Ok, the answer you’ve all been waiting for — the first half of it, anyway. Even though it is not the full story yet, you’ll find it is both self-contained and instructive.
Those of you who have been following my recent series of articles on extra dimensions of space — which include some articles on how to think about them (including some examples) and newer articles on how extra dimensions might reveal themselves to us — already know that for any type of particle that can travel in one or more extra dimensions that are unknown to us, nature will exhibit heavier versions of this particle, called Kaluza-Klein (KK) partner particles. But I haven’t yet told you why this is the case.
Today, Step 1: why the KK partner particles exist at all, and why they are heavier than the original one. But today’s argument is a bit too simple, and only partially correct: it gets the masses of the KK partners wrong. In Step 2 I’ll fix this problem by adding a little bit of quantum mechanics.