# A Measuring Quantum Vacuum Fluctuations

I have been reviewing potential methods for measuring Quantum Vacuum Fluctuations that I might be able to implement in a home hobbyist environment. Must be room temperature devices. I have seen that there are only a couple of possibilities: The Tunnel FET and the Single Electron Transistor. I have not seen that these are available for purchase. So I have a couple of questions:

1) Is the TFET or the SET commercially available or have I just missed it?
2) Is it even conceivable to measure QVF with such devices?
3) Are there any other kinds of commercially available devices that measure QVF?
4) Are there any commercially available devices that may not have the measurement of QVF as their primary function but maybe are affected by QVF and so might be exploited as a QVF measurement device?

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#### weirdoguy

I think you should start with this:

I thought it was pretty well settled that the Casimir Effect for example was the result of Quantum Vacuum Fluctuations. If true then this Casimir Effect is obviously the result of multitudes of QVFs happening all at once on the plates of the test device. I simply am exploring the possibility that some microelectronic device might already exist that could be used to scale down the detection of QVFs to an individual QVF or at least to small numbers of QVFs. So then what is the Scientific explanation for the Casimir Effect if it is not QVFs? I'm going to be disappointed if QVFs are not actually happening. How could such a lie ever get started?

#### PeterDonis

Mentor
what is the Scientific explanation for the Casimir Effect if it is not QVFs?
The term "Quantum Vacuum Fluctuations" refers to a particular feature of the theoretical model that is used to explain various phenomena, including the Casimir Effect. But it does not refer to anything that is directly measurable. Not all features of any theoretical model are directly measurable.

#### Demystifier

2018 Award
So then what is the Scientific explanation for the Casimir Effect if it is not QVFs?
Van der Waals forces, see e.g. https://arxiv.org/abs/1702.03291 and references therein.

I'm going to be disappointed if QVFs are not actually happening. How could such a lie ever get started?
For a brief history of explanations of the Casimir effect see the attached presentation, pages 7-8.

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I have seen this Van Der Waals versus QVF before. I think there is a legitimate argument that the Casimir effect could be the result of both of these phenomena. But I don't think anything here proves that QVFs do not even exist. There is too much activity involving the measurement of QVFs to think it is all a scam. Maybe you are saying the QVFs can't be measured at room temperature. It seems to me that a lot of work has been done measuring QVFs at cryogenic temperatures. This can't all be bogus. If you are saying that you don't think that QVFs are even real and if that is the thinking of this Forum then this Forum will be useless to me. Thank You for your input however.

#### vanhees71

Gold Member
Well, it's clear that the Casimir effect is more like van der Waals than vacuum fluctuations. See the excellent article

Thank You for the article. But does this mean that there is no such thing as Quantum Vacuum Fluctuations? What about the Lamb Shift? Seems like QVFs have been completely implicated in that. Lamb won a Nobel prize for this result.

#### PeterDonis

Mentor
does this mean that there is no such thing as Quantum Vacuum Fluctuations? What about the Lamb Shift?
Read the Insights articles linked to in post #2. The short answer is that you are thinking of "Quantum Vacuum Fluctuations" as the name for some real thing that causes phenomena like the Lamb Shift. It isn't. The term "Quantum Vacuum Fluctuations" is the name for a particular theoretical construct in a particular theoretical method of calculating predictions for what we expect to observe with phenomena like the Lamb Shift or the Casimir Effect. The phenomena themselves are certainly real, and the quantum fields that underlie the phenomena are real; but that does not mean that "Quantum Vacuum Fluctuations" themselves are real.

Lamb won a Nobel prize for this result.
Lamb won a Nobel Prize for measuring the effect, not for claiming or proving that "Quantum Vacuum Fluctuations" were the cause of it.

#### DarMM

Gold Member
Thank You for the article. But does this mean that there is no such thing as Quantum Vacuum Fluctuations? What about the Lamb Shift? Seems like QVFs have been completely implicated in that. Lamb won a Nobel prize for this result.
So basically when you calculate the energy levels of hydrogen in QED and Non-Relativistic Quantum Mechanics they are different. However we can't compute the QED results directly so instead we use perturbation theory.

At second order in perturbation theory we get a term that provides the largest correction to the Hydrogen atom levels. The diagram that helps one construct this integral (essentially a mnemonic device) has a loop that can be pictured as an electron-positron pair popping out of the vacuum.

So you could say that this vacuum pair "shifts" the energy levels from their Non-Relativistic values to help you think of the integral.

In truth though QED just different predicts energy levels that we approximate with a series of integrals.

Read the Insights articles linked to in post #2. The short answer is that you are thinking of "Quantum Vacuum Fluctuations" as the name for some real thing that causes phenomena like the Lamb Shift. It isn't. The term "Quantum Vacuum Fluctuations" is the name for a particular theoretical construct in a particular theoretical method of calculating predictions for what we expect to observe with phenomena like the Lamb Shift or the Casimir Effect. The phenomena themselves are certainly real, and the quantum fields that underlie the phenomena are real; but that does not mean that "Quantum Vacuum Fluctuations" themselves are real.
Since this Theoretical Construct can be used to calculate predictions for multiple disparate phenomena then it would seem to me that the Theoretical Construct begins to become more and more a real Phenomenon and less and less just a Theoretical Construct.

But anyway, I suppose then I should restate my original question as to how we might measure QVFs to: Putting aside whether QVFs actually exist, what existing devices use the Theoretical Construct of QVFs in some aspect of their operation? Do you know if there are any effects in SETs or TFETs that use the Theoretical Construct of QVFs to explain the effects?

#### PeroK

Homework Helper
Gold Member
2018 Award
Since this Theoretical Construct can be used to calculate predictions for multiple disparate phenomena then it would seem to me that the Theoretical Construct begins to become more and more a real Phenomenon and less and less just a Theoretical Construct.
What about measuring a momentum space wave-function?

Assuming you define what "real" means something is either real or it's not. The momentum space wave-function is either real or not. If you use it exclusively to do QM calculations does that make it real?

What about measuring a momentum space wave-function?

Assuming you define what "real" means something is either real or it's not. The momentum space wave-function is either real or not. If you use it exclusively to do QM calculations does that make it real?
I think that if you measure the momentum of a sub atomic particle then you are measuring or collapsing the momentum space wave function to the particular value. That's all I want to do with QVFs. Just want to find some sort of measurement device that can use the QVF Construct to, in effect, measure a QVF. Don't really care if the QVF is real or not.

#### PeroK

Homework Helper
Gold Member
2018 Award
I think that if you measure the momentum of a sub atomic particle then you are measuring or collapsing the momentum space wave function to the particular value. That's all I want to do with QVFs. Just want to find some sort of measurement device that can use the QVF Construct to, in effect, measure a QVF. Don't really care if the QVF is real or not.
Measuring the momentum of a particle doesn't imply in any way that you have measured a momentum space wave function. That is the whole point. Momentum space doesn't exist, in the sense that it is not part of our 4D universe. It's infinite dimensional for a start. You cannot put a measurement apparatus in momentum space.

I think you are chasing shadows here, to be honest.

#### DarMM

Gold Member
Since this Theoretical Construct can be used to calculate predictions for multiple disparate phenomena then it would seem to me that the Theoretical Construct begins to become more and more a real Phenomenon and less and less just a Theoretical Construct.
Well the point to note is that if we didn't use perturbation theory we wouldn't ever see these "vacuum fluctuations". They only occur in one calculation method.

Now don't get me wrong I often pictures things with them, there's plenty of effects like Finite Volume corrections where they give a nice intuitive picture (e.g. Finite Volume corrections can be seen as due to where the vacuum fluctuation pairs travel "around the world").

However they're not necessary to Quantum Field Theory, in a lattice nonperturbative calculation for example you don't have them.

#### A. Neumaier

But I don't think anything here proves that QVFs do not even exist.
It depends on your notion of ''existence''. They surely exist as mathematical abstractions, just like the terms $x^n/n!$ in the expansion of the exponential as a power series. But nobody ever suggested that these sereis terms are real just bcause you can calculate with them something real.
Since this Theoretical Construct can be used to calculate predictions for multiple disparate phenomena then it would seem to me that the Theoretical Construct begins to become more and more a real Phenomenon and less and less just a Theoretical Construct.
The term $x^n/n!$ doesn't become more real by using it to calculate an exponential in a calculation needed for analyzing some electrical circuit.
how we might measure QVFs
See my Insight article https://www.physicsforums.com/insights/vacuum-fluctuations-experimental-practice/

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#### vanhees71

Gold Member
Since this Theoretical Construct can be used to calculate predictions for multiple disparate phenomena then it would seem to me that the Theoretical Construct begins to become more and more a real Phenomenon and less and less just a Theoretical Construct.

But anyway, I suppose then I should restate my original question as to how we might measure QVFs to: Putting aside whether QVFs actually exist, what existing devices use the Theoretical Construct of QVFs in some aspect of their operation? Do you know if there are any effects in SETs or TFETs that use the Theoretical Construct of QVFs to explain the effects?
The point is that the words "vacuum fluctuations", "virtual particles", "vertex corrections", etc. are just names (abbreviations) for the perturbative series (in this case of QED).

I always emphasize that relativistic QT should be formulated as relativistic QFT, and relativistic QFT can only be solved in terms of perturbation theory (let alone ab initio numerical approaches like lattice to solve certain aspects of QCD, but that's off-topic here).

So the modern solution of the hydrogen problem starts with QED at tree level in the Coulomb gauge. That's particularly convenient for this problem, because you come already very close to the empirically correct solution. The tree level always boils down to the solution of the classical field equations, which in this case is the Dirac equation for an electron in the staticc Coulomb field of a nucleus. This leads to the famous result already found (by shear luck) in the "old quantum theory" by Sommerfeld and later lead Dirac, among other issues, to the discovery of his famous relativistic wave equation for spin-1/2 particles which bears his name, the Dirac equation.

Now this cannot be the whole truth since it doesn't take into account the quantization of the fields, and indeed one has to go to higher orders in perturbation theory. Thanks to the genius of Feynman we have a short-hand systematic notation for these calulations looking almost pictorial, the Feynman diagrams. The Feynman diagrams are, however, not more thatn precisely that, namely very clever symbolism for cumbersome calculations of corrections to the leading-order perturbative result (at "tree level", i.e., represented by Feynman diagrams without loops). The corrections symbolized by Feynman diagrams with loops are thus sometimes also called "radiative corrections", because they go beyond the tree-level result for atomic energy levels where no "radiation" is taken into account but only the static Coulomb field of the perturbative formulation of QED in the Coulomb gauge.

At one-loop level (i.e., at corrections of order $\mathcal{O}(\hbar)$) there are

-electron self-energy corrections: these are corrections describing the interaction of an electron with the quantum-fluctuating electromagnetic field, but note that we have a real electron in the game, i.e., we do not deal with the perturbative vacuum! The self-energy corrections should rather be interpreted of the electron interacting with its own flucuating em. field than thinking as if there were "vacuum fluctuations"

-photon polarizations: This is the analogy of self-energy corrections for the photon. The modern terminology would call the corresponding diagram "photon self-energy" rather than "vacuum polarization" or "photon polarization". Note again: We deal with a photon here, i.e., it's again not the perturbative vacuum, but the correction is due to the quantum fluctuations of the Dirac field due to the presence of a photon (i.e., an electromagnetic field).

-vertex corrections: This describes the fact that two electrons (or an electron and a positron) interact and this interaction is also corrected for quantum fluctuations of the electromagnetic field, but again it's not the perturbative vacuum that fluctuates, but the em. field due to the presence of the interacting charges. Among other things (charge renormalization) this diagram also corrects for the gyro-factor of the electron, not being exactly 2 as is only true at tree-level. This correction of the gyro-factor is, as the Lamb shift, among the most precise agreements between theory and experiments in the history of physics.

Anyway, all these effects together contribute to the Lamb shift, and nowhere are "vacuum fluctuations" the reason. Nowadays the evaluation of the perturbative series for the Lamb shift of the hydrogen atom (and also the muonic hydrogen-like bound state of a proton and a muon) are driven to 5th loop order, and theory and experiment agree very well.

#### PeterDonis

Mentor
Since this Theoretical Construct can be used to calculate predictions for multiple disparate phenomena then it would seem to me that the Theoretical Construct begins to become more and more a real Phenomenon and less and less just a Theoretical Construct.
No, because you don't have to use the theoretical construct to calculate the predictions; that is done out of convenience, not necessity.

#### PeterDonis

Mentor
That's all I want to do with QVFs. Just want to find some sort of measurement device that can use the QVF Construct to, in effect, measure a QVF.
Well, if QVFs can be used as theoretical constructs to calculate predictions for the Lamb Shift or the Casimir Effect, then wouldn't any measurement device that measures those phenomena count as a measurement device for QVFs?

#### A. Neumaier

This leads to the famous result already found (by shear luck) in the "old quantum theory" by Sommerfeld
Not sheer luck but because in this approximation, hydrogen is completely integrable, leading to its exactly solvable. The Bohr-Sommerfeld quantization conditions lead to exact results whenever a quantum system is completely integrable.

Anyway, all these effects together contribute to the Lamb shift, and nowhere are "vacuum fluctuations" the reason. Nowadays the evaluation of the perturbative series for the Lamb shift of the hydrogen atom (and also the muonic hydrogen-like bound state of a proton and a muon) are driven to 5th loop order, and theory and experiment agree very well.
Very good. But is there no other Phenomenon or Experiment that could indicate the existence of QVFs? QVFs are a total fiction?

#### PeterDonis

Mentor
is there no other Phenomenon or Experiment that could indicate the existence of QVFs? QVFs are a total fiction?
The series of Insights articles on vacuum fluctuations has been referred to repeatedly in this thread. It addresses all of the questions you have been asking. Please read those articles, and then, if you still have questions about what they say, you can start a new thread to ask them.

This thread is closed.

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