Re: Why physicists should pay attention to the mind
- From: Hendrik van Hees <hees@xxxxxxxxxxxxx>
- Date: Thu, 2 Jun 2005 05:39:08 +0000 (UTC)
rof@xxxxxxxxxxxx wrote:
> Perhaps you are saying that there's a silent majority of physicists
> who would not disagree with the statement "The wavefunction describes
> the actual state of the system, rather than the experimenter's
> knowledge about it."
>
> Maybe; we would need to do a poll to find that out. Perhaps it's
> been done already?
In the German physics news group (de.sci.physik), we have a quite
similar debate. From the discussion there, I get the impression that
there are as many "interpretations" of the meaning of "state" as there
are physicists using quantum mechanics.
I myself became convinced of the socalled "Statistical Interpretation"
which is due to Ballentine, because it is a minimal interpretation. It
assumes only what is really needed to apply quantum theory to
expermenter's every-day experience with quantum systems in the lab
(especially in the realm of quantum optics, where many of the former
"gedanken experiments" can be realized as true experiments).
This interpertation, which is on my opinion very well summarized in
L. E. Ballentine, The Statistical Interpretation of Quantum Mechanics,
Rev. Mod. Phys. *42* (1970) 358
or in the book by the same author
L. E. Ballentine, Quantum Mechanics, (Publisher?)
It takes the Born interpretation *really* serious and identifies the
state (i.e., the ray in a Hilbertspace in the formal language of
quantum theory) only with its inherent statistical meaning about real
systems. This means the quantum state is not describing any kind of
physical entity of a single system but only the statistics of similarly
prepared ensembles of such single systems.
With this minimal interpretation, all the problems with "spooky actions
at a distance", inherent in the orthodox Copenhagen interpretation,
where the state is attached as a physical entity to a single system and
critisized by Einstein, Poldolsky and Rosen in their famous paper. In
fact, one can read this paper as a criticism of the Copenhagen
interpretation and not so much of quantum theory itself.
As an example take a maximally entangled photon pair in the Bell state
|Psi>=1/sqrt(2) [|Hx,Vy>+|Vx,Hy>],
where |Hx> stands for a horizontally polarized photon (one might think
of a wave packet) localized in a small region around x. |Hx,Vy> is the
corresponding two-photon state with one horizontally polarized photon
"at x" and a vertically polarized photon "at y".
The reduced state of the photon at x is the mixed state of maximal
uncertainty about the polarization, i.e., setting a polarization filter
at x in any direction, the photon goes with probability 50% through it
and is absorbed also with 50% probability.
But now make a polarization measurement at x (with the polarization
filter set to H-direction). Then one immediately knows that the photon
at y must be vertically (horizontally) polarized if the photon at y
went through the polarization filter (was aborbed by the polarization
filter). Note that in principle x and y can be arbitrarily far appart.
Within the statistical interpretation, there is no problem whatsoever
with this: The state is associated only with the ensemble of similarly
prepared photon pairs, and "reduction of the state" is not more than
making use of the knowledge of the entanglement of the photon pair,
(which was established long enough before the polarization measurement,
such that the two photons could travel far appart from each other, and
the front of the correspodning wave packet indeed only moves with the
speed of light and not faster) and the measurement of the polarization
of the photon at x. The photon at x interacts locally with the
polarization filter at x and photon y is not affected by this at all.
Although before the measurement, neither photon at a defined
polarization state, there was the correlation (a statistical notion!)
encoded in the entangled Bell state, which describes our statistical
knowledge about the outcome of measurements on an ensemble of similarly
prepared photons.
According to the statistical interpretation there is not more to states
than this statistical knowledge. Indeed, we cannot not prove that the
photon pairs are in the entangled state with a given "sufficient"
certainty, other than by making measurements at a large enough
ensembles of similarly prepared photon pairs. Measuring one pair and
seeing that indeed the correlation is fulfilled doesn't tell us much,
because it could be mere chance that the predicted correlation was
really fulfilled, but if we measure a lot of photon pairs, we can
improve the statistical evidence for those correlations, the better the
more photon pairs we measure.
Now, if one takes the orthodox Copenhagen point of view, that the state
(or the wave function) of the photon pair is a real physical entity of
this pair, the whole thing changes, because then the collapse has to be
taken as a physical process, and this means measuring the polarization
of the photon at x affects instantaneously the wave function of the
photon at y, indeed a "spooky action at a distance". On the other hand,
due to the only statistical meaning of states in quantum mechanics, we
can never prove this collapse as a real process, and thus it is well
justified to give up this Copenhagen philosophy (I'd even call it
esoterics) of "action at a distance".
Another question is now, whether "Quantum mechanics can be considered a
complete theory", and here my answer is simply: "We do not know (yet)."
One might consider quantum mechanics as incomplete, if one takes the
point of Einstein's, who considered a physical theory only complete, if
it describes real physical entities of each single system in question.
Then quantum mechanics, at least if taken in the minimal statistical
interpretation, is indeed incomplete, because it cannot describe a
single physical process.
On the other hand, it is quite unclear whether such a "complete"
description of nature is possible at all. At least local deterministic
theories are very unlikely since those would mean that there are
"hidden variables" which are just not known, and the quantum behavior
is due to a usual stochastic process. At least if we assume only local
interactions (and this assumption has lead to the great success of the
standard model of elementary particles!), such a stochastic
interpretation is ruled out since, if it was true, under any
circumstances the famous Bell inequalities had to hold. It was shown
with an overwhelming statistical significance that the Bell
inequalities are violated as quantum theory predicts.
On my opinion "solutions" of this dilemma like the de Broglie-Bohm
interpretation do not really solve the problem, because the "Bohm
trajectories", because then one introduces non-local interactions which
never have been observed at all, and the formulation of these
interpretations for relativistic quantum field theory is not settled
yet.
Whether there exists a theory, which is complete and "realistic" in
Einstein's narrow sense, is a still open question. On the other hand,
as long as we cannot disprove its existence (mathematically or
empirically), we may well be on the save side if we consider quantum
theory as an incomplete but extremely successful theory to describe our
knowledge about ensembles of quantum systems. Whether we can know more
about quantum systems (ast least in principle) than the statistical
predictions of quantum theory, can neither be ruled out nor justified
at the moment.
--
Hendrik van Hees Texas A&M University
Phone: +1 979/845-1411 Cyclotron Institute, MS-3366
Fax: +1 979/845-1899 College Station, TX 77843-3366
http://theory.gsi.de/~vanhees/ mailto:hees@xxxxxxxxxxxxx
.
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