Amara Graps wrote:
If one adopts a Bayesian approach to probability, then the
Schroedinger wave equation simply becomes a posterior
probability describing our incomplete information about
the quantum system, rather than wave functions that
collapse in reality upon our observation. It could clear up
a lot of confusion.
Good point!
Heisenberg wrote (1958): "The laws of nature which we
formulate mathematically in quantum theory deal
no longer with the particles themselves but with our
knowledge of the elementary particles. ...
The conception of objective reality ... evaporated into the ...
mathematics that represents no longer the behavior
of elementary particles but rather our knowledge
of this behavior." He also wrote (1960): "The act of recording,
on the other hand, which leads to the reduction of the state,
is not a physical, but rather, so to say, a mathematical process.
With the sudden change of our knowledge also the mathematical
presentation of our knowledge undergoes of course
a sudden change".
Many more, along this path, i.e.:
Jerome Rothstein (1951) who wrote that "Wave functions contain
the information obtainable about a system from operational specification
of its preparation or measurement and describe ensembles consistent
therewith rather than single systems"
http://www.mpiwg-berlin.mpg.de/staff/segal/thesis/thesehtm/chap5/ch5btxt.htm
http://faraday.uwyo.edu/emeriti/tgrandy/infophys/node17.html
Cerf and Adami
http://arxiv.org/abs/quant-ph/9806047
http://arxiv.org/abs/quant-ph/9605039
http://arxiv.org/abs/quant-ph/9605002
Rovelli
http://arxiv.org/abs/quant-ph/9609002
Mermin
http://arxiv.org/abs/quant-ph/9609013
http://arxiv.org/abs/quant-ph/9801057
Zeilinger
http://info.uibk.ac.at/c/c7/c704/qo/philosop.html
http://www.ap.univie.ac.at/users/Anton.Zeilinger/philosop.html
http://spiro.fisica.unipd.it/usr/rmarco/philosophy.html
But why this mathematical representation of "our knowledge"
is characterized by complex quantities? We know that Wigner's
time reversal operator changes the sign of the imaginary part
of the state-vector elements. Thus, the complex nature of
the state-vector may be a manifestation of its time structure.
Is Born's probability law telling us that the probability of a particular
observation is linked to the time reverse of a state-vector component?
In the paper below (about Clifford algebra) there is
something that might be about this question (ch. 5).
http://arxiv.org/abs/quant-ph/9906040
In Sheldon Goldstein's site there is an interesting debate.
http://www.math.rutgers.edu/~oldstein/papers/qtwoe/qtwoe.html
- Anton Zeilinger says that the very austerity of the Copenhagen
interpretation, unsurpassed by that of any other interpretation,
speaks very much in its favor. Its basic attitude toward the
fundamental role of observation represents a major intellectual
step forward over naive classical realism. The revolutionary new
feature of quantum physics arises whenever there is no way,
not even in principle, to tell which of various possibilities is the
case. Then, instead of just having to acknowledge our ignorance,
as we would have to in classical physics, quantum superposition
comes in as a qualitatively new property. If the condition above
should ever be realizable for the dead and live states of Schroedinger's
cat (1), its quantum state has to be a superposition of these states.
That clearly does not mean the cat is both alive and dead.
It means only that no definite statement can be made concerning
the question of whether the poor animal is alive or dead.
Upon observation, we will find it in either state and thus the state
assigned to the cat collapses into either possibility. It is not at all
surprising that we have to change the representation of our knowledge
if that knowledge changes because of information obtained by
observation of the cat. The collapse of the state vector can be seen
only as a ``measurement paradox'' if one views this change of the
quantum state as a real physical process. In the extreme, it is often
even claimed that something happens to the cat because it is being
observed.
- But Goldstein asks: Does Zeilinger truly believe that ``quantum mechanics
is about information''? Information is always information about something.
Therefore, shouldn't quantum mechanics then be regarded as being
about that something? And does Zeilinger really wish to deny that the
change of the state vector that occurs during the measurement process
is ``a real physical process,'' even when it leads to the destruction of the
possibility of interference? Can quantum interference be genuinely
understood by invoking a wavefunction that is nothing more than
``a representation of our knowledge''?
(1) Cat's paradox, in Schroedinger's terms:
"One can even set up quite ridiculous cases.
A cat is penned up in a steel chamber, along with
the following device (which must be secured against direct
interference by the cat): in a Geiger counter there is a tiny bit
of radioactive substance, so small, that perhaps in the course
of the hour one of the atoms decays, but also, with equal probability,
perhaps none; if it happens, the counter tube discharges and through
a relay releases a hammer which shatters a small flask of hydrocyanic
acid. If one has left this entire system to itself for an hour, one would
say that the cat still lives if meanwhile no atom has decayed.
The psi-function of the entire system would express this by having
in it the living and dead cat (pardon the expression) mixed or smeared
out in equal parts. It is typical of these cases that an indeterminacy
originally restricted to the atomic domain becomes transformed into
macroscopic indeterminacy, which can then be resolved by direct
observation. That prevents us from so naively accepting as valid a
"blurred model" for representing reality. In itself it would not embody
anything unclear or contradictory. There is a difference between
a shaky or out-of-focus photograph and a snapshot of clouds
and fog banks."
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