Many Worlds, Indistinguishability, Pascal's Triangle and the Gaussian

[craigi]

Suppose we have a quantity which can take discrete equally spaced values. Iteratively, we can increase or decrease this quantity by one quantum, splitting into two new worlds each time. After multiple iterations we have some indistinguishable worlds, as described by Pascal's triangle. As the number of iterations tends towards infinity, this distribution tends towards the Gaussian distribution matching the distribution given by unbiased measurements on incoherent systems, which is pretty cool.

So my question is, where does this line of thinking go? Can we take it any further?

 

[UltrafastPED]

IMHO it leads nowhere. This is one of the "logical" problems with the Many Worlds interpretation of QM: it inverts the fact that there are multiple possibilities for the outcome of an interaction in our universe with ...

... there are many universes, and only one outcome will occur in each universe.

 

[craigi]

IMHO it leads nowhere. This is one of the "logical" problems with the Many Worlds interpretation of QM: it inverts the fact that there are multiple possibilities for the outcome of an interaction in our universe with ...

... there are many universes, and only one outcome will occur in each universe.

I'm less concerned with the interpretation in general, than how the Gaussian distribution is generated in this circumstance.

For example, the position of a particle can be predicted from infinitesimal 2-state momentum iterations. Previously, I had presumed that a Gaussian distribution on particle position was linked to a Gaussian distribution on it's momentum, but it seems that this isn't necessairily the case.

 

[UltrafastPED]

Seems to be purely a math problem. Perhaps you could run a simulation.

 

[craigi]

Seems to be purely a math problem. Perhaps you could run a simulation.

It wouldn't glean anything other than demonstrating that a Pascal triangle does converge to a Gaussian distribution.

Perhaps a deeper question is what is the relevance of this to the physical world?

 

[UltrafastPED]

Is this what you are trying to do?

"From Pascal's Triangle to the Bell-shaped Curve"
http://www.ams.org/samplings/feature-column/fcarc-normal

 

[craigi]

Is this what you are trying to do?

"From Pascal's Triangle to the Bell-shaped Curve"
http://www.ams.org/samplings/feature-column/fcarc-normal

Well that's the just the maths, but the Gaussian distribution is a feature, of nature too.

It crops up in statistics and probability theory which, as you suggest, is a mathematical problem.

In the physical world it manifests in molecular diffusion. This isn't suprising because the diffusion process is very similar to the process that I described resulting in the Pascal triangle. Many discrete interactions on a microscopic scale culminating in the continuous macroscopic distribution function.

The thing that I'm really interested in, is that it also occurs in quantum physics and I'm wondering what relation, if any, the MW splitting mechanism has to it. Could it be that here also, the distribution is produced by many small processes, or is there another explanation for how this function emerges?

I'm not really expecting anyone to give me a good answer to this, because I guess what this amounts to is asking what causes the Schrodinger equation.

 

[craigi]

Just going to bump this once in case anyone can offer any leads on it.