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* > [image: c_0 \mid 0 \rangle + c_1 \mid 1 \rangle] > <https://wikimedia.org/api/rest_v1/media/math/render/svg/ea1f5b5eb7f306860452f691348db266bc303dd9>{\displaystyle > > c_{0}\mid 0\rangle +c_{1}\mid 1\rangle } > > > > *where the coefficients 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* >
The equation above didn't copy well. It's the standard superposition for spin 1/2 particle, namely, [image: c_0 \mid 0 \rangle + c_1 \mid 1 \rangle] . AG > >>>> >>>> >>>>> Brent >>>>> >>>>> >>>>>> *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.
