Relativistic Energy: Matter & Photon

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SUMMARY

The discussion centers on the relativistic energy equations for particles, specifically addressing the equations E = γmc² and E = √(p²c² + m²c⁴). It is established that while both equations are valid for particles with mass (m ≠ 0), the first equation fails for massless particles like photons, as the Lorentz factor γ is undefined when velocity (v) equals the speed of light (c). The equivalence of the two equations for massive particles can be demonstrated using the momentum formula p = mvγ.

PREREQUISITES
  • Understanding of relativistic physics concepts
  • Familiarity with the Lorentz factor (γ)
  • Knowledge of momentum in relativistic contexts
  • Basic grasp of energy-mass equivalence
NEXT STEPS
  • Study the implications of the Lorentz factor (γ) in relativistic equations
  • Explore the concept of momentum in special relativity
  • Investigate the relationship between energy and mass for massless particles
  • Learn about the derivation of relativistic energy equations
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Students and educators in physics, particularly those focusing on relativistic mechanics, as well as researchers exploring the properties of particles and energy in high-energy physics contexts.

serverxeon
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Homework Statement


Energy of a particle may be of the form:

[tex]E = \gamma mc^{2}[/tex]
[tex]E = \sqrt{p^{2}c^{2} + m^{2}c^{4}}[/tex]

Are both valid for every particle? matter and photon?
Can they be equated?
 
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Hi serverxeon! :smile:

(have a gamma: γ and a square-root: √ :wink:)

The first one doesn't work for m = 0 (a photon), since γ is not defined for v = c,

but apart from that, yes, they're both valid for every particle. :smile:

For m ≠ 0, you can prove the equivalence by using p = mvγ.
 

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