On 7/31/2018 6:22 PM, [email protected] wrote:
On Wednesday, August 1, 2018 at 12:11:48 AM UTC, Brent wrote:
On 7/31/2018 2:43 PM, [email protected] <javascript:> wrote:
On Tuesday, July 31, 2018 at 7:14:53 PM UTC, Brent wrote:
On 7/31/2018 6:43 AM, [email protected] wrote:
On Tuesday, July 31, 2018 at 6:11:18 AM UTC, Brent wrote:
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]
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.
*But if you claim the cat decoheres in some exceedingly short
time based on decoherence theory and the wf you write taking
into account the apparatus, observer, and remaining
environment, mustn't the cat be initially isolated for this to
make sense? AG*
It never made sense. That it didn't make sense was Schroedinger's
point, he just didn't correctly identify where it first failed to
make sense, i.e. in the idea that a cat could be isolated. Since
the cat can't be isolated then |alive> and |dead> can only appear
in a mixture, not in a coherent superposition.
Brent
*
But when you include the cat in a superposition wf using decoherence
theory*
When you write that as a mathematical description you have written a
description that cannot apply to anything. Is it a description of
something? Sure. Does that something exist? No.
Weren't you the one complaining that Bruno falsely assumed every
mathematical structure exists?
Brent
*, you have a two state system using the standard interpretation of
superposition, meaning the system is in both states simultaneously,
not a mixed state. AG
*
*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.
*OK, never had a problem with this. AG**
*
Your use of the words "interpreted" and "this
interpretation" is unclear.
*I am using those words as I think Schroedinger did, where he
assumes a system in a superposition of states, is in all
component states simultaneously. It is from that assumption,
or interpretation, that he finds the contradiction or
absurdity of a cat alive and dead simultaneously. AG*
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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