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I have looked in vain for a long time for a common sense explanation of the $c$ Squared part of Einstein's famous equation. No one on Youtube or anywhere else explains this part of the equation, even when they set out to explain the equation! Why multiply $c$, for example? Why not add it? Why is it there at all?

Qmechanic
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VirtualInSeattle
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  • This clearly isn't a duplicate of the other question, why mark it as being so? – Suzu Hirose Oct 09 '16 at 07:27
  • there is a good explanation in chapter one of "Special Relativity" by A.P.French (MIT series in Physics). – Suzu Hirose Oct 09 '16 at 07:28
  • "I have looked in vain for a long time for a common sense explanation of the c Squared part of Einstein's famous equation." I sympathize, but ... Let's start with a simpler question: why does $v^2$ appear in the expression for the Newtonian kinetic energy? I know several ways to develop the expression for the total relativistic energy, but they all involve some rather careful math. – dmckee --- ex-moderator kitten Oct 09 '16 at 18:07

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Well, if you look at just the units, you would need a factor of some sort of velocity squared multiplying your mass in order to have units of energy:

$kg (\frac{m}{s})^2$ = Joules

You can not add two numbers that have different units - this is like asking what you get if you add one banana and one firetruck - nonsense! we can add one banana and 4 bananas - we get 5 bananas. So, if the units don't match, we can not add or subtract.

The actual equation $E = mc^2$ was derived using special relativity, which you can read about in many places. Note that this is just the rest energy of a massive particle - if a particle is moving (has momentum), then $E^2 = \sqrt{(Mc^2)^2 + (pc)^2}$, and if the particle has no mass (such as a photon), then E = pc

user42906
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