> On 18 Jun 2019, at 02:14, Lawrence Crowell <[email protected]> > wrote: > > The stochastic aspects of QM emerge in measurement, where the modulus square > of amplitudes are probabilities and there are these random outcomes. The > measurement of a quantum state is not a quantum process, but has stochastic > outcomes predicted by QM. Based on the Hamkin's work where I only looked at > the slides and not yet the paper, it seems possible to do this with quantum > computer. > > http://jdh.hamkins.org/computational-self-reference-and-the-universal-algorithm-queen-mary-university-of-london-june-2019/ > slides: > http://jdh.hamkins.org/wp-content/uploads/Computational-self-reference-and-the-universal-algorithm-QMUL-2019-1.pdf > I wrote a couple of elementary Python codes for the QE machine IBM has to > prepare states and run then through Hadamard gates. The thought occurred to > me that this Quining could be done quantum mechanically as a set of Hadamard > gates that duplicate a qubit or an bipartite entangled qubit. This is a part > of my ansatz that a measurement is a sort of Gödel numbering of quantum > states as qubit data in other quantum states. > Quantum computations are mapped into an orthomodular lattice that does not > obey the distributive property. The distributive law of p and (q or r) = (p > and q) or (p and r) fails. The reason is due to the Heisenberg uncertainty > principle. Suppose we let p = momentum in the interval [0, P], q = position > in the interval [-x, x] and r = particle in interval [x, y]. The proposition > p and (q or r) is true if this spread in momentum [0, P] is equal to the > reciprocal of the spread of position [-x, y] with > P = ħ/sqrt(y^2 + x^2). > The distributive law would then mean > P = ħ/|y| or P = ħ/|x| > which is clearly false. This is the major difference with quantum logic and > Boolean classical logic. These lattices of quantum logic have polytope > realizations. > This is in fact another way of realizing that QM can't be built up from > classical physics. If this were the case then quantum orthomodular lattices, > which act on convex sets on L^p spaces with p = ½ would be somehow built from > lattices acting on convex sets with p → ∞. This is for any deterministic > system, whether Newtonian physics or a Turing machine. It is this flip > between convex sets that is difficult to understand. With p = ½ and the > duality between two convex sets as 1/p + 1/q = 1 the dual to QM also has L^2 > measure. This is spacetime with the Gaussian interval. For a p → ∞ the dual > is q = 1 which is a purely stochastic system, say an idealized set of dice or > roulette wheel with no deterministic predictability. > The point of Quining statements quantum mechanically is that this might be a > start for looking at a quantum measurement as a way that quantum states > encode qubit information of other quantum states. It is a sort of Gödel > self-reference, and my suspicion is the so called measurement problem is not > solvable. The decoherence of states is then a case where p = ½ → 1 with an > outcome. That is pure randomness.
With mechanism, that randomness is reduced into the indeterminacy in self-multiplication experience. It come from the many-histories internal interpretation of arithmetic, in which all sound universal numbers converges. The quantum aspect of nature is just how the (sigma_1) arithmetical reality looks like from inside. This explains where the apparent collapse comes from, in a similar way than Everett, but it explains also where the wave comes from. Eventually quantum mechanics is just a modal internal view of arithmetic, or anything Turing equivalent. The math, and quantum physics confirms computationalism up to now, where physicalism and materialism are inconsistent, or consciousness or person eliminative. > Now of course we can ask what we mean by random, and that is undefinable. > Given any set of binary strings of length n there are N = 2^n of these, and > in general for n → ∞ there is no universal Turing machine which can compress > these into any general algorithm, or equivalently the Halting problem can't > be solved. A glance at this should indicate that N is the power set of n and > this is not Cantor diagonalizable. Chaitin found there is an uncomputable > Halting probability for any subset of these strings. Randomness is then > something that can't be encoded in an algorithm, only pseudo-randomness. > The situation is then similar to the fifth axiom of geometry. In geometry one > may consider the 5th axiom as true and remain within a consistent geometry. > One may similarly stay within the confines of QM, but there is this nagging > issue of decoherence or measurement. One may conversely assume the 5th axiom > is false, but now one has a huge set of geometries that are not consistent > with each other. Similarly in QM one may adopt a particular quantum > interpretation. QM cannot be invoked except as a toll to test Mechanism (computationalism). Bruno > LC > > -- > You received this message because you are subscribed to the Google Groups > "Everything List" group. > To unsubscribe from this group and stop receiving emails from it, send an > email to [email protected] > <mailto:[email protected]>. > To view this discussion on the web visit > https://groups.google.com/d/msgid/everything-list/504fa0ed-686e-4e17-bbdc-68dfa609008f%40googlegroups.com > > <https://groups.google.com/d/msgid/everything-list/504fa0ed-686e-4e17-bbdc-68dfa609008f%40googlegroups.com?utm_medium=email&utm_source=footer>. -- You received this message because you are subscribed to the Google Groups "Everything List" group. To unsubscribe from this group and stop receiving emails from it, send an email to [email protected]. To view this discussion on the web visit https://groups.google.com/d/msgid/everything-list/4BC35D1F-6C76-4278-8FE1-2D174DC26F26%40ulb.ac.be.
