[ExI] QT and SR (was Re: Probability is"subjectivelyobjective".)

scerir scerir at libero.it
Fri Jul 18 06:30:39 UTC 2008


> > And - speaking of the epistemic/ontic issue - interference
> > can be seen or as an algebraic effect or as an effect,
> > which takes place in abstract tensor product spaces,
> > due to the Schroedinger's "waves", which can entangle
> > particles no matter how far apart they are.

Lee: 
> Can you clarify what you mean by "epistemic/ontic issue"?

Well, the wave-function can be seen as something physical
and "real" (in Bohmian mechanics it is so; the good old
Schroedinger thought it was such a thing; etc.) or as 
something "epistemic" (that is to say just an algorithm;
a statistical representation; a mathematical representation
of preparation of quantum systems and of apparatus; a 
subjective gain in terms of information; etc.).

While in general people think that the superposition
principle applies perfectly to the amplitudes as physical
objects, people cannot easily imagine how the same principle
applies to the amplitudes if they are only representations,
potential informations, etc.

According to Heisenberg and von Neumann, and others, 
wavefunctions are both physical and epistemic, and 
there is a "psycho-physical" parallelism. 

"This probability function represents a mixture of two things,
partly a fact and partly our knowledge of a fact. It represents a
fact in so far as it assigns at the initial time the probability
unity (i.e., complete certainty) to the initial situation: the
electron moving with the observed velocity at the observed position;
'observed' means observed within the accuracy of the experiment.
It represents our knowledge in so far as another observer could
perhaps know the position of the electron more accurately. The error
in the experiment does - at least to some extent - not represent a
property of the electron but a deficiency in our knowledge of the
electron. Also this deficiency of knowledge is expressed in the
probability function." [Heisenberg, Physics and Philosophy].

J. von Neumann helps here to understand what Heisenberg
might have in mind: "It is inherenly entirely correct that 
the measurement or the related process of the subjective 
perception is a new entity relative to the physical environment 
and is not reducible to the latter. Indeed, subjective perception 
leads us into the intellectual inner life of the individual, 
which is extra-observational by its very nature". J. von Neumann, 
Mathematical Foundations of Quantum Mechanics, p.418.

J. von Neumann defined the principle of "psycho-physical
parallelism". He defines it as the principle "that it must 
be possible to describe the extra-physical process of 
the subjective perception as if it were in reality 
in the physical world - i.e., to assign to its parts 
equivalent physical processes in the objective environment, 
in ordinary space."

Heisenberg by the way goes on to say: "We can, for instance, 
predict the probability for finding the electron at a later 
time at a given point in the cloud chamber. It should be 
emphasised, however, that the probability function does not 
in itself represent a course of events in the course of time.
It represents a tendency for events and our knowledge of events."
And a little further, he says: "The observation ... breaks 
the determined continuity of the probability function by changing 
our knowledge of the system."

And also: "Therefore, the transition from the 'possible' 
to the 'actual' takes place during the act of observation. 
If we want to describe what happens in an atomic event, 
we have to realize that the word 'happens' can apply only 
to the observation, not to the state of affairs between two 
observations. It applies to the physical, not the psychical act 
of observation, and we may say that the transition from the 
'possible' to the 'actual' takes place as soon as the
interaction of the object with the measuring device, and 
thereby with the rest of the world, has come into play; it is not 
connected with the act of registration of the result by the mind 
of the observer. The discontinuous change in the probability 
function, however, takes place with the act of registration, 
because it is the discontinuous change of our knowledge in 
the instant of registration that has its image in the discontinuous 
change of the probability function."

Horodecki (if I remember well) asked something like:
"Should a more suitable approach lie between these 
[real or epistemic] extremes?". "If we insist that 
the role of the wave function is simply to describe 
probabilities, we must give up the possibility of 
treating the wave function as an isomorphic image 
of what is actually processed in the laboratory".

Using this approach (isomorphism), he says that a "quantum
information" is indeed carried by a quantum system and 
that the wave function is the "image" or the "essence" 
of this information. 

It is perhaps interesting to ask if is it possible to describe 
a quantum system on paper, by means of a sequence of classical 
symbols on the tape of a Turing machine. The answer seems
to be negative. On the contrary the wave function can be 
described on paper for sure. 

> > Coming back to the subject line let us read Dirac (1972)
> > "It [nonlocality] is against the spirit of relativity,
 
> It's against the spirit of relativity only if one thinks that
> influences spread faster than light.

"Influences". Yes, that is what both Dirac - and John Bell - 
wrote and thought. (To my knowledge Einstein did not
write that "c" was the maximum speed for "information",
this is a modern interpretation I suppose).
  
> > but is the best we can do at the present time ... and,
> > of course, one is not satisfied with such a theory.
> > I think one ought to say that the problem of reconciling
> > quantum theory with relativity is not solved."
 
> This is certainly true for General Relativity and QM, 
> of course. But I'm not aware of any problem between
> SR and QM.   EPR, for example, is easily dispatched
> by use of the MWI of QM. What other problems are
> there?

There are huge inconsistencies between MWI and the so called
Schroedinger's representation, it is difficult to define
conservation principles (energy in example) in MWI, and ...
even Bryce deWitt, in his last (I think) paper writes
that, at present time, MWI does not give a satisfactory
solution to the EPR problem.




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