# Quantum fluctuation and quantum mysticism

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1. Dec 23, 2015

### 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

2. Dec 23, 2015

### 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 possess 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).

Last edited: Dec 23, 2015
3. Dec 24, 2015

### bhobba

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

Last edited: Dec 24, 2015
4. Dec 27, 2015

### stevendaryl

Staff Emeritus
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).

5. Jan 4, 2016

### jfizzix

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).

6. Jan 4, 2016

### bhobba

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 cant 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

7. Jan 4, 2016

### jfizzix

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.

8. Jan 5, 2016

### Mentz114

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

9. Jan 5, 2016

### bhobba

IMHO quite likely.

Thanks
Bill

10. Jan 5, 2016

### bhobba

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

11. Jan 5, 2016

### Mentz114

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 ?

12. Jan 5, 2016

### Demystifier

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.

13. Jan 5, 2016

### bhobba

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

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

Thanks
Bill

Last edited: Jan 5, 2016
14. Jan 5, 2016

### bhobba

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://www.mat.univie.ac.at/~neum/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

Last edited: Jan 5, 2016
15. Jan 5, 2016

### 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?

16. Jan 5, 2016

### A. Neumaier

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.

Last edited: Jan 5, 2016
17. Jan 5, 2016

### bhobba

No idea how that happened. Now fixed.

Good idea. Will think about it.

Thanks
Bill

18. Jan 5, 2016

### vanhees71

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 ;-)).

19. Jan 5, 2016

### A. Neumaier

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.

20. Jan 5, 2016

### vanhees71

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 envoking 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.