Recent content by john baez

The principle is that the laws of nature should have symmetries that unify bosons and fermions. Since bosons describe forces - generally speaking - while fermions describe matter, this would mean a unification of forces with matter. It's surprisingly tricky to come up with laws that unify...

Yes, and that's why Einstein wanted to derive the geodesic equation for point particles as a limiting case of a deeper field-theoretic description: Einstein's equations describing the motion of "black holes" (though he didn't know they were black holes). Naively, it should be true that if you...

Whoops, I'll fix that in the FAQ. The paper by Christodoulou is too technical for the FAQ, btw. Happy New Year!

I seem to be getting pulled into the project of updating this FAQ: https://math.ucr.edu/home/baez/physics/General/open_questions_new.html. The more I look at it, the bigger the job gets. I started out rewriting the section on neutrinos, and now I'm doing the part on cosmic censorship. There...

Wow, I forgot after only 15-20 years? My memory must be getting really bad! Thanks! That's not surprising - things often get clearer after a few tries. I'll check out those Kerr papers someday. Maybe in 15-20 years. Just to help myself remember: Roy Kerr, The Lorentz-Covariant...

I haven't actually read the Einstein-Infeld-Hoffman papers, but in my post I quoted Einstein as saying So that was certainly his goal: to model particles as singular solutions of Einstein's equations.

I think that's at least one of the things they did. Einstein and Infeld wrote three papers on this stuff, and I haven't read them. That sounds hard except in the limit where the masses of the particles are very small, since otherwise they are finite-sized black holes and you have to worry...

On another thread, now closed, Intrastellar asked: Unfortunately it seems that thread is closed before anyone pointed out Einstein's papers on this question: A. Einstein, L. Infeld and B. Hoffman, The gravitational equations and the problem of motion, Annals of Mathematics 39 (1938), 65-100...

No. That's a fun puzzle! Here are some facts that may help you solve it: We shouldn't mix up energy and mass. ##E = mc^2## is only true for particles at rest, which is why another name for mass is "rest mass". As far as we can tell, neutrinos have only 3 possible values for their mass...

It all depends on how nitpicky people are. A grumpy pedant will point out that however close to the speed of light it moves, it's possible for a left-handed particle to be observed spinning counter-clockwise along its direction of motion. But I should probably not aim to please the grumpy...

Okay, so I'm not missing anything obvious! I actually think it's pretty good to take advantage of the fact that chirality reduces to helicity in the ultrarelativistic limit, since everyone can imagine a neutrino zipping along near the speed of light spinning clockwise along its axis of motion...

Thanks! Especially thanks for emphasizing how "heavily blended" the flavor eigenstates are, as linear combinations of mass eigenstates. By the way, I'm not talking about a blog, where it's easy to spend lots of time explaining stuff properly. I'm talking about the Physics FAQ, and I'm trying...

I meant the three mass eigenstates that most closely line up with the electron, muon, and tau flavor eigenstates. I need some nontechnical way to say what I mean. This is for ordinary folks, so words like "eigenstate" are not allowed. I guess the best way is something like this: "Is there...

Merry Christmas! Neutrinos are mysterious. I just blogged about some of the big open questions involving neutrinos: Neutrino puzzles. In brief, nontechnical terms they are these: What is the correct theory of neutrinos? Why are they almost but not quite massless? Do all three known...

We can think of the exceptional Jordan algebra as a funny sort of spacetime. This spacetime is 27-dimensional, with light rays through the origin moving on a lightcone given by a cubic equation instead of the usual $$ t^2 - x^2 - y^2 - z^2 = 0 $$ in 4-dimensional Minkowski spacetime. But...