Can anyone explain or correct this?

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Discussion Overview

The discussion revolves around the explanation of Einstein's equation E=mc² as presented in a one-minute physics video, specifically focusing on the use of the Doppler effect in the context of energy conservation. Participants are questioning the appropriateness of the methods used in the video and exploring the implications of classical kinetic energy in this derivation.

Discussion Character

  • Debate/contested
  • Technical explanation
  • Conceptual clarification

Main Points Raised

  • Some participants express skepticism about the video's explanation of E=mc² using the Doppler effect, suggesting that it may not be accurate.
  • There is a proposal that energy conservation could be addressed in other ways, and that the Doppler effect requires careful integration over solid angles.
  • Questions are raised about the correctness of calculating the Doppler energy gain as (1+v²/2c²) instead of (1-v²/2c²).
  • Concerns are voiced regarding the use of classical kinetic energy in deriving the formula, with some arguing that it is inappropriate and could lead to incorrect conclusions.
  • It is noted that while the classical formula may not work, deriving a new formula based on it could be problematic, as the results might align by chance rather than through valid reasoning.

Areas of Agreement / Disagreement

Participants do not reach a consensus on the validity of the video's explanation or the methods used. Multiple competing views remain regarding the application of the Doppler effect and the use of classical mechanics in this context.

Contextual Notes

Limitations include potential missing assumptions about the applicability of classical mechanics in relativistic contexts and the need for integration in the analysis of the Doppler effect.

leolee5633
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I think there would be other ways to fix energy conservation and you have to be more careful with the Doppler effect (needs an integration over the solid angle), but the basic idea is fine: The kinetic energy of the cat somehow depends on the energy content of the cat. Otherwise, "radiating+getting speed afterwards" would need the same energy as "getting speed + radiating" - but the light energy would be different.
 
mfb said:
I think there would be other ways to fix energy conservation and you have to be more careful with the Doppler effect (needs an integration over the solid angle), but the basic idea is fine: The kinetic energy of the cat somehow depends on the energy content of the cat. Otherwise, "radiating+getting speed afterwards" would need the same energy as "getting speed + radiating" - but the light energy would be different.

Thank you, but is that guy correct in calculating the Doppler energy gain to be (1+v^2/2c^2) not (1-v^2/2c^2)?
Also he is using classical kinetic energy to derive the formula, is that appropriate?
 
but is that guy correct in calculating the Doppler energy gain to be (1+v^2/2c^2) not (1-v^2/2c^2)?
That is a bit sloppy, he should integrate over all emitted photons / space directions.

Also he is using classical kinetic energy to derive the formula, is that appropriate?
That is another problem - you can derive that the classical formula does not work, but it is problematic to derive a new formula, based on the (wrong) old one. The result happens to fit, but that could be just by chance.
 
mfb said:
That is a bit sloppy, he should integrate over all emitted photons / space directions.


That is another problem - you can derive that the classical formula does not work, but it is problematic to derive a new formula, based on the (wrong) old one. The result happens to fit, but that could be just by chance.

I see, thank you very much for you help.
 

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