Derivation of Energy-Momentum Relation WITHOUT using relativistic mass?

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Discussion Overview

The discussion centers around the derivation of the energy-momentum relation without the use of relativistic mass, focusing instead on invariant mass. Participants explore various perspectives on the implications of using different definitions of mass in the context of special relativity.

Discussion Character

  • Debate/contested

Main Points Raised

  • One participant requests a derivation of the energy-momentum relation that solely relies on invariant mass.
  • Another participant provides a link to an external resource that may contain relevant information.
  • A different participant references a previous discussion that introduces mass as a scalar nonrelativistic quantity, suggesting a connection to the 4-dimensional momentum framework.
  • One participant questions the necessity of relativistic mass in the derivation of the equation E^2 = (pc)^2 + (m_0 c^2)^2, noting that it includes invariant mass.
  • Several participants express a shared sentiment that the concept of "relativistic mass" is confusing for newcomers to special relativity.

Areas of Agreement / Disagreement

Participants express disagreement regarding the utility and clarity of the concept of relativistic mass, with some advocating for its removal from discussions, while others focus on the technical aspects of the derivation itself. No consensus is reached on the best approach to the derivation.

Contextual Notes

There are unresolved questions about the definitions of mass being used and how they impact the derivation of the energy-momentum relation. The discussion does not clarify the specific derivations that utilize relativistic mass.

SamRoss
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Does anyone know of a derivation of the energy-momentum relation that does not make use of relativistic mass? In other words, a derivation that only uses invariant mass.
 
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http://www.lightandmatter.com/html_books/genrel/ch04/ch04.html#Section4.2
 
Last edited by a moderator:
Check out post #3 of earlier today in the following Special Relativity thread:

https://www.physicsforums.com/showthread.php?t=457318

Mass is introduced as a scalar nonrelativistic quantity. The mass energy is seen to correspond to the 4th component of 4-dimensional momentum from the vantage point of one observing the moving mass.
 
SamRoss said:
Does anyone know of a derivation of the energy-momentum relation that does not make use of relativistic mass?

Do you mean the equation E^2 = (pc)^2 + (m_0 c^2)^2? What derivation of it uses relativistic mass, seeing as it contains the invariant mass to begin with?
 
I wish "relativistic mass" had never been defined! :smile:

It seems to be a source of confusion for newbies in SR.
 
torquil said:
I wish "relativistic mass" had never been defined! :smile:

It seems to be a source of confusion for newbies in SR.

I couldn't agree more
 

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