For EPR, as I understand it from my too crude reading, there is an event and two particles are created and fly off in different, maybe from conservation of momentum, opposite directions. So, the two particles are a QM system with one wave function which, however, is in two parts that are separating rapidly.

As I understand the usual interpretation of the wave function, there is no, say, definite spin. We don't know what the spin of either particle is, and neither does the wave function or anything else. That is, a definite value of the spin just doesn't exist yet.

Then we measure the spin of one of the particles, and that measurement gives us a spin that apparently was determined just at our measurement. Then the wave function of the two particles has to change, and the other particle has its wave function but if we measure its spin we will get what we are supposed to, say, opposite, from what we measured from the first particle. So, the fixing of the spin of the particle we measure second was somehow transmitted faster than the speed of light. Just what was transmitted faster than the speed of light we don't know about, can't detect, and is not physics in any usual sense. Still, say, if we were trying to write a computer program to simulate this, as soon as the first measurement was made, we'd have to stop the simulation clock of the universe, go the other particle, on the simulation clock, infinitely fast, fix that particle's spin, and then continue the simulation. Strange stuff.

But, sure, that doesn't tell us how to do communications with EPR "spooky action at a distance".

I don't yet know enough QM to make well informed questions about more. I should watch the MIT QM course lectures through to the end (hold my nose on how he does his math) and pick out the more important things they are saying about how wave functions behave, when there are interactions and the wave functions disappear, etc.

Yes, pretty much need to assume the axiom of choice, and some of its consequences are tough to swallow.

> Again, currently we do not have a way of predicting the outcome of an individual experiment, but there's no reason to believe that we will never be able to do so.

Right. So, if we could so predict, what surprising things could we do with that? So, we are being forbidden to do such things. Why? Does this provide a clue about purpose?
Right, this is a long way from physics at least now.

For why SR says that information cannot be transmitted faster than light, IIRC what you said about the Lorentz transformations can say that just information, of any kind, sent any way, known to current physics or not, would permit a case of time travel or seeing into the future or some such, and we don't want to believe in that.

Yes, there is physics, say, the standard model, and first cut it looks quite simple. But the consequences are astounding beyond belief. E.g., we couldn't look at the standard model and see how DNA would work and what it would do, for green plants, earth worms, ..., humans. Heck, just looking at the standard model, we might guess that the universe would be just a fog of hydrogen or something else so simple. Even if we looked at the standard model long enough to conclude that galaxies and stars would form, some stars would explode and create some of the periodic table (the rest created otherwise), condense to planets, it's still tough to see why the planets would be more than, say, just Mars. But, no, DNA happened and after a billion or so years, we happened. That looks so astounding it looks suspiciously like part of a purpose. But you are right, that's not physics yet.