On Wednesday, May 23, 2018 at 8:53:07 AM UTC, [email protected] wrote: > > > > On Wednesday, May 23, 2018 at 8:16:07 AM UTC, Bruce wrote: >> >> From: <[email protected] >> >> On Wednesday, May 23, 2018 at 7:09:31 AM UTC, Bruce wrote: >>> >>> From: <[email protected]> >>> >>> >>> On Wednesday, May 23, 2018 at 4:44:30 AM UTC, Brent wrote: >>>> >>>> >>>> On 5/22/2018 9:41 PM, [email protected] wrote: >>>> >>>> >>>> On Wednesday, May 23, 2018 at 4:05:58 AM UTC, Brent wrote: >>>>> >>>>> >>>>> >>>>> On 5/22/2018 8:29 PM, [email protected] wrote: >>>>> >>>>> >>>>> >>>>> On Wednesday, May 23, 2018 at 2:24:07 AM UTC, Bruce wrote: >>>>>> >>>>>> From: <[email protected]> >>>>>> >>>>>> >>>>>> On Wednesday, May 23, 2018 at 1:45:39 AM UTC, Brent wrote: >>>>>>> >>>>>>> >>>>>>> >>>>>>> On 5/22/2018 5:59 PM, [email protected] wrote: >>>>>>> >>>>>>> >>>>>>> >>>>>>> On Wednesday, May 23, 2018 at 12:44:06 AM UTC, Brent wrote: >>>>>>>> >>>>>>>> >>>>>>>> >>>>>>>> On 5/22/2018 3:46 PM, [email protected] wrote: >>>>>>>> >>>>>>>> >>>>>>>> >>>>>>>> On Tuesday, May 22, 2018 at 10:41:11 PM UTC, [email protected] >>>>>>>> wrote: >>>>>>>>> >>>>>>>>> >>>>>>>>> >>>>>>>> I did, but you're avoiding the key point; if the theory is on the >>>>>>>> right track, and I think it is, quantum measurements are irreversible >>>>>>>> FAPP. >>>>>>>> The superposition is converted into mixed states, no interference, and >>>>>>>> no >>>>>>>> need for the MWI. >>>>>>>> >>>>>>>> >>>>>>>> You're still not paying attention to the problem. First, the >>>>>>>> superposition is never converted into mixed states. It >>>>>>>> *approximates*, FAPP, a mixed state* in some pointer* basis (and >>>>>>>> not in others). Second, even when you trace over the environmental >>>>>>>> terms >>>>>>>> to make the cross terms practically zero (a mathematical, not >>>>>>>> physical, >>>>>>>> process) you are left with different outcomes with different >>>>>>>> probabilities. CI then just says one of them happens. But when did >>>>>>>> it >>>>>>>> happen?...when you did the trace operation on the density matrix? >>>>>>>> >>>>>>> >>>>>>> I think the main takeaway from decoherence is that information isn't >>>>>>> lost to other worlds, but to the environment in THIS world. >>>>>>> >>>>>>> >>>>>>> But that ignores part of the story. The information that is lost to >>>>>>> the environment is different depending on what the result is. So if >>>>>>> by >>>>>>> some magic you could reverse your world after seeing the result you >>>>>>> couldn't get back to the initial state because you could not also >>>>>>> reverse >>>>>>> the "other worlds". >>>>>>> >>>>>> >>>>>> What "other worlds"? If they don't exist, why should I be concerned >>>>>> about them? AG >>>>>> >>>>>> >>>>>> I think you are ignoring the facts of the mathematics of unitary >>>>>> evolution of the wave function. Under unitary evolution the wave >>>>>> function >>>>>> branches, one branch or each element of the superposition, which is, one >>>>>> branch for each possible experimental result. These branches are in the >>>>>> mathematics. Now you can take all branches as really existing every much >>>>>> as >>>>>> the observed result exists -- that is the MWI position. Or you can throw >>>>>> them away as not representing your experimental result -- which is the >>>>>> collapse position. But in both cases, the evolution of the wave function >>>>>> shows that there is information in each mathematical branch. If you >>>>>> discard >>>>>> the branches (collapse) you throw this information away: if you retain >>>>>> the >>>>>> branches as other worlds, the information becomes inaccessible by >>>>>> decoherence and partial tracing. >>>>>> >>>>>> The situation is the same in either approach. Brent and I are not >>>>>> being inconsistent, devious, or otherwise tricky by referring to both >>>>>> MWI >>>>>> and CI approaches -- we are just recognizing the actual mathematics of >>>>>> quantum mechanics. The mathematics has to be interpreted, and different >>>>>> interpretations are available for the way in which the information in >>>>>> other >>>>>> branches is treated. >>>>>> >>>>>> Bruce >>>>>> >>>>> >>>>> Consider this interpretation of the wf, which for simplicity I >>>>> consider as a superposition of two eigenfunctions, and based on the >>>>> probability amplitudes represents a 50% probability of each outcome at >>>>> some >>>>> point in time. Since the measurement hasn't occurred, where does this >>>>> information reside? Presumably it all resides in THIS world. As time >>>>> evolves the probability distribution changes, say to 75-25, and later to >>>>> 90-10, and so on. All of this information resides in this world since >>>>> without a measurement occurring, there are no other worlds, and no >>>>> collapse. Suppose at some point in time, the values changed to 100-0, >>>>> Isn't >>>>> 100-0 as good as other pair if they sum to zero? And why would anyone >>>>> think >>>>> another world comes into existence because one of the values evolved to >>>>> 0? >>>>> I will now define, in answer to one of Brent's questions, when the >>>>> measurement occurs. I assert it occurs when one of the pair of values >>>>> equals 0, All throughout all information was in this world. Why would >>>>> another world come into existence if one of the values happened to be 0? >>>>> AG >>>>> >>>>> >>>>> First, in the cases of interest there is no mechanism for going from >>>>> 50/50 to 100/0 because it goes 0/100 as well, and it's random. You may >>>>> hypothesize there is such process, but that's equivalent to assuming a >>>>> hidden variable. And then Aspect's experiments show such a hidden >>>>> variable >>>>> transmits influence faster than light...which then cascades into problems >>>>> with special and general relativity and quantum field theory and so on... >>>>> >>>>> Brent >>>>> >>>> >>>> I was assuming the wf evolves to different probabilities via the SWE. >>>> Nothing wrong with going to 0/100 because that just means the other >>>> eigenvalue became the final state. AG >>>> >>>> >>>> That's why I wrote "in cases of interest". If it evolves to 0/100 via >>>> the SWE no problem...no interest either. >>>> >>> >>> Why no interest? Haven't I described the case of a system evolving >>> according to the SWE, then a measurement occurring, and throughout all the >>> information is residing in THIS world. >>> >>> >>> Your thought experiment does not correspond to unitary quantum evolution. >>> >> >> Why not? Would different intermediate values correspond to unitary >> quantum evolution? AG >> >> >> You describe the evolution of a quantum state to a different state -- you >> are not describing a measurement operation. If you measure a different >> state, you can expect different results. >> > > Doesn't the SWE evolve an initial quantum state into another, and another, > and so on, and the probability amplitude of each state in the original > superposition changes? If so, I was just describing how the probabilities > of each eigenstate changes, keeping the sum of probabilities equal to > unity. So far, no measurement, and all information in this world. When a > measurement occurs, the probability density of all eigenstates (except for > the eigenstate of the measured value) goes to zero, and all probability is > concentrated around the measurement value, with the result being a delta > function in probability density. Throughout, all information remains in > this world. How information associated with the other branches becomes > inaccessible under decoherence I don't understand. I'll read up on this > issue. AG >
Let's assume that the other branches are inaccessible, meaning, IIUC, that their entanglements are inaccessible and therefore that the measurement in this world can't be reversed in principle. How do you go from this conclusion, to the conclusion that all these inaccessible subspaces have MEASURED values corresponding to each of the eigenstates corresponding to each branch? AG Why would information be lost to some other world simply because one value > of the pair of probabilities equals 0? > > > If one of the probabilities is zero, it means that the wave function has > no corresponding component. If the only other part of the wave function has > probability 100%, then the outcome is certain, and no information can > reside anywhere else. > I was trying to describe a situation where the wf collapses, in terms of probability, to a delta function, where a single outcome is achieved with 100% probability, and the other does not, so it has probability of 0. AG That is a measurement on a different state, where one would expect different results. IOW, the example is meant to illustrate the fallacy of claiming some > information is lost when the measurement occurs, and now resides in some > inaccessible other world. In decoherence, isn't all the lost information > lost in THIS world, to the environment, like a heat bath? Isn't decoherence > therefore in conflict with the MWI? AG > > > No. Decoherence occurs independently for each branch of the wave function, > so information is disseminated into the environment in all branches of the > wave function independently. > OK, but how does one jump to the assumption of other worlds? Doesn't each "branch" exist in this world? AG Initially yes. But decoherence diagonalizes the density matrix FAPP, so the other branches become unreachable. That is what one means by separate worlds. Bruce > -- 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.
