What is Stochastic Quantum Mechanics (in simple terms)?

[john taylor]

Could someone, in laymen's terms explain to me what stochastic mechanics is?

 

[.Scott]

Before the position, velocity, or some QM property of a particle is measured, a probabilistic range of potential measurement results can be predicted.
But the exact measurement result cannot be fully predicted. In that sense, there is an element of randomness whenever an attempt is made at such a measurement.

The mechanics can be viewed as not fully deterministic. Thus: stochastic mechanics; mechanical rules that include an unavoidable element of randomness.

...

I am looking at this article: https://iopscience.iop.org/article/10.1088/1742-6596/361/1/012011/pdf

In the introduction, it described stochastic mechanics (SM) as an "interpretation" or quantum mechanics (QM). But it is not. One interpretation of a theory, such as QM, should yield the same predictions as any other interpretation. But the article goes on to show that the model generated by SM is not equivalent to QM. QM makes consistently accurate predictions. SM does not.

What SM does show is that there are is an awful lot of QM that results from no more than the randomness created when measurements are made - and other assumptions made by SM.

Unfortunately, as I read through the material, I cannot identify exactly what those other assumptions are.

 

[kith]

I am looking at this article: https://iopscience.iop.org/article/10.1088/1742-6596/361/1/012011/pdf

That's a nice summary. Unlike the wikipedia article, it actually gives an idea of what stochastic mechanics is about.

In the introduction, it described stochastic mechanics (SM) as an "interpretation" or quantum mechanics (QM). But it is not. One interpretation of a theory, such as QM, should yield the same predictions as any other interpretation. But the article goes on to show that the model generated by SM is not equivalent to QM. QM makes consistently accurate predictions. SM does not.

Nelson seems to claim that the predictions are the same for actual experiments. In the last paragraph of the paper you cited, he writes:
"Why do I not suggest that the experiment be done? Because if a record of the observation of the first oscillator at time t1 is made by some physical means, and similarly for the second oscillator, and the two records arecompared at a common later time t3, this is an observation at a single time, for which quantum mechanics and stochastic mechanics agree. The nonlocality of stochastic mechanics conspires to bring the records into agreement."

What SM does show is that there are is an awful lot of QM that results from no more than the randomness created when measurements are made - and other assumptions made by SM.

This doesn't seem right to me. The main feature of stochastic mechanics is to have a Brownian motion like stochastic movement of particles going on all the time which gives the Schrödinger equation the status of some kind of diffusion equation. Up to this point in the description, no measurements are involved.