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Nov16-09, 09:55 AM
P: 1,160
Quote Quote by Born2bwire View Post
I did not say that the Lamb shift is related to the vacuum energies, but the fluctuations. There is coupling with the vacuum fluctuations that is required for the correct Lamb shift to be calculated.
T. Welton (Phys. Rev. 1948) showed that it is the electron position fluctuations that modify the potential energy and cause the Lamb shift. And the electron position fluctuations are due to electron's being affected with the fields of quantum oscillators. He added the field of quantum oscillators as an external filed to the electron equation of motion and obtained an additional "electron smearing".

In fact, it is rather difficult to imagine that the quantum oscillators are not affected with the electron itself, that their weak fields are so strong that are "external" to the electron. It is much more natural to say that these oscillators are internal degrees of freedom in a compound system (electron + quantized EMF). That is why they are "decoupled" - they are just separated variables of a compound system. Then the electron in this compound system is not point-like but smeared (being a part of oscilltors) and this gives the Lamb shift.

Each charge capable of radiating is thus a compound system with its own internal degrees of freedom (its own oscillators).
And I have yet to find any classical interpretation for the vacuum fluctuations.
See the QM model described above.
Quote Quote by Born2bwire View Post
They can only arise by the quantization of the electric and magnetic fields.
It is not the fields who are directly quantized but the oscillator energies. Fields flictuate and they are just usual "fluctuations" in a compound system like an electron position in an atom (it's uncertain there).