| Topic: |
Science > Physics |
| User: |
"galathaea" |
| Date: |
24 Apr 2007 12:43:17 AM |
| Object: |
quantum randomness is BUNK |
On Apr 23, 12:06 pm, wrote:
In sci.physics.particle galathaea <galath...@gmail.com> wrote:
[...]
beables are the ontological component
of bohmian quantum fields
in bohmian theory
beables are interaction ontology
they are not particles
they are the realistic component of fields
with existents that may be measured and observed
through an "experiment" or "projection"
This is fine as an abstract, general description of the formalism. My
question, once again, is whether (and, if so, how) it can applied to
the concrete setting of interacting quantum field theory.
Let's take quantum electrodynamics, for example. To keep things
simple, you can restrict to the case that the only fields present are
the electron, the muon, and the photon. What, *specifically*, are
"the realistic component of fields" in this setting? They can't be
the fields themselves -- the field operators at different points don't
commute. As Bell explains in "Beables for Quantum Field Theory," they
can't be energy densities, for the same reason. Bell proposes fermion
number densities, but that fails when more than one species of fermion
is present; and even with only one species, it cannot distinguish between,
for example, a vacuum and and electron-positron pair in a given region.
The paper you cite, by Hyman et al., does not address this issue at
all, except to quote Bell's proposal (and, in fact, does not seem to
recognize the existence of more than one kind of fermion, replacing
Bell's fermion number with "the charge in each chunk, which is the
number of electrons minus the number of positrons in each chunk").
So, once again: if you think such a thing exists, why don't you pick
out the one paper that you feel best formulates a Bohmian quantum field
theory, in particular with a good treatment of particle creation,
annihilation, and interactions? Please note that I am *not* asking
about another reference to the general formalism, but rather one that
shows that it can be concretely implemented in an interacting quantum
field theory like QED.
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this is all classical bohmian theory
covered in, for instance, "the undivided universe"
chapter 11
now this paper shows a completely realist theory
which is also deterministic
exists for quantum fields of pretty arbitrary hamiltonian
It shows no such thing, because it does not address the *concrete*
questions of whether appropriate beables exist, how they can be
identified, and what the *specific* dynamics should be.
This is highly nontrivial for an interacting theory. Beables are
supposed to correspond to a set of commuting operators. Suppose you
choose two such operators, A(0) and B(0), at time t=0. It is easy to
check that unless they also commute with the Hamiltonian, A(0) and B(t)
will no longer commute with each other. Finding a set of operators in
an interacting theory that commute at all times is not some simple step;
it's not obvious that it's possible at all.
(Of course, if A and B commute with the Hamiltonian, there's no problem.
But this means that they're constants of motion, and searching for enough
constants of motion to give a good physical description in an interacting
field theory is a brave venture indeed.)
i am sorry you have a difficult time with the formalism
but it is something you have spend some time getting familiar with
as i mentioned in an earlier post
there is a history here
bohm was actually the first to present a realist field theory
but it applied only to bosons
his beable was the quantum field operator
that is all
1 beable
this corresponds to a similar idea in basic bohmian mechanics
that the only "beable" is position
the thing is you are assigning something existence
for almost all time
you can do it differently
you can take the basic beable to be momentum
and position just becomes another measured phenomena
but you always have to pick a commuting set
that is what you do with beables
they obviously can't be noncommutative
because that would violate the associated heisenberg inequality
which is a restriction on observables that can concurrently be real
with fermions
a different beable was chosen by bell when he bohminised
dagger
a a
the product of the annihilation / creation operators
aka the number operator over the fock space representation
####################..$$$$$$$$$$$$$$
i know you want a resource that would give you everything you want
so you can see the development all in one place
but there seem to be a lot of missing foundations
because the paper i presented
really does wrap up the question that was brought up in this thread
it really is a simple and clean resolution
of great generality
the problem is
you seem have very little familiarity with the topic
and yet keep posting assertions instead of asking questions
and it makes it hard for me to answer without getting upset at you
you have to understand
that some of your misunderstandings would seem quite naive
to those who actually are familiar with foundations research
you don't need noncommuting sets as you claimed
" Finding a set of operators
in an interacting theory
that commute at all times "
is indeed a simple step
you only need 1
_all_ bosonic fields can use the field operator
_all_ fermionic fields can use the number operator
done
different fields
different beables
now the first fermionic bohminisation
(bell)
was stochastic on a lattice
but deterministic versions of it have been around for years
and that was what was claimed
deterministic qft
the paper i gave is actually a very nice generalisation
that applies not just over fields of both statistics
but indeed is even more general in the hamiltonian
if you want to see a bohminisation
for the standard supermodel of 3+1
i can't point out resources
but i gave a huge string of resources earlier
and i might suggest
http://www.ensmp.fr/aflb/AFLB-291/aflb291p273.pdf
if you are truly going to be satisfied
seeing only QED bohminised
you will notice that it's title is
" beables in quantum electrodynamics "
it may clear up some of these issues you are having
with what the beables are in an "actual" field theory
and please understand this:
i can see you are interested enough to attempt to understand
and i appreciate that
but do not think your pretense of knowledge here
fools anyone knowledgable in foundations
or anyone willing to put the effort to understand the history
so you may want to change your tone
before you become more publicly foolish
-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-
galathaea: prankster, fablist, magician, liar
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| User: "" |
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| Title: Re: quantum randomness is BUNK |
24 Apr 2007 04:18:42 PM |
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In sci.physics.particle galathaea <galathaea@gmail.com> wrote:
[...]
bohm was actually the first to present a realist field theory
but it applied only to bosons
his beable was the quantum field operator
The quantum field operator at one position and time does not commute
with the quantum field operator at other positions and times.
Specifically, even for a free field (in TeX notation)
[\phi(x,t),\phi(x',t')] = i\Delta(x-x',t-t')
where Delta is the Schwinger function, which is *not* zero. See,
for example, Itzykson and Zuber, _Quantum Field Theory_, section
3-1-2, or Peskin and Schroeder, _An Introduction to Quantum Field
Theory_, section 2.4, or Roman, _Introduction to Quantum Field
Theory_, section 2.3, or
that is all
1 beable
this corresponds to a similar idea in basic bohmian mechanics
that the only "beable" is position
the thing is you are assigning something existence
for almost all time
you can do it differently
you can take the basic beable to be momentum
and position just becomes another measured phenomena
but you always have to pick a commuting set
that is what you do with beables
they obviously can't be noncommutative
because that would violate the associated heisenberg inequality
which is a restriction on observables that can concurrently be real
Right. Therefore, the field operator is *not* a beable.
[...]
_all_ bosonic fields can use the field operator
_all_ fermionic fields can use the number operator
The field operator at (x,t) does not commute with the field operator
at (x',t') unless the two points are spacelike separated. The number
operator is not conserved -- it does not commute with the Hamiltonian
-- so it also will not do as a beable; see the paper by Colin that
you cite below, p. 286.
So, once again, what are the beables for quantum field theory?
[...]
if you want to see a bohminisation
for the standard supermodel of 3+1
i can't point out resources
but i gave a huge string of resources earlier
and i might suggest
http://www.ensmp.fr/aflb/AFLB-291/aflb291p273.pdf
if you are truly going to be satisfied
seeing only QED bohminised
This is a nice paper. It concludes that "all the predictions
of the orthodox interpretation of quantum electrodynamics are
regained, if any measurement amounts to a measurement of the
charge density." But of course, as the authors recognize, it
is *not* the case that any measurement amounts to a measurement
of charge density. In an interaction e+ e- -> mu+ mu-, for
instance, the formalism of that paper can't distinguish the
initial and final states. Nor are there any beables associated
with photons in the paper.
Colin's paper is based on the pleasant coincidence that in QED
with only one species of fermion, fermion number density is
conserved and will do as an approximate stand-in for particle
location. This is no longer true when one has more than one
fermion species present.
[...]
and please understand this:
i can see you are interested enough to attempt to understand
and i appreciate that
but do not think your pretense of knowledge here
fools anyone knowledgable in foundations
or anyone willing to put the effort to understand the history
so you may want to change your tone
before you become more publicly foolish
This is an odd statement to hear from someone who believes that field
operators all commute.
Steve Carlip
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| User: "galathaea" |
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| Title: Re: quantum randomness is BUNK |
25 Apr 2007 01:12:25 AM |
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In article <f0ls7h$cma$1@skeeter.ucdavis.edu>,
carlip-nospam@physics.ucdavis.edu wrote:
!! In sci.physics.particle galathaea <galathaea@gmail.com> wrote:
!!
!! [...]
!! > bohm was actually the first to present a realist field theory
!! > but it applied only to bosons
!! > his beable was the quantum field operator
!!
!! The quantum field operator at one position and time does not commute
!! with the quantum field operator at other positions and times.
!! Specifically, even for a free field (in TeX notation)
!!
!! [\phi(x,t),\phi(x',t')] = i\Delta(x-x',t-t')
!!
!! where Delta is the Schwinger function, which is *not* zero. See,
!! for example, Itzykson and Zuber, _Quantum Field Theory_, section
!! 3-1-2, or Peskin and Schroeder, _An Introduction to Quantum Field
!! Theory_, section 2.4, or Roman, _Introduction to Quantum Field
!! Theory_, section 2.3, or
which is why the bosonic beable is not a particle
at least not in the treatment of bohm
though there are particle-like operators
that have been applied
these are not the field operators
at points on some manifold
which would offer a particle ontology
usually for bosonic beables
it is the functional field operator of the quantisation
in other words
not phi(x, t)
but Phi[phi(x, t)]
the fields are the dynamic variables
again
maybe i am being overly obtuse
but this is how most bohmian research formulates it
and again
you would understand if you take some time to study
this misunderstanding of yours
is explained in detail
in the first part of chapter 11
" the undivided universe "
bohm and hiley
**********..@@@@@@@
do you see why i might find this frustrating?
i know you are not stupid
steve
i read your 2001 survey on quantum gravity
shortly after it was made available online
and know you have put in the studytime
but you are wandering all over the place
trying to disprove something
you are not all that familiar with
do you know why you would do this?
you first came in
claiming that
" It's not at all clear, though, that a Bohmian
treatment can reproduce the results of quantum
field theory, which is where many of the most
precise tests exist. In particular, the Bohmian
picture has a very hard time dealing with particle
creation and annihilation. Even its most
enthusiastic proponents agree, I think, that in
this context a Bohmian model will not agree with QFT "
which i corrected by claiming that there were
many bohminisations of quantum field theory
that reproduce the predictions of the standard interpretation
not just one but plural
to which you responded
with a new challenge explicitly on determinism
above and beyond simply realist theories
" If you want to work on Bohmian mechanics
as a program that *might* eventually
lead to a deterministic alternative to QFT,
that's fine (though be careful of your citations
-- a number of the QFT models you've referred to
are explicitly *not* deterministic). But don't
confuse your hopes with what has actually
been shown to be possible. "
so it seemed you were acknowledging
that there are many models
but were concerned about the determinism
of the original thread
so i pointed you to
http://www.iop.org/EJ/article/0305-4470/37/44/L02/a4_44_l02.html
with the intent of finally putting to rest your claims
on annihilation/creation and determinism
in it
" A deterministic and time reversible Bohmian mechanics
for operators with continuous and discrete spectra is
presented. Randomness enters only through initial
conditions. Operators with discrete spectra are
incorporated into Bohmian mechanics by associating
with each operator a continuous variable in which a
finite range of the continuous variable corresponds
to the same discrete eigenvalue. In this way a
deterministic and time reversible Bohmian mechanics
can handle the creation and annihilation of particles.
The formalism does not depend on the details of the
Hamiltonian. Furthermore, many consistent choices are
available for the dynamics. Examples are given and
generalizations are discussed. "
and
" In this letter we introduce a non-stochastic,
deterministic, and time-reversible Bohmian mechanics
for any Hamiltonian and for any set of commuting beable
operators with discrete and/or continuous spectra. "
you objected that it had not demonstrated
the specific hamiltonian of quantum electrodynamics
introducing a new goalpost
somehow
without pointing to any mathematical error
you seemed to question the applicability
and needed proof that one could choose the right beables for QED
i asked you why you thought the hamiltonian in the proof
was not general enough to handle QED
you made claims that it was not possible to provide
the commutative set of beables
and that something vague about being fermionic only
so i point out that these comments
show a very big lack of understanding
in the foundational study of beables
in fermionic and bosonic fields
i gave you
http://www.ensmp.fr/aflb/AFLB-291/aflb291p273.pdf
to help clear up some of this
and show you how beables arise
here
" We show that it is possible to obtain a realistic
and deterministic model, based on a previous work
of John Bell, which reproduces the experimental
predictions of the orthodox interpretation of
quantum electrodynamics."
and he goes over some of the problems you were having
and now you come back
with all of this unrelated talk
about commutativity of the positional field operators
instead of the relevant functional field operator
and asking about photons???
????
? ?
?
?
?
?
?
you do see how you are hunting around
trying to find something
don't you?
and now you are admitting
- you don't understand bosonic bohmian theory
- you expected photons
- you don't understand bell's fermion-only approach
- you are willing to keep pretending
you have had one well developed objection
when in fact you just were unaware of literature
and to hide this you will wander around:
. they don't have a bohmian qft
. at least not deterministic
. well but not for QED
. hey this doesn't commute
. and where are the photons?
and of course
just to make sure you don't appear to be running out of objections
you'd also like to see how to interpret
+ - + -
e e --> u u
also indicating you didn't understand
how fermionic fields do have particles
and what all that chunk-charge stuff was about
even though the author of the latter paper
( colin )
is the one who gave the deterministic limit
that partly inspired the first paper
and they both discussed these developments
and you were the one
who stated so self-righteously
how you didn't want to let someone claim
to a forum that is not guaranteed to know the literature
my hopes as fact
the scary thing
steve
is that you are supposed to be a teacher
-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-
galathaea: prankster, fablist, magician, liar
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| User: "" |
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| Title: Re: quantum randomness is BUNK |
10 May 2007 07:42:31 PM |
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In sci.physics.particle galathaea <galathaea@veawb.coop> wrote:
In article <f0ls7h$cma$1@skeeter.ucdavis.edu>,
carlip-nospam@physics.ucdavis.edu wrote:
!! In sci.physics.particle galathaea <galathaea@gmail.com> wrote:
!!
!! [...]
!! > bohm was actually the first to present a realist field theory
!! > but it applied only to bosons
!! > his beable was the quantum field operator
!!
!! The quantum field operator at one position and time does not commute
!! with the quantum field operator at other positions and times.
!! Specifically, even for a free field (in TeX notation)
!!
!! [\phi(x,t),\phi(x',t')] = i\Delta(x-x',t-t')
!!
!! where Delta is the Schwinger function, which is *not* zero. See,
!! for example, Itzykson and Zuber, _Quantum Field Theory_, section
!! 3-1-2, or Peskin and Schroeder, _An Introduction to Quantum Field
!! Theory_, section 2.4, or Roman, _Introduction to Quantum Field
!! Theory_, section 2.3, or
which is why the bosonic beable is not a particle
at least not in the treatment of bohm
though there are particle-like operators
that have been applied
these are not the field operators
at points on some manifold
which would offer a particle ontology
usually for bosonic beables
it is the functional field operator of the quantisation
in other words
not phi(x, t)
but Phi[phi(x, t)]
the fields are the dynamic variables
Now I'm really confused. In
groups.google.com/group/talk.origins/msg/10a34dd3104d85e7?hl=en&
you wrote
bohm was actually the first to present a realist field theory
but it applied only to bosons
his beable was the quantum field operator
that is all
1 beable
and
" Finding a set of operators
in an interacting theory
that commute at all times "
is indeed a simple step
you only need 1
_all_ bosonic fields can use the field operator
_all_ fermionic fields can use the number operator
So, what's the beable?
Steve Carlip
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| User: "galathaea" |
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| Title: Re: quantum randomness is BUNK |
10 May 2007 08:48:39 PM |
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On May 10, 5:42 pm, wrote:
In sci.physics.particle galathaea <galath...@veawb.coop> wrote:
In article <f0ls7h$cm...@skeeter.ucdavis.edu>,
wrote:
!! In sci.physics.particle galathaea <galath...@gmail.com> wrote:
!!
!! [...]
!! > bohm was actually the first to present a realist field theory
!! > but it applied only to bosons
!! > his beable was the quantum field operator
!!
!! The quantum field operator at one position and time does not commute
!! with the quantum field operator at other positions and times.
!! Specifically, even for a free field (in TeX notation)
!!
!! [\phi(x,t),\phi(x',t')] = i\Delta(x-x',t-t')
!!
!! where Delta is the Schwinger function, which is *not* zero. See,
!! for example, Itzykson and Zuber, _Quantum Field Theory_, section
!! 3-1-2, or Peskin and Schroeder, _An Introduction to Quantum Field
!! Theory_, section 2.4, or Roman, _Introduction to Quantum Field
!! Theory_, section 2.3, or
which is why the bosonic beable is not a particle
at least not in the treatment of bohm
though there are particle-like operators
that have been applied
these are not the field operators
at points on some manifold
which would offer a particle ontology
usually for bosonic beables
it is the functional field operator of the quantisation
in other words
not phi(x, t)
but Phi[phi(x, t)]
the fields are the dynamic variables
Now I'm really confused. In
groups.google.com/group/talk.origins/msg/10a34dd3104d85e7?hl=en&
you wrote
bohm was actually the first to present a realist field theory
but it applied only to bosons
his beable was the quantum field operator
that is all
1 beable
and
" Finding a set of operators
in an interacting theory
that commute at all times "
is indeed a simple step
you only need 1
_all_ bosonic fields can use the field operator
_all_ fermionic fields can use the number operator
So, what's the beable?
i think your confusion lies in the fact that
there is a hesistancy in bohmian research
to use the term 'state vector'
instead one often sees
functional field operator
operator of the quantisation
or other terms used
the avoidance of the term 'state vector'
is because the state in bohmian mechanics
includes the ontology of beables
so the term is misleading in that interpretation
also the point is to specify that
_without_applying_a_particular_field_configuration_
the functional over fields is one potential beable for bosonic systems
( ie. a lambda abstraction is necessary)
as jim black stressed
and i pointed out earlier
questions of commutativity are trivial for 1 beable like this
if a_1 = a_2
a_1 a_2 = a_2 a_1
a single beable commutes with itself
and powers of itself
trivially
but there are always many choices of beables in bohmian mechanics
so your question doesn't make much sense
i've already pointed out the differences
between bohm's approach to qft and bell's approach
but there are many other methods of obtaining
an ontological realism for interacting quantum particles
some seek out principles of locality that can be maintained
some bring lorentz invariance to the ontological level
some bring particle ontologies to the bosonic fields
some are impulse ontologies
what beable is chosen
depends upon what properties one desires
for the underlying ontology of the theory
't hooft uses beables that exhibit local information loss
for instance
it is a very fertile theoretical framework
that many have argued is the only way to overcome
the ontological difficulties found in other quantum gravity approaches
-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-
galathaea: prankster, fablist, magician, liar
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| User: "Jim Black" |
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| Title: Re: quantum randomness is BUNK |
25 Apr 2007 10:17:39 PM |
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On Apr 24, 4:18 pm, wrote:
In sci.physics.particle galathaea <galath...@gmail.com> wrote:
[...]
bohm was actually the first to present a realist field theory
but it applied only to bosons
his beable was the quantum field operator
The quantum field operator at one position and time does not commute
with the quantum field operator at other positions and times.
Specifically, even for a free field (in TeX notation)
[\phi(x,t),\phi(x',t')] = i\Delta(x-x',t-t')
where Delta is the Schwinger function, which is *not* zero. See,
for example, Itzykson and Zuber, _Quantum Field Theory_, section
3-1-2, or Peskin and Schroeder, _An Introduction to Quantum Field
Theory_, section 2.4, or Roman, _Introduction to Quantum Field
Theory_, section 2.3, or
that is all
1 beable
this corresponds to a similar idea in basic bohmian mechanics
that the only "beable" is position
the thing is you are assigning something existence
for almost all time
you can do it differently
you can take the basic beable to be momentum
and position just becomes another measured phenomena
but you always have to pick a commuting set
that is what you do with beables
they obviously can't be noncommutative
because that would violate the associated heisenberg inequality
which is a restriction on observables that can concurrently be real
Right. Therefore, the field operator is *not* a beable.
I think you're misinterpreting this requirement. As I understand it,
the requirement is not that the set of all beables at all times be a
commuting set. The requirement is that given any time, the set of
beables at that time be a commuting set.
--
Jim E. Black
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| User: "" |
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| Title: Re: quantum randomness is BUNK |
10 May 2007 07:29:16 PM |
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In sci.physics.particle Jim Black <tramspap@yahoo.com> wrote:
[...]
I think you're misinterpreting this requirement. As I understand it,
the requirement is not that the set of all beables at all times be a
commuting set. The requirement is that given any time, the set of
beables at that time be a commuting set.
If I understand you correctly, you are describing an approach in which
one starts with the functional Schrodinger picture for quantum field
theory. (This was not obvious, since galathea's first appearance in
this thread, as far as I can tell, was in
groups.google.com/group/talk.origins/msg/e3bffc558ffc43d9?hl=en&
and started with the statement
bohmian mechanics is a completely consistent hidden variable model
that gives position and momentum to every particle at every time
and later, in groups.google.com/group/talk.origins/msg/a1b60f5d499b2b0d?hl=en&
bohm's theory is a completely deterministic quantum interpretation
it has an ontology
where there is a particle at a point in space at all times
that this set of locations is actually a trajectory
which is clearly very different from a functional Schrodinger picture, but
*is* a description of some other attempts to Bohmize QFT.)
Perhaps you can answer a question about this, then:
In standard QFT, there's a famous paper by Symanzik (Nucl. Phys. B190 (1981) 1)
that shows that to make sense of a functional Schrodinger picture in field
theory, you need an additional renormalization of the field operators. Do
you know if anyone has looked at this, or at renormalization in general, in
a Bohmian version?
Steve Carlip
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| User: "Jim Black" |
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| Title: Re: quantum randomness is BUNK |
11 May 2007 02:21:23 PM |
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On May 10, 7:29 pm, wrote:
In sci.physics.particleJim Black<trams...@yahoo.com> wrote:
[...]
I think you're misinterpreting this requirement. As I understand it,
the requirement is not that the set of all beables at all times be a
commuting set. The requirement is that given any time, the set of
beables at that time be a commuting set.
First, let me point out that my understanding is based almost entirely
on having had a look at Bell's "Beables for Quantum Field Theory."
If I understand you correctly, you are describing an approach in which
one starts with the functional Schrodinger picture for quantum field
theory.
In Bell's paper, that's definitely what he's doing. I suspect that
it's the same in the paper by Bohm about bosonic fields that Bell
references.
(This was not obvious, since galathea's first appearance in
this thread, as far as I can tell, was in
groups.google.com/group/talk.origins/msg/e3bffc558ffc43d9?hl=en&
and started with the statement
bohmian mechanics is a completely consistent hidden variable model
that gives position and momentum to every particle at every time
and later, in groups.google.com/group/talk.origins/msg/a1b60f5d499b2b0d?hl=en&
bohm's theory is a completely deterministic quantum interpretation
it has an ontology
where there is a particle at a point in space at all times
that this set of locations is actually a trajectory
which is clearly very different from a functional Schrodinger picture, but
*is* a description of some other attempts to Bohmize QFT.)
It sounds like Bohm's original, non-relativistic theory to me.
Perhaps you can answer a question about this, then:
In standard QFT, there's a famous paper by Symanzik (Nucl. Phys. B190 (1981) 1)
that shows that to make sense of a functional Schrodinger picture in field
theory, you need an additional renormalization of the field operators. Do
you know if anyone has looked at this, or at renormalization in general, in
a Bohmian version?
I have no idea.
--
Jim E. Black
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| User: "galathaea" |
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| Title: Re: quantum randomness is BUNK |
26 Apr 2007 09:42:22 AM |
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On Apr 25, 8:17 pm, Jim Black <trams...@yahoo.com> wrote:
On Apr 24, 4:18 pm, wrote:
In sci.physics.particle galathaea <galath...@gmail.com> wrote:
[...]
bohm was actually the first to present a realist field theory
but it applied only to bosons
his beable was the quantum field operator
The quantum field operator at one position and time does not commute
with the quantum field operator at other positions and times.
Specifically, even for a free field (in TeX notation)
[\phi(x,t),\phi(x',t')] = i\Delta(x-x',t-t')
where Delta is the Schwinger function, which is *not* zero. See,
for example, Itzykson and Zuber, _Quantum Field Theory_, section
3-1-2, or Peskin and Schroeder, _An Introduction to Quantum Field
Theory_, section 2.4, or Roman, _Introduction to Quantum Field
Theory_, section 2.3, or
that is all
1 beable
this corresponds to a similar idea in basic bohmian mechanics
that the only "beable" is position
the thing is you are assigning something existence
for almost all time
you can do it differently
you can take the basic beable to be momentum
and position just becomes another measured phenomena
but you always have to pick a commuting set
that is what you do with beables
they obviously can't be noncommutative
because that would violate the associated heisenberg inequality
which is a restriction on observables that can concurrently be real
Right. Therefore, the field operator is *not* a beable.
I think you're misinterpreting this requirement. As I understand it,
the requirement is not that the set of all beables at all times be a
commuting set. The requirement is that given any time, the set of
beables at that time be a commuting set.
it's probably more important
that he is misinterpreting the beable
taking operators of a field over the space
instead of the functional operator of the quantisation over fields
it is true though that this is parametrised separately by time
however
if we want to get completely technical
it is only necessary that the set is quasicommutative
although commutative sets are sufficient to be complete
there have been many algebraic investigations of beables
that have generalised the sufficient conditions
-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-
galathaea: prankster, fablist, magician, liar
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| User: "Jim Black" |
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| Title: Re: quantum randomness is BUNK |
27 Apr 2007 08:50:38 PM |
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On Apr 26, 9:42 am, galathaea <galath...@gmail.com> wrote:
On Apr 25, 8:17 pm,Jim Black<trams...@yahoo.com> wrote:
On Apr 24, 4:18 pm, wrote:
In sci.physics.particle galathaea <galath...@gmail.com> wrote:
[...]
bohm was actually the first to present a realist field theory
but it applied only to bosons
his beable was the quantum field operator
The quantum field operator at one position and time does not commute
with the quantum field operator at other positions and times.
Specifically, even for a free field (in TeX notation)
[\phi(x,t),\phi(x',t')] = i\Delta(x-x',t-t')
where Delta is the Schwinger function, which is *not* zero. See,
for example, Itzykson and Zuber, _Quantum Field Theory_, section
3-1-2, or Peskin and Schroeder, _An Introduction to Quantum Field
Theory_, section 2.4, or Roman, _Introduction to Quantum Field
Theory_, section 2.3, or
that is all
1 beable
this corresponds to a similar idea in basic bohmian mechanics
that the only "beable" is position
the thing is you are assigning something existence
for almost all time
you can do it differently
you can take the basic beable to be momentum
and position just becomes another measured phenomena
but you always have to pick a commuting set
that is what you do with beables
they obviously can't be noncommutative
because that would violate the associated heisenberg inequality
which is a restriction on observables that can concurrently be real
Right. Therefore, the field operator is *not* a beable.
I think you're misinterpreting this requirement. As I understand it,
the requirement is not that the set of all beables at all times be a
commuting set. The requirement is that given any time, the set of
beables at that time be a commuting set.
it's probably more important
that he is misinterpreting the beable
taking operators of a field over the space
instead of the functional operator of the quantisation over fields
Are you sure you're interpreting his post correctly? Or am I
misinterpreting you, perhaps? The operator $\hat{\phi}(x,t)$ is a
linear map from the Hilbert space of state vectors in quantum field
theory to itself, analogous to the position operator $\hat{x}$ in non-
relativistic one-particle quantum mechanics. These are things of
which we could ask, ``Do they commute?'' It seems to me that given $x
$ and $t$, $\hat{\phi}(x,t)$ would be an example of a suitable beable
for quantum field theory, and that $\{\hat{\phi}(x,t) : x \in
\mathbb{R}^3\}$ would be a suitable set of beables. (There's the
technicality that $\hat{\phi}(x,t)$ is a distribution, but that could
be easily taken care of by dividing $\mathbb{R}^3$ into small chunks,
and taking the integral of $\hat{\phi}(x,t)$ over a chunk to be a
beable.)
You write of the ``functional operator,'' which makes it seem to me
that you're referring to the state vector itself, expressed as a
complex-valued function (technically more of a distribution) taking
field configurations as arguments. But it wouldn't make any sense to
ask if two state vectors in the Hilbert space commuted with each
other.
--
Jim E. Black
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| User: "boson boss" |
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| Title: Re: quantum randomness is BUNK |
24 Apr 2007 05:49:26 PM |
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On Apr 24, 7:43 am, galathaea <galath...@gmail.com> wrote:
On Apr 23, 12:06 pm, wrote:
In sci.physics.particle galathaea <galath...@gmail.com> wrote:
[...]
beables are the ontological component
of bohmian quantum fields
in bohmian theory
beables are interaction ontology
they are not particles
they are the realistic component of fields
with existents that may be measured and observed
through an "experiment" or "projection"
This is fine as an abstract, general description of the formalism. My
question, once again, is whether (and, if so, how) it can applied to
the concrete setting of interacting quantum field theory.
Let's take quantum electrodynamics, for example. To keep things
simple, you can restrict to the case that the only fields present are
the electron, the muon, and the photon. What, *specifically*, are
"the realistic component of fields" in this setting? They can't be
the fields themselves -- the field operators at different points don't
commute. As Bell explains in "Beables for Quantum Field Theory," they
can't be energy densities, for the same reason. Bell proposes fermion
number densities, but that fails when more than one species of fermion
is present; and even with only one species, it cannot distinguish between,
for example, a vacuum and and electron-positron pair in a given region.
The paper you cite, by Hyman et al., does not address this issue at
all, except to quote Bell's proposal (and, in fact, does not seem to
recognize the existence of more than one kind of fermion, replacing
Bell's fermion number with "the charge in each chunk, which is the
number of electrons minus the number of positrons in each chunk").
So, once again: if you think such a thing exists, why don't you pick
out the one paper that you feel best formulates a Bohmian quantum field
theory, in particular with a good treatment of particle creation,
annihilation, and interactions? Please note that I am *not* asking
about another reference to the general formalism, but rather one that
shows that it can be concretely implemented in an interacting quantum
field theory like QED.
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this is all classical bohmian theory
covered in, for instance, "the undivided universe"
chapter 11
now this paper shows a completely realist theory
which is also deterministic
exists for quantum fields of pretty arbitrary hamiltonian
It shows no such thing, because it does not address the *concrete*
questions of whether appropriate beables exist, how they can be
identified, and what the *specific* dynamics should be.
This is highly nontrivial for an interacting theory. Beables are
supposed to correspond to a set of commuting operators. Suppose you
choose two such operators, A(0) and B(0), at time t=0. It is easy to
check that unless they also commute with the Hamiltonian, A(0) and B(t)
will no longer commute with each other. Finding a set of operators in
an interacting theory that commute at all times is not some simple step;
it's not obvious that it's possible at all.
(Of course, if A and B commute with the Hamiltonian, there's no problem.
But this means that they're constants of motion, and searching for enough
constants of motion to give a good physical description in an interacting
field theory is a brave venture indeed.)
i am sorry you have a difficult time with the formalism
but it is something you have spend some time getting familiar with
as i mentioned in an earlier post
there is a history here
bohm was actually the first to present a realist field theory
but it applied only to bosons
his beable was the quantum field operator
that is all
1 beable
this corresponds to a similar idea in basic bohmian mechanics
that the only "beable" is position
the thing is you are assigning something existence
for almost all time
you can do it differently
you can take the basic beable to be momentum
and position just becomes another measured phenomena
but you always have to pick a commuting set
that is what you do with beables
they obviously can't be noncommutative
because that would violate the associated heisenberg inequality
which is a restriction on observables that can concurrently be real
with fermions
a different beable was chosen by bell when he bohminised
dagger
a a
the product of the annihilation / creation operators
aka the number operator over the fock space representation
####################..$$$$$$$$$$$$$$
i know you want a resource that would give you everything you want
so you can see the development all in one place
but there seem to be a lot of missing foundations
because the paper i presented
really does wrap up the question that was brought up in this thread
it really is a simple and clean resolution
of great generality
the problem is
you seem have very little familiarity with the topic
and yet keep posting assertions instead of asking questions
and it makes it hard for me to answer without getting upset at you
you have to understand
that some of your misunderstandings would seem quite naive
to those who actually are familiar with foundations research
you don't need noncommuting sets as you claimed
" Finding a set of operators
in an interacting theory
that commute at all times "
is indeed a simple step
you only need 1
_all_ bosonic fields can use the field operator
_all_ fermionic fields can use the number operator
done
different fields
different beables
now the first fermionic bohminisation
(bell)
was stochastic on a lattice
but deterministic versions of it have been around for years
and that was what was claimed
deterministic qft
the paper i gave is actually a very nice generalisation
that applies not just over fields of both statistics
but indeed is even more general in the hamiltonian
if you want to see a bohminisation
for the standard supermodel of 3+1
i can't point out resources
but i gave a huge string of resources earlier
and i might suggest
http://www.ensmp.fr/aflb/AFLB-291/aflb291p273.pdf
if you are truly going to be satisfied
seeing only QED bohminised
you will notice that it's title is
" beables in quantum electrodynamics "
it may clear up some of these issues you are having
with what the beables are in an "actual" field theory
and please understand this:
i can see you are interested enough to attempt to understand
and i appreciate that
but do not think your pretense of knowledge here
fools anyone knowledgable in foundations
or anyone willing to put the effort to understand the history
so you may want to change your tone
before you become more publicly foolish
-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-
galathaea: prankster, fablist, magician, liar
Cases are created for crucial events that are taken from another type
of spectrum, randomness. But it probably won't be shown to be true.
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