2-slit puzzle in Bohm's "The Undivided Universe"
Norman D. Megill
Consider the two-slit experiment.
In the various single photon interference experiments that have been
carried out, the results have always been that if a detection mechanism
is included which can indicate which path the photon has taken the
interference pattern vanishes.
Now consider Bohm's interpretation. As I understand it, Bohm's
hidden-variable theory is a mathematically valid alternative
non-relativistic interpretation of quantum mechanics. (It is nonlocal
of course but that should not be relevant here.)
According to Bohm's interpretation, a photon is a classical-like
particle that will *actually* go through either slit A or slit B and not
both. The interference results from photons being guided by a "quantum
potential" field established by the geometry of slits A and B. Now, if
you look at sample trajectories in Fig. 3.1, p. 33 of Bohm/Hiley's _The
Undivided Universe_ (you may have to look at the book to understand what
I'm talking about), you will see that the quantum potential, in addition
to providing the interference effect, also seems to act in effect as an
"invisible barrier" that prevents a photon entering slit A from ever
crossing over to the B side and vice-versa:
| | | | photons | | | |
| | | | | | | | | | |
v v v v v v v v v v v
A B
------------| |------------| |-------------
...---------------------------> <-------------------------... target
photons from slit A always photons from slit B always
hit the target here hit the target here
(according to Bohm) (according to Bohm)
(look at Fig. 3.1 in "The Undivided Universe")
I don't have a mathematical proof of the invisible barrier effect, but
it seems "obvious" from Bohm's figure - the particle trajectories
scrunch up if they get too close to the middle and never cross over each
other.
Now, according to this model, and if this invisible barrier conjecture
is correct, we don't *need* a a detection mechanism to indicate which
path the photon has taken. We know it apriori -- if the photon landed
to the left of the middle, it passed through slit A; if it landed to the
right of the middle it passed though slit B. It is that simple.
So, we can observe the interference pattern *and* have knowledge of
a photon's path simultaneously.
Is this at odds with the standard (Copenhagen) interpretation, or am
I overlooking something?
Thanks.
--Norm
Michael Röschter
The interpretation is fine. It does not conflict quantum mechanics.
The reason being that it's completely useless, that is, it does not make
any verifiable propositions. You may also assume that photons from the
left slit always go to the right or any other pattern you like. It makes
no difference in observation.
A word about Bohm: He is the Don Quichote of quantum mechanics (please
don't misunderstand this, setting up alternative theories of the quality
Bohm does is a honorable task), but did not succeed in creating an
alternative theory with a more then philosophic value. The real value of
his scientific work is the fact that he has been exploring a universe of
alternatives and showing that they are no real alternatives that can
stand an experimental test.
A much better test (though are more difficult to understand one) is
Bells inequivilance. It rules out practically all hidden variable
theories of the simple type given in the two slit experiment.
A rough description can be found in the FAQ:
http://math.ucr.edu/home/baez/physics/faq.html
Michael
Norman D. Megill
Michael =?iso-8859-1?Q?R=F6schter?= <mic...@roeschter.de> wrote:
>The interpretation is fine. It does not conflict quantum mechanics.
>The reason being that it's completely useless, that is, it does not make
>any verifiable propositions. You may also assume that photons from the
>left slit always go to the right or any other pattern you like. It makes
>no difference in observation.
Extrapolating from the sample trajectories in figure in _Undivided
Universe_, it seems photons from the left slit cannot go to the right in
Bohm's model. That is my point.
I agree I don't have a mathematical proof of this - perhaps the sample
trajectories shown don't show cases of photons from the left slit going
to the right - but it certainly looks that way based on the ones shown.
>A much better test (though are more difficult to understand one) is
>Bells inequivilance. It rules out practically all hidden variable
>theories of the simple type given in the two slit experiment.
Bell's inequality rules out *local* hidden variable theories, but it
doesn't rule out Bohm's.
--Norm
JoJo Ramone
> I overlooking something?
This _is_ at odds with the Copenhagen interpretation, but only at an
ontological level. The fact still remains that the particular slit the
photon went through can never be directly determined experimently. If you
believe Bohm than you can, in a sense, infer which slit the photon passed
through but this is not the same as actually measuring the slit through
which the photon passed.
Now if ever an experiment was devised that could experimentally determine
that Bohm's ideas are closer to reality than the Copenhagen ideas than one
could use the Bohm theory to infer with confidence which slit the photon
passed through, but until the theories are experimentally differentiated
such inferences are more or less leaps of faith.
I would like to say, however, that this is an interesting point you brought
up. I missed it one my first reading through "Undivided Universe". I'm
actually a bit surprised that the book does not draw attention to this
point. Mabye the author go into more detail in the original journal papers.
Another interesting result is the barrier penetration or tunneling effect
(fig. 5.3, p.77). Here it is clearly shown that only the particles in the
leading edge of the wavepacket penetrate through the barrier. Once again
there is a clear division between the outcome (tunneling/reflection, like
left/right side of slits) and the initial situation (leading/trailing edge
of wavepacket, like left/right slit). This again is at odds with Copenhagen
but implies no experimentally measurable difference.
Michael Röschter
>
> >A much better test (though are more difficult to understand one) is
> >Bells inequivilance. It rules out practically all hidden variable
> >theories of the simple type given in the two slit experiment.
>
> Bell's inequality rules out *local* hidden variable theories, but it
> doesn't rule out Bohm's.
>
Nnonlocal hidden variables are possible. But, all so called paradoxes of
quantum mechanics are due to nonlocal effects. So in which way does a
"deterministic" theory with non local hidden variables offer any
advantage over quantum mechanics (at least on a philosophical, or
metaphysical level)?
Michael
JoJo Ramone
> "deterministic" theory with non local hidden variables offer any
> advantage over quantum mechanics (at least on a philosophical, or
> metaphysical level)?
Hidden variable theories, like Bohm/Hiley theory, does not need a
wavefunction collapse. By assigning particles definite position and
momenta, even if they are unmeasurable in principle, like hidden variable
theories do there is no longer a 'measurement' problem or wavefunction
collapse paradox. The double slit experiment, for example, is complete
expained in the Bohm/Hiley theory, along with the fact that the particles
seem to interfer with themselves as they pass through the slits yet are
always detected as a point object.
Hidden variable theories must be, as was previously mentionned, inherently
non-local to accurately describe nature. This, however, is not a draw back
but rather a necessity. The standard quantum theory is non-local and
experimental violation of Bell's inequality shows us that nature seems to be
non-local. Discarding a hidden variable theory because of its non-local
nature is truly a step backwards.
mjacobs
all right already. I've heard enough about this. since QM gives correct
results and special relativity gives correct results how can one imply
that the other is wrong? It is a real puzzlement. .
"JoJo Ramone" <jojor...@hotmail.com> wrote in message
news:eQiN4.145573$1C2.3...@news20.bellglobal.com...
Gerry Quinn
>
>all right already. I've heard enough about this. since QM gives correct
>results and special relativity gives correct results how can one imply
>that the other is wrong? It is a real puzzlement. .
QM has problems with general rather than special relativity. Basically,
GR is a classical theory of gravity, and the proper quantum theory to
replace it has not yet been devised.
Special relativity has no problems with QM once it is construed as
referring only to information-carrying influences, where information is
defined with respect to an observer.
Obviously this raises some philosophical questions, but in any case
those inclined towards realism will reject the conventional metaphysical
interpretation of relativity irrespective of QM.
- Gerry Quinn
mjacobs
What is your defintion of 'information'? Can an electron or a photon send a
a message 'hey buddy I just passed through slit one youd better no go
through slit two which happens to be on the other side of the solar system.
"Gerry Quinn" <ger...@indigo.ie> wrote in message
news:iSTO4.9047$sB3....@news.indigo.ie...
Gerry Quinn
>
>What is your defintion of 'information'? Can an electron or a photon send a
>a message 'hey buddy I just passed through slit one youd better no go
>through slit two which happens to be on the other side of the solar system.
Like I said, to achieve compatability between QM and SR, information
must be defined in terms of what an observer will measure. Questions
about what one electron says to another are excluded.
There are various ways to interpret what one electron says to another.
Your description is similar to the Bohm interpretation. While the
conversation of the electrons in this interpretation is faster than
light, it is not counted as being the sort of communication that SR is
about.
- Gerry Quinn
mjacobs
So you think Im taking Bohm's interpretation of SR Well it was Einseins
interpretation too and we all know he was proved to be wrong and Bohr was
proved to be right. I am content to be wrong along with Albert . After all
Einstein didnt know that much about relativity anyway. As I said it is a
puzzlement."Gerry Quinn" <ger...@indigo.ie> wrote in message
news:6WdP4.9266$sB3....@news.indigo.ie...
Gerry Quinn
>
>So you think Im taking Bohm's interpretation of SR Well it was Einseins
>interpretation too and we all know he was proved to be wrong and Bohr was
>proved to be right. I am content to be wrong along with Albert . After all
>Einstein didnt know that much about relativity anyway. As I said it is a
>puzzlement.
Hang on - Bohm's interpretation is not usually taken to be wrong as
such, although it is pretty unfashionable these days. And Einstein's
disagreement with Bohr was about realism more than locality, though to
be sure all these issues are linked.
What I am saying is that everyone accepts that even if Bohr's
interpretation is taken as true, communication within the 'pilot wave'
is not considered subject to a speed limit of c.
There are other concepts, such as the Many Worlds interpretation and the
Transactional interpretation, that give you something more closely
approaching a modified form of locality.
If you want to be a realist, you must accept that SR is a theory of
measurement. Only then can the two worldviews coexist. Operationalism
is the metaphysical claim that the measured is the same as the real
(there may be some variant formulations, but that is the nub of it).
Don't confuse the operationalist metaphysics projected by a lot of
people with the formulae that they interpret in terms of this
metaphysics. The formulae are fine, but you need to pick one way to
interpret any formulae that you are juxtaposing.
Trying to reconcile Bohr's interpretation of QM with SR's claim that no
information can go faster than light is an instance of mixing two
different ways of looking at the world. Bohr is talking about a reality
that underlies measurement, but if you want to talk about SR and Bohr
together you must consider SR to talk only about measurement. And it
works great, but it isn't able to say anything about the pilot wave.
mjacobs
If we agree that pilot wave communciation is not subject to a speed limit
then there is no problem. In that case we can just accept Bohm as gospel and
all our problems are solved. In any case your statement that there is 'no
problem' with the compatibility of QM and SR seems needs to be reformulated.news:0RSP4.9794$sB3....@news.indigo.ie...
Gerry Quinn
>
>If we agree that pilot wave communciation is not subject to a speed limit
>then there is no problem. In that case we can just accept Bohm as gospel and
>all our problems are solved. In any case your statement that there is 'no
>problem' with the compatibility of QM and SR seems needs to be reformulated.
Not all our problems, because not everybody is happy with Bohm.
But I don't think the statement needs to be reformulated. Every
interpretation of QM can be made compatible with SR by separating out
the realist aspects from the operationalist aspects. Any problems come
only from mixing two sorts of metaphysics.
- Gerry Quinn
mjacobs
. The basic axiom of QM (that the wave function is a complete description
of the state of the system) is inconsistent with the basic axiom of SR that
faster than light causal influences are possible. EPR was correct in saying
therefore that QM is incomplete if SR (as conceived by Einstein) is to be
believed. No amount of philosophical obfuscation can change that. Bohm
theory is predicated on an exemption for his pilot wave . So all that it
does is reduce the question to are there any exceptions to SR .I think we
have covered all this so I am going to quit now.
"Gerry Quinn" <ger...@indigo.ie> wrote in message
news:pGlQ4.10279$sB3....@news.indigo.ie...
Michael Kagalenko
]>
]>If we agree that pilot wave communciation is not subject to a speed limit
]>then there is no problem. In that case we can just accept Bohm as gospel and
]>all our problems are solved. In any case your statement that there is 'no
]>problem' with the compatibility of QM and SR seems needs to be reformulated.
]
]Not all our problems, because not everybody is happy with Bohm.
]
]But I don't think the statement needs to be reformulated. Every
]interpretation of QM can be made compatible with SR by separating out
]the realist aspects from the operationalist aspects. Any problems come
]only from mixing two sorts of metaphysics.
Gerry Quinn contributes another helping of his bogus pseud0scientific garbage.
*yawn* Go away, crackpot.