Cleaning up after Matt Parker

[Equations in this post may not look right (or appear at all) in your RSS reader. Go to the original article to see them rendered properly.] This video Matt Parker posted a couple of days ago really pissed me off: It’s cheating to say that a result arrived at through classical mechanics—in this case, that 12mv2 is the kinetic energy of a particle—is wrong because it’s only an approximation to relativistic physics. Of course that’s the case, and I swore at my phone when the “reveal” came. By the end of the video, though, I had calmed down because I knew I could put together a quick post of my own by rewriting the infinite series equation he derived in a better form. Also, I could provide a general expression for the individual terms. Let’s start with this result: that the kinetic energy of a particle (including relativistic effects) is mc2(γ−1) where m is the mass of the particle, c is the speed of light, and γ=11−v2c2 is the Lorentz factor, with v as the velocity of the particle. The…