Can Point Particles Have Infinite Energy in Fields?

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Discussion Overview

The discussion centers on the concept of energy stored in the electric field of point particles, specifically addressing whether point particles can possess infinite energy in their fields and the implications of this for singularities in space-time. The scope includes theoretical considerations and conceptual challenges related to classical electromagnetism and quantum electrodynamics.

Discussion Character

  • Conceptual clarification
  • Debate/contested
  • Technical explanation

Main Points Raised

  • One participant notes that the energy stored in the electric field of a point particle is infinite due to the limit as r approaches 0 in the energy density integral, questioning the implications for the field's energy and singularities.
  • Another participant acknowledges the infinite energy problem in classical electromagnetism and suggests that quantum electrodynamics provides a resolution, proposing that virtual particle pairs may shield the charge at the center.
  • A different viewpoint emphasizes that the 1/r potential is only valid outside the charged body and proposes that even fundamental particles like electrons may have a finite size, implying limitations of classical physics at small scales.
  • One participant raises a concern about the Standard Model's treatment of point particles, suggesting that it may be misleading in the context of infinite energy considerations.

Areas of Agreement / Disagreement

Participants express differing views on the implications of infinite energy in fields associated with point particles, with no consensus reached on the resolution of these issues or the validity of classical versus quantum perspectives.

Contextual Notes

The discussion highlights limitations in classical physics when addressing point particles and the potential need for quantum mechanical frameworks, but does not resolve the mathematical or conceptual challenges presented.

urnchurl
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When finding the amount of energy stored in the electric field of a point particle, one finds that it is infinite (due to the r = 0 limit in the integral of the energy density). Does this mean then that the field will never "run out" of energy?

How can the electric field of a point charge, or the gravitational field of a point mass contain an infinite amount of energy without resulting in a space-time singularity (if one considers a finite volume containing the point mass or charge)?

Thanks.
 
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It would mean that the field contained an infinite amount of energy. This was a recognized problem in classical E&M and was not really solved until Quantum Electrodynamics was completed.

One way to think of the answer is that as the energy density increases for small r, you get more and more virtual e+/e- pairs, and they "shield" the charge at the center. At least, I think the argument goes something like that.
 
The 1/r potential is valid as long as you are outside the charged body.
It is reasonable to assume that even an electron has a finite size.
Below a certain scale, classical physics is not applicable anyway.
 
lalbatros said:
The 1/r potential is valid as long as you are outside the charged body.
It is reasonable to assume that even an electron has a finite size.
Below a certain scale, classical physics is not applicable anyway.

Doesn't the Standard Model comprehend point particles? That would seem to be particularly misleading.
 

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