Why is E=pc with Light's Zero Rest Mass?

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    Derivation pc
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Discussion Overview

The discussion revolves around the equation E=pc and its application to light, particularly addressing the implications of light having zero rest mass. Participants explore the relationship between energy, momentum, and mass in the context of relativistic physics, questioning how the equation holds true for massless particles like photons.

Discussion Character

  • Exploratory
  • Technical explanation
  • Debate/contested

Main Points Raised

  • One participant questions the validity of E=pc for light, suggesting that if light has zero rest mass, then momentum p should also be zero.
  • Another participant cites the relativistic relation E^2 - (cp)^2 = (mc^2)^2, stating that setting m=0 leads to E=pc, implying that the equation is valid for massless particles.
  • A participant points out that using the equation for momentum p = m0v/sqrt(1-v^2/c^2) results in an undefined value when v=c, indicating that this equation does not apply to light.
  • There is a contention regarding whether momentum can be defined differently for light, with some arguing that the standard momentum equation should not be ignored.
  • One participant mentions finding clarity in the de Broglie wavelength equation, suggesting it provides insight into the momentum of light.
  • Another participant notes that even classically, energy and momentum densities of electromagnetic waves relate through E=pc.
  • There is a discussion about the distinction between rest mass and relativistic mass, with some suggesting that m=0 may refer to relativistic mass rather than rest mass.

Areas of Agreement / Disagreement

Participants express differing views on the implications of light's zero rest mass for momentum and energy, with no consensus reached on the interpretation of the equations involved or the definitions of momentum in this context.

Contextual Notes

Participants highlight limitations in applying certain equations to massless particles and the potential for confusion regarding definitions of mass and momentum.

Grim Shady
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I was reading the derivation of this equation on hyperphysics.com and after searching all over the internet it seems that eveywhere seems to just accept this equation is valid for light, even though a rest mass of 0 would make p equal to 0.

Sorry if I'm being stupid or if this has been asked a million times before but I can't find an explanation anywhere as to why light having zero rest mass gives the equation E = pc, despite p being proportional to the (zero) rest mass of light.
 
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For any particle, massive or massless, the relativistic relation between mass, energy, and spatial momentum is given by

E^2 - \left( cp \right)^2 = \left( mc^2 \right)^2 .

Using m = 0 in this relation results in E = cp.
 


But surely if p = m0v/sqrt(1-v2/c2), that would make p equal to 0?
 


When v = c, that equation leads you to divide by zero, which has a mathematically undefined result. So it simply doesn't apply when v = c. The equation George showed you is more general.
 


Yeah sorry my mistake, but that still would mean that p is an undefined value, despite it being in the equation George posted.
 


It means that your equation has nothing to say on a photon's momentum, while George Jones' has.
 


But you can't just ignore the equation for momentum and state that light has a momentum, p, purely for convenience.

Unless momentum can be defined as something else, other than the equation I posted.
 


Grim Shady said:
But you can't just ignore the equation for momentum and state that light has a momentum, p, purely for convenience.

Unless momentum can be defined as something else, other than the equation I posted.


E^2 = p^2 + m_0^2

is the general formula

E = gamma m_0

applies only to massive particles

where is your lack of understanding?
 


It was in the definition of momentum itself, I've found the answer the answer anyway in the de Broglie wavelength equation, which is something I knew already was just having trouble remembering it. Cheers for the help people.
 
  • #10


Even classically, the energy and momentum densities of electromagnetic waves are related by E = pc.
 
  • #11


I think he's saying that in the equation E=pc, p=mv, so that if m=0, then p=zero, then E=0.

Unless maybe saying m=0 means that relativistic mass is zero, not rest mass?
 

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