Charge Invariance & Mass Dependence: Lorentz Transformations

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Discussion Overview

The discussion revolves around the concepts of charge invariance and mass dependence in the context of Lorentz transformations. Participants explore the implications of these properties for forces, particularly gravitational and electric forces, and clarify the distinctions between rest mass and relativistic mass.

Discussion Character

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

Main Points Raised

  • One participant questions why charge is considered Lorentz invariant while mass is not, suggesting this may imply differences in how gravitational and electric forces depend on the frame of reference.
  • Another participant asserts that mass is also Lorentz invariant, possibly referring to rest mass, and distinguishes it from relativistic mass, γm.
  • A participant seeks clarification on the distinction between rest mass and relativistic mass, questioning whether the term "relativistic charge" exists.
  • One participant critiques the concept of "relativistic mass" as misleading and suggests avoiding its use, emphasizing the proper formulation of momentum in relativity.
  • The Lorentz force equation is presented, highlighting the role of γe in the context of electric and magnetic forces, but the term "relativistic charge" is also discouraged.

Areas of Agreement / Disagreement

Participants express differing views on the nature of mass in relativity, particularly regarding the validity and implications of the concept of relativistic mass. There is no consensus on the terminology or the implications for forces.

Contextual Notes

There are unresolved distinctions regarding the definitions of mass and charge in different frames of reference, and the implications of these definitions for force calculations remain unclear.

QuArK21343
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Why is it that charge is Lorentz invariant (it's a scalar, independent of the frame of reference) whereas mass is not? Does this mean that the gravitational force a body exerts depends on the frame of reference, whereas the electric force doesn't?
 
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The mass of a particle is also a Lorentz invariant. You may be thinking of the relativistic mass γm.
 
Ok, since this is new to me, could you clarify the difference between the two? Do you mean the rest mass is Lorentz invariant? Anyway, there is no analogue to relativistic mass as far as charge is concerned (no relativistic charge), right?
 
"Relativistic mass" is a highly misleading concept and should be avoided. Its use arose simply because the relativistic expression for the momentum happens to be p = γmv, and in trying to make look like the nonrelativistic formula it was written p = Mv where M = γm.

The Lorentz force equation can be written (τ is proper time)

dp/dτ = γe(E + v/c x B)

and sure enough there's the combination γe, but I would not recommend defining this as the "relativistic charge" either!
 

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