The Vacuum Fluctuation Myth - Comments

[A. Neumaier]

It seems like a Chicken-and-Egg argument: Is the Field the basis for the fluctuations, or are the fluctuations the basis for the Field?

No chicken or egg. Fluctuations are definable only after one has already defined fields. Without fields the notion of fluctuations wouldn't make scientific sense.

 

[sanman]

No chicken or egg. Fluctuations are definable only after one has already defined fields. Without fields the notion of fluctuations wouldn't make scientific sense.

That assumes they are just mere fluctuations, and not manifestations of something deeper (eg.virtual particles), which could be the basis for the Field.

We have already seen that light is quantized as photons - which is the reason that particle model has been accepted.
When the background fluctuations in the field are also quantized, why should we imagine such quantization is an intrinsic property of the field, without being open to accepting a particle model to explain the quantization?

 

[ftr]

Neumaier, I have few questions.

1. in your FAQ there is nothing about vacuum polarization, can you explain it from your point of view.

2. in QED we assume an "associated" EM field for the electron. It seems this field is a kind of pseudo-field because no real photon but a VP as its quanta, am I right.

3. do you agree that VP if they do not exist but some kind of a disturbance is generated which could be due to above field or equivalently to "vacuum fluctuation". this a view of Matt Strassler I think.

 

[A. Neumaier]

1. in your FAQ there is nothing about vacuum polarization, can you explain it from your point of view.

Vacuum polarization is the name for the radiation corrections to the photon self-energy. If computed in perturbation theory, it is given by the sum of all Feynman diagrams with two external photon lines. It is a physical effect caused by the interaction with the electron field, not by the virtual particles in the diagrams, which are pure mnemonic for the integrals used for the computation and play no causal role.
The tale told by the wikipedia page linked to is just a fairy tale, of the same kind as the myth about Hawking radiation that I discussed in the Insight article.

2. in QED we assume an "associated" EM field for the electron. It seems this field is a kind of pseudo-field because no real photon but a VP as its quanta, am I right.

I never heard about associated e/m fields for the electron. In QED there is just a single electromagnetic field and a single electron-positron field.

3. do you agree that VP if they do not exist but some kind of a disturbance is generated

The hypothesis ''they do not exist'' is false, hence there is nothing to agree to.

 

[A. Neumaier]

manifestations of something deeper (eg.virtual particles), which could be the basis for the Field.

Fields are deeper concepts than both fluctuations or virtual particles, hence the latter cannot be the basis for the former.

 

[A. Neumaier]

in your FAQ there is nothing about vacuum polarization

I just added at the end of my insight article The Physics of Virtual Particles relevant definitions of this and related items.

 

[PeterDonis]

That assumes they are just mere fluctuations, and not manifestations of something deeper (eg.virtual particles)

You are assuming that these are two different possibilities--two different ways the universe could be, and we have to figure out which.

What Arnold is saying is that they are just two different ways of trying to describe, heuristically, in ordinary language, the same single way the universe is. There is no actual difference in the physics; the only difference is in the words.

 

[ftr]

In QED there is just a single electromagnetic field and a single electron-positron field.

Ok, this is from wiki QED
https://wikimedia.org/api/rest_v1/media/math/render/svg/9277f5286335ab99c040c9c9151ab752d3bedc49 A_mu is the covariant four-potential of the electromagnetic field generated by the electron itself; do you agree with that?

Also you say

vacuum fluctuations (= nonzero vacuum expectation values)

Reference https://www.physicsforums.com/insights/vacuum-fluctuation-myth/
But I think people mean VF by the variance not the EV.

 

[Mordred]

You are assuming that these are two different possibilities--two different ways the universe could be, and we have to figure out which.

What Arnold is saying is that they are just two different ways of trying to describe, heuristically, in ordinary language, the same single way the universe is. There is no actual difference in the physics; the only difference is in the words.

Oh how true this is unfortunately often trying to describe things heuristically can cause greater confusion. I've been quilty of that on more than one occasion.

At Neumaiur now that I have a better handle on what you trying to express to me. I rectract my concerns.

 

[A. Neumaier]

vacuum fluctuations (= nonzero vacuum expectation values)

I never equated the two. Note that a nonzero variance $\sigma(X)$ is a special case $\langle(X-\bar X)^2\rangle$ of a nonzero vacuum expectation value. I clarified the final piece of my addendum to the insight article.

''The covariant four-potential of the electromagnetic field generated by the electron itself'' is sloppiness on the part of Wikipedia. The term is used solely to distinguish it from the external field mentioned in the same sentence. There is no way to separate the two parts of the field and only their sum has a measurable, hence physical meaning.

 

[ftr]

The fact that there is a variance does indicate that there is fluctuation, doesn't it

There is no way to separate the two parts of the field and only their sum has a measurable, hence physical meaning

do you mean the electron field and the EM field together "added", but the electron field does not "generate" EM.
Arnold, I think people appreciate very much what you have been trying to do, even though the issues you raised in your insight is very well known and debated endlessly but you have put them in a nice prospective story to highlight several interconnected concepts mainly regarding Feynman diagrams which were suppose to make things easier.

I also understand that it might become tiring for you, but an elaborated response might actually shorten to back and forth responses. Thank you again.

 

[Mordred]

D'oh I feel like an idiot I completely forgot the creation/annihilation operators add/subtract a quanta of energy. How embarrassing.

Ok I fully understand where you are coming from Neumaiur with regards to virtual particles.

 

[A. Neumaier]

The fact that there is a variance does indicate that there is fluctuation, doesn't it

In principle it could be interpreted as a fluctuation of the measurement results in repeatedly prepared copies of the system in identical states. But this is a sensible interpretation only for tiny systems of which one can prepare many copies in the same state. One cannot copy a quantum field. It exists only once at each point in spacetime. What is measured is always a (smeared) field expectation value. If something fluctuates there then due to turbulence, which indeed is a random field phenomenon happening in space and time. But turbulence is absent in a vacuum.

do you mean the electron field and the EM field together "added", but the electron field does not "generate" EM.

No. I mean the mathematical sum (no quotation marks) of the two physically inseparable pieces of the electromagnetic field mentioned in Wikipedia in the context of your quote, denoted there $A_\mu$ and $B_\mu$. The electron field is $\psi$ and is a separate entity that cannot be added to the e/m field as it has a completely different transformation behavior.

the issues you raised in your insight are very well known and debated endlessly but you have put them in a nice prospective story to highlight several interconnected concepts

The purpose of these insight articles is to put an end to this seemingly endless debate. Debates are always signs of using a language so imprecise that people continuously misunderstand each other. Once a clear and sufficiently authoritative language becomes widespread, misunderstanding begin to cease and debate becomes as pointless as debating irrational or imaginary numbers. The language exists already but is diluted so much by current informal practice that attempting to make sense of the whole mess is immensely confusing. It took me many years of wading through this confusion before I learned to understand things in such a way that I can point to the sources of misunderstanding in a consistent and hopefully convincing way.

 

[sanman]

You are assuming that these are two different possibilities--two different ways the universe could be, and we have to figure out which.

What Arnold is saying is that they are just two different ways of trying to describe, heuristically, in ordinary language, the same single way the universe is. There is no actual difference in the physics; the only difference is in the words.

But that's actually what I said, and not him. I pointed out that applying a particle model is just a way of describing something. He said that there can only be a Scalar Field.

Whether you want to describe the fluctuations as fluctuations in the Scalar Field, or whether you want to describe them as Virtual Particles, is just a matter of perspective.

But I would argue that quantization tends to push you towards particles, since there's no inherent need for waves to be quantized.

 

[PeterDonis]

Whether you want to describe the fluctuations as fluctuations in the Scalar Field, or whether you want to describe them as Virtual Particles, is just a matter of perspective.

No, it isn't. The scalar field is the fundamental object. "Virtual particles" is just a shorthand way of describing particular things that arise in a particular approximation.

I would argue that quantization tends to push you towards particles, since there's no inherent need for waves to be quantized.

You are making the common mistake of equating "quantized" with "discrete". That's not what quantization means.

From the standpoint of quantum field theory, quantum fields (of which the scalar field is one) are the fundamental objects. "Particles" and "waves" are just names for particular kinds of quantum field states, and there are quantum field states that are not aptly described by either of those names.

 

[Mordred]

To just add a caveat to Peterdonis excellent reply. There is alway a field even without fluctuations/particles etc. Just to stress the field is fundamental.

 

[ftr]

Arnold, I found this paper(researching a different subject) by Jaynes which you mention his name in context of entropy issues in FAQ. But This paper has some relevance to the discussion, what do you think(I kind like what he is saying, but I need to study it more)

http://bayes.wustl.edu/etj/articles/prob.in.qm.pdf

 

[sanman]

To just add a caveat to Peterdonis excellent reply. There is alway a field even without fluctuations/particles etc. Just to stress the field is fundamental.

But Mr Neumaier said that the fluctuations are intrinsic to the field. I'm saying they should be discerned from the field.

 

[Mordred]

Yes he is absolutely correct fluctuations are intrinsic to the field. Fluctuations however do not form nor define a field. Fluctuations is a property of a field much like volume is intrinsic to a 3d object. It isn't separate but an aspect of a field.

 

[sanman]

Yes he is absolutely correct fluctuations are intrinsic to the field. Fluctuations however do not form nor define a field. Fluctuations is a property of a field much like volume is intrinsic to a 3d object. It isn't separate but an aspect of a field.

He's saying there's no reason to look for a cause for those fluctuations - ie. we should just accept them "as is".

Why shouldn't we attribute a cause to the fluctuations? It's like saying there's no need to talk about energy separately from matter, because all matter is endowed with energy in some form or other.

The field may have fluctuations, but we may wish to ask why. He's saying we shouldn't ask why. To me, that's ridiculous - why can't I look for the reason why?

 

[sanman]

No, it isn't. The scalar field is the fundamental object. "Virtual particles" is just a shorthand way of describing particular things that arise in a particular approximation.
You are making the common mistake of equating "quantized" with "discrete". That's not what quantization means.

From the standpoint of quantum field theory, quantum fields (of which the scalar field is one) are the fundamental objects. "Particles" and "waves" are just names for particular kinds of quantum field states, and there are quantum field states that are not aptly described by either of those names.

http://wikidiff.com/quantum/discrete

As adjectives the difference between discrete and quantum
is that discrete is separate; distinct; individual; non-continuous while quantum is of a change, sudden or discrete, without intermediate stages.

I think I used quantum/quantized in the appropriate way.
Discrete things do not have to be of the same size. But quantum things (quanta) are supposed to be of the same size, like fundamental units or fundamental blocks. Because of that, they are like fundamental deltas or units of change.

 

[Mordred]

https://en.m.wikipedia.org/wiki/Quantum

In physics, a quantum (plural: quanta) is the minimum amount of any physical entity involved in an interaction. The fundamental notion that a physical property may be "quantized," referred to as "the hypothesis of quantization".[1] This means that the magnitude of the physical property can take on only certain discrete values

How can you possibly apply the above to a VP ?

 

[Keith_McClary]

Some people still seem to think vacuum fluctuations are a real thing.

• Theoretical estimates of various contributions to the vacuum energy density in QFT exceed the observational bound by at least 40 orders of magnitude. This large discrepancy constitutes the cosmological constant problem. One can distinguish at least two different meanings to the notion of a cosmological constant problem:
1. Calculations of Λ = 8 π G ρvac from assuming real QFT vacuum fluctuations, lead to a huge fine-tuning problem.
...
John Moffat

The value of the cosmological constant is infamously the worst prediction ever made using quantum field theory; the math says it should be 120 orders of magnitude larger than what we observe.
Sabine Hossenfelder

https://twitter.com/skdh

 

[vanhees71]

Yes, it's very hard to get wrong ideas from popular-science books (sometimes even textbooks!) out of the minds of people. Some famous guy (Feynman?) said, that for any problem there's a simple solution, which is wrong.

 

[mfb]

I don't see where the second quote would imply vacuum fluctuations. We cannot really predict a cosmological constant from QFT, but if it is non-zero, the natural scale would be the Planck density.

 

[durant35]

I have a closely related question. In the insight it is mentioned that generally, inside a superposition nothing dynamical happens. But what if the wave function is time dependent, for instance an electron in the double slit experiment, do fluctuations in the quantum state happen then?

 

[A. Neumaier]

if the wave function is time dependent, for instance an electron in the double slit experiment, do fluctuations in the quantum state happen then?

In this case the wave function changes deterministically. The wave function of the spin of an electron changes very smoothly with time, except at the moment of measurement, where it changes randomly. But this randomness has nothing to do with vacuum fluctuations.

 

[durant35]

In this case the wave function changes deterministically. The wave function of the spin of an electron changes very smoothly with time, except at the moment of measurement, where it changes randomly. But this randomness has nothing to do with vacuum fluctuations.

But would you still say that nothing dynamical happens inside the wavefunction before the measurement, even if we take into account the deterministic evolution you mentioned?

It's not like the electron is jumping from one spot to anothee. It literally is in a state without a definite position, right?

 

[vanhees71]

The wave functions evolve according to Schrödinger's equation (i.e., unitary time evolution). I don't know what you mean by "nothing happens inside the wave function". The Schrödinger equation is describing the dynamics of the system.

According to quantum theory nothing is jumping at all. It's another bad idea from "old quantum theory" that should not be used in any modern physics curriculum anymore. Indeed an electron has never a definite position (although in principle it can be quite localized, because it's a massive particle and thus admits the definition of position as an observable). Within non-relatistic quantum theory the position-probability distribution is given by $|\psi(t,\vec{x})|^2$.

 

[A. Neumaier]

But would you still say that nothing dynamical happens inside the wavefunction before the measurement

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.

To say that the electron has no definite position just means that one cannot think of it as being a point. The position of an electron is as well-defined as that of a cloud - it is located in a well-defined region but not in a well-defined point. Only the latter would have a definite position. Thus if one wants a more valid intuitive picture one needs to consider an electron as a smoothly changing cloud distributed over all electron rays with a non-negligible mass density, and contracting to a small spot upon measuring.