On Sunday, June 24, 2018 at 3:03:07 AM UTC, Brent wrote: > > > > On 6/23/2018 2:26 PM, [email protected] <javascript:> wrote: > > > > On Saturday, June 23, 2018 at 9:21:05 PM UTC, [email protected] wrote: >> >> >> >> On Saturday, June 23, 2018 at 7:52:08 PM UTC, Brent wrote: >>> >>> >>> >>> On 6/23/2018 12:02 AM, [email protected] wrote: >>> >>> >>> >>> On Saturday, June 23, 2018 at 6:25:38 AM UTC, Brent wrote: >>>> >>>> >>>> >>>> On 6/22/2018 3:13 PM, [email protected] wrote: >>>> >>>> *I've been struggling lately with how to interpret a superposition of >>>> states when it is ostensibly unintelligible, e.g., a cat alive and dead >>>> simultaneously, or a radioactive source decayed and undecayed >>>> simultaneously. If we go back to the vector space consisting of those >>>> "little pointing things", it follows that any vector which is a sum of >>>> other vectors, simultaneously shares the properties of the components in >>>> its sum. This is simple and obvious. I therefore surmise that since a >>>> Hilbert space is a linear vector space, this interpretation took hold as a >>>> natural interpretation of superpositions in quantum mechanics, and led to >>>> Schroedinger's cat paradox. I don't accept the explanation of decoherence >>>> theory, that we never see these unintelligible superpositions because of >>>> virtually instantaneous entanglements with the environment. Decoherence >>>> doesn't explain why certain bases are stable; others not, even though, >>>> apriori, all bases in a linear vector space are equivalent. These >>>> considerations lead me to the conclusion that a quantum superposition of >>>> states is just a calculational tool, and when the superposition consists >>>> of >>>> orthogonal component states, it allows us to calculate the probabilities >>>> of >>>> the measured system transitioning to the state of any component. In this >>>> interpretation, essentially the CI, there remains the unsolved problem of >>>> providing a mechanism for the transition from the SWE, to the collapse to >>>> one of the eigenfunctions when the the measurement occurs. I prefer to >>>> leave that as an unsolved problem, than accept the extravagance of the >>>> MWI, >>>> or decoherence theory, which IMO doesn't explain the paradoxes referred to >>>> above, but rather executes what amounts to a punt, claiming the paradoxes >>>> exist for short times so can be viewed as nonexistent, or solved. AG. * >>>> >>>> >>>> If you're willing to take QM as simply a calculational tool, then QBism >>>> solve the problem of wf collapse. >>>> >>>> Brent >>>> >>> >>> Thanks. I'll check it out. Is QBism a plausible theory? Do some >>> professional "heavies" accept it? AG >>> >>> >>> Asher Peres started it and he was a "heavy weight". Chris Fuchs has >>> been the main advocate, but he's kind of strange. The interpretation is >>> not widely liked because it's the extreme end of instrumentalism. >>> >>> Brent >>> >> >> *Let's go back to those little pointy things and write A = B + C, where B >> and C are basis states with appropriate multiplicative constants. Given >> this particular basis, one could interpret this equation as a superposition >> where A is understood as being in states B and C simultaneously. But A >> could be written in an infinite set of different sums using orthogonal or >> non orthogonal bases. So, given the lack of uniqueness, it seems an >> unwarranted stretch to assume any vector can be interpreted as being in two >> states simultaneously, If we drop this interpretation for quantum >> superpositions, most, possibly all the paradoxes go away. Who was the >> person who first interpreted a superposition in this way, which seems the >> root of many unnecessary, a[[ar problems in quantum mechanics? AG * >> > > ... *Who first interpreted a quantum superposition this way, which seems > the root of many unnecessary, intractable problems in quantum mechanics, > inclusive of the idea that a particle can be in more than one position > simultaneously? AG* > > > Of course in theory any pure state can be taken to be a basis vector and > there is an operator for which that state is an eigenvector, i.e. a basis > in which it is not a superposition. >
*Can't any pure state be written as a superposition using another basis? AG* > But in practice we don't know what that basis is and in general we cannot > physically realize the corresponding operator. That's why a photon passing > thru Young's slits is said to be in a superposition of passing thru slit 1 > and passing thru slit 2. We know how to create an operator that measures > "passing thru slit 1" and we know how to create an operator that measures > "passing thru slit 2", but we don't know how to construct an operator that > measures "passes thru both slit 1 and slit 2". We can write down the wf in > the basis of "passing thru slit 1" and "passing thru slit 2" and it's a > coherent sum, i.e. a superposition of those two. Decoherence theory says > that we can't construct an instrument which will measure "passes thru both > slit 1 and slit 2" because such an instrument would quickly decohere into > one of the two stable states "passed thru 1" or "passed thru 2" and the > interference pattern would not form (in repeated trials). > *In Young's double slit experiment, IIUC we assume the wave goes through both slits simultaneously in order to model the interference after repeated trials.** But you say that's NOT what decoherence theory says. I find this baffling. In the seminal quantum experiment where one could, it seems, assume simultaneity of the component wf's, you say it's denied by decoherence theory. ** Maybe I missed the content of your comment. **In general I don't see the reason to assume simultaneity for components of a quantum superposition. How would you justify that interpretation of a quantum superposition? TIA, AG* Brent > -- 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.
