use because there is no underlying math. That is a speculative statement on your part. The lectures I've watched explain virtual particles as momentum eigenstates that are summed over the wave vectors that are always produced in pairs, k and -k. Their momentum is known exactly, so the position of each is completely unknown. They exists for so short a time that no dynamics can be written for them. They are two separate plane-waves, with opposite momentum, that exist everywhere and overlap. So just exactly where and when (dynamics) they occurs is not knowable.

 

[A. Neumaier]

virtual particles as momentum eigenstates

This is simply wrong. Virtual particles do not have associated states. See post #9 of
https://www.physicsforums.com/threads/are-virtual-particles-real-or-just-math-filler.850765/

You shouldn't learn quantum mechanics from videos only and then challenge people who published research papers in quantum mechanics. I recommend that you do first some serious study based on high quality textbooks.

Weinberg's three volumes on quantum field theory are an example of books where hardly any reference to virtual particles is made. Mentioning them is not needed since they don't have an existence except in some people's mind. As samalkhaiat pointed out, Weinberg uses virtual photons in his approximate treatment of infrared divergences. But this can also be done without virtual photons, if one uses a coherent state approach.

reference to a university professor

I am a university professor, and have given several times courses on the mathematics of quantum mechanics. If knowing this makes a difference to the facts that I am presenting you are a person more gullible that desirable for someone who wants to form a correct picture of science.

Steven Weinberg whose books I just recommended is also a university professor. He is even a Nobel prize winner.

For more references see the entries in Chapter A8: Virtual particles and vacuum fluctuations of my Theoretical Physics FAQ.

 

[friend]

Since so many other university professors are using virtual particles as at least an analogy to describe the math, then perhaps you have (or should write) an article that explains why they use them (what math they are used to explain) and why they are wrong. That would be very instructive. Thank you.

 

[A. Neumaier]

denouncing virtual particles as never appropriate to use

Here you misinterpret me; I never said that. Instead I said:

It is appropriate to use them as visual aids.
But they are treated in much of the world of nonphysicists (including many wikipedia articles) as something dynamical, which is pure science fiction.

Let me emphasize:

• It is appropriate to use them only as visual aids, not in any other way.
• What really counts is only the math.

Without properly understanding the latter, any talk about virtual particles or vacuum fluctuations is likely to be highly misleading. If a physics professor is using the words, you should look for the math behind it and try to understand that. Only if you understood the latter you can claim that you understood the professor.

 

[A. Neumaier]

perhaps you have (or should write) an article that explains why they use them (what math they are used to explain) and why they are wrong. That would be very instructive.

I had done this already and had announced it on this forum a few days ago in a thread to which you contributed. But you were apparently too lazy to study the links, or too occupied with your own ideas about the matter.

Or didn't you take me seriously because you didn't know that I was a university professor?

I won't respond to you anymore until I see clear signs that you read all I wrote about the matter and linked to in the last few days.

 

[friend]

Yes, I am trying to understand better how to use t

I had done this already and had announced it on this forum a few days ago in a thread to which you contributed. But you were apparently too lazy to study the links, or too occupied with your own ideas about the matter.

Or didn't you take me seriously because you didn't know that I was a university professor?

Probably a little of all of the above. I did look at your article, and IIRC it showed that virtual particles were synonymous with Feynman diagrams. I did not see how it related to the issue of usability for theory development. If you would be so kind, could you tell me what is so speculative or wrong about my perspective in post 32 of this thread? I really wasn't using any dynamics there, ONLY that virtual particles are identical to real particles but recombine after a short time (the most common description of them). I thought that was pretty obvious, and it's key to my understanding. Now would be a good time to clear up any misconceptions. Thank you.

 

[friend]

... then the most immediate consequence would be a bare particle would recombine with one of the virtual pairs created in the vacuum nearby the bare particle, leaving the virtual partner real until it recombines with one of some other virtual pair produced nearby. In this view of things, the actual real particle is continually being traded among the nearby virtual pairs being produced in the vacuum. ... It's just a restatement that virtual pairs separate and come back together with their partners or with something identical with their partners. ...

This goes further. It seems the accelerating expansion of space results in particle creation (by ripping apart virtual pairs, or so the story goes). Since both the disentanglement of the virtual particles and accelerated expansion exist in conjunction, it's hard to say which is the cause and which is the effect. If one must always accompany the other, then the question must be asked. Does recombination (re-entanglement) of a real particle with an antiparticle cause space contraction? Then would a bare particle recombining with one of the virtual pairs produced nearby (see above) cause space contraction close by compared to space expansion further away (as the unpaired virtual partner drifts away and is disentangled)? Could this result in the curvature we see in gravity? I've already mentioned (elsewhere) where some theorists are considering how the entanglement of virtual particles cause gravity.

 

[samalkhaiat]

Weinberg's three volumes on quantum field theory are an example of books where not a single reference to virtual particles is made. Mentioning them is not needed since they don't have an existence except in some people's mind.

How sure are you? See
Weinberg Vol. 1
13.2 Virtual Soft Photons.
13.3 Real Soft Photons.

 

[A. Neumaier]

How sure are you?

I was sure until you pointed this out. Thanks a lot. I won't make again the claim that Weinberg's book doesn't mention virtual particles, and corrected my statement.

Indeed, he uses virtual soft photons in his perturbative discussion of infrared divergences and how to get rid of them. His virtual photons appear only in calculations that lead to obviously unphysical divergences, therefore are unphysical themselves.

The mathematically preferable, virtual-particle free version of this via coherent states is not in the book, not even referenced.

 

[vanhees71]

Well, here are some references:

P. Kulish and L. Faddeev. Asymptotic conditions and infrared divergences in quantum electrodynamics. Theor. Math. Phys., 4:745, 1970.
http://dx.doi.org/10.1007/BF01066485

T. W. B. Kibble. Coherent Soft‐Photon States and Infrared Divergences. I. Classical Currents. Jour. Math. Phys., 9:315, 1968.
http://dx.doi.org/10.1063/1.1664582

T. W. B. Kibble. Coherent Soft-Photon States and Infrared Divergences. II. Mass-Shell Singularities of Green's Functions. Phys. Rev., 173:1527–1535, 1968.
http://dx.doi.org/10.1103/PhysRev.173.1527

T. W. B. Kibble. Coherent Soft-Photon States and Infrared Divergences. III. Asymptotic States and Reduction Formulas. Phys. Rev., 174:1882–1901, 1968.
http://dx.doi.org/10.1103/PhysRev.174.1882

T. W. B. Kibble. Coherent Soft-Photon States and Infrared Divergences. IV. The Scattering Operator. Phys. Rev., 175:1624, 1968.
http://dx.doi.org/10.1103/PhysRev.175.1624

N. Papanicolaou. Infrared Problems in Quantum Electrodynamics. Phys. Rept., 24:229–313, 1976.
http://dx.doi.org/10.1016/0370-1573(76)90003-X

M. Swanson. Reduction formulas for quantum electrodynamics. Phys. Rev. D, 25:2086–2102, 1982.
http://dx.doi.org/10.1103/PhysRevD.25.2086