On 7/31/2018 2:43 PM, agrayson2...@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 <javascript:> 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
*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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