Particle-field(wave) duality

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SUMMARY

The discussion centers on Griffiths' assertion that the superposition principle does not apply to electrostatic energy, particularly in the context of point charge distributions. Participants agree that as charges become more localized, the electromagnetic energy increases significantly, which challenges the validity of the superposition principle. The conversation also explores the relationship between stored energy and fields, questioning whether charges can be viewed as condensed forms of electromagnetic energy and mass particles as condensed gravitational energy. The distinction between additive sources and non-additive field energies is emphasized, highlighting the complexities of wave-particle duality.

PREREQUISITES
  • Understanding of Griffiths' Electrodynamics principles
  • Familiarity with Jackson's Classical Electrodynamics
  • Knowledge of the superposition principle in electromagnetism
  • Basic concepts of wave-particle duality in physics
NEXT STEPS
  • Research Griffiths' treatment of electrostatic energy in Electrodynamics
  • Study Jackson's insights on localized charge distributions and energy magnitudes
  • Explore the implications of non-additive field energies in electromagnetic theory
  • Investigate the relationship between energy forms and wave-particle duality
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Physicists, electrical engineers, and students of electromagnetism seeking to deepen their understanding of electrostatic energy, superposition principles, and the interplay between energy and particle behavior.

Kolahal Bhattacharya
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Griffiths says the superposition principle is not valid for electrostatic energy.I understood this concept,remembering that energy,unlike potential(point function),is a field function.Is Griffiths's conclusion still correct for point charge distribution (rqn.2.43)?
I think it's correct: we know electromagnetic energy grows larger as the charge is localised more & more(Jackson).So, when we are dealing with point charges,which are localised themselves, magnitude of W is very large so that it cannot obey superposition principle.I think the principle fails when huge magnitudes are involved.Any conceptual mistake?Please help.
Next, will it be wrong to consider stored energy creates appropriate field & condensed field creates appropriate particle?i.e. can we regard a charge as a condensed form of electromagnetic energy? or, a mass particle as a condensed form of gravitational energy?I use appropriate subscripts to distinguish betweeen the fields.Can any light be thrown from here to wave -particle duality?
 
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Electric and Magnetic *fields* are the Sum of individual source contributions [which is superposition] (says classical E&M, anyway).
But the *Energies* involved go as E^2 + B^2 , even for sparse fields.
Obviously a quadratic cannot be a superposition of source contributions.

The sources themselves are additive (Q = q1 + q2 + q3 ...), so are distinct
from the NON-additive Field Energies that they engender [promulgate].
A source is most closely related to the additive Field that diverges from it.
 

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