# E = mc^2 (Why not E = mc^42 )?

• I
"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 ?

Mister T
Gold Member
"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.

jedishrfu
Mentor
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.

• bhobba
Dale
Mentor
2020 Award
"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”

bhobba
Mentor
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.