# Vacuum Fluctuations in Experimental Practice

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This Insight Article is a sequel of the Insight Articles ”The Physics of Virtual Particles”, “Misconceptions about Virtual Particles“ , and ”The Vacuum Fluctuation Myth”, which make precise what a virtual particle is, what being real means, document some of the liberties taken in physics textbooks in the use of this concept, mention the most prominent misuses, and document the origin of some of the associated myths. In short, the concept of virtual particles is well-defined and useful when restricted to its use in Feynman diagrams and associated technical discussions. But it is highly misleading when used to argue about vacuum fluctuations, as if these were processes happening in space and time. The latter is a frequent misunderstanding, a myth that has not the slightest basis in particle physics.

However, one meets occasionally mythical claims even in the scientific literature. Therefore it pays to look at a representative recent paper in which vacuum fluctuations play a seemingly prominent role, and answer the question: How do vacuum fluctuations look like in practice?

http://science.sciencemag.org/content/350/6259/420 is the official web page for accessing a paper from Science by Riek and collaborators called ”Direct sampling of electric-field vacuum fluctuations” (Science 23 Oct 2015: Vol. 350, Issue 6259, pp. 420-423). A total of nine (9!) scientists take credit for having achieved that, so their jointly presented evidence should have some weight.

The journal web page, where Science readers are introduced to the paper, tries to generate publicity for the paper by placing the vacuum fluctuation myth in front of the main text:

According to quantum mechanics, a vacuum is not empty space. A consequence of the uncertainly principle is that particles or energy can come into existence for a fleeting moment.

Scientific publications in quantum optics typically use more careful language, and so do the authors of the paper, who write in the abstract something much milder:

The ground state of quantum systems is characterized by zero-point motion. This motion, in the form of vacuum fluctuations, is generally considered to be an elusive phenomenon that manifests itself only indirectly. Here, we report direct detection of the vacuum fluctuations of electromagnetic radiation in free space.

But still, it is an extraordinary claim that gives vacuum fluctuations the appearance of reality. Thus a closer look at their paper is called for.

Towards the end of their paper, they write:

In our study, we directly monitored vacuum fluctuations without amplifying them. The only effective part […] of the operator that extracts the variance of the field in Eq. 4 indicates that vacuum fluctuations correspond to photons, which spontaneously arise and vanish in the ground state. Time-energy uncertainty demands that virtual excitations have a limited lifetime on the order of their oscillation cycle (32). The subcycle temporal resolution provided by the ultrashort probe ensures that we can directly detect effects originating from purely virtual photons.

The first sentence is still phrased in a cautious language, as the word ‘indicates’ hints at a tentative finding only. But then they assert the vacuum fluctuation myth about ”photons, which spontaneously arise and vanish in the ground state.” The reference [32] they give to justify this indication is only to another paper by one of the authors, not – as one should expect for such a revolutionary result claimed – a basic reference where one could see a detailed derivation how these photons arise spontaneously. Indeed, there are no such references since spontaneous processes happen only in unstable objects, but the vacuum is completely stable. And in the third sentence they forgot their moderation: they announce – without giving any further argument – their surprising claim ”that we can directly detect effects originating from purely virtual photons”. The justification is completely lacking….

But let us look at their experimental findings. On closer reading of the paper one finds that what fluctuates in the experiment is the electro-optical signal detected, not the vacuum. The electro-optical signal is the only thing measured, and it exhibits fluctuations. Thus they are fluctuations of the signal, not of the vacuum.

To understand what this means consider fluctuations of a visual signal seen on an oscilloscope in an ordinary experiment, and someone claims that these are a visual proof of fluctuations of the vacuum. Nobody would take such a claim serious without a proof.
To argue that fluctuations of the vacuum are measured one would have to give theoretical evidence that the signal fluctuates in the same way as the vacuum. Lack of this evidence is enough to reveal the claim as pure speculation.

So let us look at the evidence provided for their claim. The vacuum (whose fluctuations were allegedly observed) appears only indirectly – in spite of the title of the paper and the advertisement in the abstract -, namely in the form of a theoretical contribution to the variance of this signal in eq. (7), denoted $\Delta\bar E_{vac}^2$. This contribution, defined in eq. (4), is of the form $\langle X\rangle$, where $X$ can be read off from eq. (4) to be a sum of squares of Fourier components of the electric field, with the ensemble expectation taken in the ground state of the radiation field. The latter is referred to as the vacuum.

A casual reader of Science – not being an expert in quantum optics – is likely to imagine that the vacuum is a region of space devoid of matter and radiation but, indoctrinated by popular stories, filled with quantum fluctuations. Unfortunately, it is not stated in this paper where this vacuum is located: The putative vacuum appears nowhere in the description of the experimental set-up. One concludes that it does not take part in the experiment, except figuratively. How is this possible?

What is called (not only in this paper, but everywhere where quantum field theory is used) the vacuum is just a mathematical state used in the computations of quantum electrodynamics (QED) with which predictions about experimentally realizable situations are computed in perturbation theory. QED is our most successful quantum field theory. It is well-defined in perturbation theory (and at present only in this form) and leads in this form to some extraordinarily precise (10 digit) predictions, higher in relative accuracy than any other physical theory we know. It is manifestly Poincare invariant (hence valid relativistically) and gauge invariant. It is the theory that played the role model for the construction of other quantum field theories for microscopic systems, such as quantum chromodynamics (QCD). The latter is quantitatively far less well developed since its forces are far stronger, so that perturbation theory gives poor results. Compared to QED, QCD has the advantage that it is asymptotically free at large energies, with the consequence that – unlike QED – it can be studied in a lattice approximation, with enormous numerical effort ultimately rewarded by reasonable (few digit) accuracy.

QED, on the other hand, has the advantage that, because the fine structure constant is tiny at all experimentally accessible distances and energies, renormalized perturbation theory already produces very useful results at lowest order (1 loop), with closed, Poincare invariant formulas whose use needs hardly any numerical effort. The way perturbation theory works is by relating the interacting theory, i.e., the physical QED, to a mathematically well-defined but physical fiction in which electrons have physical charge zero (the so-called ”free QED”). Then everything that can be compared with experiment is expressed in terms of power series in the true electron charge $e$, with coefficients deduced by perturbation theory and expectation values of the vacuum state in this fictitious theory. The mathematically cleanest way to do this – fully Poincare invariant and completely avoiding both the infamous infinities in naive perturbation theory and the need for an energy cutoff that must be moved to infinity after all these infinities have been cancelled – is causal perturbation theory. It reproduces exactly the formulas derived earlier by mathematically more questionable methods that earned Feynamn, Tomonaga, and Schwinger the 1965 Nobel prize ”for their fundamental work in quantum electrodynamics, with deep-ploughing consequences for the physics of elementary particles”.
From the causal perturbation theoretic treatment it is clear and mathematically undisputable that everything experimentally measurable about photons, electrons, and positrons (and with appropriate extensions, also everything else) is expressible in terms of vacuum expectation values. Therefore explaining something as a consequence of hypothetical vacuum fluctuations because certain vacuum expectations occur in the quantum mechanical formula used for its calculation explains nothing, since vacuum expectations occur in all quantum field calculations, as long as they are done in a perturbation theoretic setting. In nonperturbative lattice field theoretic studies, one cannot find the slightest trace of vacuum fluctuations since the vacuum plays no role at all in the calculations.

”Explanations” by vacuum fluctuations therefore have great similarity with (and as little weight as) the absurd claim that all motion is caused by elementary arithmetic since additions, subtractions, multiplications and divisions are always used in the solution of the differential equations describing the dynamics.

For those interested, let me also remark that although causal perturbation theory serves to dispell the myths surrounding virtual particles and vacuum fluctuations, causal perturbation theory is also the origin of a true ghost story.

I am therefore I think

29 replies
1. sanman says:

Sir, you write:

"what fluctuates in the experiment is the electro-optical signal detected, not the vacuum."

Sir, by what experimental/observational means can we discern that the fluctuations are not part of the Vacuum?

It's one to say that "vacuum fluctuations" are an unsupported assertion, but it's another thing to be able tor rule them out, particularly by experimental means.

2. A. Neumaier says:

It's one thing to say that "vacuum fluctuations" are an unsupported assertion, but it's another thing to be able tor rule them out, particularly by experimental means. How can this "unsupported assertion" be ruled out, experimentally?

Claims require proof, otherwise they can be ignored. That's the rule in science. Nothing is ruled out in science; the demarcation line between science and speculation is the proof, not the disproof.

The electro-optical signal is the only thing measured, and it exhibits fluctuations. Thus they are fluctuations of the signal, not of the vacuum.

To understand what this means consider fluctuations of a visual signal seen on an oscilloscope in an ordinary experiment, and someone claims that these are a visual proof of fluctuations of the vacuum. Nobody would take such a claim serious without a proof.

To argue that fluctuations of the vacuum are measured one would have to give theoretical evidence that the signal fluctuates in the same way as the vacuum. Lack of this evidence is enough to reveal the claim as pure speculation.

3. sanman says:

Claims require proof, otherwise they can be ignored. That's the rule in science. Nothing is ruled out in science; the demarcation line between science and speculation is the proof, not the disproof.

The electro-optical signal is the only thing measured, and it exhibits fluctuations. Thus they are fluctuations of the signal, not of the vacuum.

To understand what this means consider fluctuations of a visual signal seen on an oscilloscope in an ordinary experiment, and someone claims that these are a visual proof of fluctuations of the vacuum. Nobody would take such a claim serious without a proof.

To argue that fluctuations of the vacuum are measured one would have to give theoretical evidence that the signal fluctuates in the same way as the vacuum. Lack of this evidence is enough to reveal the claim as pure speculation.

"The electro-optical signal is the only thing measured"

Sir, what is measured is "the electro-optical signal in the presence of the vacuum"

We have 2 dance partners here, and if one of them is malodorous or having squeaky shoes, we won't be able to tell which one is the culprit as long as we are only seeing them together.

If we could examine them individually apart from one another, then we might be able to tell which one is malodorous or having the squeaky shoes.

There may not be a way to measure an electro-optical signal apart from the vacuum, since we cannot step outside of spacetime, but it may be useful to look at other phenomena in the vacuum (sans electro-optical signal) to see if any similar behavior can be observed.

I do not see how you can assert that only the electro-optical signal is being measured, when that signal is occurring in the presence of the vacuum, and thus possibly interacting with the vacuum.

4. A. Neumaier says:

in the presence of the vacuum

In the presence of which vacuum? The vacuum is not part of the experimental set-up!

5. sanman says:

In the presence of which vacuum? The vacuum is not part of the experimental set-up!

Sir, we are not given a choice on whether or not to include the Vacuum in our experimental setup. The Vacuum has included itself because it is omnipresent – it is spacetime.

6. A. Neumaier says:

The Vacuum has included itself because it is omnipresent – it is spacetime.

No. Space-time is a vacuum only in a very specific state. If the two were the same we wouldn't have two different words for them.

7. mfb says:

Nice article!

Compared to QED, QCD has the advantage that it is asymptotically free at large energies, with the consequence that – unlike QED – it can be studied in a lattice approximation, with enormous numerical effort ultimately rewarded by reasonable (few digit) accuracy.

Sometimes we would be happy to have a 10% accuracy…

8. A. Neumaier says:

Nice article!Sometimes we would be happy to have a 10% accuracy…

I know. I was thinking of optimistic figures (low lying baryon spectrum to $1-9$%), and deliberately used the vague expression ''few''.

As you probably know (I write this for @atyy who thinks no continuum limit is needed), a lot needs to be done to get values that can be compared with experiment, not just calculations on a fixed lattice. From the paper just cited:

p.29: What one would ideally like to do then is to fix the N_f + 1 dimensionless bare parameters of the lattice theory, the bare quark masses and the gauge coupling, such that the N_f dimensionless observables on the lattice assume their physical values exactly and the lattice spacing a is of the desired size. One could then measure any observable on the lattice for a range of lattice spacings a and, with the appropriate functional form that is given by the discretization effects of the specific action used, extrapolate them into the continuum a = 0. […]

p.31: The removal of the cutoff, also known as continuum extrapolation, is an unavoidable part of any lattice calculation that wants to make a statement about the underlying fundamental continuum theory. The severity of the continuum extrapolation however depends very strongly on both the action used and the combination of scale setting observable and measured observable. […]

p.46: While ground state non-singlet hadron masses can be computed to a few percent accuracy today, reaching the same level of precision for excited states or singlet hadrons is still a challenging task.

The final results for the baryon masses in the infinite volume limit, together with their error margins, are given in Table 1 on p.38.

9. sanman says:

No. Space-time is a vacuum only in a very specific state. If the two were the same we wouldn't have two different words for them.

Just for clarity, which specific state are we talking about? You mean the "evacuated" state? I was speaking of the Quantum Vacuum, which exists even when matter is present, and it even affects that matter. For instance, it is the Quantum Vacuum which prevents matter from dropping below Zero Kelvin, because its fluctuations put back into the matter a basic minimum amount of energy.

So my point is that whether you measure your electro-optical signal in the presence of matter or without its presence, the Quantum Vacuum and its fluctuations are still being felt, and are still influencing the measured results.

10. A. Neumaier says:

I was speaking of the Quantum Vacuum, which exists even when matter is present, and it even affects that matter. For instance, it is the Quantum Vacuum which prevents matter from dropping below Zero Kelvin

This is not the way physicists speak about the vacuum. Maybe you should make yourself more acquainted with real science.

11. Mordred says:

I've been reading up on QFT itself and I am beginning to see where Neumaiur is coming from. Still not sure I have everything straight though. Actually positive that I don't lol, the majority of the math itself isn't the issue though. I'm currently on the Ultraviolet cutoffs and the imaginary i. Though I still need to work on the LSZ reduction formula.

Point being is from what I've gotten so far I can see the validity behind this article

12. sanman says:

This is not the way physicists speak about the vacuum. Maybe you should make yourself more acquainted with real science.

Alright, can I say that "it is the fluctuations modeled by the Quantum Vacuum Theory which prevent a body of matter from dropping to a temperature below Zero Kelvin"? (ie. even if you don't like the Quantum Vacuum model, surely you accept the existence of the fluctuations which are describable by other models of your preference)

Even if you prefer the Scalar Field as the basis for fluctuations, you haven't shown me a way to separate the Scalar Field from spacetime. Therefore, if an electro-optical signal is being measured in the Scalar Field, and that field is indistinguishable/inseparable from spacetime, then any attributes it has can be attributed to spacetime itself just as easily. How can we know better, if we can't tell them apart, or observe them apart from one another?

13. PeterDonis says:

can I say that "it is the fluctuations modeled by the Quantum Vacuum Theory which prevent a body of matter from dropping to a temperature below Zero Kelvin"?

The impossibility of a piece of matter dropping to below zero Kelvin (or even reaching zero Kelvin) is not a quantum phenomenon. It's already present in classical thermodynamics.

You might be confusing this phenomenon with the quantum phenomenon that an object at zero Kelvin (which is an idealization not realizable in practice) does not (necessarily) have zero energy.

you haven't shown me a way to separate the Scalar Field from spacetime

Have you actually looked at the math? It's obvious there.

14. A. Neumaier says:

Quantum Vacuum Theory

There is no quantum vacuum theory. Please learn the subject properly before claiming assertions about the subject matter.

15. sanman says:

The impossibility of a piece of matter dropping to below zero Kelvin (or even reaching zero Kelvin) is not a quantum phenomenon. It's already present in classical thermodynamics.

You might be confusing this phenomenon with the quantum phenomenon that an object at zero Kelvin (which is an idealization not realizable in practice) does not (necessarily) have zero energy.

Sir, I was not attempting to justify which is the most rightful explanation for why things can't go to absolute zero (or below it), I was simply referring to the Quantum Vacuum as being an explanation in its own right.

Have you actually looked at the math? It's obvious there.

Please then let me amend my statement:

"you haven't shown me an EXPERIMENTAL way to separate the Scalar Field from spacetime"

Since we were talking about measurement, and measurement is usually done through experimental observation, I assumed it was apparent that I was speaking in the context of real-world method of measurement.

The original argument here was that "Quantum Vacuum particles do not exist, they are merely mathematical constructs and are not real. Mathematical description is not enough to make something real. It is the Scalar Field which is real, not the hypothetical Quantum Vacuum particles."

And yet when I ask why the electromagnetic Scalar Field should be seen as separate from spacetime, then you are giving me the reply that

"Come on – it's all about the Math!"

I feel like we are arguing like Abbott and Costello in "Who's On First?"

I am not trying to be argumentative, but I feel that the Quantum Vacuum particles interpretation as just as legitimate as the belief in the electromagnetic Scalar Field. There has not been any proof through real world experimental measurement that rules out the existence of the Quantum Vacuum particles. That was what I was taking issue with.

16. PeterDonis says:

I was simply referring to the Quantum Vacuum as being an explanation in its own right.

Which it isn't.

you haven't shown me an EXPERIMENTAL way to separate the Scalar Field from spacetime

That's obvious too: there are different observables corresponding to measurements of the scalar field vs. measurements of spacetime (which really means measurements of times and distances).

There has not been any proof through real world experimental measurement that rules out the existence of the Quantum Vacuum particles

"Quantum vacuum particles" are just one interpretation of various measurement results. There are other interpretations, but they all predict the same measurement results. In order for "quantum vacuum particles" to be more than just an interpretation, you would have to find some measurement result that was predicted to be different if "quantum vacuum particles" exist than if other interpretations are correct. If you can find an acceptable reference to such a prediction (which I strongly doubt you can), then post it. Otherwise your speculations are off topic.

17. Daniel Kellis says:

I think virtual particles are OK in diagrams if they help solve the problem. But it is not OK to let virtual particles break the fourth wall, as is done with Hawking radiation. One virtual particle has positive energy and the other has negative energy. Hawking radiation relies on Maxwell's demon to ensure that the negative energy virtual particle always goes into the black hole and the positive energy virtual particle always escapes.

18. mfb says:

The derivation of Hawking radiation does not use virtual particles at all. That is just a pop-science description that leads to misconceptions.