On Monday, November 5, 2018 at 8:05:21 AM UTC, Pierz wrote: > > > > On Sunday, November 4, 2018 at 7:50:30 AM UTC+11, agrays...@gmail.com > wrote: >> >> >> >> On Thursday, November 1, 2018 at 11:22:46 PM UTC, Pierz wrote: >>> >>> >>> >>> On Monday, October 15, 2018 at 9:40:39 PM UTC+11, agrays...@gmail.com >>> wrote: >>>> >>>> >>>> >>>> On Sunday, October 14, 2018 at 5:08:42 PM UTC, smitra wrote: >>>>> >>>>> On 14-10-2018 15:24, agrays...@gmail.com wrote: >>>>> > In a two state system, such as a qubit, what forces the >>>>> interpretation >>>>> > that the system is in both states simultaneously before measurement, >>>>> > versus the interpretation that we just don't what state it's in >>>>> before >>>>> > measurement? Is the latter interpretation equivalent to Einstein >>>>> > Realism? And if so, is this the interpretation allegedly falsified >>>>> by >>>>> > Bell experiments? AG >>>>> >>>>> It is indeed inconsistent with QM itself as Bell has shown. >>>>> Experiments >>>>> have later demonstrated that the Bell inequalities are violated in >>>>> precisely the way predicted by QM. This then rules out local hidden >>>>> variables, therefore the information about the outcome of a >>>>> measurement >>>>> is not already present locally in the environment. >>>>> >>>>> Saibal >>>>> >>>> >>>> What puzzles me is this; why would the Founders assume that a system in >>>> a superposition is in all component states simultaneously -- contradicting >>>> the intuitive appeal of Einstein realism -- when that assumption is not >>>> used in calculating probabilities (since the component states are >>>> orthogonal)? AG >>>> >>> >>> I think because of interference. >>> >> *Are you unaware of the fact that when a superposition of states is written in the form of eigenstates of the operator, there is no interference?! Eigenstates with distinct eigenvalues are orthogonal, meaning there is no interference between any pair. AG *
Consider the paradigmatic double slit, with the single electron going >>> through it. It sure looks like the electron was in two place at once, >>> doesn't it? >>> >> *No. It's never been observed. All you "see" is an interference pattern when you don't look at the slits. AG * > >> *Yes, that's my assessment how the erroneous interpretation took hold, >> but only if you restrict yourself to the particle interpretation. If the >> electron travels as a wave, it can go through both slits simultaneously and >> interfere with itself. This is my preferred interpretation; the only one >> that makes sense. AG* >> > > Although as stated I think "being in two states at once" is a manner of > speaking quasi-classically about non-classical phenomena, it seems you > still have a very classical imagination of what's going on here, but I have > my doubts: > 1 - You say it makes sense, but I'm not sure that an electron "travelling > as a wave" but being measured as a particle makes an awful lot more sense! > *There is no satisfying model or picture of a slit experiment. However, one CAN think of a *probability* wave that interferes with itself -- they're generally used in quantum mechanics -- without being able to explain how the interfering waves coalesce into a particle when the measurement occurs. This is the great unsolved problem and I am content for now to leave it as such. But the attempt to use zig-zag paths that go forward and backward in time seems like a much worse model in terms of having explanatory value. AG * 2 - Schrödinger initially thought of his equation (the one that applies to > double slits) as being the equation for a physical wave, as you seem to be > doing. > *I never referred to a physical wave. I meant a probability wave. AG * However he was forced eventually to accept that it was something a lot more > abstract than that. The statistical interpretation formulated by Born > superseded any such notion. Interference happens whenever a quantum system > can reach the same state via more than one history. In the case of quantum > computers, complex interfering superpositions are constructed in which it > is impossible to conceive of the "wave function" as literally describing > some kind of mechanical wave. > *Not a mechanical or physical wave, but a probability wave. See above. AG * > >> I'm not sure what you mean by "that assumption is not used in calculating >>> probabilities". >>> >> >> *If the operator whose eigenvalues are being measured has a well defined >> mathematical form -- e.g., not like |alive> -- it has specific eigenvectors >> and eigenvalues, and the state function can be written as superposition of >> these eigenvectors. It can be shown that eigenvectors with distinct >> eigenvalues are orthogonal, meaning the Kronecker delta applies to their >> mutual inner products. Therefore, to calculate the probability of observing >> a particular eigenvalue, one must take the inner product of the wf with the >> eigenvector which has that eigenvalue. Due to the orthogonality, all terms >> drop out except for the term in the superposition which contains the >> eigenvector whose eigenvalue you want to measure. As you should see, there >> is nothing in this process of calculating probabilities that in any way >> implies, assumes, or uses, the concept that the system is simultaneously in >> ALL component states of the superposition (written as a sum of >> eigenvectors). AG* >> >> > Sure, but this relates to measurement *outcomes* not to the question fo > what state the system is in while not being measured. > *Not true. A superposition of states describes an isolated system prior to measurement. When the measurement occurs, the system is in one of the eigenstates of the operator (one of the postulates of QM). AG* > Clearly the fact that the vector spans more than one dimension expresses a > state that *in a mathematical sense* is a combination of more than one > component state. > *Misleading at best. Since the wf expansion can be done in many different bases, the claim that the superposition is "in" many component states is totally misleading. It's like claiming that since a vector in a plane can be expressed in some orthogonal basis, it's "in" some combination of the basis states. This is clearly false since there is an uncountable number of orthogonal bases which can represent the same vector. I've explained this many times, but few seem to understand. You will note Bruce's comment earlier on this thread, which states the same pov. AG* If it weren't for interference and entanglement (per Bell), no doubt > scientists would simply consider this combination of states a measure of > our ignorance of the underlying reaility (the hidden variables). But those > three elements of quantum weirdness make it impossible to sustain that view. > *The system is not in any particular state of the superposition, which follows from linear algebra, and thus certainly not simultaneously in all component states of any superposition, but neither does it have a pre-existing local value. AG* If you take a sum-over-histories approach it's explicitly assumed the electron went via all possible paths. *Too extravagant for my taste. Why would it go directly to the measured outcome and also do loops and zig-zags forward and backward in time? I think Feynman eventually gave up on an all-particle model of QM. AG * > >> *I don't know that method, but offhand POSSIBLE PATHS might have nothing >> to do with, and possibly independent of SUPERPOSITIONS OF STATE. AG* >> >> That's *very* offhand. Possible paths are mathematically equivalent to > the superposition that emerges from the Schrödinger picture. > *There's a subtle mathematical issue you side step. A path or history in the Feynman picture is not, on its face, a component of a superposition of states; it's a distinct mathematical entity. For simplicity, suppose there are only two paths. How would you express those paths mathematically, and wind up with a genuine superposition of states? AG* It's silly to say it might be independent of superposition if you don't > know anything about the approach. > *Am I allowed to think out loud, provisionally? AG * > > >> I don't see what the orthogonality of the basis vectors (and hence >>> component states) has to do with the question of interpretation of >>> superposition. >>> >> >> *Explained in detail above. AG* >> >> Clearly the system will be measured in only one state, and this is what >>> the orthogonal vectors represent. However the quantum state itself >>> typically spans more than one dimension of the vector space - that's what a >>> superposition is. However I think when physicists say that the >>> superposition is in all states simultaneously, it's only in a manner of >>> speaking - a way of conveying the mathematical situation in natural >>> language that is inherently classical. >>> >> >> >> *It's a totally misleading way to discuss the quantum superpositions. >> Even classically, say for the vector space of "little pointy things" in a >> plane, each vector can be expressed in uncountably many bases, both >> orthogonal and non-orthogonal. So to claim that one basis is somehow >> preferred, and the vector being expressed as a sum or superposition in that >> basis, is simultaneously in all components of that particular basis, make >> no sense whatsoever. AG* >> > > To take up your classical example, the classical system is in a > well-defined state regardless of which basis is ultimately chosen to > specify that state. In order to tell you the location of Paris (or some > little pointy thing), I need some coordinate basis, but Paris is still > located *somewhere* before I specify that basis. In some (trivial) sense > it's simultaneously at all the coordinates that could be specified were we > to be specify its location in every one of the possible bases we could > choose. The argument is that a quantum state is equally well-defined, with > no *underlying* state that is not included in the component vectors. The > difference with the Paris example of course is that it is not in a > superposition within those different bases - it has one and just one > coordinate in each of them. If there is no underlying reality beyond the > state - the hidden variables ruled out by Bell - then IMO it is not > "totally misleading" to say it is in some sense in all the states of the > superposition simultaneously. > *But if you do that, you get cats which are alive and dead simultaneously, and radioactive atoms that are decayed and undecayed simultaneously. Then you can write books about the "mysteries" of QM, but those who know basic linear algebra would see it's just a load of BS. QM has enough mysteries IMO, so we don't need to make up nonsense to sell books, or whatever motive is at work. AG* > It is *somewhat *misleading however if you don't understand QM because of > the possible confusion between a coherent and a decohered state. They are > obviously quite different things, the difference being expressed in the > density matrices of pure and mixed states. A system evolving in isolation > shouldn't be muddled up with a system post measurement. > *I didn't do that. Post measurement the system is in one of the eigenstates of the operator whose observables are being measured. It's no longer in a superposition of states. AG * > > > >> Reading Born's exchange of letters with Einstein (I'm proud to say Born >>> was my great grandfather), it's clear that Born had a conception of QM that >>> was still very realistic in the Einstein sense. Though they disagreed >>> significantly and somewhat heatedly, Born still seems to have regarded QM >>> probabilities as classical probabilities in disguise. >>> >> >> *Einstein realism seems to have been falsified due to Bell experiments. >> If that's the case, it would mean that BEFORE measurement of a quantum >> system, it is not only NOT in all states of a superposition simultaneously >> for the reasons I have argued (nothing to do with Bell), but ALSO has no >> local preexisting value. AG* >> >> > I don't think he would ever have endorsed the notion that a particle is >>> truly in all of the states of the superposition simultaneously. >>> >> >> *Thanks for your input. 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 firstname.lastname@example.org. Visit this group at https://groups.google.com/group/everything-list. For more options, visit https://groups.google.com/d/optout.