Re: Nonlocality from space-time zigzags

Date: Sat, 30 Dec 1995 14:39:38 -0800
From: Vic Stenger <vjs@uhheph.phys.hawaii.edu>
To: quantum-d@teleport.com
Subject: Re: Nonlocality from space-time zigzags

On Fri, 29 Dec 1995, Mitchell Porter wrote:

> In Chapter 9 of _The Undivided Universe_, Bohm and Hiley discuss
> stochastic models and conclude that they must be nonlocal. In
> Section 9.7 they say that Nelson reached the same conclusion.

Yes, that's why I have tried to distinguish nonlocal from superluminal.
Bohm's deterministic model is nonlocal and superluminal, while the 
stochastic zigzag is only nonlocal.  I think the title of Bohm and 
Hiley's book should make it clear that they are thinking superluminal, 
holistic, etherial, deterministic and nonlocal.

> The idea that one can obtain effective nonlocality from a local
> physics through space-time zigzags strikes me as very interesting,
> but in need of quantitative expression. Something like a law of
> motion needs to be proposed, from which one can ultimately derive
> quantum-mechanical transition probabilities.
> 
> There are apparently relationships between quantum field theory in n 
> (space) dimensions and the statistical mechanics of Euclidean field 
> theory in n+1 dimensions, so perhaps one could construct such a 
> derivation starting with a "random Euclidean field". I don't know how 
> to go about doing that for the continuum case, but I can see a way to 
> work on a lattice of space-time points.
> 
> A possible history would consist of an assignment of field values to
> the lattice points (or of a set of particle trajectories along the edges
> connecting them). One would assign probabilities to each possible 
> field-value (or trajectory component) - I shall call these the
> "elementary probabilities" - and calculate the total probability of a 
> history or history segment by multiplying the elementary
> probabilities of its constituents, in the usual fashion of
> probability theory. (Note that these are ordinary probabilities, not 
> complex probability amplitudes.) 
> 
> Finally, one can obtain a transition probability between an initial
> condition on one space-like surface, and a final condition on some
> other surface, by simply summing the probabilities of all possible 
> connecting histories. (I am assuming that the "elementary probabilities"
> are chosen so we have unitarity/normalization.)
> 
> If one can recover quantum-mechanical transition probabilities from
> such a starting point, an obvious interpretation suggests itself.
> Ontologically, the world consists of a random Euclidean field -
> "random" in that it doesn't follow a law of motion, but admitting
> of a simple characterization in terms of those elementary probabilities.
> Probabilities here would admit of relative frequency interpretation:
> the probabilities assigned to the fundamental processes above would
> simply be the relative frequency of those processes in space-time.
> Unfortunately, as I said, I don't have a precise idea regarding
> the continuum case.

As far as I'm concerned, you do not have to worry about the continuum.  
Space and time, energy and momentum, are all fundamentally discrete.  The 
continuum spacetime is only an approximation to allow us to use calculus, 
which works fine at most scales above the Planck scale.

> Just to reemphasize: the notion here is that one could get spacelike
> correlations out of locally-defined elementary probabilities because
> of the existence of back-and-forth-in-time event-chains affecting
> spacelike conditional probabilities.
> 
> Rafael Sorkin also has some ideas in "Quantum Measure Theory and
> Its Interpretation" (gr-qc/9507057). He proposes three principles
> ("Realism", "the Space-time Character of Reality", and "the
> Single World") which are consistent with this approach.
> 
> -mitch
> http://desire.apana.org.au/~qix
> 
> PS A recent realization concerning Gell-Mann and Hartle's "decoherent
> histories": since their scheme of assigning "a priori probabilities"
> to each of a set of histories works only if the histories are
> coarse-grained, I had assumed that GM&H were supposing a
> "coarse-grained" _ontology_ as well - e.g., a universe in which
> there are fields taking values only on some discrete lattice of
> space-time points. But in several places (for example, a recent
> preprint on "Strong decoherence", gr-qc/9509054), they define a
> coarse-grained history as an equivalence class of fine-grained 
> histories (namely all those f-g histories which pass within the limits
> defining the c-g history). So when one assigns a probability to
> a coarse-grained history, one is really stating the probability
> that the universe belongs to a particular set of possible
> fine-grained histories.

Thanks for all these references.  I will look them up.
 
>   (see further:
>    http://www.teleport.com/~rhett/quantum-d/posts/vjs_12-19.html
>    and related postings...
>   
>     &
>       http://www.phys.hawaii.edu/vjs/www/visual.ps
>       http://www.phys.hawaii.edu/vjs/www/visual.txt
> 
>    - rhett)

Note: New, greatly revised version as of 27 Dec. now on web.

Welcome back, Mitch!

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Vic Stenger
http://www.phys.hawaii.edu/vjs/www/vjs.html
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