Interesting Coincidence with Classical/Modern View of Mass and Energy

[Cadaei]

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?

 

[A.T.]

The units in a physical formula actually do work out? What a coincidence!

 

[Doc Al]

Creepy!

 

[mfb]

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.