Bell’s Theorem is only correct if this assumption holds. Hossenfelder is arguing that the assumption is incorrect: that Bell’s Theorem is incorrect precisely because there ARE hidden variables and that these ARE correlated with measurement settings.
She also argues that all mentions of free will in all related discussions are meaningless red herrings that have distracted physicists from properly interpreting Bell’s Theorem and observed violation of Bell’s Inequality.
Superdeterminism, arguably misnamed, simply argues that QM is deterministic, where Bell and others have argued it is not.
Thanks, I will keep trying to make sense out of Bell's work.
I keep getting stuck trying to read quantum mechanics: One place was the claim that the wave functions form a Hilbert space. Nope: As I read in W. Rudin, Real and Complex Analysis, a Hilbert space is a complete inner product space where complete means that every Cauchy convergent sequence is convergent. Well, while the wave functions are likely points in a suitable Hilbert space, they can't be complete, e.g., they can converge to a point in the space, i.e., a function, that is not continuous and, thus, not differentiable in contradiction to the assumption that all wave functions are differentiable. I admit that this is a small point, but I was trying to take quantum mechanics seriously and be careful.
Closer to the OP, another place I got stuck was in the approaches of physics to independent and uncorrelated: In probability theory those two are not the same: For two real valued random variables, independence implies uncorrelated. As in W. Feller, in the case of two real valued random variables with joint Gaussian probability density function, uncorrelated implies independence. Generally, however, uncorrelated does not imply independence. Independence is a much stronger property than uncorrelated. Maybe eventually I will figure out what physics means by "uncorrelated", especially for Bell's work.
To me, we can take the Ace of Hearts and the Ace of Spades, shuffle them, and deal them out, face down, one each to Bob and Sally. Bob can go a light year away. Sally then looks at her card and knows right away, nothing faster than the speed of light needed, what Bob's card is.
We know all the associated probability distributions for Bob and Sally. And we know that as soon as the cards are dealt what each of Bob and Sally have is determined -- so far unknown but still determined.
I'm guessing that this Bob-Sally thought experiment may have something to do with entanglement, the EPR (Einstein, Podolsky, Rosen) paradox, "spooky action at a distance", collapse of quantum mechanics wave functions, and Bell's results -- but I need to keep studying.
1. When we measure the first particle, we alter the second particle to produce the desired correlation. This is the communication loophole. If you move the particles far enough apart, it requires superluminal communication, which GR says is impossible. This is what Einstein was getting at in the EPR paper; if what the Copenhagen interpretation of QM says is true, and the particle is in both states at once, measuring it collapses it to a given state, and the other particle suddenly "knows" what it should be, even though the propagation of information through the universe has a speed limit.
2. We could define an additional hidden variable in [0,1], and do rejection sampling at the detector. Anything that is rejected is not detected, and we only deal with detected particles. This is the detection loophole. I'm not an expert, but this is the only one that really makes sense to me as a good candidate for a hidden variables theory, and I believe it's been ruled out by experiment.
3. We could bias the initial sampling of our hidden variables. The problem is, this requires that we know the setting of the detector ahead of time. As far as I understand it, this is essentially what superdeterminism comes down to: you know the experiment setting ahead of time because everything is completely deterministic, like a movie reel being rolled forwards. You can thus bias the initial sampling step to produce the QM correlation function. Aside from being unfalsifiable, it still leaves open the question of why this would happen. It essentially means that all QM experiments have predetermined outcomes, and for whatever reason, those outcomes are the outcomes we observe.
Ultimately, it seems to me that Bell's inequality is more a statement about the fundamental incompatibility of quantum probability with classical mechanics and probability. If QM is correct, and it seems that it is, then you have to give up certain assumptions such as locality.
The standard computational approach to this is to define the distribution as lazily evaluated based on some future state. That's exactly what Sabine is suggesting for a superdeterministic theory.
> It essentially means that all QM experiments have predetermined outcomes, and for whatever reason, those outcomes are the outcomes we observe.
More or less. This doesn't seem to bother anyone when spin 1/2 particles are all governed by the Dirac equation "for whatever reason", but somehow people really seem to think it matters in this case.
> We know all the associated probability distributions for Bob and Sally. And we know that as soon as the cards are dealt what each of Bob and Sally have is determined -- so far unknown but still determined.
Right, so that's a hidden variable theory. But the Bell Inequalities give you a set of measurements that can't be explained by hidden variables - one simpler variation is Conway's "free will theorem": Bob and Alice each have something like 29 envelopes, and if he opens one of several sets of 3, then he will always find two black cards and one white card (and Alice will always find the opposite). But there's no way to "statically" assign black and white cards to envelopes so that all of these sets of 3 have that property. So either which cards are in which envelopes really is undetermined until Bob opens a set of 3, or you somehow know which envelopes Bob is going to open at the point where you're putting the cards in the envelopes.
I don't get it. Alice knows it right away only if she knows the rules of the game, electricity in her brain doesn't need to move a light year away. Though, if she's braindamaged, it can take longer than a light year for her to figure that out or may never happen at all.
No, this is completely wrong. Super-determinism is more than determinism. Super-determinism is about conspiratorial coincidences – so the measurement settings you choose just happen to be the ones which will make it look like the world is quantum.
Other quantum interpretations are also deterministic, like many worlds and pilot wave theory. Bell's theorem doesn't assume determinism, but most importantly (1) locality (2) counterfactual definiteness (3) a single classical world (4) no retro-causality and (5) no super-determinism.
The laws of physics were there before people started studying physics. Didn't make it less interesting for those who were interested.
Everything we do is a mockery - life expectation is 75 if you are lucky and universe doesn't care about your achievements
>you can't learn anything about what causes have what effects because you can't ever change a causal variable.
[shrugs]If you don't have free will, then how can you change smth? What part of a computer "learns" during gradient descent?
But they're interesting because they are laws - because there's some structure there, because the same causes consistently have the same effects. Superdeterminism denies all that.
> If you don't have free will, then how can you change smth?
I'd say that if you're an inherent part of the causal chain that makes something happen then it's fair to say that you changed it. You don't have to assume free will to acknowledge that we affect our environment.
> What part of a computer "learns" during gradient descent?
I don't know or particularly care, but the learning happens - you can't understand the behaviour of the system otherwise.
Wait, how does it deny it?
> i'd say that if you're an inherent part of the causal chain that makes something happen then it's fair to say that you changed it. You don't have to assume free will to acknowledge that we affect our environment.
it's separating us from the environment and saying that one part changed the other, but that's just a simplification as our heads can't contain the whole system with all it's events. A blurry reflection. So now we "look" at this reflection and say : this is wrong, it makes no sense
Without simplification, we had some "initial" state and it "goes" somewhere. Like sand in a clock. We all know where the sand goes and what will happen in an hour.
We have words like "interesting, learn, understand" which don't really mean anything when we think about determinism. Science requires an observer but who is looking?
To be able to talk about cause and effect you have to have a concept of independence. Superdeterminism's basic premise is essentially that everything in the past can affect everything in the future - you chose which direction to measure because the particle was polarised a particular way (or because of some common underlying cause). So how can you possibly talk about what caused you to measure a particular direction when apparently it was magically due to this thing that has no visible connection to it?
> We have words like "interesting, learn, understand" which don't really mean anything when we think about determinism. Science requires an observer but who is looking?
And yet science does work. We're able to make predictions and see them borne out.
You mean a connection we can measure.
as i understand, our measurements rely on what we know and what we know relies on previous events. Its like what and how we measure something is simultaneosly determined by that something. We can't measure the size of a cat's soul because we don't have instruments for it but if we invent the instruments there will be no other choice than measuring them in a particular way the soul allows us to measure it.
Don't know if it make sense at all, but i tried to make sense of it.
If the cat's soul changed the usual laws of physics around the cat, it would destroy our ability to do physics when cats were nearby. It's not about whether we can measure it but about whether we can isolate its effects. If you can't do an experiment that doesn't depend on the state of the entire universe, you can't do an experiment.
There can be structure without cause and effect. Take any static physics problem, for example a flexible sheet that’s stretched over some frame. Since there is no time dimension there is no cause and effect but at every point in the sheet there is structure (Poisson’s law).
Both QFT and GR are the same order in time and space dimensions. Now, time is special among the dimensions because of the second law of thermodynamics, but I still have this feeling that it’s our being part of the universe and our brains having sufficient complexity for self reference that causes the illusion of a linear flow of time, while in fact all time happened in one ‘instant’ and one of the requirements for our universe to exist is that it is self consistent (causing these weird conspirational coincidences).
Up to a point - that kind of structure still depends on a notion of spatial distance and "influence" where you can reason locally about subsets. It's fairly fundamental that some parts of the sheet are more closely related to each other than other parts of it. If you had a model where every point of the sheet was equally closely related to every other point, you wouldn't be able to have any nontrivial structure, I think.
Pilot wave theory is deterministic, but non-locality is retrocausal influence under GR.
I also don't think your take on superdeterminism is entirely correct. As Sabine says, "statistical independence" is the "no superdeterminism" assumption, and some superdeterministic theories can be conspiratorial, but that doesn't mean all such theories are conspiratorial. This is the mistake.
It is deterministic. The experimenter ends up in all of them.
This is incorrect. QM is already deterministic. Where oh where do people get the idea that it is not?
E.g. the master equation for a quantum density matrix governs its evolution when the environmental conditions are not completely known or modelled. Classical ensembles or 'decohered' states occur as a consequence.
QM is formulated as a deterministic theory. When you try to model an open, interacting system without tracking its environment, you have to sacrifice determinism in that model, because you are failing to track all the information in the system. You settle for probabilistic quantities. Nothing quantum about it either-- same thing happens in classical mechanics. They call this "classical thermodynamics".