> On 1 Aug 2018, at 22:50, [email protected] wrote: > > > > 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?
To be sure I do NOT assume every mathematical structure exists. That was my earlier critics of Tegmark, which seems to have understood the point. Eventually I assume only the semi-computable part of arithmetic, which is an extremely tiny part of mathematics. Basically, I assume only K and S and their combination, and the laws Kxy = x, and Sxyz = xz(yz), and nothing else. It is not just physics which becomes phenomenological, but analysis and set theories too. Infinities and continua, like matter, belongs only to the imagination of the numbers or equivalent, like combinators. Bruno > > 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] > <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.
