One of the challenges for a person trying to explain physics to the non-expert — and for non-experts themselves — is that scientific language and concepts are often frustratingly confusing. Often two words are used for the same thing, sometimes words are used that are fundamentally misleading, and often a single word is used for two very different but related concepts. You’d think we’d clear this stuff up, but no one has organized a committee dedicated to streamlining and refining our terminology.
A deeply unfortunate case, the subject of today’s post, is the word “mass”. Mass was confusing before Einstein, and then Einstein came along and (accidentally) left the word mass with two different definitions… both of which you’ll see in first-year university textbooks. (Indeed, this confusion even extended to physicists more broadly, causing the famous particle physicist Lev Okun to make this issue into a cause celebre…) And it all has to do with how you interpret E = mc² — the only equation everybody knows — which relates the energy stored in an object to the mass of the object times the square of the universal speed limit c, also known as “the speed of light”.
Here are the two possible interpretations of this equation. Modern particle physicists (including me) only use the first interpretation. The purpose of this post is to alert you to this fact, and to point you to an article where I explain more carefully why we do it this way.