🚀 go-pugleaf

jtwamley@physics.adelaide.edu.au (Jason Twamley) writes:

Greetings Jase :),

>Question:
>Assume the the while universe can be described by a quantum theory.ie. there
>exists a wave function for the universe. There have been a number of proposals
>for the quantum boundary conditions for this wavefunction at the begining of
>the universe.

My first remark would be that modern quantum cosmology doesn't use
a wavefunction, or even a density matrix. The alternative decohered
histories approach does not have an intermediate state in general (at
best a density matrix, which has many superselection sectors, and
thus describes, roughly, an ensemble of states). A single quantum
state, at best, has old-fashioned decoherence (loss of diagonal
terms in the Schroedinger picture density picture rather than the
Heisenberg picture decoherence functional) and thus reality is
a tad fuzzy.

If one of these boundary conditions succeed in specifiying
>a unique wavefunction what does this say concerning the uncertainty in the
>evolution of the everyday classical world and free will? Frequently the 
>wavefunction of the universe is called on to calculate the characteristics
>of large structures ie. inflation, density perturbations etc. However,
>in principle, how far can the information content of this wavefunction reach?
>Can it (is it suposed to?) describe the milk mixing in my tea? The standard
>probabalistic interpretation of QM is not clear here as we are attempting to
>describe the one universe by a single wavefunction and attempting to make
>predictions. Or is the Many-world description more appropriate?

Again, in generalized quantum mechanics, this has little meaning.
ADH, of course, supersedes many-worlds, but many worlds comes close
to the paradigm (As Jim Hartle likes to say, though, it's really
a many _histories_ interpretation). A single state probably lacks
the information for a realistic quantum cosmology.

>To put my
>question another way.. do the correlations contained in the quantum 
>cosmological boundary conditions contain all the information necessary to
>describe the complete future of the `classical' world deterministically?

<grin>, that's a hard one. That's the entire quasiclassical domain
problem, of course. You basically have to come up with a definition
of _classical_world_ first to answer that one. Do that, and we
can finally make generalized quantum mechanics into a real internal
QM interpretation scheme. In general, you _expect_ many quasiclassical
domains and thus many different histories for the universe. If we
had a SINGLE domain for our (generalized) quantum state, you could
almost say that we have a unique classical world. It's a little more
complicated that that, though, because further finegraining would
give you incompatible histories, and thus there's still a certain
quantum fuzziness in the system.

>Jason Twamley

				Steve Braham
--
| Name: Stephen P. Braham | Perversion: Quantum Cosmologist|
| Hangout: UBC physics    | Signature:  Euclidean          |
|          Vancouver, BC  |--------------------------------+
|          Canada         | E-mail: braham@physics.ubc.ca  |

In article <jtwamley.711766649@adelphi> jtwamley@physics.adelaide.edu.au (Jason Twamley) writes:
>Question:
>Assume the the while universe can be described by a quantum theory....
(Lots of stuff deleted here.  Let me summarize.)

The question, as I understand it, is this:  If we had a theory that predicted the
wavefunction of the Universe uniquely at time t=0, would that mean that the 
evolution of the Universe thereafter was completely deterministic?

Admittedly, we're in somewhat murky waters here, but I'll give an opinion.

No.  The indeterminism of quantum mechanics would still apply.  Let's suppose
that either the standard "collapse" interpretation or the so-called "many-worlds"
interpretation of quantum mechanics is right.  In the first case, observations
will (frequently) cause the collapse of the wavefunction, and this collapse
will be a nondeterministic event.  It is perhaps even more unclear than usual
what counts as an "observation" that can collapse this wavefunction, but the
fact that the wavefunction collapses under some circumstances is certain.

I'm not really up on the many-worlds interpretation, but my understanding of it
is that the evolution of the wavefunction is deterministic, but that the results
of any particular quantum experiment will still be random.  This is true whether
the wavefunction in question belongs to a single electron or the entire Universe.
If anybody wants to do a better job explaining this, be my guest.

-Ted
(ted@physics.berkeley.edu)

A quick comment on the role of the wavefunction/density matrix
in consistent histories (ala Hartle & Gell-Mann):
There is an initial condition (i.e. initial density operator) to be specified
in the decoherence functional.  The initial conditions will  determine in part
which histories decohere, and are quasi-classical.  The specific dynamics, and
choice of coarse graining will also be important.


A variation of this scheme included two density operators for both initial and
final conditions. This seemed to be an attempt to remove the apparent
introduction of time asymetry by hand. I hope the proposal has died a quiet and
painless death. :)

-mike gallis
mrg3@psuvm.psu.edu

In article <jtwamley.711766649@adelphi> jtwamley@physics.adelaide.edu.au (Jason Twamley) writes:
>Question:
>Assume the the while universe can be described by a quantum theory.ie. there
>exists a wave function for the universe. There have been a number of proposals
>for the quantum boundary conditions for this wavefunction at the begining of
>the universe. If one of these boundary conditions succeed in specifiying
>a unique wavefunction what does this say concerning the uncertainty in the
>evolution of the everyday classical world and free will? Frequently the 
>wavefunction of the universe is called on to calculate the characteristics
>of large structures ie. inflation, density perturbations etc. However,
>in principle, how far can the information content of this wavefunction reach?
>Can it (is it suposed to?) describe the milk mixing in my tea? 

I have seen various equations for the wavefunction of the universe
(these are rather speculative proposals of course) and none of them
seems to predict that you decided to have tea yesterday.  I will repeat
Gell-Man's joke to Hartle: "If you know the wavefunction of the
universe, why aren't you rich?"  Alas, the stock prices simply cannot be
derived from the wavefunction of the universe as given by quantum
cosmology, not even in principle.   This of course is not surprising: if
I know that the wavefunction of an electron is spin-up along the z axis,
I know very little about what to expect when I measure it's spin along
the x axis.  Any given wavefunction only gives sharp predictions for
observables for which it is almost an eigenfunction.

But as another poster pinted out, speaking of "the wavefunction of the
universe" is easily misleading.  People are busy trying to come up with
somewhat deeper ways of understanding quantum mechanics.  If I may make
my own suggestion (which I may regret), it would be to regard the
wavefunction (or more generally, density matrix) of a quantum system as
a mathematical model of what we know, or can imagine knowing, about the
state of the system.  From this we can calculate probabilistic answers
to questions.  "The wavefunction of the universe" as given by various
formulas in quantum cosmology is a proposal for what we might be
expected to know about the state of the universe knowing ONLY THE LAWS
OF PHYSICS and not having, say, bothered to take into account the fact that we
know the solar system exists, etc. etc..  Of course, this is rather
tautologous since the wavefunction of the universe as given by these
proposals would BE one of the laws of physics -- the "boundary
conditions" as opposed to the dynamical equations, roughly speaking.  

In any event, asking "what's the chance that Jason will make tea, pour
milk in it, and see the milk mix in the tea just like this, GIVEN the
information contained in the wavefunction of the universe" would be
quite hard to calculate, but we can imagine it would be possible once we made
ourselves much clearer about what counts as a "Jason" in the
language of elementary particle physics, what counts as "tea," "milk,"
"just so" etc..  The narrower we made our definitions of these terms the
lower the probability would be, but in any case, it would hardly be a
useful calculation.  

On the other hand, asking "what's the chance that the milk will mix in
the tea just like this, GIVEN that Jason makes tea and pours milk in it"
can (again throwing the practical difficulties to the winds) be
calculated from a wavefunction which models the situation in which you
make tea and pour in some milk.  The wavefunction, in short, is part of
mathematical formalism closely related to that of CONDITIONAL PROBABILITY in
probability theory.

I probably should have used the example of two electrons colliding,
rather than Jaons pouring milk in his tea, because the latter brings in
all sorts of red-herring issues like whether we can ever define complex
events precisely enough to do sensible calculations about them from
first principles.  So it would be better to ponder "what's the chance
that an atom of gold will form, given this proposal for a wavefunction
of the universe" -- already too hard to answer in practice.

In article <braham.711770201@physics.ubc.ca> braham@physics.ubc.ca (Stephen Braham) writes:

>My first remark would be that modern quantum cosmology doesn't use
>a wavefunction, or even a density matrix. The alternative decohered
>histories approach does not have an intermediate state in general (at
>best a density matrix, which has many superselection sectors, and
>thus describes, roughly, an ensemble of states). 

What do you mean by an "intermediate state"?

By the way, lots of mathematicians use "state" to refer both to pure
states (typically represented by unit vectors in Hilbert space) and
mixed states (aka density matrices).

What is the most lucid and interesting single reference on the
alternative decohered histories approach?  I've read a bit about it but
could stand some more.

jbaez@riesz.mit.edu (John C. Baez) writes:

>In article <braham.711770201@physics.ubc.ca> braham@physics.ubc.ca (Stephen Braham) writes:

>> [stuff by me deleted]

>What do you mean by an "intermediate state"?

>By the way, lots of mathematicians use "state" to refer both to pure
>states (typically represented by unit vectors in Hilbert space) and
>mixed states (aka density matrices).

Yes, I'd better be careful- I used state in that sense later. I'm
really talking about an intermediate density matrix or wavefunction
here, vs. a more general quantum state (or quantum description
of the system). By intermediate, I mean intermediate in time, i.e.,
between 'measurements.' In ADH, we try to give meaning to just
HISTORIES, and we bury the idea of a density matrix or wavefunction
at a particular time. For a _Hamiltonian_ ADH (which isn't general
enough for quantum cosmology, probably), one can go to a generalized
approach with both final and initial conditions, and you get a system
that cannot be described by a density matrix at any intermediate time,
but is fully predictive. Wehn the final state density matrix is
just the identity, you get back to pretty standard Copenhagen
style Hamiltonian quantum mechanics, and you can almost say that
each projection operator IS a Cophenhagen style collapse. I prefer
Jim's way of looking at it though, in which you say that you're
looking at a purely conditional question, and the collapse is
nothing except the standard conditional probability rule. This
shouldn't be confused with the _dynamical_ collapse of the
wavefunction, induced by decoherence processes- that's a statement
on a Shroedinger picture density matrix, and ADH is a lot more
general than that.

>What is the most lucid and interesting single reference on the
>alternative decohered histories approach?  I've read a bit about it but
>could stand some more.

Ewww, hard one. I think I'll have to give you two, because things
are in flux, and Gell-Mann and Hartle are redefining their
concept of quasiclassical domains. The Jerusalem Winter School (1989)
notes are probably the best single description, they're in
Quantum Cosmology anb Baby Universes, ed. S. Coleman, J. B. Hartle and
T. Piran (World Scientific, Singapore, 1990). The later, modified,
stuff is Alternative Decohering Histories in Quantum Mechanics,
UCSBTH-90-56.

			Steve 
--
| Name: Stephen P. Braham | Perversion: Quantum Cosmologist|
| Hangout: UBC physics    | Signature:  Euclidean          |
|          Vancouver, BC  |--------------------------------+
|          Canada         | E-mail: braham@physics.ubc.ca  |

<MRG3@psuvm.psu.edu> writes:
> [some stuff deleted]

>A variation of this scheme included two density operators for both initial and
>final conditions. This seemed to be an attempt to remove the apparent
>introduction of time asymetry by hand. I hope the proposal has died a quiet and
>painless death. :)

HEY! <grin> It's quite a useful thing to do- it's more of an example
than anything though. The idea it to try to understand what we may
or may not get out of, say, a sum-over-histories, formulation of
quantum cosmology. There are ways of formulating the path integral
in such as way that you have, effectively, both past and future
conditions. You can simulate the effect in old-fashioned Hamiltonian
quantum mechanics by adding the final density matrix in. It IS useful
in certain circumstance, though. Tony leggett and others (including
my boss :)) have pointed out that you CAN do time-symmetric experiments
and you need this insertion of final conditions to get the right result.
In this situation, you have no density matrix at intermediate times
that can describe probabilities- you NEED the final condition part.
Tony's hoping to verify this with his squid experiments, of course.
Hmmmm, the reference part of this posting now has three members of
the same PhD graduating class in it <chuckle>. Go lions! <grin>

>-mike gallis
>mrg3@psuvm.psu.edu

			Steve

--
| Name: Stephen P. Braham | Perversion: Quantum Cosmologist|
| Hangout: UBC physics    | Signature:  Euclidean          |
|          Vancouver, BC  |--------------------------------+
|          Canada         | E-mail: braham@physics.ubc.ca  |

MRG3@psuvm.psu.edu writes:
>A quick comment on the role of the wavefunction/density matrix
>in consistent histories (ala Hartle & Gell-Mann):
>There is an initial condition (i.e. initial density operator) to be specified
>in the decoherence functional.  The initial conditions will  determine in part
>which histories decohere, and are quasi-classical.  The specific dynamics, and
>choice of coarse graining will also be important.

This is interesting.  I assumed that the initial density operator was
in fact a partial description of some pure state, unknown because of
our ignorance of the microscopic variables-- like an ensemble of experiments
repeatedly performed in which controllable variables interact with a
complicated environment.  You get a diagonal density matrix for the
macroscopic variables after decoherence, but in this view the state
after any one measurement would actually be some unknown superposition of
the various eigenstates of the measured observable, with the density
matrix giving average results.  Someone recently mentioned that in 
quantum cosmology, though, there might be such a thing as a truly mixed
state-- that the universe might be describable only by a density matrix,
not a single state vector or wave function.  Is this related to the idea
of degrees of freedom disappearing behind event horizons?  What does
it mean?  Am I babbling?

-- 
Matt McIrvin   mcirvin@husc.harvard.edu   Long live short .sigs

Hi everyone...glad to see there are people interested in discussing these
topics...:

John and Stephen both emphasize the conditional probability interpretation
given to the density matrix or decohereing histories formulation of
quantum cosmology. However, in QM the density matrix contains not only our
ignorance of the details of the ensembe but also the QM uncertainty. Even,
if we can enumerate completely the position and momentum of every particle of
the tea and cup and surrounding enviroment to the limit imposed by the 
uncertainty principle we still cannot proceed deterministically... can we?
Also...when Steve admits a final and initial density matrix in the ADH what
exactly is fixed uniquely? Is it that collection of 
quasi-classical coarse grained histories which maximize the information 
content (ie. most finely grained histories compatible with quasi-classisity).
If this collection is not unique then we do not have complete prediction
of these histories. Also.. these histories presumably refer to suitably gross
collective coordinates ie. the path of a football through the air... if I
decide to ask ADH about the evolution of coordinates of a molecule of leather
in this football then ADH looses a degree of predictive power as we may be
going beyond that above mentioned  quasi-classically-optimised graining.


Jason

---------------------------------------------------------------------------
Jason Twamley                            | "WHY must I treat the measuring
Univ. of Adelaide Math. Physics          | device classically??  What will
GPO Box 498, Adelaide                    | happen to me if I don't??"
South Australia 5001                     |       -- Eugene Wigner
jtwamley@physics.adelaide.edu.au         
                                         

braham@physics.ubc.ca (Stephen Braham) writes:

>shouldn't be confused with the _dynamical_ collapse of the
>wavefunction, induced by decoherence processes- that's a statement
>on a Shroedinger picture density matrix, and ADH is a lot more
>general than that.
                                          ^^^^^^^^^^^^^^^^^^^^^^

Hmmmm... I have head it said that ADH may be too restrictive for any
system to match up to the Gell-Mann Hartle (GMH) criterion of quai-classical.
Even Omnes believes that the GMH decoherence criterion is too tough...
It must be checked in some actuall models.. Halliwell and Dowker 
(FERMILAB-PUB-92-44-A, CTP # 2071) have
ploughed through some awfull calculations for a very simple system of
a free particle coupled to a thermal bath (the Caldeira-Leggett model)
and have found that the histories do not decohere (ala ADH) completely
but to the extent that they do they seem to be peaked around the
classical paths in (x,p) phase space. But this is perhaps one of the
simplest models one can have and also there are still ambiguties
concerning how does one quantify how good the decoherence is, the
concept of peaking about the classical path, etc. How model dependent
are the results? Another model using ADH with inflation shows no
decoherence  whatsoever (in preperation). Harmonic oscillators, while
the testbed for many theories, possess many special properties not
found in even slightly more complicated models. 

Jason

Matt (mcirvin@husc8)writes:
>MRG3@psuvm.psu.edu writes:
>>A quick comment on the role of the wavefunction/density matrix
>>in consistent histories (ala Hartle & Gell-Mann):
>>There is an initial condition (i.e. initial density operator) to be specified
>>in the decoherence functional.  The initial conditions will determine in part
>>which histories decohere, and are quasi-classical. The specific dynamics, and
>>choice of coarse graining will also be important.

>This is interesting.  I assumed that the initial density operator was
>in fact a partial description of some pure state, unknown because of
>our ignorance of the microscopic variables-- like an ensemble of experiments
>repeatedly performed in which controllable variables interact with a
>complicated environment.  You get a diagonal density matrix for the
>macroscopic variables after decoherence, but in this view the state
>after any one measurement would actually be some unknown superposition of
>the various eigenstates of the measured observable, with the density
>matrix giving average results.  Someone recently mentioned that in
>quantum cosmology, though, there might be such a thing as a truly mixed
>state-- that the universe might be describable only by a density matrix,
>not a single state vector or wave function.  Is this related to the idea
>of degrees of freedom disappearing behind event horizons?  What does
>it mean?  Am I babbling?

You are certainly not babbling, but suffer from a cultural bias in the way
QM is generally taught.:)  Generally, when the density matrix is introduced,
it is in terms of some level of ignorance (unknown measurement results, quantum
entanglement with other systems, etc.). While this may be a useful viewpoint
at first, I tend to think it results in confusion in the long run.
QM can be expressed solely in terms of density operators, without ever
referring to a state vector.  A pure state is merely a minimum entropy
density operator.  Evolution of isolated systems (in normal QM) is unitary
and preserves entropy (i.e. pure states stay pure), although alternatives
to standard QM, such as Quantum Mechanics with Spontanious Localization,
have nonunitary evolution(where we can only say entropy is nondecreasing).
In open quantum systems, there has a great deal of work done on
phenomenological evolution equations.  When you start looking at
quantum open systems, or variants of the Schroedinger equation, paying
attention to things like "where did the information go" is distraction and
irrelevant (unless you are considering foundational issues). I think a
fairly good intro to density operators can be found in von Neuman's
Mathematical Foundarions  of Quantum Mechanics.

 The effective dynamics of an  open quantum system tend to
reduce the coherence terms of the density operator of the
system of interest.  They don't go away in a finite time, rather, the
the decoherence decays away (hopefully exponentially) with time.
The density operator can never be diagonal in a continuous
basis (such as position): it would not be normalizable.
Decoherence and the "superselection" are necessarily
approximate.
  With regards to quantum coherence down the wormhole:
This strikes me as just another open quantum system with inaccessible
regions (to the observable universe, as opposed to the entire universe).
A minor point is that it is not degrees of freedom that go down the wormhole,
but rather, there is quantum entanglement between degrees of fredom (field
amplitudes) out here and degrees of freedom down in there.
There is still no dynamical mechanism for collapsing the wave function.

mike gallis
mrg3@psuvm.psu.edu

jtwamley@physics.adelaide.edu.au (Jason Twamley) writes:

>braham@physics.ubc.ca (Stephen Braham) writes:

>>shouldn't be confused with the _dynamical_ collapse of the
>>wavefunction, induced by decoherence processes- that's a statement
>>on a Shroedinger picture density matrix, and ADH is a lot more
>>general than that.
>                                          ^^^^^^^^^^^^^^^^^^^^^^

>Hmmmm... I have head it said that ADH may be too restrictive for any
>system to match up to the Gell-Mann Hartle (GMH) criterion of quai-classical.
>Even Omnes believes that the GMH decoherence criterion is too tough...

Well, the definition of a quasiclassical domain is VERY strong, and
classicality is being redefined. I tend to lean towards the approximate
decoherence ideas, but that causes LOTS of problems (the statements
that Gell-Mann and Hartle make really do need EXTENSIVE improvement).
I'm presently spending time worrying about that, in fact. My biggest
worry is that you then seemed to be forced into needing an interpretation
of the off-diagonal elements in the decoherence functional. These
are NOT connected to the off-diagonal elements in the density matrix,
by the way- old-fashioned S-picture decoherence and ADH are produced
by similar effects (state squeezing, primarily), or so it seems, but
they are very different creatures in reality.


>Jason
		Steve

--
| Name: Stephen P. Braham | Perversion: Quantum Cosmologist|
| Hangout: UBC physics    | Signature:  Euclidean          |
|          Vancouver, BC  |--------------------------------+
|          Canada         | E-mail: braham@physics.ubc.ca  |

MRG3@psuvm.psu.edu writes:

> [stuff deleted]

>QM is generally taught.:)  Generally, when the density matrix is introduced,
>it is in terms of some level of ignorance (unknown measurement results, quantum
>entanglement with other systems, etc.). While this may be a useful viewpoint
>at first, I tend to think it results in confusion in the long run.
>QM can be expressed solely in terms of density operators, without ever
>referring to a state vector.  A pure state is merely a minimum entropy
>density operator.  Evolution of isolated systems (in normal QM) is unitary
>and preserves entropy (i.e. pure states stay pure), although alternatives
>to standard QM, such as Quantum Mechanics with Spontanious Localization,
>have nonunitary evolution(where we can only say entropy is nondecreasing).
>In open quantum systems, there has a great deal of work done on
>phenomenological evolution equations.  When you start looking at
>quantum open systems, or variants of the Schroedinger equation, paying
>attention to things like "where did the information go" is distraction and
>irrelevant (unless you are considering foundational issues). I think a
>fairly good intro to density operators can be found in von Neuman's
>Mathematical Foundarions  of Quantum Mechanics.


Yes, at, in some sense, ADH goes even further; once you define everything
in terms of decoherence functionals, you can even get rid of the
idea of a density matrix, or the concept of a state at a given time.
It's this that interests us in QC, of course, where time is a dirty
word.

> The effective dynamics of an  open quantum system tend to
>reduce the coherence terms of the density operator of the
>system of interest.  They don't go away in a finite time, rather, the
>the decoherence decays away (hopefully exponentially) with time.
>The density operator can never be diagonal in a continuous
>basis (such as position): it would not be normalizable.
>Decoherence and the "superselection" are necessarily
>approximate.

Exactly, and this connects up with an earlier statement by Jase on
the difficulty is getting perfectly decohered histories. Approximate
decoherence seems to be the way to go, but it's hard to QUANTIFY
it. I really worry that coarse graining may not preserve approximate
decoherence (unlike perfect decoherence). We can almost see what
needs to be done in the old density matrix, S-picture, type decoherence,
but, as I said in another post, the ADH off-diagonal terms are not
really connect to the off-diagonal terms in the effective density
matrix (when that matrix exists, which, in general, it doesn't).
There's a DYNAMICAL connection- the same squeezing together of the
trajectories in the configuration space path integral produces
both types of decoherence, but that's not enough for an _interpretation_.
It helps, though :).

>  With regards to quantum coherence down the wormhole:
>This strikes me as just another open quantum system with inaccessible
>regions (to the observable universe, as opposed to the entire universe).
>A minor point is that it is not degrees of freedom that go down the wormhole,
>but rather, there is quantum entanglement between degrees of fredom (field
>amplitudes) out here and degrees of freedom down in there.
>There is still no dynamical mechanism for collapsing the wave function.

Oh goody, I get to be in wormie mode for a bit; yeah, I know tend to
believe that wormies don't help as much in that regard. On the other hand,
I think we're pushing our paradigm a little far when we talk about
information going down 'em- it's hard to give them a physical meaning
outside the Euclidean path integral, and the interpretation of THAT
is getting tougher. At a certain point, I'd go along with Jim Hartle
and say let's define QM _by_ the decoherence functional, and forget
about fields at a particular time.

>mike gallis
>mrg3@psuvm.psu.edu

			Steve

--
| Name: Stephen P. Braham | Perversion: Quantum Cosmologist|
| Hangout: UBC physics    | Signature:  Euclidean          |
|          Vancouver, BC  |--------------------------------+
|          Canada         | E-mail: braham@physics.ubc.ca  |