> On 1 Mar 2019, at 20:42, Philip Thrift <[email protected]> wrote: > > > > On Friday, March 1, 2019 at 8:49:54 AM UTC-6, Bruno Marchal wrote: > >> On 1 Mar 2019, at 01:42, Lawrence Crowell <[email protected] >> <javascript:>> wrote: >> >> >> >> On Monday, February 25, 2019 at 9:42:01 AM UTC-6, Bruno Marchal wrote: >> >>> On 25 Feb 2019, at 12:39, Lawrence Crowell <[email protected] <>> >>> wrote: >>> >>> On Monday, February 25, 2019 at 2:44:14 AM UTC-6, Bruno Marchal wrote: >>> >>>> On 24 Feb 2019, at 15:24, Lawrence Crowell <[email protected] <>> >>>> wrote: >>>> >>>> On Friday, February 22, 2019 at 3:18:01 PM UTC-6, Brent wrote: >>>> >>>> >>>> On 2/22/2019 11:39 AM, Lawrence Crowell wrote: >>>>> This sounds almost tautological. I have not read Masanes' paper, but he >>>>> seems to be saying the Born rule is a matter of pure logic. In some ways >>>>> that is what Born said. >>>>> >>>>> The Born rule is not hard to understand. If you have a state space with >>>>> vectors |u_i> then a quantum state can be written as sum_ic_i|u_i>. For >>>>> an observable O with eigenvectors o_i the expectation values for that >>>>> observable is >>>>> >>>>> sum_{ij}<u_j|O|u_i> = sum_{ij}<u_j|o_i|u_i> = sum_ip_io_i. >>>>> >>>>> So the expectations of each eigenvalue is multiple of the probability for >>>>> the system to be found in that state. It is not hard to understand, but >>>>> the problem is there is no general theorem and proof that the eigenvalues >>>>> of an operator or observable are diagonal in the probabilities. >>> >>> I am not sure I understand this. >>> >>> >>> >>> >>>>> In fact this has some subtle issues with degeneracies. >>>> >>>> Doesn't Gleason's theorem show that there is no other consistent way to >>>> assign probabilities to subspaces of a Hilbert space? >>>> >>>> Brent >>>> >>>> It is close. Gleason's theorem tells us that probabilities are a >>>> consequence of certain measurements. So for a basis Q = {q_n} then in a >>>> span in Q = P{q_n}, for P a projection operator that a measure μ(Q} is >>>> given by a trace over projection operators. This is close, but it does not >>>> address the issue of eigenvalues of an operator or observable. Gleason >>>> tried to make this work for operators, but was ultimately not able to. >>> >>> It should work for the projection operator, that this is the >>> yes-no-experiment, but that extends to the other measurement, by reducing >>> (as usual) the question “what is the value of A” into the (many) question >>> “does A measurement belong to this interval” … Gleason’s theorem assures >>> that the measure is unique (on the subspaces of H with dim bigger or equal >>> to 3), so the Born rule should be determined, at least in non degenerate >>> case (but also in the degenerate case when the degeneracy is due to tracing >>> out a subsystem from a bigger system. I will verify later as my mind >>> belongs more to the combinator and applicative algebra that QM for now. >>> >>> >>> >>>> >>>> Many years ago I had an idea that since the trace of a density matrix may >>>> be thought of as constructed from projection operators with tr(ρ_n) = >>>> sum_n |c_n|^2P_n, that observables that commute with the density matrix >>>> might have a derived Born rule following Gleason. Further, maybe operators >>>> that do not commute then have some dual property that still upholds Born >>>> rule. I was not able to make this work. >>> >>> I will think about this. Normally the measure is determine by the “right" >>> quantum logic, and the right quantum logic is determined by the any >>> “provability” box accompanied by consistency condition (like []p & p, []p & >>> <>t, …). The main difference to be expected, is that eventually we get a >>> “quantum credibility measure”, not really a probability. It is like >>> probability, except that credibility is between 0 and infinity (not 0 and >>> 1). >>> >>> Bruno >>> >>> >>> I think I ran into the issue of why Gleason's theorem does not capture the >>> Born rule. Not all operators are commutative with the density matrix. So if >>> you construct the diagonal of the density matrix, or its trace elements, >>> with projector operators and off diagonal elements with left and right >>> acting projectors (left acting hit bra vectors and right acting hit ket >>> vectors) the problem is many operators are non-commutative. In particular >>> the usual situation is for the Hamiltonian to have nontrivial commutation >>> with the density matrix. >> >> >> It seems to me that Gleason theorem takes this into account. It only means >> that the probabilities does not make the same partition of the multiverse, >> but that is not a problem for someone who use physics to see if it confirms >> or refute the “observable” available to the universal numbers/machines in >> arithmetic. >> >> Gleason's theorem applies for just one set of commuting operators, > > > I am astonished by this. Are you sure you refer Gleason’s original work? I > have seen many “simplified” proof, which sometimes add simplifying > hypothesis. > > I’m afraid you will have to wait that I find the time to revise my proof of > Gleason theorem ... > > > > >> and in particular those that commute with the density matrix. The Born rule >> holds for all operators, and especially the Hamiltonian that does not >> commute with the density matrix. >> >> >> I am not completely sure. You raise a doubt, and I’m afraid it will take >> some time I come back to Gleason theorem. But I appreciate. My conversation >> with Bruce and Brent makes me think that the notion of multiverse is far >> from clear. At least with mechanism things are crystal clear! There is only >> the sigma_1 sentences, and the nuances imposed by incompleteness for the >> “Löbian number” who “lives” through them (them for the sigma_sentences, >> which “realises” the computations). >> >> I would not confuse the multiverse with this. There are several levels of >> multioverse. The first is just the world beyond what we can ever observe due >> to the cosmic horizon. > > > If mechanism, that is only a sharable dream/video games played by numbers. > > That a tiny part of arithmetic realise all computation is entirely proved in > Gödel 1931 already, except that Gödel missed the Church-Turing thesis, and so > this will only be explicitly seen by Turing, Kleene, etc. > > But that is enough to doubt that “there is” a primary physical universe, and > with Mechanism there is no choice: we have to retrieve physics from number > (Turing universal) relations. > > Have you study my papers? I can explain this here if you are interested. To > get the quanta, we can extrapolate relations from our observation, but to get > both the quanta and the qualia, we need to extract the quanta from the > Gödel-Löb-Solovay “true” modal logic of self-reference. It seems to work. > Would it not work, we would get some empirical evidences that Mechanism (in > cognitive science) is wrong. But up to now, thanks to QM, it seems that > Mechanism fits very well. In fact QM without collapse is very close to what a > solution of the mind-body problem should resemble if Mechanism is true. > > > > > >> The second is the vacuum pocket worlds in an inflationary de Sitter >> spacetime. A third may be how these are connected to anti-de Sitter >> spacetimes and how the landscape or swampland is generated. The fourth is >> the idea that many worlds interpretation is the grand or ultimate many >> worlds. This last one I would not take that seriously. Many worlds >> interpretation, as with all interpretations, is an addition to quantum >> mechanics that is less about physics and more about metaphysics. > > I disagree. Here I am OK with Deutsch. Quantum theory without collapse is > automatically a “many-relative state theory”. I avoid the word “world” > because that one *is* metaphysically charged. > > Anyway, elementary arithmetic is a many computations theory, too, without any > added metaphysics. Then, what the machines perceive from inside arithmetic, > taking into account the fact that they cannot distinguish their computation > (of themselves) with a quasi-continuum of computations, we can extract the > appearance of the physical reality, and its stability/persistence, from their > sharable first person points of view. > > With mechanism, both matter and consciousness are explained entirely from > just two equations: > > Kxy = x > Sxyz = xy(yz) > > And three rules: > > If A = B and A = C then A = C > If B = C then AB = AC > If B = C then BA = CA > > Together with some definitions, motivated by the Mechanist hypothesis and/or > Plato’s analysis of knowledge. > > We cannot add anything more. The extensionality axioms (like If AC = BC then > A = B, equivalent with ([x](Ax) =A (x not occurring in A); not to be confused > with the definition of elimination ([x]A)x) = x (true for all combination A) > are already phenomenological. > > > >> >> >> Of course I come from the other side, but if mechanism is correct, I can >> only cross physics when and where physics is correct. For now, physics is >> not yet a solved problem, as GR does not fit with QM. The very notion of >> “force” or “interaction” seems conceptually very different in GR and QM. We >> can expect surprise, but with Mechanism, the quantum weirdness is welcomed, >> and we are far from having any notion of physical space, and why 3D or 11D >> or 26D. Mechanism is a 0 dimension theory of the mind, à la Plato, where the >> ideas are the numbers i, and the partial recursive function phi_i, and the >> operator phi_phi_i, etc. >> >> Spacetime is likely emergent from quantum entanglements. Quantum >> entanglements are entirely nonlocal, so it seems strange that something that >> is local should be so defined. However the Einstein field equation R_{ab} - >> 1/2Rg_{ab} = T_{ab} has a curious duality about it. It says that high energy >> quantum gravity on the left is equal to low energy ordinary quantum fields. >> Further, the T_{ab} is for local quantum fields and these are dual to >> nonlocal physics as gravitation in the spacetime bulk. > > > Very interesting and rather compelling. OK. But to solve the mind body > problem, both space and time must be recovered from self-reference, itself > deducible from the little theory above. > > Bruno > > > > I still think this semantics of qualia is ultimately "joy eliminativism" (a > great term introduced here by someone before).
Why do you think that. N the contrary, Mechanism makes the notion of person, including its first person soul, central in metaphysics, but also quite opposed to anthropomorphism, and panphsyicsime. It is more a Turing-universal-machine-centered points of view foundations. All universal number are born equal, if I may say. You are the one introducing a reductionism of person and machine. You are the one depriving them of joy, apparently. I’m afraid you are the one who will be angry if your daughter decide to marry a man-machine, like a guy having said yes already to the doctor. If you don’t them the right to vote, no doubt that they will feel less joy … Bruno > > > > > George Eliot [(link: > https://books.google.com/books?id=NskZTEr8Td8C&pg=PA520&lpg=PA520) > books.google.com/books?id=NskZT… <https://t.co/ZgU6zMLiiF?amp=1>] > <https://twitter.com/philipthrift/status/1101565464373805062/photo/1>1:30 PM > · Mar 1, 2019 · Twitter Web App > <https://help.twitter.com/using-twitter/how-to-tweet#source-labels> > > - pt > > -- > 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 post to this group, send email to [email protected] > <mailto:[email protected]>. > Visit this group at https://groups.google.com/group/everything-list > <https://groups.google.com/group/everything-list>. > For more options, visit https://groups.google.com/d/optout > <https://groups.google.com/d/optout>. -- 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 post to this group, send email to [email protected]. Visit this group at https://groups.google.com/group/everything-list. For more options, visit https://groups.google.com/d/optout.
