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Interesting Coincidence with Classical/Modern View of Mass and Energy

  1. Jun 12, 2012 #1
    Has anyone ever noticed that, even in classical physics, energy is shown as a scalar multiple of mass?

    For example, consider the joule;

    1 J = 1 kg*(m/s)^2

    If you consider the units of motion (m/s) to be a vector quantity, then squaring such a vector would be interpreted as a dot product that produces a scalar.

    1 J (energy) = [mass in kg]*[scalar speed]

    Which is eerily similar to E=MC^2. Thus, whether anyone in the past realized it or not, did they inadvertently stumble on the mass-energy equivalence just by dealing with these units?
  2. jcsd
  3. Jun 12, 2012 #2


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    The units in a physical formula actually do work out? What a coincidence!
  4. Jun 12, 2012 #3

    Doc Al

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    Staff: Mentor

    Creepy! :bugeye:
  5. Jun 12, 2012 #4


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    Staff: Mentor

    If you set the speed of light to 1, mass and energy have the same units. This is not a coincidence, and shows that the concepts are related in relativity.

    If, for some strange reason, nonrelativistic kinetic energy would be something like mv^3, the rest energy of objects should be something like mc^3. But I do not think this would give meaningful physics.
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