Energy of photons vs classical physics energy

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Discussion Overview

The discussion centers on the comparison of energy expressions for photons in the context of relativity and classical physics. Participants explore the differences between the relativistic energy-momentum relationship and classical kinetic energy formulas, particularly as they relate to the behavior of particles at high speeds.

Discussion Character

  • Debate/contested
  • Technical explanation
  • Conceptual clarification

Main Points Raised

  • One participant notes that relativity describes photon energy as E=pc, while classical physics describes energy as E=1/2 pv, questioning the apparent discrepancy.
  • Another participant asserts that classical physics does not address photons, as they are not part of classical physics, and emphasizes that E=pc can be derived from Maxwell's equations without any missing factors.
  • A third participant introduces the general energy-momentum relationship E = √(p²c² + m²c⁴), explaining how it simplifies for massless particles like photons and massive particles at rest.
  • A later reply expresses an interest in understanding the energy of protons as they are accelerated to speeds approaching that of light, indicating a shift in focus to practical calculations related to particle acceleration.

Areas of Agreement / Disagreement

Participants do not reach a consensus on the interpretation of energy formulas across different contexts. There are competing views regarding the applicability of classical physics to photons and the nature of energy as speed increases.

Contextual Notes

Some limitations include the dependence on definitions of energy in classical versus relativistic contexts, and the unresolved nature of how energy expressions transition as particles approach the speed of light.

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Relativity says photons have energy E=pc. Classical physics says E=1/2 pv. There seems to be a factor of 2 missing in one case or the other or does the energy formula change as the speed of light is reached? There must be a simple explanation but I have not found it yet. I did not know where to put this question-under classical physics of quantum physics. Thanks for any help.

hjr
 
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Classical physics says E=1/2 pv
There are no photons in classical physics, so classical physics cannot say anything about them.

With the Maxwell equations and classical physics, you can derive E=pc for electromagnetic waves. There is no factor of 2.
 
The single relationship between energy and momentum that applies to both massive and massless particles is E = √(p2c2 + m2c4). For a massless particle, set m = 0 and it reduces to E = pc. For a massive particle at rest, set p = 0 and it reduces to E = mc2.

For a massive particle that's slowly moving, keep both terms and expand in a power series in p. The first two terms give you the usual Newonian expression, E = mc2 + p2/2m.
 
Energy of photon vs classical physics energy

Thanks for the replys. I was trying to understand what happens to energy of a proton as a proton is accelerated from rest to almost the speed of light as in the LHA. I think I can calculate that now.

hjr
 

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