Rohrlich's derivation of E=mc2 wrong?

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    Derivation E=mc2
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Discussion Overview

The discussion centers on the validity of Rohrlich's derivation of the mass-energy equivalence formula E=mc², particularly in the context of the relativistic Doppler effect. Participants examine the appropriateness of different equations under relativistic conditions and the implications for the derivation.

Discussion Character

  • Debate/contested
  • Technical explanation
  • Mathematical reasoning

Main Points Raised

  • Some participants argue that the Doppler shift factor 1-\frac{v}{c} is incorrectly applied under relativistic conditions, suggesting that the formula \frac{1}{1+\frac{v}{c}} should be used instead.
  • Others claim that Rohrlich's formula does not fit into the relativistic Doppler effect equation.
  • It is noted that at low velocities, the expressions 1-v, 1/(1+v), and \sqrt{(1-v)/(1+v)} are similar to first order in v, which raises questions about the derivation's accuracy.
  • One participant points out that the relativistic Doppler formula is derived by dividing by the Lorentz factor, questioning the use of the first equation if time dilation is minimal.
  • Another participant emphasizes that while both equations may appear similar at low velocities, the derivation is mathematical rather than a numerical approximation, noting significant deviations at approximately 0.1c.

Areas of Agreement / Disagreement

Participants express disagreement regarding the validity of Rohrlich's derivation and the appropriate equations to use under relativistic conditions. No consensus is reached on the correctness of the derivation or the equations involved.

Contextual Notes

Limitations include the assumption of low velocities and the dependence on specific definitions of the Doppler effect equations. The discussion does not resolve the mathematical steps involved in the derivation.

Lamarr
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http://en.wikipedia.org/wiki/Mass–energy_equivalence#Alternative_versionAccording to Wikipedia,

"The velocity is small, so the right-moving light is blueshifted by ... Doppler shift factor 1-\frac{v}{c}

But 1-\frac{v}{c} should not be applied under relativistic conditions.
The formula \frac{1}{1+\frac{v}{c}} should be used instead.So wouldn't this invalidate Rohrlich's derivation?
 
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The formula used by Rohrlich does not even fit into the relativistic doppler effect equation.
 
That's why they say, "The velocity is small,..." Taking units where c=1, the expressions 1-v, 1/(1+v), and \sqrt{(1-v)/(1+v)} are all the same to first order in v.
 
but the relativistic doppler formula is derived by dividing the second equation by the lorentz factor.

So if time dilation is minimal, why use the first equation? He should've used the second one.

The first equation is for a detector approaching a stationary wave source, passing the wavefronts faster than their speed in a medium.

The second is for a wave source approaching a detector, and the position that each wavefront was generated changes.

The principles the first equation is based on seems to violate relativity, as one cannot approach light waves faster than their speed of propagation.
 
yes, it is true that both equations are similar at low velocities, but this a mathematical derivation of an equation and not a numerical approximation.

I plotted the graphs of both equations, and from what i can see, both show significant deviations at about 0.1c
 

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