What Happened to Potential Energy in E=m[tex]c^2[tex]

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Discussion Overview

The discussion revolves around the treatment of potential energy in the context of the energy-mass equivalence formula E=mc². Participants explore whether potential energy should be included in total energy calculations, particularly when dealing with charged particles in electric fields.

Discussion Character

  • Exploratory
  • Technical explanation
  • Debate/contested

Main Points Raised

  • One participant questions why potential energy is not included in the total energy calculation of E=mc², suggesting that it could be significant for charged particles in electric fields.
  • Another participant cites the energy-momentum relation E²=(pc)²+(mc²)², noting that it is typically applicable to free particles where potential energy is not considered.
  • A later reply proposes a modified relation (E-V)²=(pc)²+(mc²)², indicating that potential energy (V) should be accounted for separately from rest mass energy (m).
  • Another participant reiterates the modified relation (E-V)²=(pc)²+m²c⁴, emphasizing the distinction between rest mass and potential energy.

Areas of Agreement / Disagreement

Participants express differing views on the inclusion of potential energy in energy calculations, with no consensus reached on how it should be integrated into the framework of E=mc².

Contextual Notes

Participants reference various formulations of energy relations, indicating potential dependencies on definitions and contexts, such as whether the particle is free or influenced by external fields.

bhthiang
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I have been wondering why is potential energy not included in the calculation of total energy E=m[tex]c^2[tex]?<br /> I know that m[tex]c^2[tex]includes the rest energy and the kinetic energy. Suppose the particle or object is charged and is moving in a strong electric field, its potential energy will be sdgnificant wouldn't it?<br /> If we have to include the PE, how should we do it?<br /> Thanks[/tex][/tex][/tex][/tex]
 
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The energy-momentum relation that you see in a standard general physics textbook is:

[tex]E^2=(pc)^2+(mc^2)^2[/tex]

It is typically advertised as the energy-momentum relation for a *free* particle (so [itex]V=0[/itex]). If memory serves, Goldstein's "Classical Mechanics" treats relativistic mechanics with a potential, via the Lagrangian formalism.
 
Properly,
[tex](E-V)^2=(pc)^2+(mc^2)^2[/tex]
where V is the potential energy and m, the rest mass, does NOT contain the kinetic energy.
 
Properly,
[tex](E-V)^2=(pc)^2+m^2c^4[/tex]
where m is the rest mass and V the potential energy
 

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