I Why is the term "fluctuations" objectionable?

[nomadreid]

TL;DR Summary

The term "quantum fluctuation" is supposedly only a popular science expression. Whereas I can understand the objection to some explanations of quantum distributions, the fact that the values in the distribution change at different intervals of spacetime make it a change, i.e., fluctuation, no?

I have read in several places (e.g., https://physics.stackexchange.com/q...ing-of-quantum-fluctuations-and-vacuum-energy) that "quantum fluctuations" is an expression to be consigned to the sixth or eighth Circle of Dante's Inferno. OK, I can sympathize with this when the said fluctuations are linked too directly to an uncertainty principle, or some other incorrect explanation. However, what "quantum fluctuations" usually refer to is a change of a value over space or time, and as the values of a distribution are indeed dependent on intervals of spacetime, and they are not necessarily constant, and since a synonym for "fluctuation" is "change", then I do not see what is so objectionable about the term. What am I missing?

 

[jedishrfu]

It’s objectionable because it brings up memories of past discarded theories Or of fields that already use the word for a specific reason. In math and physics, words may appear to have the usual layperson meaning but instead are often selected and used in a specific and mostly consistent manner across the fields that is in direct conflict with how laypeople use them.

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

Bottomline, learn the jargon of the field, understand the meaning and describe things using that jargon. Don’t inject words that aren’t used in an attempt to simplify or bring out some analogy that seems to make sense to you.

 

[Klystron]

Along with a storied history as a scientific term, fluctuate encompasses contradictory definitions. From an online dictionary:

1. to change continually; shift back and forth; vary irregularly.
2. to move back and forth in waves; vary regularly.

Italics added for emphasis.

 

[PeterDonis]

This Insights article is relevant:

https://www.physicsforums.com/insights/vacuum-fluctuation-myth/

 

[nomadreid]

Thanks, PeterDonis, Klystron and jedishrfu. Good explanations, good links. The Insights article was magnificent.

One could probably make a long list of terms/concepts which have suffered this fate.

In satirizing the popular explanations of string theory, Terry Pratchett, in his Discworld novel "Making Money", has one of his characters saying, "That is a very graphic analogy which aids understanding wonderfully while being, strictly speaking, wrong in every possible way."

 

[atyy]

The Feynman path integral picture is a useful calculational tool in which the system takes all possible paths, instead of just one path. This picture in which all paths are taken, rather than just one path, is called "quantum fluctuations" by some.
http://hitoshi.berkeley.edu/221A/pathintegral.pdf
http://eduardo.physics.illinois.edu/phys582/582-chapter5.pdf

Many quantum systems can be treated using Feynman path integrals, including some rigorously-constructed quantum field theories (that do not describe our universe). However, the Feynman path integral is not the most fundamental conception of quantum mechanics. In the sense that the path integral is not fundamental, one can do without "quantum fluctuations".

@PeterDonis linked @A. Neumaier's discussion of the issue. There you can see that his warning also involves the Feynman path integral method, and taking too literally some usual pictures associated with steps in its calculation.

 

[A. Neumaier]

However, what "quantum fluctuations" usually refer to is a change of a value over space or time

That this is implied by many is the main reason why the term is completely unsatisfactory.

Quantum fluctuations have nothing to do with changes in time; they are completely unlike fluctuation of stock market prices, say. They refer instead to nonvanishing expectation values of quantities (like vacuum expectation values of field products) that ae impossible to measure by making statistics. For vacuum expectation values indicating fluctuations in time it would have to be measurements of the field in vacuum nd seeing it wildly changing with time. Instead, measuring the vacuum gives always constant values, for whatever you are repeatedly measuring.

 

[nomadreid]

Thanks for the further helpful replies, atty and (the author of the great Insight articles) A. Neumaier.

To check how close (or far) my understanding is on this,

measuring the vacuum gives always constant values, for whatever you are repeatedly measuring

How far off is it to say that the wave function calculates the quantum field at any interval in space to give the probability of measuring a particle in that interval, so that the "whatever you are repeatedly measuring" refers to the operators involved?

 

[A. Neumaier]

How far off is it to say that the wave function calculates the quantum field at any interval in space to give the probability of measuring a particle in that interval, so that the "whatever you are repeatedly measuring" refers to the operators involved?

Totally off.

In a vacuum, nothing happens, so one cannot measure any temporal change or fluctuation.

In textbook quantum field theory one never calculates wave functions but time-independent S-matrix elements related to scattering cross sections. What is repeatedly measured to compare this with are probabilities of random particle detection events with specified momentum range..

In nonequilibrium quantum field theory one never calculates wave functions but space- and time-dependent expectations or correlation functions of field operators. What is repeatedly measured to compare this with are (nonfluctuating local integrals of) macroscopic fields or response functions, or again random particle detection probabilities.

The only things fluctuating are the observational results, and these are fluctuations comparable to the fluctuations in the number of eyes shown by randomly casting dice.

 

[nomadreid]

Thank you very very much, A. Neumaier. This is extremely helpful, giving me something to chew on for quite some time.

 

[PGaccount]

The word quanqtum fluctuations" can refer to the zero-point fluctuations of fields in empty space. These can manifest as measurable effects such as the Casimir force. The word vacuum fluctuations" is also used to refer to the vacuum feynman diagrams.

 

[PeterDonis]

The word quanqtum fluctuations" can refer to the zero-point fluctuations of fields in empty space. These can manifest as measurable effects such as the Casimir force.

Please read the Insights article linked to earlier in the thread. This is one of the misconceptions it discusses.