Karl,

You certainly recall Bohr's famous dictum "It is wrong to think that the task of physics is to find out how Nature is. Physics concerns what we can say about Nature."

In Bohr's sense, the best what we can say about a photon is contained in Feynman's formulation of QED of the years 1949/50: Here I read: "[QED is] a description of direct interaction at a distance (albeit retarded in time) between charges." (I wonder how many today's users of QED are aware of this.) Following Feynman I understand (real) photons as virtual photons exchanged over a long distance. Virtual photons, in turn, are artifacts of the perturbation algorithm. They refer to the structure of momentum-entangled two-particle states that can be described as being generated by the exchange of quanta of momentum (=virtual photons) between charged particles. In this sense a photon refers to the structure of entangled two-particle states rather than to an independent physical entity. So the 'existence' of photons depends on answering the question: Why are two-particle states momentum entangled? But that is different story.

Karl,

Would you kindly tell us how many physicists there are in the world and what is the idea of each one of them about the photon? I "heard" all sort of exotic opinions about the photon - the imagination of people is very creative, especially when they are not exactly at home with the quantum theory formalism.

So, if you want an answer, then please state your question more precisely. The quantum optics shows us indeed how to introduce quantization in the expression of the electromagnetic field. You can see that for example in the "Quantum Optics" of Walls and Milburn.

Now, can you formulate more clearly your doubts?

Dear @Walter,

There is something not so clear in what you explained. You said:

==> "Following Feynman I understand (real) photons as virtual photons exchanged over a long distance."

What goes there? Virtual photons travelling a long distance become real? As far as I know virtual particles are very short-lived. For travelling a long distance a particle needs time, therefore it can't be short lived.

So, would you explain?

Dear Sofia,

don't believe these silly stories about 'virtual particles popping in and out of existence' (Scientific American, Oct. 6, 2006). Instead, you better read Feynman's original papers of 1949/50, especially the third paper (Phys. Rev. 80, 440-457 (1950), Appendix B). There you will find the explanation. There is no reason, why virtual photons should be 'short-lived'. 'Virtual particles' are not particles but functions, therefore the uncertainty relation, which sometimes is wrongly invoked, does not apply.

Dear Walter,

By the way I had a look at an article of yours dealing with momentum entanglement. I liked the article, but I want to stress the following statement that I saw there:

==> "In an irreducible two-particle representation of the Poincar´e group, the particles exchange virtual quanta of momentum"

Where from comes this statement? I don't see a proof. I only see that individual linear momenta of the particles are not conserved quantities, and that's correct.

You see, the two particles are supposed to fly apart, and at the measurement time they may be at a huge distance from one another. I never heard, even about virtual photons, that they propagate with infinite velocity. But, besides that, why should the two particles exchange something between themselves? Why should something pass from one particle to the other?

Best regards,

Sofia

Dear Sofia,

Thank you for reading my paper "Noether's Theorem and its complement in multi-particle systems" ( arXiv:1604.05965 or on RG). In this paper I show that in an irreducible two-particle representation of the Poincaré group the momenta of the individual particles are not conserved. On the other hand, the total momentum is conserved, if the two-particle state is an eigenstate of the total momentum. Therefore, such a two-particle state must have an entangled structure. In the language of quantum electrodynamics such a structure is described as being generated by the 'exchange of virtual quanta'. I think this diction was first used by Feynman in his famous papers of 1949/50. There is no real exchange, only a 'potential' to exchange momentum, therefore 'virtual'. However, the exchange may become real in a scattering experiment.

I do not understand what you mean by 'two particles are supposed to fly apart' or by 'virtual photons [propagating] with infinite velocity'. I never mentioned such things.

Dear Walter,

It was another paper of yours that I read, " Momentum entanglement in relativistic quantum mechanics". The paper does what you say, examines the Poincaré group vs. momenta.

Now, I am aware that you didn't say that the two entangled particles fly apart from one another, but this is what we do in experiments for revealing the nonlocal character of the entanglements. We let the two particles fly at big distances from one another, and perform on them simultaneous (with respect to the lab) measurements.

Therefore, those virtual photons of which you speak, should have infinite velocity with respect to the lab.

In a measurement on the entangled pair, the individual results produced by the two particles is consistent with the value of the total momentum. Then, if you believe that this consistence is realized by exchanging of virtual photons, then these photons have to fly at infinite velocity.

Best regards,

Sofia

Dear Sofia,

I think, I now understand what you mean. Your objection is obviously based on the idea that in an experiment of the EPR-type a virtual photon is 'generated' at the moment of the measurement on one of the particles. This is, of course, not the case. The virtual photons that describe an entangled two-particle state are 'generated' at the moment when this two-particle state is formed, e.g., within the experimental setup of a scattering experiment. Furthermore, you are talking about virtual photons in space-time, whereas I am talking about energy-momentum space. When we transform from the energy-momentum picture into the space-time picture, then the maximum 'velocity' of a virtual photon is the speed of light. Recall Feynman's wording: "...action at a distance ...albeit retarded in time...".

Best regards,

Walter

Dear Walter,

I thought that you are trying to say that the entangled particles correlate among themselves (agree on) the responses to measurements, by means of virtual photons. If you don't mean this, then it's O.K. However, please see what you say in the end of section 3:

==> "Nevertheless, if the state is an eigenstate of the total momentum, the

particle momenta will always add up to the (conserved) value of the total momentum. Hence an unbiased experimenter will conclude that the particles exchange momentum."

What you mean by "unbiased experimenter"?

But, leaving aside the unbiased experimenter, let's consider that Walter talks with Sofia. At the preparation step the two particles are in contact through different fields, and indeed may exchange among themselves all sort of field carriers, including virtual ones. But when the different momenta of the particles takes them away from one another, the particles don't exchange anything among themselves anymore. The entangled state remains in the form

(1) |ψ> = (1/sqrt(2)) { |p1>A |p2>B + |p3>A |p4>B },

where A and B are the two particles, and p1 + p2 = p3 + p4. There is no room in the RHS of Eq. (1) for an additional particle, real or virtual.

By the way, about what Feynman said, we cannot stick all the time to what our teachers said. We have to know what they said, though make OUR judgement. It's OUR turn to take responsibility.

Kind regards,

Sofia

Dear Sofia,

By an unbiased experimenter, I mean an observer who looks at the results of an experiment without having any pre-formed ideas of what is going on inside the experiment, e.g., a person who is interested in the S-matrix only. 

I am talking about elementary quantum mechanics of two 'free' (incoming) particles initially described by a product representation. At the preparation step (in the 'interaction region'), an eigenstate of the total linear momentum and the orbital angular momentum is prepared. (There are neither 'different fields' nor 'all sorts of field carriers'.) Such a state is momentum entangled. You are right to say that the entanglement is not changed, when the particles move away, and, of course, there is no room for additional particles. This cannot prevent us from writing the entangled state in the form

|ψ> = (1/sqrt(2)) { |p1>A |p2>B + |p1 - k>A |p2 +k>B }, where k = p3 - p1 = p4 - p2.

Here k is the momentum of the 'virtual particle', which is just an alternative in talking about entangled states.

My remarks about Feynman were intended to point out that Feynman saw certain things more clearly than many of his followers do (in my judgement). They were definitely not intended as an invitation to uncritically stick to what our teachers said or not to take responsibility.

Best regards,

Walter

Dear Walter,

I confess that I am not enthousiastic about that virtual particle that you speak of. Please see, people may take it literally, i.e. that there is indeed a virtual particle passing between the two real particles in the entanglement. 

Let me give you a counter-example, I mean a case that at least casts doubt on an exchange of a virtual particle. For this purpose let's move from momentum entanglement to spin entanglement. Here is the spin part of the entanglement of two spin 1 bosons (two particles with rest-mass, not photons), the so-called spin 1 singlet. In the z-projection of the spin it looks as follows:

|S1> = (1/sqrt(3)) { |+1>A |-1>B + |0>A |0>B +  |-1>A |+1>B}.

Can you tell me what is the spin z-projection of the virtual particle passing between the two bosons? Is it 0? Is it +2? Is it -2?

But we can pass from the z-projection to the projection on whatever other axis. The form of the function is absolutely the same. It's obvious that the virtual particle has spin 2, but along which axis is it polarized? And why doesn't it have spin-projections ±1?

My best regards,

Sofia

Dear Sofia,

It is not me who invented the notion of a 'virtual particle'. I don't like it also, but since this term is well-established in particle physics, I fear that we have to use it, when we want to make ourselves understood by the physics community. Indeed too many, even experienced physicists, who should know it better, are taking this term literally.

You may have noticed that in my papers I point out that a 'virtual particle' has nothing in common with a 'real' particle. Therefore, you are preaching to the converted, when you try to give me a 'counter-example'.

Best regards,

Walter

Dear Walter,

I believe that we quite understood one another. Now, you see, I insisted in this dialogue between us, because in other cases, different from the one we discussed, I have the feeling that these so called "virtual particles" are something more than just a mathematical tool in Feynman diagrams.

But this issue does not belong to Karl's question and is much more complicated. Maybe we'll have the occasion to talk about it.

Best regards,

Sofia