Quantum fluctuation and quantum mysticism

[David Maroto]

Hello,

searching for information about debunking quantum mysticism I stumbled upon this article: http://www.csicop.org/si/show/quantum_quackery/ , where one of the main arguments seems to be based on quantum fluctuation to explain Einstein´s famous "spooky effect on a distance". You can check it after Figure 2 (which you should have a look on to understand the next):

"On the left, an electron (e-) is moving along a well-defined path. An electron-positron pair (e-e+) is produced at point C by a quantum fluctuation of the vacuum, allowed by the uncertainty principle. The positron annihilates the original electron at point A while the electron from the pair continues past point B. Since all electrons are indistinguishable, it appears as if the original electron has jumped instantaneously from A to B."

My question now is: isn´t that quantum fluctuation of the vacuum not another "weak point" when trying to debunk quantum mysticism? I´m a telecommunication engineer with, sadly, not much quantum physics knowledge, but this "out-of-the-blue" fluctuation seems also pretty spooky to me. Am I missing something?

Thank you and cheers,
David

 

[DrChinese]

Welcome to PhysicsForums, David!

Trying to comprehend quantum vacuum fluctuations through a diagram (such as the one you reference) is going to be difficult. There are a lot of issues with the diagram, I don't even consider it something I would point to for any discussion of quantum non-locality anyway.

Please keep in mind that it is generally accepted that electrons do not possesses simultaneously well defined momentum and position. So a diagram showing such is going to have problems anyway. So this would not be the thing to reference for your strongest arguments against quacks. How about instead considering QM's experimental record?

And by the way, I strongly object to something stated in the article you reference. Victor says "...an objective reality, ... is consistent with all observations." This viewpoint is generally rejected (although not by all interpretations of QM). I would agree with Victor that consciousness does not seem to be a factor (as far as anyone knows, but this is technically unprovable at this point).

 

[bhobba]

"On the left, an electron (e-) is moving along a well-defined path. An electron-positron pair (e-e+) is produced at point C by a quantum fluctuation of the vacuum, allowed by the uncertainty principle. The positron annihilates the original electron at point A while the electron from the pair continues past point B. Since all electrons are indistinguishable, it appears as if the original electron has jumped instantaneously from A to B."

Be very careful of anything you read using Quantum Field Theory outside a QFT textbook. Its likely wrong. The above is an example. In QFT actual particles are not produced by quantum fluctuations despite what you may have read. There are many, sometimes heated, threads discussing this so no need to go into the details.

BTW there is no 'mysticism' in QM. Conciousness being involved is not true, or rather its a very fringe and weird interpretation these says because the original reason for its introduction is no longer valid without going into the history of it.

Since you are a telecommunication engineer the following gives the modern view based on reasonable assumptions showing QM is not quite as weird as some make out:
http://arxiv.org/pdf/quant-ph/0101012.pdf

Thanks
Bill

 

[stevendaryl]

BTW there is no 'mysticism' in QM.

I interpreted the phrase "quantum mysticism" to mean various wacky beliefs that the adherents claim is supported by quantum mechanics, (for example, stuff by Deepak Chopra).

 

[jfizzix]

Be very careful of anything you read using Quantum Field Theory outside a QFT textbook. Its likely wrong. The above is an example. In QFT actual particles are not produced by quantum fluctuations despite what you may have read. There are many, sometimes heated, threads discussing this so no need to go into the details.

It's worth noting that in the scientific literature, the production of entangled pairs of particles can be seeded by vacuum fluctuations.
In quantum nonlinear optics, spontaneous parametric down-conversion is a process where one high energy (pump) photon is destroyed, and in that same instant, two low energy daughter photons are created. It is widely accepted that fluctuations in the electromagnetic quantum vacuum are responsible for seeding this process. These photons don't come from nowhere, though (the pump photon was destroyed).

 

[bhobba]

It is widely accepted that fluctuations in the electromagnetic quantum vacuum are responsible for seeding this process. These photons don't come from nowhere, though (the pump photon was destroyed).

It is also widely accepted that Lattice Field Theory, which has no virtual particles, hence no quantum vacuum fluctuations, reproduces all the predictions of QED. Hence it can't be the cause.

Spontaneous emission is generally said to be caused by vacuum fluctuations, and indeed the textbooks I have studied explain it that way. However my understanding is this isn't really true - the real reason is due to the interaction with the quantum EM field electrons in atoms are not in a stationary state.

I would appreciate someone more knowledgeable than me confirming this, as well as exactly what's going on with the pump process mentioned. I suspect like spontaneous emission vacuum fluctuations are not the real reason. If it is we are in deep do do because it would mean lattice field theory is wrong.

Thanks
Bill

 

[jfizzix]

I suspect like spontaneous emission vacuum fluctuations are not the real reason. If it is we are in deep do do because it would mean lattice field theory is wrong.

Could it not just be that both mathematical formulations give the same results, like the Heisenberg vs Schrodinger picture?

As far as I know, the concept of vacuum fluctuations help us not just make sense of spontaneous emission, but in how spontaneous emission can be altered by placing the emitter in differently shaped cavities even with no photons inside beforehand. If lattice QED can do this as well, then they could just be complementary descriptions of the same observable phenomena.

 

[Mentz114]

It is also widely accepted that Lattice Field Theory, which has no virtual particles, hence no quantum vacuum fluctuations, reproduces all the predictions of QED. Hence it can't be the cause.

Spontaneous emission is generally said to be caused by vacuum fluctuations, and indeed the textbooks I have studied explain it that way. However my understanding is this isn't really true - the real reason is due to the interaction with the quantum EM field electrons in atoms are not in a stationary state.

I would appreciate someone more knowledgeable than me confirming this, as well as exactly what's going on with the pump process mentioned. I suspect like spontaneous emission vacuum fluctuations are not the real reason. If it is we are in deep do do because it would mean lattice field theory is wrong.

Thanks
Bill

How does the lattice theory deal with the Lamb effect ? The virtual photons are possibly artifacts of the perturbative process here, so I assume they don't appear.

For those who are not familiar with the Lamb shift there is a (semi-fictitious ?) account here

https://en.wikipedia.org/wiki/Lamb_shift

 

[bhobba]

Could it not just be that both mathematical formulations give the same results, like the Heisenberg vs Schrodinger picture?.

IMHO quite likely.

Thanks
Bill

 

[bhobba]

How does the lattice theory deal with the Lamb effect

Well lattice theory is done on a computer so getting intuitive pictures such as in perturbation theory isn't really possible. As far as I know it predicts exactly the same results.

Thanks
Bill

 

[Mentz114]

Well lattice theory is done on a computer so getting intuitive pictures such as in perturbation theory isn't really possible. As far as I know it predicts exactly the same results.

Thanks
Bill

Thank you. I expect lattice theory must give the same result as the one-loop expansion or someone would have noticed.

The shift is attributed to a virtual photon created by a vacuum fluctuation neither of which exists in the lattice theory. Do you have a reference where I can read how it's done ?

 

[Demystifier]

the following gives the modern view based on reasonable assumptions showing QM is not quite as weird as some make out:
http://arxiv.org/pdf/quant-ph/0101012.pdf

Even the author of this paper does not like it so much as you do.
Perhaps you could write a simplified review of arguments in that paper? It might be very useful for a wider community and you might be a right person to do that.

 

[bhobba]

Even the author of this paper does not like it so much as you do.

It was a real eye opener to me. The first time I had seen QM derived from reasonable assumptions. It led me to investigate the whole generalised probability model approach, which in itself is very interesting, not just for QM but statistical modelling in general, which is something that always fascinated me in even in my undergrad days.

The other interesting connection is white noise theory with Rigged Hilbert Spaces and Hida Distributions:
http://www.asiapacific-mathnews.com/04/0404/0010_0013.pdf

Perhaps you could write a simplified review of arguments in that paper? It might be very useful for a wider community and you might be a right person to do that.

Good idea. Let me think about it. I was thinking of one about Rigged Hilbert Spaces - maybe after that.

Thanks
Bill

 

[bhobba]

The shift is attributed to a virtual photon created by a vacuum fluctuation neither of which exists in the lattice theory. Do you have a reference where I can read how it's done ?

I don't quite follow what you mean by how the shift is done. It simple. When you do calculations in lattice theory virtual particles do not appear.
http://arnold-neumaier.at/physfaq/topics/quantum_fields.html
'Depending on the ways the quantum field is analyzed, one may ascribe parts of the fields to certain particles. In schemes that do so, these particles are thought to be free (although they cannot be, which results in renormalization problems); they are called virtual particles, and correspond to the internal lines of corresponding Feynman diagrams. They are off-shell, and different schemes for analyzing the quantum field during a collision assign different portions of the field to different and differently interacting virtual particles. Nonperturbative schemes such as lattice gauge theory do not permit such an analysis in terms of virtual particles. Thus the presence and meaning of virtual particles is scheme-dependent, and one cannot ascribe any objective reality to them.'

Thanks
Bill

 

[Demystifier]

@bhobba

First, something is wrong with your quotation in #14. I never said that.

Second, what do you think about my proposal for you in #12?

 

[A. Neumaier]

vacuum fluctuations are not the real reason

The interpretation of vacuum fluctuations as dynamical events (via virtual particles) is spurious. It is a misunderstanding based on the ambiguity of the word ''cause''. See Chapter A8: ''Virtual particles and vacuum fluctuations'' of my theoretical physics FAQ.

Vacuum fluctuations exist as mathematical entities (even in lattice models, where virtual particles are absent); but in quantum mechanics they do not have a dynamical interpretation as something happening. When someone reasonably respectable says that ''vacuum fluctuations are the cause of the Casimir effect'' (which I take as example since it is a loose formulation based on a clear fact) they mean that ''vacuum fluctuations appear in the mathematical derivation of formulas for the Casimir effect that can be empirically checked'' (which is the fact), and not that ''because a vacuum fluctuation happened, the Casimir effect is observable'' (which is pure fiction). The fact is based on a logical explanation (called ''cause''), while the fiction is based on a dynamical explanation (also called ''cause'').

In case of the Casimir effect (as for most other events ''caused'' by vacuum fluctuations) there are alternative derivations that are not based on vacuum fluctuations, proving that the latter cannot be the ''real cause'' of the effect.

 

[bhobba]

@bhobba
First, something is wrong with your quotation in #14. I never said that.

No idea how that happened. Now fixed.

Second, what do you think about my proposal for you in #12?

Good idea. Will think about it.

Thanks
Bill

 

[vanhees71]

In case of the Casimir effect (as for most other events ''caused'' by vacuum fluctuations) there are alternative derivations that are not based on vacuum fluctuations, proving that the latter cannot be the ''real cause'' of the effect.

In fact the usual hand-waving derivation is the limit of perfect conductivity, i.e., a strong-interaction limit. The Casimir effect is not due to the "vacuum fluctuations" but due to the presence of charges and charge fluctuations.

R. L. Jaffe. The Casimir effect and the quantum vacuum. Phys. Rev. D, 72:021301, 2005.
http://dx.doi.org/10.1103/PhysRevD.72.021301
http://arxiv.org/abs/hep-th/0503158

As was stressed by you and many people in this thread already, "vacuum fluctuations" are a notion of perturbation theory. I'd rather call them "higher-order corrections" or as also often used notion, because QED was the first relativistic QFT in the early days of quantum theory, "radiation corrections".

If you could evaluate the hydrogen spectrum exactly by lattice theory, you'd just get the exact spectrum without corrections, and that's it. If you calculate the energy levels exactly there are no more corrections to them ;-)).

 

[A. Neumaier]

"vacuum fluctuations" are a notion of perturbation theory

No. What you say is the case for virtual particles only. But vacuum fluctuations address the fact that the variance of an operator in the vacuum state need not be zero, and that fields may have nontrivial correlations in the vacuum state. This is independent of perturbation theory.

 

[vanhees71]

No. What you say is the case for virtual particles only. But vacuum fluctuations address the fact that the variance of an operator in the vacuum state need not be zero, and that fields may have nontrivial correlations in the vacuum state. This is independent of perturbation theory.

Ok, that's superficially true, if you mean that the expectation value $\langle \Omega \phi^2(x)| \Omega \rangle \neq 0$ for a real Klein-Gordon field $\phi$ as the most simple example. I'm not so sure which sense to make of this, however. If you evaluate this for the free-field case you get a divergent result, and you have to give some sense to this quantity in terms of observables. The usual way is to normal order quantities like this, e.g., when defining quantities like the total energy (Hamiltonian). There this makes a lot of sense, since you want to define the energy of the ground state to be 0, and then count all energy values from this ground-state energy, which then necessarily are positive. However, how do you justify normal order the above field operator when calculating the standard deviation of the field in the vacuum state? To clarify this, one would have to relate it to some observable quantity, but it's not clear to me, what should be such an observation? The same is of course also true for the electromagnetic field. There, however you have to use a gauge-invariant property, i.e., $\vec{E}^2$ or $\vec{B}^2$, which are related to the electromagnetic field energy, whose density is $\mathcal{H}=\frac{1}{2} (\vec{E}^2+\vec{B}^2)$. Again, you have trouble with the vacuum expectation value and then normal order it with the same argument as given above for the KG field. Now, what's left of "vacuum fluctuations" now? Either you say the variance of the field vanishes in the vacuum state by invoking normal ordering (and you have the same trouble when calculating any other higher (even) moment, so that also for them you have to regularize the expression) or you find another way to define the meaningless diverging expectation value, but also then you need some physical interpretation to make sense out of it, and that can only be given in terms of some observable (it's clear that renormalized perturbative QFT is well defined, because the renormalization prescription is based on defining quantities like masses and couplings from observations, i.e., within a given renormalization scheme you fit the renormalized parameters to appropriate cross sections of scattering processes, i.e., you are referring to observables of the theory, namely S-matrix elements). But what's an observable proving "vacuum fluctuations"? I've never seen any clear physis definition of such an observable, and usually that's why you read about "vacuum fluctuations" in popular science books rather than true QFT textbooks.

So let me put it differently. To observe vacuum fluctuations you need a detector, but then you don't have a vacuum anymore. So pure vacuum fluctuations are a non-observable thing and thus fictitious. The paradigmatic example, which started modern QFT and renormalization theory in 1947/48 is the Lamb shift of the hydrogen atom. Another is the anomalous magnetic moment of the electron, which is also measured at high accuracy, but these are of course all concerning observations on a non-vacuum state, and you can interpret them in terms of perturbative QED as the deviation from the result of the approximation that the electromagnetic field is unquantized. For the hydrogen levels you solve the problem of an electron in an electrostatic field (usually one uses a Coulombfield despite the fact that the proton has a non-trivial form factor already in this semiclassical level). Deviations from the radiative corrections of QED are then called Lamb shift, und if you wish that can be interpreted of the fact that the electromagnetic field has quantum fluctuations (due to the uncertainty relations electric and magnetic field components cannot be simultaneously determined), but these are not fluctuations in the vacuum but at the presence of a proton and an electron bound to hydrogen. The same holds for the anomalous magnetic moment. It's deviation from the Dirac equation with unquantized fields (where you have a Lande factor of precisely 2) can again be interpret as due to quantum fluctuations of the quantized electromagnetic field.

You an also calculate the deviations of a point charge's electrostatic field from the Coulomb field due to "quantum fluctuations". I'm not sure whether this is somehow measurable, but it's in principle observable, but again it's nothing in the vacuum but at presence of at least this charge, creating the field.

So, I don't know what the popular-science term "vacuum fluctuation" really means. The Casimir effect is clearly no proof for them, as Jaffe's paper clearly demonstrates, but it's an observable and, I think, even really unambiguously observed quantum effect.

 

[A. Neumaier]

If you evaluate this for the free-field case you get a divergent result

An infinite variance is no disaster in statistics; you can have it in classical statistics, too - the Cauchy distribution has infinite variance, and the Wiener process is mathematically well-defined although its variance is infinite.
If you want to have finite results, take the vacuum correlation function $\langle vac|\phi(x)\phi(y)|vac\rangle$. for distinct x and y. The correlations are nonzero and have a physical meaning. But although they are vacuum expectations, they don't say anything about the vacuum but about single-particle states.

Nonexperts listen to the word only and interpret every nonzero vacuum expectation value as a property of the vacuum, and fill their imagination by projecting fictitious properties (something fluctuates ... people speak of virtual particles ... the Heisenberg uncertainty relation ... borrowing for a very short time energy from nothing ... so virtual particles pop in and out of existence, and everything seems to make sense to them) into the vacuum so that it can have these properties in an intuitively appealing way.
Since they are just storytellers unconstrained by theory, the outcome is very magical.

So, I don't know what the popular-science term "vacuum fluctuation" really means.

The word is taken from the existence of nonzero vacuum expectation values, which don't mean anything observable about the true vacuum (which is completely inert). But the sense it is given to it (by misunderstanding) by the general public is ''virtual particles popping in and out of the vacuum''. This is evident from wikipedia; see, e.g., all the superficially scientific nonsense in
https://en.wikipedia.org/wiki/Casimir_effect#Vacuum_energy
https://en.wikipedia.org/wiki/Quantum_fluctuation
https://en.wikipedia.org/wiki/Vacuum_energy

 

[vanhees71]

I couldn't agree more to #21 :-)).

 

[friend]

In accelerating frames (big bang, black holes, Unruh effect, etc), quantum fluctuations in the fields actually produce particles. So it would seem quantum fluctuations (virtual particles) are MORE real than real particles, since real particles come from quantum FUCTUATIONS to begin with. I would be very interested in seeing how you renormalize your way out of that one.

 

[A. Neumaier]

quantum fluctuations in the fields actually produce particles.

Your statement misrepresents what happens.

The Unruh effect says that a field that appears to an observer at rest to be in the vacuum state appears to an accelerated observer as being in a coherent state with an indefinite particle content. This has nothing to do with quantum fluctuations; it is a statement about the observer-dependent interpretation of the same state.

It is like saying that what in ordinary life appears to a close observer as big appears to a far away observer as small. The objective meaning of this is that the apparent size (and shape) of an object is not its true size, but must be calculated from it by the rules of perspectivity.

By analogy, the Unruh effect therefore contains the message that the particle content of the same field is not something objective but something observer-dependent. Objective is only the underlying quantum field and its state, from which the observer views can be derived.

Thus the Unruh effect confirms what I had already said in the context of the double slit experiment - that the field description is the one universally valid, while the particle description is derived and inferior - it depends both on a semiclassical approximation and on the dynamics of the observer.

 

[friend]

By analogy, the Unruh effect therefore contains the message that the particle content of the same field is not something objective but something observer-dependent. Objective is only the underlying quantum field and its state, from which the observer views can be derived.

I am told that the unaccelerated observer will see photons, etc. coming from the Unruh radiation of that accelerating object.

 

[A. Neumaier]

I am told

Who told you? Please add a reference for the claim.

 

[friend]

Who told you? Please add a reference for the claim.

I'm presently watching a series by Prof. Achim Kempf of the Primeter Institute here on QFT in curved spacetimes. In one of those lectures (I don't remember which one, sorry) He responds to a question (thus it is not in his notes (I looked)) to a student asking if this Unruh radiation was real. The professor says something to the effect that the Unruh radiation would not cook an egg in the unaccelerated frame. But we would see photons from the accelerated body produced by the accelerating body interacting with the Unruh radiation. The accelerating body would feel the heat of the thermal bath of Unruh radiation, get warm, and throw off photons.

Now my question for you is when are real particles ever produced apart from acceleration exciting the vacumm state of quantum fluctuations? I think perhaps your alternate interpretation using renormalization probably only works in flat spacetimes.

 

[A. Neumaier]

when are real particles ever produced apart from acceleration exciting the vacuum state of quantum fluctuations?

Real photons are produced when an electron is captured or goes from an excited state into a lower state. They are also produced when a particle and its antiparticle annihilate, The Unruh effect is the least observable of all known photon generating processes.

Nothing of this has to do with vacuum fluctuations but with differences in how different observers see the same thing. It is like length contraction in special relativity.

The electromagnetic field changes, and an observer who interprets the field in terms of photons will believe to see photons, while an an observer who interprets the field in terms of coherent states of the field will believe to see coherent light. There are very good reasons why quantum electrodynamics is called a quantum field theory and not a quantum particle theory! Newton had believed that light was particles, ans was disproved by ancient diffraction experiments. Since then the field point of view has remained the coherent one (pun intended), so why exchange it for a weird view in terms of particles with weird properties?

My thesis in this thread and its companion is that QM is weird if and only if one chooses an inappropriate language for talking about it, and this is a good example. There are several ways of talking about the same situation. It is up to you to choose the coherent one or the weird one.

 

[friend]

This has nothing to do with vacuum fluctuations but with differences in how different observers see the same thing. It is like length contraction in special relativity.

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.

 

[A. Neumaier]

how the fluctuations of the vacuum state can be excited to produce particles

Let me repeat what I said brfore:

When someone reasonably respectable says that ''vacuum fluctuations are the cause of the Casimir effect'' (which I take as example since it is a loose formulation based on a clear fact) they mean that ''vacuum fluctuations appear in the mathematical derivation of formulas for the Casimir effect that can be empirically checked'' (which is the fact), and not that ''because a vacuum fluctuation happened, the Casimir effect is observable'' (which is pure fiction). The fact is based on a logical explanation (called ''cause''), while the fiction is based on a dynamical explanation (also called ''cause'').

The same holds for the Unruh effect: ''producing particles by vacuum fluctuations'' means ''vacuum fluctuations appear in the mathematical derivation of formulas that predict particle production'' (fact) and not: ''because a vacuum fluctuation happened, particles are produced" (fiction).

One must always distinguish between formal explanations (on paper or in a video) and dynamical events (that actually happen).

 

[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.