The Vacuum Fluctuation Myth - Comments

[durant35]

The smooth evolution of the wave function is dynamically happening while it passes a magnet. It is not the wave function but the intuitive semiclassical picture of an electron as a moving point that ''causes'' the apparent jumps.

Got it. To me, to say that the electron ia fluctuating in its position is roughly to say that it is jumping between one position and another when not measured which is clearly related to the semiclassical picture you (and vanhees) described. And which is of course false.

When I said nothing happens in the wf, I meant that. Electron isn't jumping between the spots, it literally is in a state of variance which may change over time. But it is still only a variance - nothing happens 'inside' the wf. This is a different context of happening than deterministically evolving which applies to the wf as a whole. For something to happen, you need measurement. Would you agree with this line of reasoning?

 

[A. Neumaier]

This is a different context of happening than deterministically evolving which applies to the wf as a whole. For something to happen, you need measurement.

No. In more complicated contexts, a lot may happen, and this is expressed in the evolution of the state. Indeed, ''the moment of measurement'' is itself a gross simplification of a very complicated interaction that happens between the electron and the measurement device, described not by the state of the electron alone but by the state of the combined system electron+device+environment. The apparent randomness in the fate of the electron state alone is due to this additional complexity.

 

[Keith_McClary]

I used to know a bit about the "toy model" $\phi^4_2$ QFT in 1+1 dimensions (Glimm & Jaffe). They rigorously construct interacting particle states with bound states and scattering. AFAIK there is nothing corresponding to vacuum fluctuations in this mathematically well defined theory. I can't think how you could even rigorously ask "are there vacuum fluctuations?" in this context.
"Vacuum fluctuations" seem to be an artifice of trying to apply perturbation theory when you don't know that the perturbed theory is mathematically well defined.

 

[A. Neumaier]

I used to know a bit about the "toy model" $\phi^4_2$ QFT in 1+1 dimensions (Glimm & Jaffe). They rigorously construct interacting particle states with bound states and scattering. AFAIK there is nothing corresponding to vacuum fluctuations in this mathematically well defined theory. I can't think how you could even rigorously ask "are there vacuum fluctuations?" in this context.
"Vacuum fluctuations" seem to be an artifice of trying to apply perturbation theory when you don't know that the perturbed theory is mathematically well defined.

Vacuum fluctuations refer to the fact that smeared field operators have in the vacuum state a nonzero variance. This is captured by the Wightman distribution functions, hence a fact even in $\phi^4_2$ QFT in 1+1 dimensions.

On the other hand, interpreting (as in most popular accounts of quantum phenomena) these vacuum fluctuations as happenings in time is completely fictitious.

 

[Fred Wright]

If vacuum fluctuations are fictitious, then what is the proper explanation of the Casimir effect?

 

[A. Neumaier]

If vacuum fluctuations are fictitious, then what is the proper explanation of the Casimir effect?

https://www.physicsforums.com/threads/vacuum-fluctions-and-the-casimir-effect.828475/

 

[bhobba]

If vacuum fluctuations are fictitious, then what is the proper explanation of the Casimir effect?

Its actually a manifestation of Van Der Walls forces you probably learned about in HS chemistry::
https://arxiv.org/pdf/hep-th/0503158v1.pdf
'The Casimir effect is a function of the fine structure constant and vanishes as α → 0. Explicit dependence on α is absent from eq. (3) because it is an asymptotic form, exact in the α → ∞ limit. The Casimir force is simply the (relativistic, retarded) van der Waals force between the metal plates'

See also:
https://arxiv.org/abs/1605.04143

Thanks
Bill

 

[Fred Wright]

Thank you Dr. Neumaier and Dr. Bill for taking the time to respond to my post. I have been perplexed and annoyed by the term "vacuum fluctuation" for many years. After reading the paper by Jaffe my angst has been lifted and I have a renewed appreciation for the incredible predictive power of QFT. Alhamdu lila!
Salam,
Fred

 

[jtbell]

Vacuum fluctuations refer to the fact that smeared field operators have in the vacuum state a nonzero variance. [...]

On the other hand, interpreting (as in most popular accounts of quantum phenomena) these vacuum fluctuations as happenings in time is completely fictitious.

The source of this (mis)interpretation is surely the fact that in normal English usage, the word "fluctuation" does mean "variation with respect to time." At least, that's how I always understand it in everyday language.

This is of course not the only case in people are confused by the re-purposing of everyday words into physics jargon with specific technical meaning. Consider "work", "energy", and "power", which introductory physics students often struggle with at first. Or "speed" and "velocity".

 

[Mordred]

The word vacuum is also problematic when you look at the definitions from classical to quantum.

 

[bhobba]

Dr. Bill

Many that post here have doctorates, including Dr. Neumaier. I however am not one. Just a guy with a degree in applied math and computing who is now retired from 30 years spent programming, so can indulge his fascination for and interest in physics.

Thanks
Bill