Determinism

In plain terms

Prepare two systems as identically as any procedure allows, measure them identically, and quantum mechanics happily reports different outcomes, offering no reason why this one rather than that. Either the world contains genuine chance, or the preparations weren't actually identical.

Determinism takes the second answer. The two systems agreed on everything the procedure fixed and differed in what it couldn't fix, so the observed spread is that hidden variation showing through, and probability is bookkeeping for ignorance. This is the same move classical statistical mechanics has always made about gases, as the temperature and pressure of a gas fix its state only coarsely, the exact positions and speeds of its molecules vary from one sample to the next, and the statistics come from that variation.

Whether the answer is still available after the no-go theorems isn't a matter of taste. It survives, at a stated price, as the theory must be contextual, meaning that the outcome of a measurement can depend on which other measurements are made alongside it, and non-local, meaning that what happens here can depend on a choice made far away. The entries on contextuality and hidden variables carry the receipts.

In CSD

The substrate's motion is deterministic and volume-preserving, carrying every region of the underlying state space to a region of the same size, and chance appears nowhere in the dynamics. Probability enters exactly once, as ignorance of the microstate within the region a preparation fixes, and the forced measure, the one rule for sizing regions the symmetries of the state space allow, turns that ignorance into unique numbers.

The debt is recorded rather than buried, and it's the interesting part. The frequency argument assumes independent trials. A deterministic substrate with memory would violate that assumption, and the violation would show up as deviations from ordinary shot noise, the statistical scatter expected in counts of independent events, in high-statistics data. This is one of the very few places CSD could differ measurably from quantum mechanics, and testing it needs no Planck-scale machine, just patience and statistics.

Mathematically

This entry is positional. The formal content is the measure-preserving flow and the volume-ratio weights, and determinism is the reading of that structure.

The nearest formal object is the preservation field itself, carried as an ontic postulate and listed as such in the axiom ledger, so it's assumed for physical admissibility and not derived.

Related entries

• Single trajectoryThere's one world and it follows one path, so probability lives in how experiments are repeated and not in how the world evolves, and theorems rather than wording keep the two apart.
• If CSD is deterministic, where do probabilities come from?They come from ignorance of the exact starting point, as the dynamics never rolls dice, and the probabilities are the sizes of the sets of microstates a preparation can't tell apart, measured with a ruler nobody was free to choose.
• Is CSD superdeterministic?No. In CSD's Bell model the distribution of hidden states is provably the same whatever settings the experimenters choose, and the escape from Bell's theorem runs through outcomes that depend on the measurement context and not through settings arranged in advance.
• TypicalityTypicality is probability without randomness, as the world is deterministic, you don't know which state you have, and the odds are the sizes of the possibilities.
• Constraint surfaceThere's one arena, it's deterministic, and it doesn't grow, and everything else in the programme is bookkeeping about how much of it a measurement context lets you see.