Hard Determinism and Bell's Theorem

[Technical Ben]

Say I have a pair of particles in (1_up, 2_down) + (1_down, 2_up) entangled state. Now observer A comes in and does the measurement of the first particle's state. Instead of collapse, according to MWI, observer becomes part of the state.

(A_up, 1_up, 2_down) + (A_down, 1_down, 2_up)

Now, observer B does measurement of particle 2.

(A_up, 1_up, B_down, 2_down) + (A_down, 1_down, B_up, 2_up)

Now, suppose observer A goes to observer B to compare the notes. What's the state here? (A_up and B_down compare notes) + (A_down and B_up compare notes).

Despite the fact that collapse never happened, observer A that experienced outcome up can only meet with observer B who experienced outcome down. And it doesn't matter who did measurements first, or if the two measurements happened at the exact same time, while the two observers were separated by great distance. When observers compare notes, they'll always find that despite each one having random result by himself, if one got up, the other got down.

That's entanglement. And it's clear why you can't use it for communication. Everything is intuitive and there are no paradoxes.

Ah, that's very different. With dice, if you had perfect information about initial conditions, you could, in principle, compute the output. There is Deterministic Chaos involved, which says that if you have even a tiniest uncertainty in initial conditions, such as you don't know exactly where every molecule of air around the die is, then your predictions ten to diverge with time. Dice, specifically, undergo several mechanical catastrophes as they hit the table, which allow for small errors due to chaotic nature of the system become discrete differences in outcome.

In Quantum Mechanics, you cannot have sufficient information to make predictions about the outcome of the measurement. It's fundamentally impossible. The dynamics, in contrast, is still entirely deterministic. But there is Quantum Chaos as well, which is way, way worse than classical.

Thanks. Why can I not just explain it away by saying both measured the same particle (I throw out locality, and say they made the reading of the same particle, thus have to get the correct readings)? Why can they not just have an additional dimensionality within this universe, or for just that particle, for the collapse/reading/observation? Why does it need to branch out into additional universes?

For the dice, I'm assuming quantum dice. "Dice" used just to be simple with the terminology (the same way "up" is not a direction with QM). I have 1 quantum particle. I can know for a certainty the probabilities are "50% up and 50% down". I cannot know if it will be up or down.

"The dynamics, in contrast, is still entirely deterministic." AFAIK the calculations are deterministic only in their probabilities, not in their results. I can say it will give a result, with 100% certainty, up or down. I cannot say it will be down. AFAIK this is proven scientifically, mathematically and through observations. Thus, how is it "deterministic" if there is no actual determined result?

Basically, I can assume all dice rolls result in alternate realities which spawn additional dice, so they all appear with each side facing up. This is not possible and not considered correct, because it's classical and we accept no such universe exists. Do we suggest such universes exist for quantum particles? If so, why?

Edited July 18, 2014 by Technical Ben