## Are virtual particles really there?

 Quote by tom.stoer Why do we have to discuss virtual particles every other week? Isn't it possible to have a sticky thread named "virtual particles are virtual particles because they are virtually virtual"?
It doesn't seem to me that such a sticky would stop a lot of these posts, which boil down to arguing, not asking a question.

 It doesn't seem to me that such a sticky would stop a lot of these posts, which boil down to arguing, not asking a question.
I ask a painfully clear question: how do you explain Coulomb force between two charged quantum particles without virtual particles? No one answered.

 That is what Zee is saying, yes. Zee dislikes virtual particles so much that he only mentions them about 10 times in the book, apparently each time as a shorthand for an internal line or similar concept.
He most certainly is not referring to real particles as transmitting forces. Are you trying to tell me that in a Coulomb force you can measure individual photons???

Have you read page 19 of the book where he writes about vacuum? Let me quote:"Incidentally, the vacuum in quantum field theory is a stormy sea of quantum fluctuations", it goes on on the next page "watching a boiling sea of quantum fluctuations. We would like to disturb the vacuum..."

You picked here the wrong text to argue against the idea of virtual particles, tiny-tim. And P&S can be found in every library or at amazon.

I follow you peoples argumentation here and see your point, but saying quantum field theory is just computing S-matrices and everything else just tricks and tools and fictious does not convince.

But what the heck, I was even childish enough to write Prof. Zee an email to come clean about this virtual business. I also wrote Edward Witten and Frank Wilczek an email. Zee did not answer yet, Witten and Wilczek did! Obviously must be very kind people.(If you don't believe me, I can redirect you the emails.)

My question to them was:

 Hi, I'm a physic student with a quick question. Are virtual/ off mass particles really out there, do they really exist or are they just mathematical artifacts of pertubation theory and thus fictious? I would be very grateful for any answer.
Witten answered rather shortly
 This is a not such a simple question, because the meaning of real'' is a little subtle in quantum mechanics. A precise statement, but one that may not satisfy you, is that virtual particles do not exist as asymptotic states.
Wilczek wrote
 Hi, It comes down to what you mean by "really there". When we use a concept with great success and precision to describe empirical observations, I'm inclined to include that concept in my inventory of reality. Buy that standard, virtual particles qualify. On the other hand, the very meaning of "virtual" is that they (i.e., virtual particles) don't appear *directly* in experimental apparatus. Of course, they do appear when you allow yourself a very little boldness in interpreting observations. It comes down to a matter of taste how you express the objective situation in ordinary language, since ordinary language was not designed to deal with the surprising discoveries of modern physics. All the best, Frank W.

 Quote by kexue I ask a painfully clear question: how do you explain Coulomb force between two charged quantum particles without virtual particles? No one answered.
Let me be clear: virtual particles allow the math to work for something like the Coulomb force(s), and there is a real effect to be observed, but I don't believe anyone expects a better theory to include virtual particles.

I can describe the magnetic force in terms of the exchange of <insert noun>... and the EM force is real, but that doesn't mean that my description is an accurate one. It's just unfortunate that the name "virtual particle" ever came along... without it these discussions wouldn't exist.

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 Quote by kexue I ask a painfully clear question: how do you explain Coulomb force between two charged quantum particles without virtual particles? No one answered.
The last time I answered your question (!) was on 28th of November (!) in this thread http://www.physicsforums.com/showthread.php?t=445730 post #5,7. Unfortunately you didn't respond but started this new thread.

I repeat my statement:

 Quote by tom.stoer One can formulate QED in Coulomb gauge which contains the Coulomb potential w/o any sumation over radiative corrections. One has to use the appropriate gauge for this problem. It is a common misconception (which I see quite often here in the PF) that QED does contain only perturbative photons. This is not correct in general.
Have you studied the paper I proposed you to read?

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 Quote by tom.stoer Why do we have to discuss virtual particles every other week? Isn't it possible to have a sticky thread named "virtual particles are virtual particles because they are virtually virtual"?
But if we keep posting in threads on virtual particles so that they stay at the top then we virtually have a virtual sticky.

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 Quote by Born2bwire But if we keep posting in threads on virtual particles so that they stay at the top then we virtually have a virtual sticky.

 Quote by kexue I ask a painfully clear question: how do you explain Coulomb force between two charged quantum particles without virtual particles? No one answered.
No one denies that. They are needed to explain Coulomb force.

Still, all virtual particles or virtual transitions I know are equally well described by a more technical term - 'perturbative corrections'.

Can you give me any example that a virtual particle arises in a non-perturbative context?

 Quote by kexue But what the heck, I was even childish enough to write Prof. Zee an email to come clean about this virtual business. I also wrote Edward Witten and Frank Wilczek an email. Zee did not answer yet, Witten and Wilczek did! Obviously must be very kind people.(If you don't believe me, I can redirect you the emails.) My question to them was: "Are virtual/ off mass particles really out there, do they really exist or are they just mathematical artifacts of pertubation theory and thus fictious?" Witten answered rather shortly "This is a not such a simple question, because the meaning of real'' is a little subtle in quantum mechanics. A precise statement, but one that may not satisfy you, is that virtual particles do not exist as asymptotic states." Wilczek wrote "Hi, It comes down to what you mean by "really there". When we use a concept with great success and precision to describe empirical observations, I'm inclined to include that concept in my inventory of reality. Buy that standard, virtual particles qualify. On the other hand, the very meaning of "virtual" is that they (i.e., virtual particles) don't appear *directly* in experimental apparatus. Of course, they do appear when you allow yourself a very little boldness in interpreting observations. It comes down to a matter of taste how you express the objective situation in ordinary language, since ordinary language was not designed to deal with the surprising discoveries of modern physics. All the best, Frank W."
Right, so they are both saying the same thing - there is a precise mathematical machinery for doing calculations and virtual particles are mathematical constructs in the formalism but the point of the calculations is to make probabilistic predictions for empirical measurements of quantities we would normally identify with "real", whilst the intermediary constructs are not generally considered "real".

It's rather like asking if a photon "really" goes off to alpha centuri and whizzes around it a couple of times when doing a double slit experiment, since we have a mathematical formalism which considers such behaviour (path integral) and predicts correct results for the interference pattern observed.

The intermediary mathematical constructs in QFT should surely not be considered "real" in any sense, in fact nothing should be considered "real" unless it can be observed, which essentially restricts "reality" to stable macroscopic constructs, since everything at the microscopic level is in probabilistic flux.
 To clarify, by "microscopic" I mean ~planck scale. And I realise Wilczek is suggesting that virtual particles are "real" by his definition. It's possible that with a "correct" simulation of reality at the scale of electrons and protons we may really see these virtual particles shooting around between particles, so it's possible Wilczek is right to think they are "real". On the other hand there may be a better way to mathematically model the microscopic, and with another model we may have no such particle exchanges. My feeling is that we will see something that can partially support the case for "reality" of the particles.

I could not resist to send the same question to Curtis Callan.

 The "virtual" particle is real enough, since its existence leads to perfectly measurable effects on "real" particles with which it interacts. A classic example is the way the interaction of the electron in the hydrogen atom with "virtual photons" leads to the Lamb shift which splits the 2S and 2P levels (which are degenerate in the Schrodedinger equation solution). The terminology "virtual" lends an air of mystery, but it reflects a general concept in quantum mechanics which you will find perfectly understandable once you have studied "perturbation theory" in your first year of taking quantum mechanics. CGC
 Recognitions: Science Advisor I repeat my question: Have you studied the paper I proposed?

 Quote by tom.stoer I repeat my question: Have you studied the paper I proposed?
No, not yet, Tom. Can you roughly explain what it says?

 Quote by kexue I could not resist to send the same question to Curtis Callan. His answer "The "virtual" particle is real enough, since its existence leads to perfectly measurable effects on "real" particles with which it interacts. A classic example is the way the interaction of the electron in the hydrogen atom with "virtual photons" leads to the Lamb shift which splits the 2S and 2P levels (which are degenerate in the Schrodedinger equation solution). The terminology "virtual" lends an air of mystery, but it reflects a general concept in quantum mechanics which you will find perfectly understandable once you have studied "perturbation theory" in your first year of taking quantum mechanics. CGC"
By that logic, epicycle orbits of planets could be considered real too.

At least Wilczek clearly demarcates between mathematical concept and reality.
 Recognitions: Science Advisor In this paper a "quantum gauge fixed" Hamiltonian is constructed for QED, which contains a static Coulomb term. The gauge fixing is implemented via unitary transformations. There is a simple example in 1-dim. QM, a two-particle system with interaction V(x-y). Instead of going to the c.o.m system, setting the total momentum P=0 and quantizing in x,p one first quantizes in x,y, ... and implementes P~0 as a constraint. The space of physical states is then described by the states |p, P=0>, but X and P are still qm operators. In QED the constraint P~0 is replaced by the Gauss law constraint G~0. By a (complicated) unitary transformation the space of physical states is described via |transversal photons, G=0>. The resulting Hamiltonian consists of - a kinetic photon term - a kinetic fermion term - an interaction term where fermions couple to dynamical photons to (*) - an interaction term where fermions couple to a static Coulomb potential (**) (*) would result in virtual particles in a perturbation expansion (**) is the well-known Coulomb potential which looks like $$\hat{V}_C = e^2 \int d^3x\,d^3y\,\frac{\rho(x)\,\rho(y)}{|x-y|}$$ The charge density in the numerator is just the 0th component of the four-vector current density and looks like $$\rho = \bar{\psi}\gamma^0\psi$$ i.e. it is bilinear in the fermion fields. The conclusion is that virtual particles from (*) do not generate the Coulomb potential but only perturbations to the Coulomb potential. [This approach is heavily used in canonical, non-perturbative quantization of QCD. One applies unitary operators to define "dressed" fermion fields. Via this dressing the color-Coulomb potential (which contains gluon fields!) changes. The color-Coulomb potential is terribly complicated. One has to define a partial differential operator D[A] where A is the gluon field. In order to construct V one has to invert D which means that you have an A-dependend integral operator with a kernel that has formally an A-dependent denominator. You are not allowed to make a perturbation expansion as you would lose all information regarding the non-perturbative structure contained in 1/D which is responsible for color confinement.] Lessons learned: both the interaction potential and the definition of fermion fields are gauge dependent. Therefore the concept of virtual particles is gauge dependent, too. The Coulomb potential itself is not necessarily generated by one-particle exchange but can (depending on the gauge) be described as a static term.
 Thanks Tom for the very elaborated explanation, it's very much appreciated. Since you seem much more knowledgeable than me, I might need some time to understand what you just wrote here. One reason why I did not read the paper by myself was because it looked a bit over my head. I'm still learning QFT, you know!

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 Quote by tom.stoer In this paper a "quantum gauge fixed" Hamiltonian is constructed for QED, which contains a static Coulomb term....be described as a static term.
"And, therefore, by process of elimination, the electron must taste like grape-ade."

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