Regards,
Quentin
We have no choice on this. Without incompleteness, all modalities
corresponding to
the arithmetical definitions of the points of view would collapse, and in
that
case, but only in that case, physics would have been reduced to an empty
set, or to
a boolean logic, and all physical facts would have been shown to be
geographical.
That case is ruled out by incompleteness. So we have a non trivial (non
empty) set
of physical laws, and we have that the observable obeys a different logic
than
boolean logic. Indeed the math shows already a quantum logic.
Now we can test quantitatively if our observable verifies that logic.
Indeed the
quantitative result already obtained rules out boolean logic, and are given
by
quantum logic, and comp predicts and explains exactly that.
From each Kripke model of the translation of that quantum logic in G, which
is an
the output of the theorem prover for the logics Z1* (and S4Grz1, and X1*),
you can
build experimental devices refuting classical computationalism.
You argument based on the fact that comp entails all and every simulations,
does
not work, because physics is given by the first person indeterminacy on the
points
of view, and so to get the number exact, you need the exact *proportions*
on the
relative continuations, which is what today is given by quantum
probabilities, and
comp confirms and explain that.
The rest are open problem, and it is just a (difficult) exercise to see if
qZ1* can
justifiy the presence or not of a "real time" quantum computer. As I tend to
believe QM (as physical, not geographical), if neither qS4Grz1, qZ1*, qX1*
can
emulate a quantum computer, I would consider that as making classical comp,
if not
comp itself, refuted.
Note that it would be very astonishing that the Comp Quantum Logic is equal
to von
Neuman main quantum logics, because their modal descriptions are not
exactly the
same (we lost the necessitation rules), and so get plausibly some different
physical predictions already, but without progressing in some optimization
of the
theorem prover of those modal logics, we cannot say having isolate the
experimental
device making the difference.
The P = 1/2 in the WM-duplication, is a physical law, but the events "I am in
W"
and "I am in M" are contingent. "Once in M I stay in M" is physical, well
it should
be, and it is the case when you do the math.
By UDA comp generalizes QM. Instead of Everett quantum relative
computational
states, we have *all* comp relative computational states, and the
appearance of the
universal wave is already partially explained (and retrodict) by the
universal
machine introspection (or the arithmetical UDA-reflexion). The point of UDA
is that
we *have to do* that generalization, if saying yes to the doctor is correct
at some
level, so that Everett's work is not completed.
At first sight the probabilities can only add in the UD*, but that is
exactly what
the machine explains as not obeying a boolean logic, and obeying a quantum
logic.
The arithmetical quantization are given, the rest is technical, highly
technical
(and that is a weakness if you want, as philosophers fear math, and
mathematicians
fear philosophy, today).
If classical comp is false, the qZ1* machinery provides a tool to measure
experimentally our divergence from comp.
My feeling is that somewhere you might forget that physics is 1p (plural)
and non
Turing emulable a priori, as you cannot emulate at each physical instant
the entire
UD*. You can fail a simulated observer either by simulating the right
quantum logic
below its substitution level, but then from his point of view, he is in all
versions of that "correct" simulation, or by building a lie and revised
infinitely
often your program along with the observation progress of the simulated
observer.
I guess more precisions will be given in the math thread.
Bruno
http://iridia.ulb.ac.be/~marchal/ <http://iridia.ulb.ac.be/%7Emarchal/>
