E = mc^2, so how can anything have zero mass?

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Discussion Overview

The discussion revolves around the implications of the equation E = mc², particularly in relation to the concept of mass, especially zero mass in particles such as photons. Participants explore the theoretical framework of special and general relativity, the definitions of mass and momentum, and the conditions under which these equations apply.

Discussion Character

  • Technical explanation
  • Conceptual clarification
  • Debate/contested

Main Points Raised

  • Some participants assert that E = mc² leads to c² = E / m, raising concerns about division by zero when mass is zero.
  • Others point out that E = mc² is a special case of the more general equation E² = (m₀c²)² + (pc)², where massless particles have rest mass m₀ equal to zero but possess non-zero momentum p.
  • One participant questions the logic of using total mass versus rest mass in the context of momentum, suggesting it may lead to circular reasoning.
  • Some argue that E = mc² only applies when considering particles in their rest frame, noting that photons do not have a rest frame.
  • Another participant mentions that while momentum is typically defined as m * v, this does not hold for massless particles like photons, which have momentum despite having zero mass.

Areas of Agreement / Disagreement

Participants express differing views on the implications of E = mc² for massless particles, with no consensus reached on the definitions and relationships between mass, energy, and momentum.

Contextual Notes

There are unresolved assumptions regarding the definitions of mass and momentum, particularly in the context of massless particles and the applicability of the equations in different frames of reference.

goldust
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E = mc^2 results in c^2 = E / m, and division by 0 is undefined.
 
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Oops, my bad. Should be in the Special & General Relativity section.
 
goldust said:
Oops, my bad. Should be in the Special & General Relativity section.
Done.
 
goldust said:
E = mc^2 results in c^2 = E / m, and division by 0 is undefined.

##E=mc^2## is a special case of the more general ##E^2=(m_0{c}^2)^2+(pc)^2##. The massless particles have ##m_0## equal to zero but ##p## non-zero.
 
E also equals FD: so how can force or distance ever be zero?
 
E = mc^2 only applies in the special case where the particle in question is in its rest frame. Photons do not have a rest frame.
 
Nugatory said:
##E=mc^2## is a special case of the more general ##E^2=(m_0{c}^2)^2+(pc)^2##. The massless particles have ##m_0## equal to zero but ##p## non-zero.

The 'p' in that is momentum, correct?
Yet momentum is m * v, mass times velocity. I understand that photons have a velocity of c, but their mass...? If you use the argument that it isn't talking about rest mass, but total mass, then isn't it sort of circular logic?
 
goldust said:
E = mc^2 results in c^2 = E / m, and division by 0 is undefined.

Please read the Relativity FAQ subforum.

https://www.physicsforums.com/forumdisplay.php?f=210

Zz.
 
Last edited by a moderator:
ModestyKing said:
Yet momentum is m * v, mass times velocity.
Not in general. Photons have momentum but 0 mass, and for massive objects momentum is unbounded as v approaches c.
 

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