On Wednesday, August 1, 2018 at 9:36:18 PM UTC, Brent wrote: > > > > On 8/1/2018 1:50 PM, agrays...@gmail.com <javascript:> wrote: > > > > On Wednesday, August 1, 2018 at 4:41:02 AM UTC, agrays...@gmail.com > wrote: > > > > On Wednesday, August 1, 2018 at 2:09:45 AM UTC, Brent wrote: > > > > On 7/31/2018 6:22 PM, agrays...@gmail.com wrote: > > > > On Wednesday, August 1, 2018 at 12:11:48 AM UTC, Brent wrote: > > > > On 7/31/2018 2:43 PM, agrays...@gmail.com wrote: > > > > On Tuesday, July 31, 2018 at 7:14:53 PM UTC, Brent wrote: > > > > On 7/31/2018 6:43 AM, agrays...@gmail.com wrote: > > > > On Tuesday, July 31, 2018 at 6:11:18 AM UTC, Brent wrote: > > > > On 7/30/2018 9:21 PM, agrays...@gmail.com wrote: > > > > On Tuesday, July 31, 2018 at 1:34:58 AM UTC, Brent wrote: > > > > On 7/30/2018 4:40 PM, agrays...@gmail.com wrote: > > > > On Monday, July 30, 2018 at 7:50:47 PM UTC, Brent wrote: > > > > On 7/30/2018 8:02 AM, Bruno Marchal wrote: > > *and claims the system being measured is physically in all eigenstates > simultaneously before measurement.* > > > > Nobody claims that this is true. But most of us would I think agree that > this is what happens if you describe the couple “observer particle” by QM, > i.e by the quantum wave. It is a consequence of elementary quantum > mechanics (unless of course you add the unintelligible collapse of the > wave, which for me just means that QM is false). > > > This talk of "being in eigenstates" is confused. An eigenstate is > relative to some operator. The system can be in an eigenstate of an > operator. Ideal measurements are projection operators that leave the > system in an eigenstate of that operator. But ideal measurements are rare > in QM. All the measurements you're discussing in Young's slit examples are > destructive measurements. You can consider, as a mathematical convenience, > using a complete set of commuting operators to define a set of eigenstates > that will provide a basis...but remember that it's just mathematics, a > certain choice of basis. The system is always in just one state and the > mathematics says there is some operator for which that is the eigenstate. > But in general we don't know what that operator is and we have no way of > physically implementing it. > > Brent > > > *I can only speak for myself, but when I write that a system in a > superposition of states is in all component states simultaneously, I am > assuming the existence of an operator with eigenstates that form a complete > set and basis, that the wf is written as a sum using this basis, and that > this representation corresponds to the state of the system before > measurement. * > > > In general you need a set of operators to have the eigenstates form a > complete basis...but OK. > > *I am also assuming that the interpretation of a quantum superposition is > that before measurement, the system is in all eigenstates simultaneously, > one of which represents the system after measurement. I do allow for > situations where we write a superposition as a sum of eigenstates even if > we don't know what the operator is, such as the Up + Dn state of a spin > particle. In the case of the cat, using the hypothesis of superposition I > argue against, we have two eigenstates, which if "occupied" by the system > simultaneously, implies the cat is alive and dead simultaneously. AG * > > > Yes, you can write down the math for that. But to realize that physically > would require that the cat be perfectly isolated and not even radiate IR > photons (c.f. C60 Bucky ball experiment). So it is in fact impossible to > realize (which is why Schroedinger considered if absurd). > > > * CMIIAW, but as I have argued, in decoherence theory it is assumed the > cat is initially isolated and decoheres in a fraction of a nano second. So, > IMO, the problem with the interpretation of superposition remains. * > > > Why is that problematic? You must realize that the cat dying takes at > least several seconds, very long compared to decoherence times. So the cat > is always in a *classical* state between |alive> and |dead>. These are > never in superposition. > > > > * When you start your analysis /experiment using decoherence theory, don't > you assume the cat is isolated from the environment? It must be if you say > it later decoheres (even if later is only a nano second). Why is this not a > problem if, as you say, it is impossible to isolate the cat? AG * > > > That it is impossible to isolate the cat is the source of the > absurdity...not that it exists in a superposition later. > > > *But if you claim the cat decoheres in some exceedingly short time based > on decoherence theory and the wf you write taking into account the > apparatus, observer, and remaining environment, mustn't the cat be > initially isolated for this to make sense? AG* > > > It never made sense. That it didn't make sense was Schroedinger's point, > he just didn't correctly identify where it first failed to make sense, i.e. > in the idea that a cat could be isolated. Since the cat can't be isolated > then |alive> and |dead> can only appear in a mixture, not in a coherent > superposition. > > Brent > > > * But when you include the cat in a superposition wf using decoherence > theory* > > > When you write that as a mathematical description you have written a > description that cannot apply to anything. Is it a description of > something? Sure. Does that something exist? No. > > > *I am just applying the standard interpretation to a superposition. > Nothing more. Probabilities are calculated differently for superpositions > vs mixed states. In the former, there are interference terms arising from > the inner product with the wf itself, and each eigenstate (and then > calculating the norm-squared). Mixed states probabilities are, I believe, > just the normed squared of the amplitude of each of component state > separately. In any event, when one sees the PLUS sign between the component > states, one generally means a standard superposition, not a mixed state, > unless otherwise informed. So the two-state superposition in decoherence > theory which includes the cat must be a standard superposition, and > Schroedinger believed that the standard interpretation was that the system > is in both states simultaneously, thus leading to his cat paradox. What > interpretation do you assume for this superposition if not Schroedinger's? > Are you writing a superposition of something that doesn't exist? AG* > > > Weren't you the one complaining that Bruno falsely assumed every > mathematical structure exists? > > > *Yes Brent, it was me, but I was objecting to the assumption that every > mathematical structure and prediction exists AFTER I gave examples where > this hypothesis is falsified, such as plane waves and advanced waves in > E&M. But in the case we're discussing, the two state wf written in > decoherence theory for the cat problem, the wf is specifically given to > represent a physical system consisting of cat* > > > And Conan Doyle specifically gave descriptions of an English detective. >
*Is this supposed to be a meaningful reply? I have no idea how this relates to our discussion. AG * > > *, detector, radioactive source, and remaining environment. If it doesn't > represent anything as you now claim, ISTM we're in woo-woo land. I mean, > you're asserting a wf which has no discernible meaning or interpretation. * > > > Where did I assert that? > *Here; your words! Brent: When you write that as a mathematical description you have written a description that cannot apply to anything. Is it a description of something? Sure. Does that something exist? No.AG* > > *If the cat is always in a mixed state, discussing decoherence times in > the context of this wf make no sense, at least to me. But if you insist on > this, mustn't the overall wf be a mixed state, making the radioactive > source, and so forth, also mixed states? * > > > An atom can be in a superposition of decayed and not decayed because it is > relatively isolated. It doesn't radiate IR photons or have othseer > interactions with the environment. *I know that, of course. But if you have an eigenstate consisting of several tensor products and one is a mixed state, such as the cat,and the others not, is the overall eigenstate pure or mixed?Is it even an eigenstate? don't think you can legitimately write such an "eigenstate". You can write it of course, you can write anything, but how is it interpreted? AG* > Haven't you read Schlosshauer's paper yet? > *Irrelevant. AG * > > Brent > > *AG* > > > * Unrelated to this issue AFAICT. If the superposition with the cat used > as a starting point for your decoherence analysis doesn't exist as > representing anything, it's baffling that any conclusions can be reached. > OTOH, if the two component states are mixed, that's a fact that seems never > in evidence, certainly not in what I have read about decoherence theory. AG > * > > > Brent > > > > > > > *, you have a two state system using the standard interpretation of > superposition, meaning the system is in both states simultaneously, not a > mixed state. AG * > > > *Isn't this the standard interpretation of a superposition of states? AG* > > ... -- 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 post to this group, send email to everything-list@googlegroups.com. Visit this group at https://groups.google.com/group/everything-list. For more options, visit https://groups.google.com/d/optout.
