The Full Equation for Mass-energy Equivalence

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Discussion Overview

The discussion revolves around the mass-energy equivalence equation, commonly expressed as E=mc², and its extended form E²=(mc²)²+(pc)², where p represents momentum. Participants explore the definitions of mass used in these equations and the implications of these definitions on the understanding of mass-energy equivalence.

Discussion Character

  • Exploratory
  • Technical explanation
  • Debate/contested

Main Points Raised

  • Some participants note that the equation E=mc² is a special case where momentum p=0.
  • There is a discussion about the definitions of mass: E=mc² uses "relativistic mass," which increases with velocity, while the extended equation uses "rest mass." Some argue that both equations are correct based on their definitions of mass.
  • One participant suggests that starting from E=mc² and substituting m with m₀/√(1 - v²/c²) leads to the extended form of the equivalence equation.
  • Another participant expresses skepticism about the relevance of the relativistic mass concept in contemporary discussions, suggesting that the rest mass definition is more widely accepted today.

Areas of Agreement / Disagreement

Participants express differing views on the relevance and usage of relativistic mass versus rest mass in the context of mass-energy equivalence. There is no consensus on which definition is preferable or more accurate in modern physics discussions.

Contextual Notes

Participants highlight the dependence of the equations on the definitions of mass, indicating that the interpretations may vary based on the context in which they are applied. The discussion does not resolve the implications of these definitions.

Jason Kim
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Hi.

I've seen a video by MinutePhysics that talked about the mass-energy equivalence equation,
usually known as E=mc^2.

It said that there is an extra part to it, and I didn't really understand what it meant.

(E^2)=((mc^2)^2)+((pc)^2) seems to be the full one (p being momentum)

So, any ideas?

By the way:
 
Last edited by a moderator:
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Jason Kim said:
Hi.

I've seen a video by MinutePhysics that talked about the mass-energy equivalence equation,
usually known as E=mc^2.

It said that there is an extra part to it, and I didn't really understand what it meant.

(E^2)=((mc^2)^2)+((pc)^2) seems to be the full one (p being momentum)

So, any ideas?

By the way:


Each equation uses a different definition of mass. e=mc^2 uses m="relativistic mass," which increases the faster the mass is moving relative to the observer. The second equation uses m="rest mass." The first equation was Einstein's, the second is used more these days because it is usually more convenient and less confusing.

Each equation is correct, given its definition of m.
 
Last edited by a moderator:
If one starts from E = mc^{2} and replaces m by \frac{m_{0}}{\sqrt{1 - \frac{v^{2}}{c^{2}}}} where m_{o} is the mass at rest, one gets the other version of the equivalence equation.
 
E=mc2 is just the special case where p=0.

ImaLooser said:
Each equation uses a different definition of mass. e=mc^2 uses m="relativistic mass," which increases the faster the mass is moving relative to the observer. The second equation uses m="rest mass." The first equation was Einstein's, the second is used more these days because it is usually more convenient and less confusing.

I don't think this interpretation works, since nobody today uses relativistic mass, but everyone uses E=mc2.
 

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