On Tuesday, July 10, 2018 at 11:23:55 PM UTC-6, scerir wrote: > > > Il 11 luglio 2018 alle 0.01 [email protected] <javascript:> ha scritto: > > > > On Monday, July 9, 2018 at 11:55:45 PM UTC-6, scerir wrote: > > > Il 9 luglio 2018 alle 22.46 [email protected] ha scritto: > > > > On Saturday, July 7, 2018 at 4:48:51 PM UTC-6, [email protected] wrote: > > > > On Saturday, July 7, 2018 at 12:19:23 PM UTC-6, [email protected] wrote: > > > > On Friday, July 6, 2018 at 1:56:12 PM UTC-6, [email protected] wrote: > > > > On Friday, July 6, 2018 at 1:22:03 PM UTC-6, Brent wrote: > > > > On 7/6/2018 11:44 AM, [email protected] wrote: > > > > On Thursday, July 5, 2018 at 5:14:34 PM UTC-6, Brent wrote: > > > > On 7/5/2018 3:55 PM, [email protected] wrote: > > > > On Thursday, July 5, 2018 at 2:03:46 PM UTC-6, Brent wrote: > > > > On 7/5/2018 11:27 AM, [email protected] wrote: > > > > On Wednesday, July 4, 2018 at 10:57:06 AM UTC-6, Brent wrote: > > > > On 7/4/2018 1:57 AM, 'scerir' via Everything List wrote: > > > *No. I am asserting that the INTERPRETATION of the superposition of states > is wrong. Although I have asked several times, no one here seems able to > offer a plausible justification for interpreting that a system in a > superposition of states, is physically in all states of the superposition > SIMULTANEOUSLY before the system is measured. If we go back to those little > pointing things, you will see there exists an infinite uncountable set of > basis vectors for any vector in that linear vector space. For quantum > systems, there is no unique basis, and in many cases also infinitely many > bases, So IMO, the interpretation is not justified. AG* > > ***SIMULTANEOUSLY*** was used by EPR in their paper, but that did not have > much meaning (operationally, physically). > > Can we say that the observable, in a superposition state, has a > ***DEFINITE*** value between two measurements? > > No - in general - we cannot say that. > > > It's in some definite state. But it may be a state for which we have no > measurement operator or don't intend to measure; so we say it is in a > superposition, meaning a superposition of the eigenstates we're going to > measure. So it does not have one of the eigenvalues of our measurement. > > Brent > > > *So for the radioactive source, the superposed state, Decayed + Undecayed, > does NOT imply the system is in both states simultaneously? * > > > No, it is in a state that consists of Decayed+Undecayed. So in a sense it > is in both simulatnaeously. If you are sailing a heading of 45deg you are > on a definite heading. But you are simultaneously traveling North and > East. And if someone was watching you with a radar that could only output > "moving north" or "moving east" it would oscillate between the two and you > might call that a superposition of north and east motion. > > Brent > > > *I see. But as I have pointed out, there are uncountably many sets of > basis vectors that result in the same vector along the 45 deg direction. > Thus, it makes no sense to single out a particular basis and claim it is > simultaneously in both. * > > > That's where you're wrong. It makes perfect sense if that's the only > basis you can measure in. That's why I gave the hypothetical example of a > radar that could only report motion as northward or eastward. In some > cases, like decayed our not-decayed, we don't have instruments to measure > the superposition state. In other cases like sliver atom spin we can > measure up/down or left/right or along any other axis. > > *ISTM, this is the cause of many of the apparent paradoxes in QM such as > Schroedinger's cat, or a radioactive source which is decayed and undecayed > simultaneously. I have no objection using such a state to do a calculation, > but I think it's an error to further interpret a superposition in terms of > simultaneity of component states. What say you? AG* > > > I say use what's convenient for calculation. Don't imagine your > calculation is the reality. > > > > *But the consensus, perhaps unstated or subliminally, is that the > superposition is imagined as reality, which leads to cats and radioactive > sources being (respectively) alive and dead, and decayed and undecayed, > simultaneously. Isn't this what Schroedinger was arguing against? I have > rarely, if ever, seen it argued NOT to interpret a superposition as reality > as a proposed solution to these apparent paradoxes. AG * > > > You just go around and around. You never put together the explanations > you get. Decoherence shows that, in the presence of an environment, the > wave function FAPP collapses into orthogonal quasi-classical states in > fractions of a nano-second. That's why the Schroedinger cat story doesn't > show what Schroedinger thought it did. BUT there are experiments, like > silver atoms thru and SG in which superpositions of left+right persist, > they are up polarizations for example; and we know they exist because we > can prepare up states and then measure them left/right or measure them > up/down. The latter, up/down measurement, would always yield "up" showing > they were in an up eigenstate, even though they were also in a left+right > superposition. But there are other cases where we can't measure the > eigenstate (e.g. neutrino family) so we always describe them as being in a > superposition because the eigenstate is operationally unmeasurable and we > can't prepare them in an eigenstate. > > Brent > > > *You also go round and round without answering a key question about > decoherence theory. You refer to the infinitesimally short decoherence time > of, say, the apparatus, but ISTM it has already decohered way before it is > employed in any experiment. What then is the reasoning for including the > apparatus in the superposition for the entire system, and claiming this wf > represents the total system before any environmental interaction? BTW, what > is a right + left superposition in SG measurement, and how is it relevant > to this discussion? TIA, AG * > > *(My computer is being repaired, so I have limited library time for > possibly a week or more. This means I will have to study some of your > examples later before possibly responding.)* > > > *Thinking about this some more, I agree that if one measures in a > particular basis, it is natural to express the wf of the system in a > superposition of this basis. However, where I disagree with your analysis > is that one doesn't need decoherence theory to resolve Schroedinger's > apparent cat paradox. This is because regardless of the natural basis used, > there is nothing in QM to allow, or compel us to interpret the > superposition as meaning the system is simultaneously in all component > states (which interpretation seems to produce an alleged paradox). > Moreover, although we cannot measure in other bases, the wf can > nevertheless be expressed in other bases, and sometimes the set of bases is > uncountable, again casting doubt on the legitimacy of interpreting the > superposition in terms of simultaneity of component states. Do you agree or > disagree? * > > *Also, when doing an SG spin measurement, I don't see that right-left is > well defined for a well-defined Up / Dn measurement. I also don't see why > the system is assumed to be in a superposition of right + left, or why it > persists after the measurement, or in what way these facts -- if they are > facts -- is in any way enlightening. I would appreciate your comments on > these issues. * > > *TIA, AG* > > > > *From Wiki; * *https://en.wikipedia.org/wiki/Quantum_superposition > <https://en.wikipedia.org/wiki/Quantum_superposition>* > > *The principle of quantum superposition states that if a physical system > may be in one of many configurations—arrangements of particles or > fields—then the most general state is a combination of all of these > possibilities, where the amount in each configuration is specified by > a complex number <https://en.wikipedia.org/wiki/Complex_number>.* > > *For example, if there are two configurations labelled by 0 and 1, the > most general state would be* > > > A|Up> + B|Dn> > > *where the coefficients A and B are complex numbers describing how much > goes into each configuration.* > > > *The principle was described by Paul Dirac > <https://en.wikipedia.org/wiki/Paul_Dirac> as follows:* > > *The general principle of superposition of quantum mechanics applies to > the states [that are theoretically possible without mutual interference or > contradiction] ... of any one dynamical system. It requires us to assume > that between these states there exist peculiar relationships such that > whenever the system is definitely in one state we can consider it as being > partly in each of two or more other states. The original state must be > regarded as the result of a kind of superposition of the two or more new > states, in a way that cannot be conceived on classical ideas. Any state may > be considered as the result of a superposition of two or more other states, > and indeed in an infinite number of ways. Conversely any two or more states > may be superposed to give a new state... (underlining my emphasis)* > > > *IMO, he's mistaken. There's no need for the underlined assumption. If > anyone here disagrees, please offer your *argument*. TIA, AG* > > > *Cat got your tongue Brent? Bruce out to lunch? No genuine seekers of > truth here? What's the rationale for Dirac's claim? I am all ears. AG* > > "The non-classical nature of the superposition process is brought out > clearly if we consider the superposition of two states, *A* and *B*, such > that there exists an observation which, when made on the system in state > *A*, is certain to lead to one particular result, *a* say, and when made > on the system in state *B* is certain to lead to some different result, > *b* say. What will be the result of the observation when made on the > system in the superposed state? The answer is that the result will be > sometimes *a* and sometimes *b*, according to a probability law depending > on the relative weights of *A* and *B* in the superposition process. It > will never be different from both *a* and *b*. *The intermediate > character of the state formed by superposition thus expresses itself > through the probability of a particular result for an observation being > intermediate between the corresponding probabilities for the original > states, not through the result itself being intermediate between the > corresponding results for the original states. (PAM Dirac, The Principles > ......, second edition, 1947, page 12 ).* > > > *IIRC, the above quote is also in the Wiki article. It's not a coherent > argument; not even an argument but an ASSERTION. Let's raise the level of > discourse. It says we always get a or b, no intermediate result when the > system is in a superposition of states A and B. Nothing new here. Key > question: why does this imply the system is in states A and B > SIMULTANEOUSLY before the measurement? AG * > > Let us imagine the system is in state A or in state B before measurement. > Would that be consistent with outcomes of experiments? >
*I'm not exactly clear what Dirac means by states A and B. I think he means the Up/Dn states of a spin measurement. Generally, If A and B are eigenstates of the operator whose observable is being measured, the system will remain in those eigenstates after measurement. OTOH, if A or B are superpositions of other states, the system will be some eigenstate after the measurement, possibly A or B if they are eigenstates of the operator being measured. AG * Let us imagine the state of system is a mixture of A and B. Would that be > consistent with outcomes of experiments? > *A mixture isn't a superposition, so your question doesn't seem relevant to my issue here; namely, the proper interpretation of a superposition of states. AG * > *Same for cat, Alive + Dead? Same for ( (Undecayed, Alive) + (Decayed, > Dead) ) for Schroedinger's composite system? If that's the case, why would > anyone think these states are in any way paradoxical or contradictory? 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. > > > -- > 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. > > > -- > 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. > > > > -- > 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. > > > -- > 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] <javascript:>. > To post to this group, send email to [email protected] > <javascript:>. > Visit this group at https://groups.google.com/group/everything-list. > For more options, visit 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.
