Bohm interpretation
Ulmo
If the Bohm interpretation of quantum mechanics is supposed to be
based on hidden variables, then why is it not totally refuted by
Bell's Inequality and the Aspect Experiment?
David
backdoorstudent
ul...@cheerful.com (Ulmo) wrote in message news:<53ca460a.0407...@posting.google.com>...
Because it allows nonlocal influences via a quantum potential. Bell's
theorem refutes local hidden variables theories, i.e., ones that claim
quanta are in a single state prior to measurement.
Although Bohm's theory is completely deterministic, one could not
exploit the quantum potential to transmit information instantaneously.
Nevertheless, it does not fit together very well with relativistic
physics which is it's main problem.
alistair
backdoo...@yahoo.com (backdoorstudent) wrote in message news:<750f5e99.04072...@posting.google.com>...
> ul...@cheerful.com (Ulmo) wrote in message news:<53ca460a.0407...@posting.google.com>...
> Nevertheless, it does not fit together very well with relativistic
> physics which is it's main problem.
Alistair writes:
The Pilot wave in Bohm's theory can change instantaneously throughout
its length.This is probably one reason why his theory does not go well
with relativity.But can the behaviour of the Pilot wave be modified?
backdoorstudent
alis...@goforit64.fsnet.co.uk (alistair) wrote in message news:<861c1b21.0407...@posting.google.com>...
In the case of an EPR pair the position phase space is 6 dimensional.
You can see how this can get ridiculously complex with multiple
particles. In Bohm's theory the "hidden variables" are the actual
positions of particles - the instantaneous (why it's hard to make
lorentz invariant) values of which give the quantum potential.
> But can the behaviour of the Pilot wave be modified?
Yes. Start here:
http://www.google.com/search?q=relativistic+bohmian+mechanics
People have come up with similar theories that don't assume the same
kind of particle trajectories:
http://arxiv.org/abs/quant-ph/0403156
Igor
alis...@goforit64.fsnet.co.uk (alistair) wrote in message news:<861c1b21.0407...@posting.google.com>...
IIRC, any hidden variable theory that is compatible with QM has to
have superluminal transfer of information at some level. That would
seem to be what puts it at odds with relativity.
Frank Hellmann
ul...@cheerful.com (Ulmo) wrote in message news:<53ca460a.0407...@posting.google.com>...
The right way to think about Bohm is as a MWT where the particle keeps
track of what branch we are on (it doesn't quite make sense
epistemologically since Bohmians on every branch would assume the
particle is with them, but that's how the mathematics of the theory
look).
It is however, a many worlds interpretation where all the results of
an experiment do exist. The so called hidden variable in Bohms theory
contains no physics, and furthermore and more importantly, it is not
local therefore it doesn't fit under Bell's inequality which rules out
local hidden variable theories.
cheers,
frank
backdoorstudent
thoo...@excite.com (Igor) wrote in message news:<d434b6c6.04072...@posting.google.com>...
> IIRC, any hidden variable theory that is compatible with QM has to
> have superluminal transfer of information at some level.
Not necessarily. It only has to have the same nonlocality as ordinary
QM which is simply a fact of nature. In the case of Bohm's theory the
"information" is in principle unattainable so it is irrelevant whether
it is superluminal or not.
Nonlocality does not necessarily mean superluminal information
transfer. This has been discussed here many times before.
kurious
Can Bohm's theory shed any new light on the problem of
unifying quantum mechanics and general relativity?
------------------------------------------------------------------------
This post submitted through the LaTeX-enabled physicsforums.com
To view this post with LaTeX images:
http://www.physicsforums.com/showthread.php?t=36368#post266788
kurious
Ulmo:
If the Bohm interpretation of quantum mechanics is supposed to be
based on hidden variables, then why is it not totally refuted by
Bell's Inequality and the Aspect Experiment?
Kurious:
Here's a discussion of Bohm's theory in which it
is mentioned that John Bell pointed out that his theorem did not
rule out Bohm's theory and that Bohm welcomed the
result's of Alain Aspect's experiments on non-locality.
http://www.uncletaz.com/library/scimath/pilotwave.html
------------------------------------------------------------------------
This post submitted through the LaTeX-enabled physicsforums.com
To view this post with LaTeX images:
http://www.physicsforums.com/showthread.php?t=36368#post266778
Franz Heymann
"kurious" <alis...@goforit64.fsnet.co.uk> wrote in message
news:kurious...@physicsforums.com...
>
> Can Bohm's theory shed any new light on the problem of
> unifying quantum mechanics and general relativity?
No. It does not concern itself with gravity at all. It is quite
simply an attempt at a causal and deterministic interpretation of
quantum mechanics.
Franz
Igor
That's interesting. Wasn't it deBroglie that came up with the pilot
wave theory in the first place? I think he sometimes referred to it
as the theory of double solution, because he basically interpreted one
solution as the quantum probability wave, whereas the other one was a
more physical notion of a guiding or "pilot" wave that actually told
the particles how to move. And additionally, wasn't deBroglie using
the relativistic Klein-Gordon equation (or perhaps the Dirac) to
demonstrate his points? I remember reading some of his early papers
on the subject, but it has been a while now. I do know that Bohm
began referring to the pilot wave model in later papers, but I don't
recall him mentioning it in his first papers on hidden variables from
1952.
Igor
backdoo...@yahoo.com (backdoorstudent) wrote in message news:<750f5e99.04072...@posting.google.com>...
Yeah, I hear what you saying, but I don't think I really understand
it. Frankly, I've never understood how you can have a nonlocal theory
that does not have any kind of superluminal connection. I know it has
been demonstrated again and again that the basis of QM is nonlocal.
But how can you explain how information is transferred that has that
characteristic, yet is not superluminal in nature?
backdoorstudent
thoo...@excite.com (Igor) wrote in message news:
> That's interesting. Wasn't it deBroglie that came up with the pilot
> wave theory in the first place?
Yes. Curiously, both Einstein and Bohr thought of the idea as well
(even before deBroglie, I think), but did not work out any details.
And then Bohr went on to give up believing in objective reality :)
> I think he sometimes referred to it
> as the theory of double solution, because he basically interpreted one
> solution as the quantum probability wave, whereas the other one was a
> more physical notion of a guiding or "pilot" wave that actually told
> the particles how to move. And additionally, wasn't deBroglie using
> the relativistic Klein-Gordon equation (or perhaps the Dirac) to
> demonstrate his points?
I'm not sure, but if so I can see why Bohm's version became more
popular.
> I remember reading some of his early papers
> on the subject, but it has been a while now. I do know that Bohm
> began referring to the pilot wave model in later papers, but I don't
> recall him mentioning it in his first papers on hidden variables from
> 1952.
I think Bohm's name has stuck to it because his presentation was so
straight-forward. It's just a quantum Hamilton-Jacobi equation from
which you can easily get Schrodinger's eq., yet it's free of
metaphysical duality and ambiguous division of the world into observed
and unobserved.
backdoorstudent
"Franz Heymann" <notfranz...@btopenworld.com> wrote in message news:<ce3s6c$6u7$8...@hercules.btinternet.com>...
All these people would disagree you, Franz:
http://www.google.com/search?q=bohmian+quantum+gravity
backdoorstudent
thoo...@excite.com (Igor) wrote in message news:<d434b6c6.04072...@posting.google.com>...
> backdoo...@yahoo.com (backdoorstudent) wrote in message news:<750f5e99.04072...@posting.google.com>...
> > thoo...@excite.com (Igor) wrote in message news:<d434b6c6.04072...@posting.google.com>...
> > > IIRC, any hidden variable theory that is compatible with QM has to
> > > have superluminal transfer of information at some level.
> >
> > Nonlocality does not necessarily mean superluminal information
> > transfer. This has been discussed here many times before.
>
>
> Yeah, I hear what you saying, but I don't think I really understand
> it. Frankly, I've never understood how you can have a nonlocal theory
> that does not have any kind of superluminal connection. I know it has
> been demonstrated again and again that the basis of QM is nonlocal.
> But how can you explain how information is transferred that has that
> characteristic, yet is not superluminal in nature?
That has what characteristic? What do you mean exactly by
"information"? Quantum nonlocality refers to the perfect correlations
(or anti-correlations) between outcomes of measurements. But because
the outcomes are random there is no information being transmitted,
i.e., there is no causal connection.
This means that you could not modulate a signal between entangled
streams of particles; the intrinsic randomness makes for only noise
which is the opposite of information.
Now, many people wonder why these correlations are perfect over
spacelike (and even timelike) separations. But superluminosity is the
most likely incorrect answer. Perhaps the answer has nothing to do
with spacetime? Or maybe it means superdeterminism? Or maybe it means
something our cognition is incapable of grasping? Sadly, we can only
speculate at this point.
Perhaps in the future (or the present :) physicists will look back on
all this as nonsense.
Igor
And another really big question is just how would you actually define
timelike and spacelike separations over N-body configuration space?
That seems to be where the non-local properties tend to sneak into
Bohm's theory in the first place.
Franz Heymann
"backdoorstudent" <backdoo...@yahoo.com> wrote in message
news:750f5e99.0407...@posting.google.com...
The complete exposition of Bohm's interpretation of quantum mechanics
is contained in the book "The Undivided Universe", by Bohm and Hiley.
Neither of the words "gravity" or "gravitation" occur in the index.
Incidentally, it is not a "theory", in the sense that it makes no
predictions for experiments which may support it and at the same time
negate any other presently accepted theory. It offers only an
interpretation of quantum mechanics.
Furthermore, there is no quantum theory of gravity yet,
Franz
backdoorstudent
"Franz Heymann" <notfranz...@btopenworld.com> wrote in message news:<ce8ujo$dv0$1...@sparta.btinternet.com>...
> The complete exposition of Bohm's interpretation of quantum mechanics
> is contained in the book "The Undivided Universe", by Bohm and Hiley.
Much more has been done by many different people since that book was
published. So it cannot be considered the "complete exposition".
Follow some of those links I posted.
> Incidentally, it is not a "theory", in the sense that it makes no
> predictions for experiments which may support it and at the same time
> negate any other presently accepted theory.
Why are you so sure that it makes no predicitons that are different
from textbook quantum mechanics?
Urs Schreiber
news:750f5e99.04072...@posting.google.com...
There are two aspects of Bohm's approach.
The first is the observation that the complex Schroedinger equation is
_equivalent_ to two real equations, one being a continuity equation, the
other being the classical Hamilton-Jacobi equation corrected by a term
proportional to hbar.
This is just a mathematical truth and not even a very deep one. And it
applies to all systems, to the single nonrelativistic particle, the single
relativistic Klein-Gordon particle, to the first quantized string, to (even
relativistic) field theory, to anything. (Recall that the Hamiltonian of
field theory describes the propagation of a single point in the space of all
field configurations.). It also applies to theories where the Hamiltonian is
a constraint. This is why somebody managed to find links which talk about
Bohmian quantum cosmology, because there we have the Wheeler-deWit equation
which is nothing but a Hamiltonian constraint.
So this first aspect is just ordinary quantum mechanics/quantum field theory
written in a somewhat unusual way. By the very nature of equivalence, this
alone cannot change anything about QM/QFT at all!
The second aspect is that the above mathematical truth makes people wonder
if it is maybe telling them something. And if it is telling them something,
they ask, is it maybe suggestive of certain modification of quantum
mechanics that they should consider?
One should be very carefule here.
In any case the answer to your question is:
As long as one is only concerned with Bohm's equivalent rewriting of the
Schroedinger equation, there cannot, by the very meaninng of the word
'equivalent', be any distinction to textbook quantum mechanics.
If, on the other hand, Bohm's equivalent rewriting of the Schroedinger
equation inspires you to make all kinds of changes to textbook quantum
mechanics, then, of course, there will in general be differences. But then
you are also probably walking on Feynman's blind alley.
I know of (only) two examples where people inspired by Bohm's reformulation
have actually produced something potentially insteresting, which is not
crazy from the outset.
That's first Edward Nelson, who has identified the conditions on a
stochastic process to be governed preciely by Bohm's two real equations. For
those who can read german a review can be found here:
http://www-stud.uni-essen.de/~sb0264/stochastic.html .
Note that this is again a mathematical truth which is only suggestive of a
reinterpretation of QM.
Then there is Lee Smolin, who claims to have identified an interesting model
which actually reproduces a stochastic process with the strange property
that Nelson identified. Namely he claims that the eigenvalues of certain
ensembles of large matrices are described by such a strange stochastic
process. This can be found discussed here:
http://xxx.uni-augsburg.de/abs/hep-th/0201031 .
I know only one further person whose opinion on these matters I would
readily take serious:
backdoorstudent
"Urs Schreiber" <Urs.Sc...@uni-essen.de> wrote in message news:<41091d6b$1...@news.sentex.net>...
> I know of (only) two examples where people inspired by Bohm's reformulation
> have actually produced something potentially insteresting, which is not
> crazy from the outset.
>
> That's first Edward Nelson, who has identified the conditions on a
> stochastic process to be governed preciely by Bohm's two real equations. For
> those who can read german a review can be found here:
>
> http://www-stud.uni-essen.de/~sb0264/stochastic.html .
>
Didn't Nelson develop his Stochastic Mechanics independently from and
at the same time as Bohm?
> I know only one further person whose opinion on these matters I would
> readily take serious:
>
> http://golem.ph.utexas.edu/string/archives/000400.html .
What's his opinion?
Are you aware of this guy?
http://arxiv.org/find/quant-ph/1/au:+Floyd_E/0/1/0/all/0/1
And these guys?
http://arxiv.org/find/hep-th/1/AND+au:+faraggi+au:+matone/0/1/0/past,all/0/1?
backdoorstudent
> _equivalent_ to two real equations, one being a continuity equation, the
> other being the classical Hamilton-Jacobi equation corrected by a term
> proportional to hbar.
>
> This is just a mathematical truth and not even a very deep one.
>
> written in a somewhat unusual way. By the very nature of equivalence, this
> alone cannot change anything about QM/QFT at all!
Yes, but I think you're missing the point. It's not just "this alone".
Mathematically equivalent does not mean physically equivalent. It
depends on with what you identify the terms. In textbook quantum
mechanics the only physically real terms are eigenvalues. In the case
of Bohm's theory particles and waves are each physically real, and
trajectories of particles are physically real. And this is also where
people started tacking on supplementary mathematical details which is
the second aspect you mentioned. I'm not saying they're right - just
that they're physically different. Or am I missing the point?
Franz Heymann
>
>
> "Franz Heymann" <notfranz...@btopenworld.com> wrote in message
news:<ce8ujo$dv0$1...@sparta.btinternet.com>...
> > The complete exposition of Bohm's interpretation of quantum
mechanics
> > is contained in the book "The Undivided Universe", by Bohm and
Hiley.
>
> Much more has been done by many different people since that book was
> published. So it cannot be considered the "complete exposition".
> Follow some of those links I posted.
Yes. But that would not be Bohm's interpretation. Much of that
exists only as unrefereed pseudo-publications.
>
> > Incidentally, it is not a "theory", in the sense that it makes no
> > predictions for experiments which may support it and at the same
time
> > negate any other presently accepted theory.
>
> Why are you so sure that it makes no predicitons that are different
> from textbook quantum mechanics?
Read Bohm and Hiley "The Undivided Universe".
The Bohm interpretation does not present a new theory at all. It
simply reorganises the Schrodinger equation in order to interpret it
anew. It still retains quantum mechanics as we know it. It is only
an interpretation of quantum mechanics, in the same sense as the
Copenhagen interpretation is only an interpretation of quantum
mechanics and not an independent theory.
Franz
kurious
Franz Heymann:
>The Bohm interpretation does not present a new theory at all. It
>simply reorganises the Schrodinger equation in order to interpret it
>anew.
Kurious:
The Bohm interpretation is a new theory because the pilot wave
physically
pushes particles around.There is no such interaction in standard
quantum mechanics.
------------------------------------------------------------------------
This post submitted through the LaTeX-enabled physicsforums.com
To view this post with LaTeX images:
http://www.physicsforums.com/showthread.php?t=36368#post272100
Franz Heymann
"kurious" <alis...@goforit64.fsnet.co.uk> wrote in message
news:kurious...@physicsforums.com...
>
>
>
> Franz Heymann:
> >The Bohm interpretation does not present a new theory at all. It
> >simply reorganises the Schrodinger equation in order to interpret
it
> >anew.
>
> Kurious:
>
> The Bohm interpretation is a new theory because the pilot wave
> physically
> pushes particles around.There is no such interaction in standard
> quantum mechanics.
The Bohm approach does not lead to a prediction of the outcome of any
experiment which can distinguish it from predictions of quantum
theory. It is therefore categorically not a new theory.
For exactly the samr reason, the Copenhagen interpretation is not a
theory. It is an interpretation of a pre-existing theory. The Bohm
interpretation is yet another interpretation of quantum theory.
Franz
Aaron Denney
On 2004-08-12, kurious <alis...@goforit64.fsnet.co.uk> wrote:
>
>
>
> Franz Heymann:
>>The Bohm interpretation does not present a new theory at all. It
>>simply reorganises the Schrodinger equation in order to interpret it
>>anew.
>
> Kurious:
>
> The Bohm interpretation is a new theory because the pilot wave
> physically pushes particles around. There is no such interaction in
> standard quantum mechanics.
Well, yes, but any actual measurements get the same results as standard
quantum theory. The particles being pushed around by the pilot waves
have no "back-reaction" on the pilot waves, nor do they affect each
other, so they might as well not be there.
--
Aaron Denney
-><-