Wave Function Collapse and Bayesian Probabilty

[unchained1978]

I'm curious as to whether or not there is a connection to be drawn between the phenomenon of wave function collapse and the idea of Bayesian inference. I began thinking about this within the context of one of the variants of the Monty Hall problem. If you have one kid, what's the probability that you will have a girl, given that the first is a boy. Before you learned that the first was a boy, the probability that the kid would be a girl is just .5. We could treat that probability as a sort of probabilistic wavefunction (loosely speaking). Now when we learn that one child is a boy, the probability of the next being a girl changes to 2/3. (BB BG GB GG) The last option is now excluded given the new information, giving rise to a new "wavefunction" which effectively collapses the previous wavefunction. It seems strikingly similar to a particle in a box, in which the observation of a rightward moving particle collapses the wavefunction and vice versa. Any thoughts?

 

[lugita15]

There is indeed an interpretation of quantum mechanics in which uncertainty just reflects our ordinary classical ignorance of the system. It is known as the Bohmian interpretation, and it says that particles have well-defined positions and momenta at all times, we just may not know what they are. The only price you have to pay is nonlocality: particles are able to influence each other faster than the speed of light.

 

[unchained1978]

I remember reading about this some time ago, but I don't seem to recall how non locality arises in such a system. Could you elaborate?

 

[atyy]

Discussed by
Pusey et al, On the reality of the quantum state, What is the quantum state?
"From the 'state of knowledge' view, the argument goes, collapse need be no more mysterious than the instantaneous Bayesian updating of a probability distribution upon obtaining new information."

Older work
David Deutsch, Quantum Theory of Probability and Decisions

 

[lugita15]

I remember reading about this some time ago, but I don't seem to recall how non locality arises in such a system. Could you elaborate?

It has to do with quantum entanglement and Bell's theorem, which is an absolutely fascinating topic. I suggest you read the excellent, yet easy to understand explanation "quantumtantra.com/bell2.html" .

 

[DrChinese]

I'm curious as to whether or not there is a connection to be drawn between the phenomenon of wave function collapse and the idea of Bayesian inference. I began thinking about this within the context of one of the variants of the Monty Hall problem. If you have one kid, what's the probability that you will have a girl, given that the first is a boy. Before you learned that the first was a boy, the probability that the kid would be a girl is just .5. We could treat that probability as a sort of probabilistic wavefunction (loosely speaking). Now when we learn that one child is a boy, the probability of the next being a girl changes to 2/3. (BB BG GB GG) The last option is now excluded given the new information, giving rise to a new "wavefunction" which effectively collapses the previous wavefunction. It seems strikingly similar to a particle in a box, in which the observation of a rightward moving particle collapses the wavefunction and vice versa. Any thoughts?

There has been discussion of this by a number of authors, as has been mentioned. You should be aware that this is no simple answer for anything. The issue is that the context of a measurement controls the resulting statistical correlations. In other words, we live in an observer dependent reality. Either that, or as mentioned, there are non-local influences (or both).

For example: There are a lot of different ways to generate entanglement, and it is possible to entangle particles AFTER the fact. You would have to admit that it gets pretty tricky to explain (using Bayesian probabilities) how you can entangle particles that have never even been in causal contact.

http://arxiv.org/abs/quant-ph/0201134