On 6/23/2018 2:26 PM, [email protected] 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? AGAsher 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. 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).
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