On 8/1/2018 2:57 PM, agrayson2...@gmail.com wrote:
On Wednesday, August 1, 2018 at 9:36:18 PM UTC, Brent wrote:
On 8/1/2018 1:50 PM, agrays...@gmail.com <javascript:> 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.
*Is this supposed to be a meaningful reply? I have no idea how this
relates to our discussion. AG *
Specifically giving a a wf to represent a physical system doesn't mean that it does.
*, 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? *Here; your words!Brent: 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.*
So I referred back to "that" wf as not applying to anything. How does that comport with, "*...you're asserting a wf which has no discernible meaning or interpretation." *I'm /*not*/ asserting a wf.
Brent**
* AG* *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 photonsor have othseer interactions with the environment.*I know that, of course. But if you have an eigenstate consisting of several tensor products and one is a mixed state, such as the cat,and the others not, is the overall eigenstate pure or mixed?Is it even an eigenstate? don't think you can legitimately write such an "eigenstate". You can write it of course, you can write anything, but how is it interpreted? AG*Haven't you read Schlosshauer's paper yet? *Irrelevant. AG * 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* ... --You received this message because you are subscribed to the Google Groups "Everything List" group. To unsubscribe from this group and stop receiving emails from it, send an email to everything-list+unsubscr...@googlegroups.com <mailto:everything-list+unsubscr...@googlegroups.com>. To post to this group, send email to everything-list@googlegroups.com <mailto:everything-list@googlegroups.com>.Visit this group at https://groups.google.com/group/everything-list. For more options, visit https://groups.google.com/d/optout.
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