On 7/30/2018 9:21 PM, [email protected] wrote:
On Tuesday, July 31, 2018 at 1:34:58 AM UTC, Brent wrote:
On 7/30/2018 4:40 PM, [email protected] <javascript:> wrote:
On Monday, July 30, 2018 at 7:50:47 PM UTC, Brent wrote:
On 7/30/2018 8:02 AM, Bruno Marchal wrote:
*and claims the system being measured is physically in all
eigenstates simultaneously before measurement.*
Nobody claims that this is true. But most of us would I
think agree that this is what happens if you describe the
couple “observer particle” by QM, i.e by the quantum wave.
It is a consequence of elementary quantum mechanics (unless
of course you add the unintelligible collapse of the wave,
which for me just means that QM is false).
This talk of "being in eigenstates" is confused. An
eigenstate is relative to some operator. The system can be
in an eigenstate of an operator. Ideal measurements are
projection operators that leave the system in an eigenstate
of that operator. But ideal measurements are rare in QM.
All the measurements you're discussing in Young's slit
examples are destructive measurements. You can consider, as
a mathematical convenience, using a complete set of commuting
operators to define a set of eigenstates that will provide a
basis...but remember that it's just mathematics, a certain
choice of basis. The system is always in just one state and
the mathematics says there is some operator for which that is
the eigenstate. But in general we don't know what that
operator is and we have no way of physically implementing it.
Brent
*I can only speak for myself, but when I write that a system in a
superposition of states is in all component states
simultaneously, I am assuming the existence of an operator with
eigenstates that form a complete set and basis, that the wf is
written as a sum using this basis, and that this representation
corresponds to the state of the system before measurement. *
In general you need a set of operators to have the eigenstates
form a complete basis...but OK.
*I am also assuming that the interpretation of a quantum
superposition is that before measurement, the system is in all
eigenstates simultaneously, one of which represents the system
after measurement. I do allow for situations where we write a
superposition as a sum of eigenstates even if we don't know what
the operator is, such as the Up + Dn state of a spin particle. In
the case of the cat, using the hypothesis of superposition I
argue against, we have two eigenstates, which if "occupied" by
the system simultaneously, implies the cat is alive and dead
simultaneously. AG *
Yes, you can write down the math for that. But to realize that
physically would require that the cat be perfectly isolated and
not even radiate IR photons (c.f. C60 Bucky ball experiment). So
it is in fact impossible to realize (which is why Schroedinger
considered if absurd).
*
CMIIAW, but as I have argued, in decoherence theory it is assumed the
cat is initially isolated and decoheres in a fraction of a nano
second. So, IMO, the problem with the interpretation of superposition
remains. *
Why is that problematic? You must realize that the cat dying takes at
least several seconds, very long compared to decoherence times. So the
cat is always in a /*classical*/ state between |alive> and |dead>. These
are never in superposition.
*It doesn't go away because the decoherence time is exceedingly short. *
Yes is does go away. Even light can't travel the length of a cat in a
nano-second.
*And for this reason I still conclude that Schroedinger correctly
pointed out the fallacy in the standard interpretation of
superposition; namely, that the system represented by a superposition,
is in all components states simultaneously. AG
*
It's not a fallacy. It just doesn't apply to the cat or other
macroscopic objects, with rare laboratory exceptions. Any old plane
polarized photon can be represented as being in a superposition of left
and right circular polarization. It is */not/* the case that a system
is in all basis states at once unless you count being in state /|x>/
with zero amplitude as being in /x/.
Brent
**
Brent
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