On Tue, Dec 21, 2021 at 1:12 AM Bruce Kellett <bhkellet...@gmail.com> wrote:
> On Tue, Dec 21, 2021 at 4:40 PM Jesse Mazer <laserma...@gmail.com> wrote: > >> On Mon, Dec 20, 2021 at 8:10 PM Bruce Kellett <bhkellet...@gmail.com> >> wrote: >> >>> On Tue, Dec 21, 2021 at 11:53 AM Jesse Mazer <laserma...@gmail.com> >>> wrote: >>> >>>> >>>> But one of the big selling points of the MWI is to give some sort of >>>> objective picture of reality in which "measurements" have no distinguished >>>> role, but are simply treated using the usual rules of quantum interactions. >>>> >>> >>> At one time, that might have been a point on which to prefer MWI over >>> Bohr's version of the CI, but that is no longer true. Modern collapse >>> theories do not have to distinguish particular "measurement" events, and do >>> not have to assume a classical superstructure . In modern fGRW, for >>> example, everything can be treated as quantum, and the theory is completely >>> objective. >>> >>> fGRW has the added advantage that it is an inherently stochastic theory. >>> Probability is treated as a primitive notion that is not based on >>> anything else. MWI struggles with the concept of probability, and while it >>> has to reject a frequentist basis for probability, it cannot really supply >>> anything else. Self-locating uncertainty does not, in itself, serve to >>> define probability. You have to have some notion of a random selection from >>> a set, and that is not available in either the Schrodinger equation or in >>> self-locating uncertainty. >>> >> >> What does fGRW stand for? >> > > It is short for Flash-GRW, in which the random collapse interactions of > GRW are replaced by "flashes". The point here is that this formulation is > Lorentz invariant and completely relativistic. > I assume the flashes are collapses to eigenstates, with probabilities given by the Born rule, even if these collapses are not necessarily caused by interactions? If so, what factors affect the probability a collapse happens at any given moment? Does it depend on the mass of the entangled system (thus becoming more likely as the system becomes entangled with its environment), as in Penrose's suggestion? > > If it's stochastic, do you mean it's one of those theories that involves >> stochastic spontaneous collapse? Such theories are usually in principle >> experimentally distinguishable from QM, would that be true of this theory >> as well? >> > > In principle this collapse model is distinguishable from no-collapse > models. The experiments to detect this might be outside current > capabilities. > > If you have to say "OK, I believe in the MWI plus Born rule for >>>> measurements" with there being no dynamical definition of what qualifies as >>>> a measurement, where the moments we call 'measurements' are just something >>>> we feed into the theory on a know-it-when-I-see-it basis, then this claim >>>> to objectivity is lost and it's not clear what theoretical appeal it has >>>> over the Copenhagen interpretation. >>>> >>>> Personally I still lean towards some version of the MWI being true >>>> mainly because you can come up with a toy model with MWI-style splitting >>>> that deals with Bell style experiments in a way that preserves locality >>>> >>> >>> No you can't. >>> >>>> but doesn't require hidden variables (see >>>> https://www.mdpi.com/1099-4300/21/1/87/htm ) but I see it as a sort of >>>> work in progress rather than a complete interpretation. >>>> >>> >>> They set up a contrast between realism and locality. >>> >> >> I wasn't linking to the paper for the argument about semantics (there >> doesn't seem to be any agreed-upon definition of 'realism' distinct from >> local realism in physics, from what I've seen) but rather for the toy model >> they provide in section 5 with the experimenters being duplicated when they >> try to measure the entangled particle. The point is that Alice is locally >> duplicated when she measures her particle, and Bob is locally duplicated >> when he measures his, but there is no need for the universe to decide which >> copy of Bob inhabits the same "world" as a given copy of Alice, or vice >> versa, until there's been time for signals limited by the speed of light to >> pass between them (or to a third observer). This is not the sort of "local >> realist" theory that Bell was trying to refute (one of the implicit >> assumptions in his derivation was that each spin measurement produces >> exactly one of two possible outcomes), but the dynamics of such splitting >> can be perfectly local, and it can still be true that if you randomly >> select one of the copies of an observer in a Bell type experiment, the >> probabilities that your randomly selected copy will see various outcomes >> can be made to match the QM predictions that violate Bell inequalities. >> > > This seems to be the hand-waving way in which this is usually argued. I > was asking for something a little more concrete. > > There is a fairly simple argument that shows that many worlds ideas can > have no role to play in the violation of the Bell inequalities. In other > words, there is an indirect no-go theorem for the idea that MWI makes these > experiments completely local. > > The argument goes like this. Take Alice and Bob measuring spin states on > members of entangled pairs of particles -- they are presumed to be distant > from each other, and independent. Alice, say, measures a sequence of > particles at random polarizer orientations, randomizing the polarizer angle > between measurements. She records her results (up or down) in a lab book. > After N such pairs have been measured, her lab book contains a sequence of > N 0s or 1s (for up/down), with a record of the relevant polarizer angle for > each measurement. If MWI is correct, there are 2^N copies of Alice, each > with a lab book containing a similar binary sequence. Over the 2^N copies > of Alice, all possible binary sequences are covered. Bob does the same, so > he has a lab book with some binary sequence of 0s and 1s (and 2^N copies > with different lab books). For each copy of Bob, and each lab book, all N > measurements were necessarily made in the same world (because individuals > cannot move between worlds). > > After all measurements are complete, Alice and Bob meet and compare their > lab books in order to calculate the correlations between results for > different relative measurement angles. Once Alice and Bob meet, they are > necessarily in the same world. And since they carry their lab books with > them, the measurements made in each lab book must all have been made in > that same, single, world. The correlations that Alice and Bob calculate are > shown to violate the Bell inequality. (That is experimentally verified). > But this violation of the inequality takes place in just one world, as has > been seen by the above construction. The alternative copies of Alice and > Bob also meet to compare results. As before, all these meetings take place > in the same worlds as all the relevant measurements were made. > Consequently, the many-worlds analysis for each Alice-Bob pair is exactly > the same as the single world analysis obtained if collapse is assumed. > Many-worlds adds nothing to the analysis, so MWI cannot give any > alternative explanation of the correlations. In particular, MWI cannot give > a local account. > You seem to be assuming one copy for each distinct measurement outcome, and given that assumption it's true you can't reproduce the statistics of arbitrary Bell type experiments, but if you are allowed to assume *multiple* copies for any given outcome it can be made to work. For example, you could simply assume a huge (approaching infinity) population of copies at the start, and then in a given spin measurement, half the copies see spin-up and half see spin-down--I believe the many-minds interpretation discussed at https://plato.stanford.edu/entries/qm-everett/#ManyMind would work this way. But if we just want to construct a toy model, it may be simpler to assume that each new measurement splits each member of a finite population of copies into further copies. For example, let's say that each measurement splits each existing copy into 8 copies, 4 seeing the result spin-up (which we can denote '1') on that trial, and 4 seeing the result spin-down (which we can denote '0'). So if we start with a single version of Bob who measures 2 particles in a row, there will then be 8^2 = 64 copies of Bob, with 1/4 of them (i.e. 16 copies) recording the result 00, 1/4 recording the result 01, 1/4 recording 10, and 1/4 recording 11. And exactly the same local splitting will occur for Alice when she measures the two entangled twins of the particles Bob measured. One commonly discussed Bell type experiment allows each experimenter to choose between 3 detector settings on each trial, with the quantum prediction being that on any trial where they both chose the same detector setting they both get the same result with probability 1 (or opposite results with probability 1 depending on the type of particle and the experimental setup, but let's say same results for the sake of simplicity), whereas on any trial where they chose two different detector settings, they have only a 1/4 probability of getting the same result. Bell's theorem would say that given the first condition about the *same* detector settings, we should conclude that when they choose *different* detector settings, any local realist theory would predict they should get the same result at least 1/3 of the time, so the quantum prediction of 1/4 is incompatible with local realism. But as I noted before, it's an implicit condition of "local realism" that each measurement gives a single unique outcome--if we instead have a local model with local copying as I described above, can we subsequently match up the copies of Bob with the copies of Alice in a one-to-one way, such that in a randomly selected matched pair, the probability they saw the same result on any trial with different detector settings was only 1/4? The answer is yes, and the matching rule is fairly straightforward. Assume for the sake of the argument that both Bob and Alice chose their sequence of detector settings before receiving any particles (and so before they started to get copies), so that in the sequence of two measurements I discussed above, all copies had the same series of detector settings, and can only differ in what results they observed with those settings. Further assume that Alice and Bob chose different detector settings for each measurement, so we want to match up copies in a way that ensures that with a randomly selected matched pair, there is a 1/4 chance they got the same result on the first measurement, and likewise a 1/4 chance they got the same result on the second measurement (and likewise a 3/4 chance they got a different result on each measurement). So, we can match them like this: --Of the 16 Bobs that got 00, (1/4)*(1/4) = 1/16 are matched with an Alice that got 00, (1/4)*(3/4) = 3/16 are matched with an Alice that got 01, (3/4)*(1/4) = 3/16 are matched with an Alice that got 10, and (3/4)*(3/4) = 9/16 are matched with an Alice that got 11. --Of the 16 Bobs that got 01, (1/4)*(3/4) = 3/16 are matched with an Alice that got 00, (1/4)*(1/4) = 1/16 are matched with an Alice that got 01, (3/4)*(3/4) = 9/16 are matched with an Alice that got 10, and (3/4)*(1/4)=3/16 are matched with an Alice that got 11. --Of the 16 Bobs that got 10, (3/4)*(1/4) = 3/16 are matched with an Alice that got 00, (3/4)*(3/4) = 9/16 are matched with an Alice that got 01, (1/4)*(1/4) = 1/16 are matched with an Alice that got 10, and (1/4)*(3/4) = 3/16 are matched with an Alice that got 11. --Of the 16 Bobs that got 11, (3/4)*(3/4) = 9/16 are matched with an Alice that got 00, (3/4)*(1/4) = 3/16 are matched with an Alice that got 01, (1/4)*(3/4) = 3/16 are matched with an Alice that got 10, and (1/4)*(1/4) = 1/16 are matched with an Alice that got 11. If you add up the numbers for Alice, to do this matching you need 1 + 3 + 3 + 9 = 16 Alice-copies that get 00, 3 + 1 + 9 + 3 = 16 Alices that get 01, 3 + 9 + 1 + 3 = 16 Alices that get 10, and 9 + 3 + 3 + 1 = 16 Alices that get 11. So, this works out perfectly with the local splitting rule that says when each performs two measurements, each is split into 64 copies with 16 seeing 00, 16 seeing 01, 16 seeing 10, and 16 seeing 11. And the matching rule above was constructed so that if you pick a matched pair at random, on each of the two trials there is a 1/4 chance both had the same result and a 3/4 chance they had different results. In this case I only looked at a pair of measurements where they chose different detector settings on both, what if we had a mixed series where they both chose the same detector settings on some trials, different detector settings on others? For example let's say they each made 4 measurements, and on the first and last they both chose the same detector setting, while on the middle two they chose different detector settings. Then we will have 8^4 = 4096 copies of Bob, of whom 1/16 = 256 got results 0000, 256 got results 0001, and so forth, and likewise for Alice. So now imagine our matching algorithm first sorting all the Alices and all the Bobs into four "piles" that each have 1024 Bobs and 1024 Alices--in the first pile we will have Bob-copies and Alice-copies that got the result 0 on the first measurement and 0 on the fourth measurement, in the second pile those that got 0 on the first measurement and 1 on the fourth measurement, in the third pile those that got 1 on the first measurement and 0 on the fourth measurement, and in the fourth pile those that got 1 on the first measurement and 1 on the fourth measurement. If we now restrict ourselves to only matching copies of Bob and Alice that are from the same pile, we guarantee that all matched pairs get the same result for the first and fourth measurements, when they were both using the same detector settings. And now if we look at a given pile and concentrate on what each copy got on the second and third measurement (when their detector settings were different), we see that 1/4 of the Bobs in that pile got 00 for their 2nd and 3rd measurements, 1/4 got 01, 1/4 got 10, and 1/4 got 11, and likewise for the Alice copies in that pile (since each pile had 1024 Bobs and 1024 Alices, there will be 256 Bobs and 256 Alices in a pile that have each of the 4 possible middle two measurement results). So the within-pile matching of Alice-copies to Bob-copies can proceed the same way as before--for example, of the 256 Bob-copies in a pile that got 00 for their middle measurements, 1/16 are matched with an Alice that got 00 for her middle measurements, 3/16 are matched with an Alice that got 01, 3/16 are matched with an Alice that got 10, and 9/16 are matched with an Alice that got 11. So, this local-copying-and-later-matching rule does guarantee that if you choose a matched pair at random (with all the pairs equally likely), there's a probability 1 that they got the same result on each trial where they both chose the same detector setting, and a probability 1/4 they got the same result on each trial where they chose different detector settings. It's easy to generalize this rule to arbitrary sequences of N measurements with arbitrary combinations of the same detector setting on some trials, and different detector settings on others. > > >> As I said this can only be shown clearly in a toy model like the one in >> section 5 of that paper, but a number of physicists including David Deutsch >> do think that the full MWI would also respect a principle of "local >> splitting", although even if this can be shown in terms of the quantum >> formalism we still have the problem of deriving probabilities. The article >> on the MWI by Lev Vaidman at >> https://plato.stanford.edu/entries/qm-manyworlds/ discusses work on the >> notion of local splitting in the MWI: >> >> 'Deutsch 2012 claims to provide an alternative vindication of quantum >> locality using a quantum information framework. This approach started with >> Deutsch and Hayden 2000 analyzing the flow of quantum information using the >> Heisenberg picture. After discussions by Rubin 2001 and Deutsch 2002, >> Hewitt-Horsman and Vedral 2007 analyzed the uniqueness of the physical >> picture of the information flow. Timpson 2005 and Wallace and Timpson 2007 >> questioned the locality demonstration in this approach and the meaning of >> the locality claim was clarified in Deutsch 2012. Rubin 2011 suggested that >> this approach might provide a simpler route toward generalization of the >> MWI of quantum mechanics to the MWI of field theory. Recent works >> Raymond-Robichaud 2020, Kuypers and Deutsch 2021, Bédard 2021a, clarified >> the meaning of the Deutsch and Hayden proposal as an alternative local MWI >> which not only lacks action at a distance, but provides a set of local >> descriptions which completely describes the whole physical Universe. >> However, there is a complexity price. Bédard 2021b argues that “the >> descriptor of a single qubit has larger dimensionality than the Schrödinger >> state of the whole network or of the Universe!”' >> > > I did suggest that you made the argument yourself rather than giving a > long list of references. > > B. > > -- > 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 everything-list+unsubscr...@googlegroups.com. > To view this discussion on the web visit > https://groups.google.com/d/msgid/everything-list/CAFxXSLSo_am0G4ncg2FqCNeULXNR2AdwqLsf%2B0tnUQwuVmbC5Q%40mail.gmail.com > <https://groups.google.com/d/msgid/everything-list/CAFxXSLSo_am0G4ncg2FqCNeULXNR2AdwqLsf%2B0tnUQwuVmbC5Q%40mail.gmail.com?utm_medium=email&utm_source=footer> > . > -- You received this message because you are subscribed to the Google Groups "Everything List" group. 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