Energy Stored in Charged Capacitor: Kaluza-Klein Theory

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Discussion Overview

The discussion revolves around the interpretation of stored electromagnetic energy in a charged capacitor through the lens of Kaluza-Klein theory. Participants explore the relationship between charge, momentum, and geometrical interpretations of electrostatic energy within this theoretical framework.

Discussion Character

  • Exploratory
  • Technical explanation
  • Conceptual clarification
  • Debate/contested

Main Points Raised

  • One participant questions how Kaluza-Klein theory views the stored electromagnetic energy in a capacitor.
  • Another participant states that Kaluza-Klein theory incorporates standard electrodynamics, suggesting that it would explain the stored energy in a capacitor similarly to conventional theories.
  • A participant proposes that in Kaluza-Klein theory, charge can be interpreted as momentum in the 5th dimension and seeks a geometrical interpretation of electrostatic energy.
  • Further clarification is provided that charge relates to the velocity of a particle in the 5th dimension, but uncertainty remains regarding how this interpretation applies to the energy stored in the field.
  • It is noted that in standard 4-dimensional general relativity, localized energy in the gravitational field cannot be defined as a geometric object, raising questions about the interpretation of electromagnetic energy as a form of energy stored in the gravitational field in Kaluza-Klein theory.

Areas of Agreement / Disagreement

Participants express differing views on the interpretation of charge and energy within Kaluza-Klein theory, and the discussion remains unresolved regarding the application of these concepts to the energy stored in a capacitor.

Contextual Notes

There are limitations in defining localized energy in gravitational fields within standard general relativity, which may affect interpretations in Kaluza-Klein theory. The discussion also reflects uncertainty about extending geometrical interpretations to the energy stored in the electromagnetic field.

Spinnor
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In terms of Kaluza-Klein theory how does one view the stored electromagnetic energy between the plates of a charged capacitor.

Thanks!
 
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I'm not sure what you're asking. Kaluza-Klein theory is equivalent to the Einstein Field Equation + Maxwell's Equations. So it includes standard electrodynamics, which can explain the stored energy in a capacitor, and Kaluza-Klein theory would just use that same explanation.
 
In Kaluza_Klein charge can be thought of as momentum in the 5th dimension?

I guess I was looking for some kind of geometrical interpretation of electrostatic energy.
 
Spinnor said:
In Kaluza_Klein charge can be thought of as momentum in the 5th dimension?

Sort of, yes; charge relates to how fast a particle is going around the small circle that is the 5th dimension. But I don't know how (or if) that interpretation can be extended to cover the energy stored in the field. In standard (4-dimensional) GR there is no way to define a localized "energy in the gravitational field" as a geometric object, and in Kaluza-Klein theory what we call "electromagnetic" energy would be a form of "energy stored in the gravitational field" (interpreting "gravitational field" as the underlying 5-dimensional geometry).
 

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