No, it is not a coincidence [0]. It is a direct result of the fact that in relativity temporal and spatial information has to be unified into a single vector (

No, it is not a coincidence [0]. It is a direct result of the fact that in relativity temporal and spatial information has to be unified into a single vector (a four-vector [1]). Since (in the Noether theorem sense [2]) energy is the conserved quantity related to symmetry of displacements in time and momentum is the conserved quantity related to symmetry under displacements in space, it is quite natural to unite them into one four vector, related to symmetry of displacements in spacetime. What's peculiar is that the temporal entry of the four vector gets the "opposite sign" for the Pythagorean theorem. That is, if you have a vector (t, x, y, z), then the "hypotenuse" (called an invariant) is t^2 - x^2 - y^2 - z^2 (up to a conventional choice of overall sign). What's surprising is that the hypotenuse is the thing that's the same for different observers. So, if you do a Lorentz transformation [3], t and the spatial entries will change, but the invariant combination won't. Everybody knows E = mc^2 is the relationship between a particle's mass and its energy. But what is its energy if it's moving? Certainly the particle gains energy the faster it moves, right? Yes. E = mc^2 is the 0-momentum version of a relativistic expression. Since E is temporal and momentum p is spatial, the four vector can be written (E, pc), which has an invariant E^2 - (pc)^2. We call this invariant the rest mass[4], up to some factors of c. Algebraically moving things around gives us the "Pythagorean" form. [0] https://en.wikipedia.org/wiki/Energy%E2%80%93momentum_relation https://en.wikipedia.org/wiki/Energy%E2%80%93momentum_relati... [1] https://en.wikipedia.org/wiki/Four-vector https://en.wikipedia.org/wiki/Four-vector [2] https://en.wikipedia.org/wiki/Noether%27s_theorem https://en.wikipedia.org/wiki/Noether%27s_theorem [3] https://en.wikipedia.org/wiki/Lorentz_transformation https://en.wikipedia.org/wiki/Lorentz_transformation [4] https://en.wikipedia.org/wiki/Invariant_mass https://en.wikipedia.org/wiki/Invariant_mass