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

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SUMMARY

The equation E=mc², which defines energy as mass times the speed of light squared, is derived from the principles of Special Relativity and classical physics. The exponent of 2 is essential for unit consistency, linking it to the classical kinetic energy formula E=1/2 mv². The discussion emphasizes that energy is not a "flat planar thing" but rather a consequence of Noether's theorem and the relativistic Lagrangian formulation. Understanding this relationship is crucial for grasping the constraints of frame invariance in relativity.

PREREQUISITES
  • Special Relativity principles
  • Noether's theorem
  • Classical mechanics, specifically kinetic energy formulas
  • Understanding of Lagrangian mechanics
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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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