On 6/23/2018 9:20 PM, agrayson2...@gmail.com wrote:
On Sunday, June 24, 2018 at 3:03:07 AM UTC, Brent wrote:
On 6/23/2018 2:26 PM, agrays...@gmail.com <javascript:> wrote:
On Saturday, June 23, 2018 at 9:21:05 PM UTC, agrays...@gmail.com
wrote:
On Saturday, June 23, 2018 at 7:52:08 PM UTC, Brent wrote:
On 6/23/2018 12:02 AM, agrays...@gmail.com wrote:
On Saturday, June 23, 2018 at 6:25:38 AM UTC, Brent wrote:
On 6/22/2018 3:13 PM, agrays...@gmail.com 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*
Sure.
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. **
Pay attention. I said we couldn't make a measuring device for that.
NOT that we didn't calculate it that way
Brent
**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
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