# Envariance and Bohm

1. Oct 2, 2010

### atyy

The Bohmian interpretation says quantum mechanics is deterministic.

The environmental darwinism approach tries to derive the Born rule, and make quantum mechanics deterministic.

If darwinism succeeds, would it be compatible with Bohm, since both aim to make QM deterministic?

2. Oct 2, 2010

Can you quote a reliable source?

3. Oct 2, 2010

### atyy

http://arxiv.org/abs/quant-ph/0312059
"Bohmian mechanics, on the other hand, upholds a unitary time evolution of the wavefunction, but introduces an additional dynamical law that explicitely governs the always-determinate positions of all particles in the system."

4. Oct 2, 2010

But this statement in the paper:

"Thus the particles follow determinate trajectories described by Q(t), with the distribution of Q(t) being given by the quantum equilibrium distribution $$\rho=|\psi|^2$$"

is inaccurate. To make it accurate one would have to add: "provided it is given by this distribution at some time instant t0."

Last edited: Oct 2, 2010
5. Oct 2, 2010

Quoting from Goldestein, Struyve, "On the Uniqueness of Quantum Equilibrium in Bohmian Mechanics", Journal of Statistical Physics 128, 1197-1209 (2007)

"Bohmian mechanics (often called the deBroglie-Bohm theory) yields the same predictions as standard quantum theory provided the conﬁguration of a system with wave function ψ is random, with distribution given by $$|\psi|^2$$ This distribution, the quantum equilibrium distribution [1, 2], satisfies the following natural property: If the distribution of the conﬁguration at some time t0 is given by $$|\psi_{t_0}|^2$$, then the distribution of the conﬁguration at any other time t will be given by $$|\psi_t|^2$$ — i.e., with respect to the wave function it will have the same functional form at the other time—provided, of course, that the wave function evolves according to Schrodinger’s equation between the two times and the conﬁguration evolves according to the law of motion for Bohmian mechanics."

6. Oct 4, 2010

### Demystifier

Probably not, because the two approaches have different ontologies. Yet, there could be a relation between the two approaches not yet seen explicitly (at least by me).

7. Oct 4, 2010

### atyy

Thanks, Demystifier. I guess have to wait and see, but I would hope it'd be something like a different foliation of the same spacetime.