What are quantum fluctuations ?

[Aidyan]

What are quantum "fluctuations"?

We get to know that vacuum is not really empty but that its energy ground state is non zero. Is this what is represented by quantum "fluctuations"? As far as I understand QM this seems to me a very misleading representation of things. If we believe that something is "fluctuating" we imply that there is something with definite properties (say position and momentum) but its values changing quickly in time. I think this is a gross misrepresentation and also against quantum complementarity, which, as I understand it, says that non-commuting observables can't be measured at the same time, i.e. are "non-definite", "indeterminate", "uncertain", or whatever you might call it, but something very different than saying that they are "fluctuating" in time (like Brownian motion or thermal fluctuations). Moreover, if there would be really "fluctuations" a particle like an electron should 'zizzag' throughout space and, being electrically charged, emit continuously radiation, i.e. energy would not be conserved. So, I tend to think that there is nothing such as a "fluctuating" vacuum, but that there are quantum objects which properties (like position, momentum, spin, etc.) have some probability of "actualization" at the time of interaction or measurement. Before that instant there is no fluctuation, but only state of indetermination. The idea to describe vacuum as quantum foam seems to me simply wrong. Can someone please direct me to a document, link, article or whatever that clarifies better this point?

 

[sheaf]

Have you seen Arnold Neumaier's FAQ entry ?

Quantum fluctuations are a popular buzzword for the statistical
triviality that the variance <A^2> of a random variable A with zero
mean is typically not zero - except that A is now an operator.
Some people therefore think that this deserves a much more mysterious
name.

 

[Aidyan]

Thank you. Neumaier's faq look interesting. But I think that to sweep vacuum fluctuations under the carpet saying that it can be explained away also with other theories is not enough. I think he should have argued better about that. Because first of all why can it be explained with quantum fluctuations in the first place? Then, common wisdom is that it is the simplest explanation, and according to Occam's razor it should then be preferred. Moreover, it is not only about static but also dynamical Casimir effect (e.g. see: motion induced radiation http://arxiv.org/abs/1105.4714 ). These people claim to have converted 'virtual' particles in 'real' ones. Is this all rubbish? What is not clear to me in Neumaier's words, is what his alternative explanations are beyond saying that it is only about perturbative terms in the calculations or "statistical triviality as the variance of an operator", etc.? So, while I'm philosophically inclined to share Neumaier's perspective, I'm afraid that unless we won't come up with other convincing interpretations of the formalism, the 'fluctuation' and 'virtual' particles interpretation will continue to annoy me...

 

[sheaf]

Thank you. Neumaier's faq look interesting. But I think that to sweep vacuum fluctuations under the carpet saying that it can be explained away also with other theories is not enough. I think he should have argued better about that. Because first of all why can it be explained with quantum fluctuations in the first place? Then, common wisdom is that it is the simplest explanation, and according to Occam's razor it should then be preferred. Moreover, it is not only about static but also dynamical Casimir effect (e.g. see: motion induced radiation http://arxiv.org/abs/1105.4714 ). These people claim to have converted 'virtual' particles in 'real' ones. Is this all rubbish? What is not clear to me in Neumaier's words, is what his alternative explanations are beyond saying that it is only about perturbative terms in the calculations or "statistical triviality as the variance of an operator", etc.? So, while I'm philosophically inclined to share Neumaier's perspective, I'm afraid that unless we won't come up with other convincing interpretations of the formalism, the 'fluctuation' and 'virtual' particles interpretation will continue to annoy me...

Yes, in that reference, they mention in the abstract the notorious "virtual particles popping in and out of existence" phrase, but in the main body of the paper - the actual calculations - there is no mention of virtual particles - no creation of them from the vacuum state etc. As I understand it (I'm only an armchair physicist, so my opinion may not be worth a great deal!), the real photons are created from changing screening currents due to a boundary moving in the vacuum. The vacuum contains an electric field which, in a classical world should be zero (hence no screening currents and no radiated photons), but in a quantum world, any repeated measurement of the field will yield fluctuating results. I'm thinking of the (effective) moving mirror as making measurements of the electric field in the vacuum state.

I'd be interested if someone more knowledgeable could comment if this is the right interpretation...

Interestingly, Hawking's particle creation by black holes paper does the same thing - mentions a virtual particle picture in the introduction, but does not treat it mathematically in the main body. The calculation presented is just based on the usual Bogoliubov transformation.

 

[Aidyan]

Since my knowledge so far does not go much beyond the classical non relativistic QM I uphold any final judgement, but in fact, 'virtual particles' seems to be a mere juxtaposition for something the mathematical formalism misleadingly suggests to our anthropomorphic understanding leaving a lot of space to our personal subjective fantasies. If so, I think physicists are fooling themselves. It is unfortunate that there is no desire to put things a bit into a coherent conceptual order. I suppose this comes from the devastating effect the "shut up and calculate" approach had on generations.

 

[IsometricPion]

I think there is a certain sense in which you are right about "quantum fluctuations". If all that exists is the ground state vacuum, the system is in an energy eigenstate. However, this state is not in general a particle number eigenstate. So, measurements of the number of, e.g., photons in a given region of vacuum in QED will yield a distribution of results (rather than always zero). I say that this agrees with your assertion about "quantum fluctuations" because these probabilities are not time dependent (so there can be no fluctuation in the expectation value of the number of photons one will measure). However, as soon as one introduces a time varying component of the system, it is certain that the system is no longer in an energy eigenstate. In this case the number probabilities will, in general, vary with time (as will the associated expectation value). These results are entirely separate from the perturbation theory approach. Wikipedia- Jaynes-Cummings model is an example of an exactly solvable system in QED (so there is no perturbation theory necessary) that exhibits a time varying photon number in for an atom in a vacuum (with or without a zero expectation value for the number of photons present in the region).

 

[sheaf]

I think there is a certain sense in which you are right about "quantum fluctuations". If all that exists is the ground state vacuum, the system is in an energy eigenstate. However, this state is not in general a particle number eigenstate. So, measurements of the number of, e.g., photons in a given region of vacuum in QED will yield a distribution of results (rather than always zero). I say that this agrees with your assertion about "quantum fluctuations" because these probabilities are not time dependent (so there can be no fluctuation in the expectation value of the number of photons one will measure). However, as soon as one introduces a time varying component of the system, it is certain that the system is no longer in an energy eigenstate. In this case the number probabilities will, in general, vary with time (as will the associated expectation value). These results are entirely separate from the perturbation theory approach. Wikipedia- Jaynes-Cummings model is an example of an exactly solvable system in QED (so there is no perturbation theory necessary) that exhibits a time varying photon number in for an atom in a vacuum (with or without a zero expectation value for the number of photons present in the region).

Re highlighted bit, I thought the QED vacuum was a number eigenstate, namely the state with number zero. You would see a varying number of photons if you observed this vacuum from an accelerated frame (like the mirror is doing when it's moving backwards and forwards) ?

 

[IsometricPion]

Sorry, yes, you must be correct. The vacuum is defined in part by the application of the annihilation operator yielding zero, so it must be a number eigenstate. The only way I can think of for the sentance you highlighted to apply is in a context where you have the vacuum plus other objects (but then you don't really have a vacuum). I must not have been thinking very clearly.