On Wednesday, August 1, 2018 at 4:41:02 AM UTC, [email protected] wrote: > > > > On Wednesday, August 1, 2018 at 2:09:45 AM UTC, Brent wrote: > > > > On 7/31/2018 6:22 PM, [email protected] wrote: > > > > On Wednesday, August 1, 2018 at 12:11:48 AM UTC, Brent wrote: > > > > On 7/31/2018 2:43 PM, [email protected] wrote: > > > > On Tuesday, July 31, 2018 at 7:14:53 PM UTC, Brent wrote: > > > > On 7/31/2018 6:43 AM, [email protected] wrote: > > > > On Tuesday, July 31, 2018 at 6:11:18 AM UTC, Brent wrote: > > > > On 7/30/2018 9:21 PM, [email protected] wrote: > > > > On Tuesday, July 31, 2018 at 1:34:58 AM UTC, Brent wrote: > > > > On 7/30/2018 4:40 PM, [email protected] 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, 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. 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? 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* > > > > > *It doesn't go away because the decoherence time is exceedingly short. * > > > Yes is does go away. Even light can't travel the length of a cat in a > nano-second. > > > *And for this reason I still conclude that Schroedinger correctly pointed > out the fallacy in the standard interpretation of superposition; namely, > that the system represented by a superposition, is in all components states > simultaneously. AG * > > > It's not a fallacy. It just doesn't apply to the cat or other macroscopic > objects, with rare laboratory exceptions. > > > *Other than slit experiments where superposition can be interpreted as the > system being in both component states simultaneously, why is this > interpretation extendable to all isolated quantum systems? AG * > > > ?? Any system can be mathematically represented as being in a > superposition of different basis states. It's just a consequence of being > a vector in a vector space. Any vector can be written as a sum of other > vectors. > > > *OK, never had a problem with this. AG* > > > Your use of the words "interpreted" and "this interpretation" is unclear. > > > *I am using those words as I think Schroedinger did, where he assumes a > system in a superposition of states, is in all component states > simultaneously. It is from that assumption, or interpretation, that he > finds the contradiction or absurdity of a cat alive and dead > simultaneously. 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 [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.
