On 08 May 2014, at 18:52, meekerdb wrote:
On 5/8/2014 6:18 AM, Bruno Marchal wrote:
On 07 May 2014, at 17:39, Quentin Anciaux wrote:
2014-05-07 17:20 GMT+02:00 Bruno Marchal <[email protected]>:
On 07 May 2014, at 11:41, Quentin Anciaux wrote:
2014-05-07 11:13 GMT+02:00 Bruno Marchal <[email protected]>:
On 06 May 2014, at 20:22, [email protected] wrote:
<snip>
But you do not ever make a hard prediction Bruno.
I have no clue why you say that. It is the object of the whole
work. You seem to misunderstand something in the UDA.
I have to agree with ghibbsa... your actual prediction are vague,
there isn't any numerical hard predictions that we could do an
experiment and compare and refute or not...
And even if you would give any, you can always ascribe the non-
corresponding result to geography... I asked you several time
what in comp is not "geography" ? As comp entails all and every
simulations (as precise as we can imagine them to be), it
contains all numericable value for any observable... so it must
be geography... so what *hard* prediction does comp make that can
falsify it here and now ? I really mean hard prediction, not some
vague retrodiction of current theories.
Comp, and to my knowledge, only classical comp, gives a precise
criteria to distinguish physics and geography.
Physics concerns laws, that is physical rules of prediction true
for all universal machine. Geographies concern only prediction
which are contingently verified.
So what are physical facts that comp predict ? what laws ? what
can I measure in this universe that would not be *geography* but
*true for all universal machine* and be able to falsify comp ?
what is it ? what is the predicted value ? How comp predict it ?
How can I measure it and confront it to comp prediction ?
You can test the boolean tautologies, like this simple form of
Bell's inequality:
(A & B) -> (A & C) V (B & ~C)
Both QM and comp predicts that it can be violated. That means comp
predicts the existence of three observable A, B and C such that a
measurement of A, B and C gives a result violating it. That is the
measurement of A, and B gives 1, and neither A & C nor B V ~C gives
1.
The Kripke structure providing the comp counter-example (through
the modal translation of that inequality) can provide constructive
tools to build the experimental device to make the violation
experimental.
So what is the counter-example?
For that formula, its explicit description would be too long to run on
the theorem prover for Z1*, but it would be given if it was optimized.
But other quantum modalities have been tested. If the logic was
boolean, it would give NIL (the empty list), and well, it is not NIL.
Then nature, through EPR, Bell aspect illustrate those counter-
example. The comp counterexample does not say explicitly the nature of
the observable, but their existence, and indeed they defined abstract
projection operator in some linear base.
More systematically, you can test all boolean tautologies in comp,
and it has been verified, with those not being too much complex,
that they are violated by comp if and only if they are violated by
QM.
Is there a list of these somewhere?
I provide the programs generating the list. I did no more run those
programs since a long time. But I proved them correct, and the
relation with quantum logic.
As we get not B, but B without the necessitation rule, there might be
discrpancies, and thus set of observable not being match by nature,
but up to now, no-one has find them, not that many have search for
them too, of course.
The point was just that classical comp is testable. If you grasp well
UDA, the physics must be determined by the logic of measure one, and I
give it.
I am just opening a door. No doubt that a lot of work is needed to see
better the picture, but it provides already an explanation (may be
wrong, may be not) of where the laws of physics come from, (the Gödel-
Löb quantization of the sigma_1 arithmetic), and this with an
explanation of why some part are sharable, and non sharable between
machines. To explain more I have to progress on the representation
theorems. When the simple Bell formula is translated in G (the last
step before being arithmetical), it becomes a formula a dozen of pages
long. Better to understand what happens than looking at a listing
given the counterexample.
Bruno
Brent
There are reasons to expect the measure on sigma_1 sentences to be
deducible from that comp quantum logic, although this is without
doubt quite difficult to do, but in principle possible (and by UDA
+ classical theory of knowledge) necessary. More on this much later
in the math thread.
Best,
Bruno
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/
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