How is E=mc^2 connected to the speed of light?

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Discussion Overview

The discussion revolves around the connection between the mass-energy equivalence equation E=mc^2 and the speed of light, exploring its theoretical underpinnings and implications in the context of Special Relativity.

Discussion Character

  • Exploratory, Technical explanation, Conceptual clarification

Main Points Raised

  • Some participants note that E=mc^2 is derived from the postulates of Special Relativity, specifically the invariance of the speed of light and the consistency of physical laws across inertial frames.
  • One participant provides a breakdown of the dimensions of energy and mass, suggesting that the conversion factor in the equation must have dimensions of velocity squared, with the speed of light being the only non-arbitrary choice for this role.
  • Another participant emphasizes the importance of dimensional analysis in understanding the relationship between mass and energy in the equation.

Areas of Agreement / Disagreement

Participants generally agree on the connection of E=mc^2 to the speed of light through the framework of Special Relativity, but the discussion includes varying levels of detail and emphasis on different aspects of the derivation and implications.

Contextual Notes

The discussion does not resolve the deeper implications of the relationship between mass and energy, nor does it address potential limitations or assumptions inherent in the derivation of the equation.

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In the mass-energy equivalent equation, E=mc^2, why is it related to the speed of light?
 
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That is the formula for rest energy predicted by Special Relativity.

From the postulates of SR (Invariance of c, physical laws are the same in all inertial frames) one can derive the equations describing energy:
[tex]E_{tot}=\gamma mc^2[/tex]
[tex]E_k=(\gamma -1)mc^2[/tex]
which lead to the conclusion that a mass has a rest energy [tex]E_0=mc^2[/tex] which is called the mass-energy equivalence.

So the the short answer is that it follows from the postulates of SR.

For a more in depth description detailing how the equation is derived, see
http://en.wikipedia.org/wiki/Mass-energy_equivalence#Background
 
Merry Christmas!

DeadCat_86 said:
In the mass-energy equivalent equation, E=mc^2, why is it related to the speed of light?

He DeadCat_86! Have a bouncy Christmas! :smile:

e is energy, which is ML2/T2, while m is of course just M,

so the conversion factor must have dimensions of L2/T2, ie it has to be a velocity squared …

and c is the only non-arbitrary velocity for such a general equation! :wink:
 
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tiny-tim said:
He DeadCat_86! Have a bouncy Christmas! :smile:

e is energy, which is ML2/T2, while m is of course just M,

so the conversion factor must have dimensions of L2/T2, ie it has to be a velocity squared …

and c is the only non-arbitrary velocity for such a general equation! :wink:

Dimensional analysis saves the day yet again!
 

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