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

  1. Oct 6, 2018 #1
    "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 ?
  2. jcsd
  3. Oct 6, 2018 #2

    Mister T

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    Science Advisor
    Gold Member

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

    You need the exponent of 2 to make the units come out right.
  4. Oct 6, 2018 #3


    Staff: 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.
  5. Oct 7, 2018 #4


    Staff: Mentor

    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”
  6. Oct 7, 2018 #5


    Staff: 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.

    Last edited: Oct 7, 2018
  7. Oct 7, 2018 #6
    Thanks for the replies.
    Working on it.
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