On 7/31/2018 6:43 AM, agrayson2...@gmail.com wrote:
On Tuesday, July 31, 2018 at 6:11:18 AM UTC, Brent wrote:
On 7/30/2018 9:21 PM, agrays...@gmail.com <javascript:> wrote:
On Tuesday, July 31, 2018 at 1:34:58 AM UTC, Brent wrote:
On 7/30/2018 4:40 PM, agrays...@gmail.com 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.
*
When you start your analysis /experiment using decoherence theory,
don't you assume the cat is isolated from the environment? It must be
if you say it later decoheres (even if later is only a nano second).
Why is this not a problem if, as you say, it is impossible to isolate
the cat? AG *
That it is impossible to isolate the cat is the source of the
absurdity...not that it exists in a superposition later.
*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.
*Other than slit experiments where superposition can be interpreted as
the system being in both component states simultaneously, why is this
interpretation extendable to all isolated quantum systems? AG *
?? Any system can be mathematically represented as being in a
superposition of different basis states. It's just a consequence of
being a vector in a vector space. Any vector can be written as a sum of
other vectors. Your use of the words "interpreted" and "this
interpretation" is unclear.
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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