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In electrostatics, charged particles attract or repel via exchange of virtual photons. But when charges wiggle (or more generally accelerate), they generate electromagnetic waves which are often called "real" photons. For such a photon to be a real particle, its dispersion relation must sit on-shell. This requires the precise measurement of its momentum and energy. However, uncertainty principle says we can't get precise measurement unless the field is indefinite in time and space.

In my head, a massless spin-1 photon field exists indefinitely without any beginning or end. On the other hand, the EM field generated by a wiggling charge has a beginning so that it can't be infinite in time and space. So, why is this EM field called a "real" photon? Or is it an asymptotically real photon but indeed virtual? Or am I misunderstanding something?

I read the Wikipedia article about virtual particle. According to the article, the Casimir effect is due to virtual photons interacting with metal plates. I don't understand why the photon here is virtual. Can anybody explain it, too?

For more clarification, the notion of real particle conflicts in my head. I think it is on-shell particle and it has either a beginning or end or none of these in a Feynman diagram. However these two concepts are conflicting because for the particle newly annihilated or created, the energy and momentum relation must remain vague due to uncertainty principle. I can say a particle or field is on-shell only when it exists indefinitely like a planewave. Can anybody resolve it?

ACuriousMind
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Liberty
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2 Answers2

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To start with there is no Heisenberg uncertainty between energy and momentum; the HUP is between momentum and position, there do exist additional uncertainty relations , but not between energy and momentum. The mass is a fixed real number , the "length" of the four vector in special relativity. So particles which are on mass shell are called real, because they do have an energy and momentum constraining the four vector to the mass of a given particle.

Secondly virtual particles are in the realm of quantum mechanics , quantum field theory and the attendant Feynman diagrams. Please see my answer here on what a virtual particle is.

In electrostatics, charged particles attract or repell via exhange of virtual photon.

That is not correct. Electrostatics emerges from the underlying quantum mechanical level. The interactions between atoms and molecules constituting the macroscopic surfaces studied can be described quantum mechanically with virtual photon exchanges, but the build up to the classical static field is not as simple addition.

You may get an idea of the complexity by reading this blog, of how classical electromagnetic waves emerge from the quantum substrate. ( My answer here might help in visualizing how photons build up a classical wave). The "wiggling charge" is releasing real photons, shich can be measured one photon at a time.

So, how this EM field is called "real" photon? Or is it asymptotically real photon but indeed virtual?

The EM field as a classical light wave is not called a "photon". The field theoretical photon field, which fills all space and is acted upon by creation and annihilation operators to model the motion of a photon is the one you are confusing with the EM field.

From the linked blog entry one can understand the complexity of going from the atoms and molecules ( 10^23 per mole) to a charged surface, it is not a simple addition of virtual photons that will give the coulomb field macroscopically.

Community
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anna v
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The total EMF contains two addenda (see the solution in a textbook): a "near field" (like a Coulomb one) and a "radiated field". Their behavior, as a function of the distance, differs. The "near field" does not propagate even though it is wiggling too. In terms of its total flux, it decays with distance.

The radiated field total flux does not decay. Far away from the source the radiated field can be represented as a superposition of plane waves, which are associated with real photons. The near field is then called "virtual photons".

Vladimir Kalitvianski
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