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

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Energy is defined as E=mc^2 because the exponent of 2 is necessary for unit consistency, linking it to classical physics equations like E=1/2 mv^2. The term "flat planar thing" is not applicable in this context, as energy and mass are derived from fundamental principles in relativity and Noether's theorem. The relationship is constrained by the requirements of frame invariance in relativistic physics. Alternative definitions, such as using different exponents, would lead to inconsistencies with classical mechanics. Understanding these derivations is crucial for grasping the foundations of energy-mass equivalence.
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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
 
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Thanks for the replies.
Working on it.
 

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