On 8/1/2018 1:50 PM, agrayson2...@gmail.com wrote:
On Wednesday, August 1, 2018 at 4:41:02 AM UTC, agrays...@gmail.com
wrote:
On Wednesday, August 1, 2018 at 2:09:45 AM UTC, Brent wrote:
On 7/31/2018 6:22 PM, agrays...@gmail.com wrote:
On Wednesday, August 1, 2018 at 12:11:48 AM UTC, Brent wrote:
On 7/31/2018 2:43 PM, agrays...@gmail.com wrote:
On Tuesday, July 31, 2018 at 7:14:53 PM UTC, Brent
wrote:
On 7/31/2018 6:43 AM, agrays...@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 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.
*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.
*I am just applying the standard interpretation to a
superposition. Nothing more. Probabilities are calculated
differently for superpositions vs mixed states. In the former,
there are interference terms arising from the inner product with
the wf itself, and each eigenstate (and then calculating the
norm-squared). Mixed states probabilities are, I believe, just the
normed squared of the amplitude of each of component state
separately. In any event, when one sees the PLUS sign between the
component states, one generally means a standard superposition,
not a mixed state, unless otherwise informed. So the two-state
superposition in decoherence theory which includes the cat must be
a standard superposition, and Schroedinger believed that the
standard interpretation was that the system is in both states
simultaneously, thus leading to his cat paradox. What
interpretation do you assume for this superposition if not
Schroedinger's? Are you writing a superposition of something that
doesn't exist? AG*
Weren't you the one complaining that Bruno falsely assumed
every mathematical structure exists?
*Yes Brent, it was me, but I was objecting to the assumption that
every mathematical structure and prediction exists AFTER I gave
examples where this hypothesis is falsified, such as plane waves and
advanced waves in E&M. But in the case we're discussing, the two state
wf written in decoherence theory for the cat problem, the wf is
specifically given to represent a physical system consisting of cat*
And Conan Doyle specifically gave descriptions of an English detective.
*, detector, radioactive source, and remaining environment. If it
doesn't represent anything as you now claim, ISTM we're in woo-woo
land. I mean, you're asserting a wf which has no discernible meaning
or interpretation. *
Where did I assert that?
*If the cat is always in a mixed state, discussing decoherence times
in the context of this wf make no sense, at least to me. But if you
insist on this, mustn't the overall wf be a mixed state, making the
radioactive source, and so forth, also mixed states? *
An atom can be in a superposition of decayed and not decayed because it
is relatively isolated. It doesn't radiate IR photons or have other
interactions with the environment. Haven't you read Schlosshauer's
paper yet?
Brent
*AG*
*
Unrelated to this issue AFAICT. If the superposition with the cat
used as a starting point for your decoherence analysis doesn't
exist as representing anything, it's baffling that any conclusions
can be reached. OTOH, if the two component states are mixed,
that's a fact that seems never in evidence, certainly not in what
I have read about decoherence theory. AG *
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
*
*Isn't this the standard interpretation of a superposition of
states? 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*
...
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