[ExI] Bell's Inequality

Thu Dec 1 17:41:01 UTC 2016

On Thu, Dec 1, 2016 at 10:24 AM, Stuart LaForge <avant at sollegro.com> wrote:

> Jason Resch wrote:
> <Are you familiar with:
> https://en.m.wikipedia.org/wiki/Compatibilism ?
> [...]
> I am a compatibilist when it comes to freewill and determinism.>
>
> Thanks for the link, I will look into it.
>
> Jason Resch wrote:
> <Someone earlier stated Bell's Inequality implies we have to give up one
> of: locality, determinism, or realism. This list is incomplete, we must
> give up one of: locality, determinism, realism, or counterfactual
> definiteness.
> Counterfactual definiteness means experiments have only one outcome. MWI
> gives up counterfactual definiteness and retains locality, determinism and
> realism.>
>
> My understanding of counterfactual definiteness is that it is very
> specific type of realism. It is the notion that objects have measurable
> properties that have a definite value even if measurements are not made.
>
> For example, whenever you list your weight on a driver's license
> application without weighing yourself beforehand, you are assuming a
> counterfactual definiteness to your weight. Even if you were off by a few
> pounds, the idea is that if you were to weigh yourself, you would measure
> a certain weight and that's how much you actually weigh even if you didn't
> bother weighing yourself.
>
> If you give up counterfactual definiteness, it means you don't have a
> weight when you are not standing on a scale. So I am not sure what you
> mean by saying that "MWI gives up counterfactual definiteness".
>

It is giving up the part that only one possible result will be measured for
a particular value. I would point you towards this explanation for question
32 from the many worlds FAQ (
http://www.anthropic-principle.com/preprints/manyworlds.html ):

The decomposition into four worlds is forced and unambiguous after

communication with the remote system. Until the two observers

communicated their results to each other they were each unsplit by each

others' measurements, although their own local measurements had split

themselves. The splitting is a local process that is causally

transmitted from system to system at light or sub-light speeds. (This

is a point that Everett stressed about Einstein's remark about the

observations of a mouse, in the Copenhagen interpretation, collapsing

the wavefunction of the universe. Everett observed that it is the mouse

that's split by its observation of the rest of the universe. The rest

of the universe is unaffected and unsplit.)

When all communication is complete the worlds have finally decomposed

or decohered from each other. Each world contains a consistent set of

observers, records and electrons, in perfect agreement with the

predictions of standard QM. Further observations of the electrons will

agree with the earlier ones and so each observer, in each world, can

henceforth regard the electron's wavefunction as having collapsed to

match the historically recorded, locally observed values. This

justifies our operational adoption of the collapse of the wavefunction

upon measurement, without having to strain our credibility by believing

that it actually happens.

To recap. Many-worlds is local and deterministic. Local measurements

split local systems (including observers) in a subjectively random

fashion; distant systems are only split when the causally transmitted

effects of the local interactions reach them. We have not assumed any

non-local FTL effects, yet we have reproduced the standard predictions

of QM.

So where did Bell and Eberhard go wrong? They thought that all theories

that reproduced the standard predictions must be non-local. It has been

pointed out by both Albert [A] and Cramer [C] (who both support

different interpretations of QM) that Bell and Eberhard had implicity

assumed that every possible measurement - even if not performed - would

have yielded a *single* definite result. This assumption is called

contra-factual definiteness or CFD [S]. What Bell and Eberhard really

proved was that every quantum theory must either violate locality *or*

CFD. Many-worlds with its multiplicity of results in different worlds

violates CFD, of course, and thus can be local.

Thus many-worlds is the only local quantum theory in accord with the

standard predictions of QM and, so far, with experiment.

[A] David Z Albert, _Bohm's Alternative to Quantum Mechanics_

Scientific American (May 1994)

[As] Alain Aspect, J Dalibard, G Roger _Experimental test of Bell's

inequalities using time-varying analyzers_ Physical Review Letters

Vol 49 #25 1804 (1982).

[C] John G Cramer _The transactional interpretation of quantum

mechanics_ Reviews of Modern Physics Vol 58 #3 647-687 (1986)

[B] John S Bell: _On the Einstein Podolsky Rosen paradox_ Physics 1

#3 195-200 (1964).

[E] Albert Einstein, Boris Podolsky, Nathan Rosen: _Can

quantum-mechanical description of physical reality be considered

complete?_ Physical Review Vol 41 777-780 (15 May 1935).

[S] Henry P Stapp _S-matrix interpretation of quantum-theory_ Physical

Review D Vol 3 #6 1303 (1971)

There is also this article which seems to cover exactly the subject at
hand: https://arxiv.org/pdf/0902.3827.pdf

> My biggest concern with MWI is that it requires the Universal Wave

Function to be objectively real, not merely a mathematical abstraction. So
> if the UWF is objectively real then that means the infinite-dimensional
> Hilbert space that describes it is objectively real. So where is this
> gigantic Hilbert space hiding? Why do we only perceive 3+1 dimensions in a
> multiverse controlled by an infinite dimensional Wave Function? What is
> the relationship of our percievable space-time to the Universal Wave
> Function and the Hilbert space in which It dwelleth?
>

The wave function is a standard assumption of all QM
theories/interpretations that accurately describes the evolution of any
isolated system. The *universal* wave function just treats the entire
universe as an isolated system, and applies the regular rules of QM to
determine how it evolves.

Jason
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