Protons have mass? I didn’t even know they were Catholic. –Woody Allen
Albert Einstein as a young man, before his crazy-hair days. (Credit: Lucien Chavan, public domain)
As is often the case, this story began with a misquote.
Someone on Twitter quoted the above, but wrote “photons” instead of “protons”. When another person (not me) challenged him on it, he doubled down and said that everything has mass because of E = mc2 : anything possessing energy could be considered to have an effective mass equal to m = E/c2. Of course, you could do that—write a mass value for anything, including stuff like energy released in a chemical reaction—but that’s not what mass is. It may feel intuitively right, but it’s not meaningful from a physics point of view. Photons are indeed massless in a fundamental sense, but to see why that’s important, it’s good to understand mass, energy, and their role in the most famous equation in physics.
(A quick aside on what I’m not going to talk about: mass has another purpose in gravity, where it is sometimes called gravitational mass. In both Newtonian physics and general relativity, gravitational mass is equivalent to the more ordinary form ...