The wavelength of the virtual photons of the Coulomb force

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Discussion Overview

The discussion revolves around the properties of virtual photons in the context of the Coulomb force, specifically focusing on whether these virtual photons can be assigned a wavelength, frequency, or energy. The scope includes theoretical considerations and conceptual clarifications regarding the nature of virtual particles.

Discussion Character

  • Debate/contested
  • Conceptual clarification

Main Points Raised

  • One participant inquires about the possibility of calculating the wavelength, frequency, or energy of virtual photons exchanged between charges in the Coulomb force.
  • Another participant suggests that the wavelength of virtual photons corresponds to the distance between interacting charges, proposing that if an electron is half an angstrom away from a proton, the wavelength would be half an angstrom.
  • A different participant challenges this view, asserting that virtual photons do not carry energy, implying that their frequency is zero and their wavelength is unbounded.
  • Another participant questions the validity of the previous claim, arguing that virtual photons do not propagate and do not satisfy the wave equation, thus raising doubts about the meaning of wavelength in this context.
  • One participant introduces the concept that virtual particles can break conservation of energy in a classical sense, suggesting a relationship between the maximum extra energy and the distance between particles, leading to a calculation of wavelength based on this energy.
  • A subsequent reply expresses confusion, stating that having a length scale does not equate to having a wavelength, and emphasizes the conservation of 4-momentum at interaction vertices, questioning the notion of non-conservation of energy.
  • A final participant acknowledges the ambiguity in their understanding of virtual photons, indicating a misconception about their similarity to regular photons.

Areas of Agreement / Disagreement

Participants express differing views on the existence and properties of wavelengths associated with virtual photons, with no consensus reached on the matter. The discussion remains unresolved regarding the implications of virtual particles on energy conservation and their characteristics.

Contextual Notes

Participants highlight ambiguities in the definitions and properties of virtual photons, particularly concerning their energy, wavelength, and the implications for conservation laws. The discussion reflects a range of interpretations and assumptions that are not fully reconciled.

diagopod
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Is there a way to calculate the wavelength, frequency or energy (per photon) of the virtual photons that charges exchange to account for the Coulomb force? This is assuming that it's always the same wavelength, of course.
 
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They have wavelength just of the length between interacting bodies. If an electron is half angstrem away of a proton, the wavelength of the virtual photons will be half an angstrem.
 
I think this is wrong. It would mean they carried energy and they don't. The frequency is zero and the wavelength is unbounded.
 
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I don't see how that can be correct.

Virtual photons don't propagate; they don't satisfy the wave equation, so how can they have a wavelength? What does a wavelength even mean in this case?
 
What does a wavelength even mean in this case?
Virtual particles break conservation of energy in the classical sense. The maximum amount of extra energy can be [tex]\Delta E = \hbar / d[/tex], where [tex]d[/tex] is the distance between interacting particles. If you now count the wavelength of a photon of such energy, you will get exactly [tex]d[/tex].
 
I don't follow. The fact that you have a length scale d is not the same as saying it's a wavelength. Also, 4-momentum (one term of which is energy) is conserved at every vertex, so I don't see where this non-conservation of energy is coming from.
 
Thanks everyone. Didn't realize it was ambiguous. I thought that virtual photons were more like regular photons than they actually are I suppose. Thanks for the insight.
 

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