Hidden variables

In plain terms

If the quantum state describes knowledge rather than the world, there has to be something the knowledge is about, an underlying state of affairs that's definite whether or not anyone looks. Theories that supply one are called hidden-variable theories, and a famous sequence of theorems is widely reported to have ruled them out.

The reports are wrong, in an instructive way. What Bell and his successors actually ruled out are the well-behaved hidden-variable theories, the local ones, in which what happens here can't depend on a choice made far away, and the non-contextual ones, in which the value a system gives for one quantity doesn't depend on which other quantities are measured alongside it. Hidden variables survive, at the stated price of locality and non-contextuality.

That isn't a loophole, as it's the actual content of the theorems. Bohmian mechanics has been paying the price since 1952, and it remains the standing proof that the reports of death were exaggerated.

In CSD

The constraint surface is a hidden-variable theory in the technical sense, and the programme says so plainly rather than hoping nobody asks. It's contextual and non- local, exactly the two properties whose absence the theorems forbid, and it proves the relevant obstructions in-house rather than citing them, since a reconstruction resting on trust in the theorems that constrain it would be oddly built.

Two standard misreadings are worth heading off. First, CSD isn't a repair of quantum mechanics, as it reproduces the same predictions at leading order, and candidate departures are recorded as owed by the papers and not claimed. Second, the quantum state isn't the hidden variable. The state is the summary, and the hidden variable is the point of the constraint surface underneath, which is why the state can be epistemic without the theory being about nothing.

Mathematically

No product partition of a shared hidden-state space reproduces the singlet correlations, at any setting pair, and likewise GHZ. This is proved over arbitrary measurable state spaces, so the constraint hits the class and not one construction.

The positive half is also in the corpus, an explicit contextual, non-local assignment that does reproduce the singlet. Together the pair delimits the viable region from both sides, what can't work and one thing that does.

Related entries

• ContextualityFor some sets of quantum questions no consistent answer sheet exists at all, and CSD's response is to stop demanding one answer per question and to say instead what the answer depends on.
• Bell and CHSHNo pre-written answer sheet for all four measurement settings can match what a singlet pair of particles does, and the corpus proves this as a theorem about every possible answer sheet.
• Is CSD a hidden-variable theory?Yes, in the technical sense, as something definite underlies the quantum state in CSD, and the programme openly pays the two prices the no-go theorems demand, dependence on measurement context and correlations beyond what locality permits.
• Bohmian mechanicsBohmian mechanics is CSD's nearest neighbour, deterministic, with definite states, and openly non-local, and the dispute between them is over where the probabilities come from.
• Psi-epistemicThe quantum state is what you know and not what exists, and the hard part was always saying what it's knowledge of, so CSD's whole architecture is an answer to that.