The Vacuum Fluctuation Myth - Comments

[A. Neumaier]

A. Neumaier submitted a new PF Insights post

The Vacuum Fluctuation Myth

Continue reading the Original PF Insights Post.

 

[A. Neumaier]

The article is a slightly polished version of my much-liked posting at https://www.physicsforums.com/posts/5453034

 

[Greg Bernhardt]

Nice Insight Arnold!

 

[Drakkith]

Nice article!

 

[Collin237]

But Hawking radiation itself is a myth. All we know about black holes is that there are things that match the description as deduced from billions of miles away.

 

[Nugatory]

But Hawking radiation itself is a myth. A

Only if you're willing to put Hawking's derivation (the real thing, not the heuristic upon which Professor Neumaier is heaping scorn) in the category of "myth".

 

[Drakkith]

All we know about black holes is that there are things that match the description as deduced from billions of miles away.

The same is true of stars, nebulas, exoplanets, galaxies, etc.

 

[houlahound]

I usually steer away from such insights because to me the specialists writing them assume too much prior knowledge in both the content and notation department.

This insight I got a lot out of, thank you.

 

[Collin237]

The same is true of stars, nebulas, exoplanets, galaxies, etc.

Those are taken seriously as objects. If a physicist has a new idea about them, it's explored, refined, etc., and goes through an ordinary Kuhnian trial. Ideas about black holes, however, are argued on merely theoretical merit.

Only if you're willing to put Hawking's derivation (the real thing,

What else would you call it? Already in just the abstract, the remarks about "entropy" are a huge red flag.

 

[houlahound]

Observed orbital motion around massive objects that appear as black holes of some sort kind of suggest black holes as predicted by GR.

 

[Vanadium 50]

Ideas about black holes, however, are argued on merely theoretical merit.

False.

As an example, the "chirp" of GW150914 depends on the horizon radius of the merged black hole. If you don't have a horizon, or have it in another place, the chirp no longer matches the GR predictions.

Now I will make a prediction - when confronted with the evidence, your reaction will not be "I was wrong". It will be some argument that somehow this doesn't count.

 

[jonjacson]

Minute 48 and 49.

 

[HyperStrings]

It was a very strong description. I was curious about a few pieces in your explanation. In, the paper, Direct Observation of Quantum Phonon Fluctuations in a One-Dimensional Bose Gas[1] it is shown that quantum fluctuations result from 'acoustic vibrations'. Lending strong correlation with the analog of the fluctuation in very still and ice cold states. It is then repeated in 2016 [2] as "we prove that quantum fluctuations stabilize the ultracold gas far beyond the instability threshold imposed by mean-field interactions.". With analog vibrations having a seemingly strong subadvity for quantum fluctuations and the experiment involving analog hawking radiation of black holes using "dumb holes"[3], we could say the quantum fluctuation is relative to the energy of the black hole. Quantum fluctuations are also observed through the lamb shift [4].
[1] http://journals.aps.org/prl/abstract/10.1103/PhysRevLett.108.225306
[2] http://journals.aps.org/prx/abstract/10.1103/PhysRevX.6.041039
[3] http://journals.aps.org/prl/abstract/10.1103/PhysRevLett.85.4643
[4]http://physics.aps.org/articles/v9/139

 

[bhobba]

Quantum fluctuations are also observed through the lamb shift [4].

Gee - I always thought it was simply including higher orders and re-normalization.

Its a total myth that quantum fluctuations, virtual particles yada, yada, yada exist. Its part of the pictorial language that has grown up with Feynman diagrams - but are really just terms in a Dyson series:
https://en.wikipedia.org/wiki/Dyson_series

Thanks
Bill

 

[A. Neumaier]

Quantum fluctuations are also observed through the lamb shift [4].

The paper [4] states: ''It arises because zero-point fluctuations of the electromagnetic field in vacuum perturb the position of the hydrogen atom’s single bound electron.'' The truth - shown by all sources that actually do the calculations - is that the electromagnetic field interacting with the hydrogen atom’s single bound electron introduces radiative corrections into the corresponding Dirac equation. According to standard quantum mechanical perturbation theory, these corrections result in the Lamb shift. Nothing with vacuum fluctuations or ''virtual photons popping in and out of existence'' as your source claims.

I didn't check the other papers but it is unlikely that they provide harder evidence for what you want to imply.

 

[stevendaryl]

Its a total myth that quantum fluctuations, virtual particles yada, yada, yada exist. Its part of the pictorial language that has grown up with Feynman diagrams - but are really just terms in a Dyson series:
https://en.wikipedia.org/wiki/Dyson_series

Of course you (and A. Neumaier) are right. However, it is interesting that respectable physicists (most recently, I saw a video lecture by Alan Guth where this happens) very often present their informal reasoning in terms of vacuum fluctuations. It seems like it's a useful heuristic for reasoning about what's possible, even though the mathematical details, when you actually try to calculate things, don't actually resemble the "fluctuation" reasoning much at all.

For an example from Guth, http://web.mit.edu/physics/people/faculty/guth_alan.html

One of the intriguing consequences of inflation is that quantum fluctuations in the early universe can be stretched to astronomical proportions, providing the seeds for the large scale structure of the universe. The predicted spectrum of these fluctuations was calculated by Guth and others in 1982. These fluctuations can be seen today as ripples in the cosmic background radiation, but the amplitude of these faint ripples is only about one part in 100,000. Nonetheless, these ripples were detected by the COBE satellite in 1992, and they have now been measured to much higher precision by the WMAP satellite and other experiments. The properties of the radiation are found to be in excellent agreement with the predictions of the simplest models of inflation.

 

[HyperStrings]

They were virtual phonons, and I do not ascribe to the theory that phonons are particles, or even 'virtual particles'. though it is upsetting you didn't check the other papers. These fluctuations were not to be meant as a cohesive description upon one anothers papers. They do certainly outline quantum fluctuations. I don't see how your retort disproves acoustic quantum fluctuations. Considering you didn't take the time to read them nor cite any paper yourself, I find your assessment, illogical.

 

[A. Neumaier]

Of course you (and A. Neumaier) are right. However, it is interesting that respectable physicists (most recently, I saw a video lecture by Alan Guth where this happens) very often present their informal reasoning in terms of vacuum fluctuations. It seems like it's a useful heuristic for reasoning about what's possible, even though the mathematical details, when you actually try to calculate things, don't actually resemble the "fluctuation" reasoning much at all.

It is a very useful (and historically sanctioned) tool to capture the imagination of an audience without presenting any formula, although it does not resemble at all what happens. The latter is discovered only if one wants to see what the talk means - and one discovers that it means nothing. ''vacuum fluctuations'' are just a buzzword for ''field theoretic effects'', nothing more.

 

[A. Neumaier]

I don't see how your retort disproves acoustic quantum fluctuations.

Quantum fluctuations are everywhere, but calling an unexcited crystal a quantum vacuum, as the authors of your source [4] do, is quite a misnomer. Analogies don't create truth.

''The authors measured an energy shift in the presence of the quantum vacuum, finding a value in good agreement with theoretical expectations. In addition to providing the first quantitative measurement of the phononic Lamb shift, the result confirms the validity of the theoretical framework that describes the effect. ''

The author measured an energy shift in the presence of a crystal (producing of course an interaction that changes all energy levels), finding a value in good agreement with theoretical expectations. But this sounds too unexciting to be worth reporting.

 

[Haelfix]

It is a very useful (and historically sanctioned) tool to capture the imagination of an audience without presenting any formula, although it does not resemble at all what happens. The latter is discovered only if one wants to see what the talk means - and one discovers that it means nothing. ''vacuum fluctuations'' are just a buzzword for ''field theoretic effects'', nothing more.

I'm a little uneasy by some of these discussions, b/c its a little difficult to know what the claim is, and whether its just a matter of terminology. I'm fine with saying the quantum vacuum is a subtle creature, and it's a little hard to define what a 'fluctuation' actually means considering that we are by assumption talking about stationary states (and then there are all the complicated renormalization scheme caveats associated with what we mean by this). However, I'm a little uneasy by the implication that the 'real' thing when properly understood is trivial or empty. That has definitely not been demonstrated.

The only way you can measure the quantum vacuum, is by doing an experiment, and it's always an inferred counterfactual property (this is what we would measure if we thought the vacuum was trivial or empty). So when people talk about polarizing the vacuum like for the Lamb shift, its basically about feynman diagrams that sort of look like bonafide vacuum diagrams except that there are external legs present, and there is always a strong background field (as well as the presence of a hydrogen atom as a spectator). Of course real vacuum diagrams have no external legs, and there is no background field present, so it is technically true that the presence of a measured nonzero effect for the Lamb shift doesn't necessarily tell us about the nature of the real quantum vacuum.

Then there is the temptation to think that the nonzero quantum vacuum is then only some sort of perturbative artifact. But this is also wrong. For instance, one can show that instantons can contribute to the QCD vacuum. Also, one of the virtues of supersymmetric theories, is that they are sometimes exactly solvable, and we can actually demonstrate that the vacuum is nonzero in certain cases.

I guess I don't understand what the claim is specifically.

 

[A. Neumaier]

whether its just a matter of terminology. I'm fine with saying the quantum vacuum is a subtle creature, and it's a little hard to define what a 'fluctuation' actually means

That's the problem. It is nowhere meaningfully defined, but used a lot in informal talk.

One can meaningfully talk about fluctuations of an observable $X$, meaning that the variance of $X$ is nonzero, but there is no formal definition of vacuum fluctuation, hence it is meaningless. How can you meassure something that doesn't even have a proper definition? One can measure spectral shifts, or forces, but claiming that in this way one has measured vacuum fluctuations needs more than saying that some nonzero vacuum expectation is used somewhere in the calculations. For the latter is the case in any perturbative computation of anything in quantum field theory, hence doesn't say anything nontrivial.

The informal meaning most often used, e.g., in [4], that these fluctuations consist of virtual particles popping in and out of existence, is plainly wrong.

one can show that instantons can contribute to the QCD vacuum.

This isn't about vacuum fluctuations, but about the proper definition of what the vacuum state means in QCD.

we can actually demonstrate that the vacuum is nonzero in certain cases.

A nonzero vacuum expectation value doesn't mean in any sense that the vacuum is fluctuating. Otherwise the ground state of a single harmonic oscillator would also be fluctuating...

 

[HyperStrings]

Analogies don't create truth

There is a good physics lecture on 'The Dangers of Analogies' and I agree with you, we should be very discerning of analogy. Though, in the lecture/paper he gives rules to how to properly use analogies safely when discussing/teaching physics and admits that sometimes there is no other way to explain something. Just as all Gaileleo had to prove his theory was an analogy. Its a double edged sword, as we must also be aware, we are heading into a time of where experiments will need to be able to represent complex Planckian scale effects, so we may very well have to bite the bullet and start to understand analogous experiments. As it is very possible for them to be useful. With that being said, I will try to be more discreet and specific as I can respect your position.

Quantum fluctuations are everywhere,

So, in your opinion, what is causing the ''field theoretic effects'' that oscillate the atom, 'up the slope of the bowl' in a dead, zero point BEC well?

The paper observed the BEC well oscillations, mathematically predicted the subtle nuance of effects of acoustic oscillations that match the 'vibration' of the field to exactly match the 'field theoretic effect' of the oscillations or quantum fluctuations of the atoms in the BEC well. Then showed, precisely, those same exact quantum fluctuations, with their mathematically predicted phonon model. I have tried to put together any various combination of small changes in the atomic structure that would allow the equivalent of such oscillations but I can't find any correlation that would create these specific, exactly replicated, oscillations. So I am in agreement with the paper.

(and then there are all the complicated renormalization scheme caveats associated with what we mean by this

Which brings me to another point that, we are using normalization because of Planck scale discrepencies, and 'science' is okay with that, but if you try to isolate those discrepencies with a mathematical application of a 'mistake fixing, re-normalization', science is not okay with that? The very process of normalization is in essence, 'blurring the clarity of the image'. Then a proper re-normalization can result with 'sharpening of the image'.

As I see it, the vibration of the atoms field creates virtual phonon wave oscillations, the atoms wiggle up the bowls slope and the quantum fluctuations are the wiggle of those vibrations.

 

[Haelfix]

A nonzero vacuum expectation value doesn't mean in any sense that the vacuum is fluctuating. Otherwise the ground state of a single harmonic oscillator would also be fluctuating...

We completely agree then, although I'm now wondering if the origin of the word in textbooks is precisely when discussing simple harmonic oscillators, particles in a box, and other simple nonrelativistic quantum mechanics. There it would presumably me a fluctuation relative to a classical zero.

 

[A. Neumaier]

if the origin of the word in textbooks is precisely when discussing simple harmonic oscillators, particles in a box, and other simple nonrelativistic quantum mechanics. There it would presumably mean a fluctuation relative to a classical zero.

I have seen the word used only in the context of (relativistic or nonrelativistic) quantum field theory. It doesn't make sense for a harmonic oscillator or a particle in a box. The quantum mechanical ground state is dynamically completely inert under the quadratic Hamiltonian that defines the oscillator. Nothing fluctuates. There is an uncertainty about the values of observables not commuting with the energy, but this is because it is impossible to measure them more accurately, not because these would fluctuate in time. The traditional interpretations refrain from saying what happens in between measurememt; none of them claims that these observables have all the time exact but fluctuating values.

 

[A. Neumaier]

, what is causing the ''field theoretic effects'' that oscillate the atom

Well, the interaction with the crystal, or if you wish, the field defined by it cause these effects. Switch the interaction or the mean field off and the effect is gone. This proves that these are the responsible agents. Not mystical quantum fluctuations.

 

[RockyMarciano]

Mixing nrqm and qft may lead to confusions. To me quantum fluctuations are defined by the fact that the ground state in qm must also obey the Heisenberg principle, that is what in graphic language fluctuates in quantum fluctuations. When going to the quantum field picture there are so many things that change(for one thing position is no longer a operator while what used to be states are operators,etc...) that there is no longer a good mathematical translation of this, and the vacuum state of the field theory doesn't qualify when formally defined. There, no more mystique.

 

[Haelfix]

. The quantum mechanical ground state is dynamically completely inert under the quadratic Hamiltonian that defines the oscillator. Nothing fluctuates.

Yep, they are clearly stationary states in the nrqm case.

So, I would say I have heard the word used more when discussing things like barrier penetration in nrqm. So an author will write something like "classically you will never measure a particle here, but b/c of 'quantum fluctuations' or 'quantum jitters' you will see a tunneling phenonemon on the other side and the nonzero possibility for the detection of a particle". So there the word would presumably mean some sort of deviation from classical expectations.

In the context of inflation, the same sort of pedagogical word choice is frequently used informally in the context of a potential term for a scalar field, where you have either tunneling between false and true vacuums, or alternatively where you have oscillatory behavior at the bottom of a well analogous to the phenomenon which leads to the longitudinal mode in the Higgs phenomenon.

 

[A. Neumaier]

To me quantum fluctuations are defined by the fact that the ground state in qm must also obey the Heisenberg principle

The Heisenberg uncertainty relation is not about quantum fluctuations but about the intrinsic uncertainty in measuring noncommuting observables. Nothing fluctuates there.

 

[A. Neumaier]

I have heard the word used more when discussing things like barrier penetration in nrqm. So an author will write something like "classically you will never measure a particle here, but b/c of 'quantum fluctuations' or 'quantum jitters' you will see a tunneling phenomenon on the other side and the nonzero possibility for the detection of a particle".

Though this is somewhat unrelated to the present topic, let me mention that quantum tunneling is a misnomer. It is motion over the barrier and not through the barrier. For the ''tunneling'' probability tends to zero as the barrier gets higher, and is zero when the barrier is infinitely high. No matter how long a tunnel through the barrier would have to be! Thus it is like the motion of a classical particle with a random kinetic energy - it has a small probability of being kicked over the barrier and ending up outside the well it was in originally.

Again nothing that fluctuates!

 

[RockyMarciano]

The Heisenberg uncertainty relation is not about quantum fluctuations but about the intrinsic uncertainty in measuring noncommuting observables. Nothing fluctuates there.

This is purely semantic but both the insight and thread are about semantics so why not get it right?. Fluctuation is a word that is synonim both of oscillation and of indeterminacy or uncertainty. All it means in the quantum context is the Heisenberg indeterminacy of the ground state, and what fluctuates(vacillates i.e. it is intrinsically uncertain) is precisely the noncommuting observables. Of course many people by extension thinks about something moving or oscillating, that I guess it is what you understand if you disregard the meaning of fluctuation as vacillation/indeterminacy. Since Heisenberg indeterminacy lies at the heart of the quantum departure from classical physics, quantum fluctuations by extension are also referred by many as this departure from classicality.

On the other hand if one is strict with the math not even the fields or the waves actually oscillate, since the math always describes a rigid picture, a shortcoming of analysis. But this should show just how ridiculous can blind strictness get.

 

[ftr]

This is purely semantic but both the insight and thread are about semantics so why not get it right?. Fluctuation is a word that is synonim both of oscillation and of indeterminacy or uncertainty. All it means in the quantum context is the Heisenberg indeterminacy of the ground state, and what fluctuates(vacillates i.e. it is intrinsically uncertain) is precisely the noncommuting observables. Of course many people by extension thinks about something moving or oscillating, that I guess it is what you understand if you disregard the meaning of fluctuation as vacillation/indeterminacy. Since Heisenberg indeterminacy lies at the heart of the quantum departure from classical physics, quantum fluctuations by extension are also referred by many as this departure from classicality.

On the other hand if one is strict with the math not even the fields or the waves actually oscillate, since the math always describes a rigid picture, a shortcoming of analysis. But this should show just how ridiculous can blind strictness get.

But it seems vacuum fluctuation is mentioned more in QED and you are talking about "quantum fluctuations"
https://en.wikipedia.org/wiki/Quantum_fluctuation
https://en.wikipedia.org/wiki/QED_vacuum
https://en.wikipedia.org/wiki/Vacuum_polarization

so some "fluctuation" is related to vacuum in the vicinity of interactions others to an otherwise empty interstellar vacuum. It sound like many concepts being mixed up.

 

[A. Neumaier]

Fluctuation is a word that is synonim both of oscillation and of indeterminacy or uncertainty.

No. Fluctuation in today's usage always means change, not just being uncertain! All the major dictionaries agree on that:

http://www.dictionary.com/browse/fluctuation
1. continual change from one point or condition to another.
2. wavelike motion; undulation.
3. Genetics. a body variation due to environmental factors and not inherited.

http://dictionary.cambridge.org/dictionary/english/fluctuate
fluctuate: to change, especially continuously and between one level or thing and another

https://en.oxforddictionaries.com/definition/fluctuation
An irregular rising and falling in number or amount; a variation

https://www.merriam-webster.com/dictionary/fluctuate
fluctuate:
1. to shift back and forth uncertainly
2. to ebb and flow in waves

https://www.vocabulary.com/dictionary/fluctuation
The noun fluctuation refers to the deviations along the path from one point to another. We see frequent fluctuations in the stock market, as prices go up or down, and also in the weather, which is always changing.

http://www.macmillandictionary.com/dictionary/british/fluctuation
frequent changes in the amount, value, or level of something

Even wikipedia describes it as a change, though in a completely unscientific manner (not surprisingly, since it also promotes lots of other nonsense about virtual particles):
''In quantum physics, a quantum fluctuation (or quantum vacuum fluctuation or vacuum fluctuation) is the temporary change in the amount of energy in a point in space [...] the field's lowest-energy or ground state, often called the vacuum state, is not, as one might expect from that name, a state with no particles, but rather a quantum superposition of particle number eigenstates with 0, 1, 2...etc. particles.''

The quality of the Wikipedia statement can be assessed from the second sentence quoted, which is absurd. The vacuum state is always the eigenstate of the number operator with exactly zero particles. There is no uncertainty in the number of particles, since it is an eigenstate.

what fluctuates(vacillates i.e. it is intrinsically uncertain) is precisely the noncommuting observables.

This is only your private interpretation of the term. Never before I heard of someone talk about quantum vaccilations! And even that word means not just uncertainty but wafering uncertainty - a process in time!

 

[ftr]

Arnold

What do you think this statement is saying then in wiki

"So what does the spacelike part of the propagator represent? In QFT the vacuum is an active participant, and particle numbers and field values are related by an uncertainty principle; field values are uncertain even for particle number zero. There is a nonzero probability amplitude to find a significant fluctuation in the vacuum value of the field Φ(x) if one measures it locally (or, to be more precise, if one measures an operator obtained by averaging the field over a small region)."

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

 

[A. Neumaier]

What do you think this statement is saying

As stated, it is meaningless since $\Phi(x)$ is not an operator, hence not an observable. As remarked in your quote, one has to use a smeared version (averaging over a small open region in space-time) to produce an operator. Even with this amendment, the statement is misleading. The ''vacuum value'' is not a commonly used expression. The nearest expression with a formal meaning is the vacuum expectation value, but this is completely determined and hence certain. What is probably meant is that if one could measure the local value of a smeared field in the vacuum state (don't ask how this ever can be done, as the vacuum contains no particles, hence no observer), the result would have a significant uncertainty, i.e., there is a nonzero probability of getting a result significantly different from the vacuum expectation value. This is formally true if one assumes (as is commonly done) that the Born interpretation holds in this (counterfactual) case.

But in the statement quoted, the mistake already pointed out is made - that uncertainty and fluctuation are equated. This turns an unconspicuous statement that some measurement result has a significant uncertainty (we know this holds for most measurements) into the remarkable and wrong statement that the value fluctuates - with the implied, equally wrong consequence that the vacuum is ''active''. This is typical for the exaggerations made when turning banal truths into exciting stories for everyone.

 

[A. Neumaier]

The passage
''In terms of virtual particles, the propagator at spacelike separation can be thought of as a means of calculating the amplitude for creating a virtual particle-antiparticle pair that eventually disappear into the vacuum, or for detecting a virtual pair emerging from the vacuum. In Feynman's language, such creation and annihilation processes are equivalent to a virtual particle wandering backward and forward through time, which can take it outside of the light cone.''
from the same wikipedia article is also misleading. Creation and annihilation operators only exist for time-like, on-shell momenta; hence the associated creation and annihilation processes all refer to real particles.