[extropy-chat] Be[ing] or Not Be[ing]
scerir
scerir at libero.it
Sun Apr 18 18:41:28 UTC 2004
> Critique the simulation argument all you want, but do so on a valid basis.
> Don't reject it just because it's built out of logic and not science.
> Hal
What appears to be more frightening: a clocklike universe which
is totally governed by deterministic laws, or a lawless universe
which is totally unpredictable and random? Asked once Karl Svozil ...
http://tph.tuwien.ac.at/~svozil/publ/2000-vreal.htm
I do not know if the simulation argument sounds or not. But I
think the argument saying that QM, especially Bell's theorem,
rules out the simulation argument is not so strong, at least on
conceptual grounds.
Bell imposed two conditions. 1) Hidden variables, that is to say,
determinism. 2) Local realism. But there are, in Bell's reasoning,
many more hidden assumptions. In example he uses the same lambda
(hidden variables description) for both space-like separated wings
of his gedanken set-up. There is another hidden assumption: that
reality is single valued (no Everett here). There is another
assumption: that observers are free (to choose observables,
parameters, angles, and so on). If observers were not free, that
is to say if they too were pre-determined, i.e. by hidden variables,
Bell's result is completely meaningless.
If A is one of the two wings of a typical Bell apparatus, i the
observable to be measured in A and x its possible value, and if
B is the other of the two wings, j is the observable to be measured
in B and y its possible value, and if Lambda is the hidden variables
joint state description of the composite system, we can write,
following Bell .....
p[A,B,Lambda] (x,y|i,j) = p[A,Lambda] (x|i) p[B,Lambda] (y|j)
which just means that the joint probability of outcomes x and y, for
measurements of observables i and j, in the A and B wings, is equal
to the product of the the separate probabilities. We know that so
many experiments have shown the expression above is far from
reality.
The above condition is equivalent (after Jarrett, 1983/1984) to the
conjunction of two (double) independent conditions ....
Locality condition
p[A,Lambda] (x|i,j) = p[A,Lambda] (x|i)
p[B,Lambda] (y|i,j) = p[B,Lambda] (y|j)
Separability condition
p[A,Lambda] (x|i,j,y) = p[A,Lambda] (x|i,j)
p[B,Lambda] (y|i,j,x) = P[B,Lambda] (y|i,j)
It is possible to show (following Jarrett, Shimony, Ghirardi, Howard,
Cushing, Eberhard, maybe van Fraassen, maybe Fine, etc.) that QM
violates violates the Separability condition but does not violate
the Locality condition. In physical terms the above means that QM does
not allow FTL *signalling* (signalling is different from "influences",
"passions", "fashions" at a distance). (Eberhard, Nuovo Cimento, 46B,
1978, 392; Ghirardi et al., Found. Phys., 23, 1993, 341).
It is possible to show (following Jarrett, Shimony, Ghirardi, Howard,
Eberhard, Cushing, maybe van Fraassen, maybe Fine, etc.) that a
a (phantomatic) *deterministic* theory (i.e. one in which the range
of any probability distribution of outcomes is the set 0 or 1) reproducing
predictions of QM implies the violation of the Locality condition but does
not imply the violation of the Separability condition. Just the reverse
of what the *indeterministic* usual version of QM does.
So, it is also possible to argue that a *deterministic* simulation might
have something to do with Non-Locality, while an *indeterministic*
simulation might have something to do with Non-Separability.
In any case it is important to stress here that our reality (simulated
or not) is something "in between". I mean, between perfect determinism
(and total non-locality) and perfect randomness (and total separability).
In a certain sense our reality (simulated or not) is a good, smart choice.
Diversity, in unity, for evolution.
s.
Dictionary.
Non-Locality. Given any two space-like separated systems, A and B,
the separate state of A is influenced by events (such as the choice
of an observable to measure) in the vicinity of B, and viceversa.
Non-Separability. Regardless of their past history (interaction),
any two systems A and B, separated by some spatio-temporal interval,
do not possess their own separate states, in such a manner that the
joint state is not completely determined by their separate states.
Causality vs. FTL. As far as I remember (but I'm wrong very often!)
Matt Visser http://www.arxiv.org/abs/gr-qc/0107091 or Erasmo Recami
(the man of the tachyons) do not think that Non-Locality means,
necessarily, Non-Causality, or A-Causality. They say (?) we can easily
re-define causality here.
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