On 26 Nov 2017, at 21:56, Lawrence Crowell wrote:
On Sunday, November 26, 2017 at 8:22:37 AM UTC-6, Bruno Marchal wrote:
On 24 Nov 2017, at 00:15, Lawrence Crowell wrote:
I am new to this list and have not followed all the arguments here.
In weighing in here I might be making an error of not addressing
things properly.
Consider quantum entanglements, say the entanglements of two spin
1/2 particles. In the singlet state |+>|-> + |->|+> we really do
not have the two spin particles. The entanglement state is all that
is identifiable. The degrees of freedom for the two spins are
replaced with those of the entanglement state. It really makes no
sense to talk about the individual spin particles existing. If the
observer makes a measurement that results in a measurement the
entanglement state is "violently" lost, the entanglement phase is
transmitted to the needle states of the apparatus, and the
individual spin degrees of freedom replace the entanglement.
We have some trouble understanding this, for the decoherence of the
entangled state occurs with that state as a "unit;" it is blind to
any idea there is some "geography" associated with the individual
spins. There in fact really is no such thing as the individual
spins. The loss of the entangled state replaces that with the two
spin states. Since there is no "metric" specifying where the spins
are before the measurement there is no sense to ideas of any causal
action that ties the two resulting spins.
I agree. But we can trace out locally the prediction possible, and
this explains locally the results in the MW view, not so in the mono-
universe view which requires some (incomprehensible) action at a
distance. That is why I took the Aspect confirmation that QM violate
Bell's inequality (well the CHSH's one) as a confirmation of the
physical existence of the parallel computations/worlds, and not of
action at a distance.
The MWI has worlds in superposition, which as you say is preferable
to the idea of some action at a distance. I have had many email
battles with people over this, but this idea of action at a distance
or its space plus time version of retrocausality keeps coming up. It
is like shooting ducks in a carnival shooting gallery; you can shoot
them down but the damned things keep popping back up. This does not
mean I am a convert to the MWI interpretation. In many ways M-theory
of D-branes is more friendly to the Copenhagen Interpretation, where
D-branes are condensates of strings that form a classical(like)
structure that act in ways as decoherence systems on strings. The ψ-
epistemic viewpoint has some merits with respect to looking at the
classical world as a way that information or Bayesian updates can be
made on quantum systems. The problem of course with this is it leads
into a sort of quantum solipsism The converse ψ-ontological
perspective avoids this classical-quantum dichotomy, but I have
always found problems with the issue of contextuality. This goes
back to my pointing out how MWI fails to indicate how an observer is
"pushed" into a particular eigenbranch of the world and how this
occurs at a given time. With the lack of simultaneity in special
relativity and spacetime in general what is the spatial surface at
which the world wave function appears to split according to an
observer?
Such question needs in fine a quantum theory of space-time/gravitation.
I am personally convinced that EPR-BELL violation + a mono-universe +
minimal physical realism do lead to action at a distance. But I do
think such action disappear when seen in the big wave or matrix picture.
This chaffs our idea of physical causality, but this is because we
are thinking in classical terms. There are two ways of thinking
about our problem with understanding whether quantum mechanics is
ontic or epistemic. It could be that we are a bit like dogs with
respect to the quantum world. I have several dogs and one thing
that is clear is they do not understand spatial relationships well;
they get leashes and chains all tangled up and if they get wrapped
up around a pole they simply can't figure out how to get out of it.
In this sense we human are simply limited in brain power and will
never be able to understand QM in some way that has a completeness
with respect to causality, reality and nonlocality. There is also a
far more radical possibility. It is that a measurement of a quantum
system is ultimately a set of quantum states that are encoding
information about quantum states. This is the a quantum form of
Turing's Universal Turing Machine that emulates other Turing
machines, or a sort of Goedel self-referential process. If this is
the case we may be faced with the prospect there can't ever be a
complete understanding of the ontic and epistemic nature of quantum
mechanics. It is in some sense not knowable by any axiomatic
structure.
I agree and much more can be said. In fact quantum weirdness can be
proved to be a consequence of Mechanism (informally with some
thought experience), and formally with the Gödel-Löb-Solovay theory
of self-reference (which is *the* theory provided by the universal
machine itself when looking inward deep enough.
I can give you references if you are interested. And yes, it is
radical ... for Aristotelian materialists, which believes that
physics *is* metaphysics. The arithmetical explanation of the
quantum is of course rather natural for platonic Pythagorean people.
What is nice, is that the Gödel-Löb logics explains also the quanta
as the sharable part of a more general consciousness or qualia
theory. You might look at:
Marchal B. The computationalist reformulation of the mind-body
problem. Prog Biophys Mol Biol; 2013 Sep;113(1):127-40
Marchal B. The Universal Numbers. From Biology to Physics, Progress
in Biophysics and Molecular Biology, 2015, Vol. 119, Issue 3, 368-381.
B. Marchal. The Origin of Physical Laws and Sensations. In 4th
International System Administration and Network Engineering
Conference, SANE 2004, Amsterdam, 2004. Available here: http://iridia.ulb.ac.be/~marchal/publications/SANE2004MARCHALAbstract.html
Bruno
I am familiar with Löb's theorem, if it can be shown a statement "a
proposition is provable in a system" is true then the proposition is
provable in that system.
Precisely, if you can prove "provable(p) ->p" in the system, then p is
provable in the system.
That sounds almost tautological,
Not at all. It is the most amazing formula in mathematics. In his 1993
book, Boolos can't resist to express his awe: "Löb's theorem is
utterly astonishing for at least five reasons". I will come back on
this, I think you get it wrong.
and in modal logic it is □p → p.
No, that is the reflexion formula, typically not provable in general
(for exemple Bf -> f, with f representing the constant falsity, or "0
= 1") expresses consitency (~Bf), which is not provable.
Löb's theorem asserts that the machine will say Bp -> p only when she
actually prove p, which is a statement of modesty. Obviously if she
proves p, she can prove Bp -> p, because p / (q -> p) is a valid rule
in classical logic. But the machine, by Löb's theorem says the
converse, if ever she proves Bp -> p, she proves p.
The formal modal formula is B(Bp -> p) -> Bp.
It looks also like wishful thinking. If you succeed in convincing a
Löbian entity (whose beliefs are close for the Löb rule, or having
Löb's theorem for its bewesibar predicate) that if she ever believes
that some medication will work, then it work, then she will believe
the medication works!
It solves Henkin's problem about the status of the proposition
asserting their own provability: p <-> Bp. We know with Gödel that
those asserting their own non-provability to a consistent system must
be true and unprovable by the system, that is not obvious for the
Löbian sentences, as they could a priori be false and non provable, or
true and provable, but it happens that they are always true (and
provable).
The modus tolens is ⌐p → ⌐□p (⌐ = NOT) which is not the
same as p → □p. The □ means necessarily and ⌐□⌐ means not
necessarily not or possibly abbreviated as ◊ and so ⌐p →
◊⌐p. Godel's theorem illustrates a case where p → □p is false;
Indeed: ~Bf -> ~B (~Bf) (consistency implies non-provability of
consistency).
a proposition about an math system is true, but is not necessarily
or provably true.
Well the Löbian systems are completely captured by G, for the provable
statement on provability, and G* for the true statement on provability.
G has axioms
B(p -> q) -> (Bp -> Bq)
Bp -> BBp (redundant, follows from Löb).
B(Bp -> p) -> Bp (Löb)
With the rule of modus ponens and necessitation a/Ba.
G* has as axioms all theorem of G, +
Bp -> p
But lost the necessitation rule. I let you show that G* is
inconsistent if you add the necessitation rule.
If that is false then ⌐□p → ⌐p is false or ◊⌐p → ⌐p
is false. We can then only say that p being true is "possible." This
seems to have some connection with quantum measurement and the
update on knowledge of a system with prior probabilities =
plausible estimates.
I wrote a paper involving Gödel's theorem, but it was not that well
received. I will take a look at the paper on the web. I have a
certain cautionary issue with these sorts of issues. I have learned
lots of physicists take some umbrage with it.
Penrose has repeated old errors in the field, already well addressed
in the literature. That a great mathematician could be wrong on Gödel
wary a bit the physicists. I decided to do mathematics and
mathematical logic to masteries metamathematics, as it solved already
many problem I was interested in in biology and genetics. I can give
you reference on this. Gödel's theorem is only a first big theorem in
a very rich field, and it has important relation with computer
science, and, by consequence, in the computationalist approach of the
mind-body problem.
Bruno
LC
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