Bohmian mechanics

In plain terms

The question Bohm settled in 1952 was whether a deterministic account of quantum mechanics is possible at all, one in which the present state of the world fixes the future by law, with no randomness. The folklore of the time, leaning on von Neumann's flawed impossibility proof, said it couldn't be done, and Bohm answered by construction, as he wrote one down.

In his theory particles have definite positions at all times, and a wave, evolving by the ordinary Schrodinger equation, guides them, so every quantum prediction comes out exactly. The price is explicit non-locality, as each particle's guidance depends instantaneously on where all the others are, across any distance. Bell, who admired the theory, showed that this price isn't Bohm's clumsiness but everyone's obligation, since any account that reproduces the quantum predictions must pay it in some form.

Bohmian mechanics remains the standing counterexample to every claim that quantum mechanics rules out determinism, so whatever else is true, that claim is dead.

In CSD

This is CSD's closest relative, and the family resemblance is real, with determinism, a definite underlying state, non-locality accepted with open eyes, and probabilities that express ignorance of the exact state rather than randomness in the world. A reader placing CSD on the map of interpretations should put it nearest here.

The differences concern what exists, and on one point they're sharp. Bohm has a dual ontology, a physical guiding wave together with particle positions, while CSD has one object, the constraint surface, and demotes the quantum state to epistemic bookkeeping, a summary of what's known rather than a thing in the world, so nothing guides anything. The probability postulates also differ in kind. Bohmian statistics require the quantum equilibrium hypothesis, an assumed initial distribution of particle positions, possibly one the dynamics relaxes into, whereas CSD's measure is forced by a symmetry theorem, so where Bohmians must defend an initial condition CSD points at uniqueness. That's the standing objection to Bohm this programme claims to escape.

Mathematically

There's no formal content in the corpus about the rival itself.

The shared formal shape is that both derive probabilities from a measure on an underlying state space rather than postulating the Born rule, so both owe an account of the measure, and the accounts differ (assumed equilibrium there, forced uniqueness here).

Related entries

• How does CSD differ from Bohmian mechanics?They're cousins rather than twins, as both theories pay the price the no-go theorems demand of any deterministic account, but Bohmian mechanics postulates its equilibrium distribution where CSD proves its measure unique, and the arenas underneath the two are different kinds of object.
• Hidden variablesThe no-go theorems don't kill hidden variables, as they price them, and CSD reads the price tag and pays it.
• Many-Worlds interpretationMany-Worlds keeps the smooth quantum evolution and gives up the single outcome, and CSD makes the opposite choice, one trajectory and one world, as a settled commitment.
• 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.
• DeterminismThe substrate has no dice, so the spread in the data is variation in what your preparation couldn't pin down.
• Nelson stochastic mechanicsNelson derived the Schrodinger equation from a diffusion, so the same continuity equation that lets Bohm read a velocity off the wavefunction lets Nelson read a drift with noise against it, and the Born density solves both.