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fox26

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weak force is, and of course virtually nothing about the quantized theory of the

gravitational force, which mostly doesn’t exist, so the following arguments and

questions may be somewhat wrongly based where they refer to such theories.

I will talk specifically about the quantized theory of the electromagnetic field, but

the considerations may generalize to the other three forces. A stationary,

non-time-varying electrostatic field was said, in my classical E&M course, to have

an energy of its own which was calculated, in the case of the field between the

plates of a capacitor, by determining the energy required to charge the capacitor

to create the field and assuming conservation of energy. The energy density at

each point turned out to be proportional to the square of the magnitude of the

field there. In the quantized theory of the E-M field, as I understand, there is

nothing similar to the continuous E-M field in classical theory. What is observed

macroscopically as a stationary electrostatic field, such as that of a stationary

electron, is popularly said according to QED to be due to photons, real or virtual.

My question is: How is this possible?

Julian Schwinger asked why people insist on the existence of theoretical objects,

such as atoms, electrons, and E-M fields or photons, and are not satisfied with

just the mathematics of physical theories, and the observable predictions it

makes, as a description of nature. Whatever the reason, most people, including

most physicists and myself, want a description that includes physical entities of

some sort. Quantum Field Theory provides this for such things as electrons, in a

way that is at least semi-satisfactory, as excitations of some quantum field. Is

there a corresponding description by Quantum Electrodynamics (QED) of the

electromagnetic field?

If, according to QED, an electrostatic field is somehow composed of photons,

are these real or virtual, or is this supposed question, according to QED,

meaningless? Even in QED, energy expectation value is conserved, so the

energy used in charging a capacitor must go somewhere, and would that not be

into the E field between the plates of the capacitor, or QED’s substitute for that?

Surely the E(

**r**) field of a stationary electron must, as in the case of the field in a

capacitor, have an energy density expectation value at a point

**r**proportional to

|E(

**r**)|

^{2}(with E(

**r**) being the classical field). The problem is, why don’t the photons

comprising the field, whether they are real or virtual, for an electron in otherwise

empty space, fly off to infinity? Even virtual photons, which some people writing

in PF or elsewhere, such as Arnold Neumaier in his PF article “The Physics of

Virtual Particles”, claim are unobservable (or nonexistent), surely (?) would fly

off to ∞. The electron couldn’t renew its supply of energetic photons, real or

virtual, which in this view its E field must be composed of, all of which would be

going to ∞, since that would cause its own mass to decrease.

It may be that the claim that a quantized E-M field is composed of photons, real

or virtual, is another case of misrepresentation by popularizers. If that is so, what

is a quantized (supposedly all are) E-M field composed of? Must we, according

to present theory, give up the picture of such a field as being made up of physical

entities?