Why Is Energy Defined as E=mc^2 and Not Another Dimension?

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Discussion Overview

The discussion revolves around the definition of energy as E=mc², questioning why this specific formulation is used and whether other dimensions or forms could be valid. Participants explore theoretical implications and connections to classical physics, as well as the mathematical reasoning behind the equation.

Discussion Character

  • Exploratory
  • Technical explanation
  • Debate/contested

Main Points Raised

  • Some participants question why energy is defined as E=mc² and suggest alternative formulations, such as E=mc^42.
  • Others argue that the exponent of 2 is necessary for the units to be consistent, implying a mathematical requirement rather than a physical one.
  • A participant references the derivation of Special Relativity and its connection to classical physics, specifically E=1/2 mv².
  • One participant introduces Noether's theorem and discusses the implications of defining mass in relation to the relativistic Lagrangian, suggesting that the formulation is constrained by the principles of relativity.
  • Another participant expresses confusion over the term "flat planar thing," indicating a lack of clarity in the discussion.

Areas of Agreement / Disagreement

Participants express differing views on the nature of the equation E=mc² and its implications, with no consensus reached on the validity of alternative formulations or the interpretation of dimensionality.

Contextual Notes

Some claims depend on specific definitions and assumptions about mass and energy, and the discussion does not resolve the mathematical steps or implications of alternative formulations.

rootone
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"Energy equals mass times the speed of light squared."
OK, but why is it considered to be a flat planar thing?
Why not cubed or any dimension you fancy/
Why not E = mc^42 ?
 
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rootone said:
"Energy equals mass times the speed of light squared."
OK, but why is it considered to be a flat planar thing?

It's not considered to be a flat planar thing.

You need the exponent of 2 to make the units come out right.
 
Study the derivation of Special Relativity and you’ll see it’s got a connection to E=1/2 m v^2 of classical physics.
 
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rootone said:
"Energy equals mass times the speed of light squared."
OK, but why is it considered to be a flat planar thing?
Why not cubed or any dimension you fancy/
Why not E = mc^42 ?
What are the units of E and what are the units of mc^42

I have no idea what you mean by “flat planar thing”
 
Its a simple consequence of Noether and the only reasonable relativistic free particle Lagrangian k*dτ where τ is the proper time and k is a constant to be determined. By definition mass, m, is defined as k/c so the Lagrangian is mcdτ. Apply Noether and you get E = mc^2.

Relativity is strange like that - frame invariance is very constraining.

Why not define m as k/c^42? Try it - you will see that classical mechanics is not correct in the low speed limit.

Thanks
Bill
 
Last edited:
Thanks for the replies.
Working on it.
 

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