Dear Lars-Göran, Andrei and Hans,
As you (I hope) have seen, I am trying to see how the evolution of macroscopic
processes can be described in terms of changing probabilities, and I am
encouraged to believe this is possible. If you allow the extension from QM, all
of the following would seem to allow this
(I am not concerned about whether QM itself becomes more or less complex):
1. Andrei confirms that the probability (in LIR, degree of potentiality or
actuality) of a phenomenon can have a direction.
2. Lars-Göran says that probability amplitudes can represent real physical
features.
3. Even though /a contrario/, Hans wrote:
In order to make contact with real, measurable quantities, it (the probability
amplitude) must be multiplied by its complex conjugate. This recipe is called
the Born rule, and it is an ad hoc addition to the quantum theory. It lacks any
motivation except that it works.
In my Logic in Reality, since there is a reciprocal relation between actuality
and potentiality, each should be the complex conjugate of the other. I have no
problem in the two summing to 1 if the values of 0 or 1 are excluded for either
of them. This non-quantum aspect of reality could provide the missing
motivation for the recipe in quantum theory ;-)
I am certainly looking for a measurable (or estimatable) quantity of the
actuality and potentiality of interactive processes that is not a standard
probability of outcomes, but of changing macroscopic states. This is of course
an 'underdeveloped' concept, but I am encouraged to believe that this idea of
another set of "very special probabilities" is neither totally wrong nor
totally trivial.
Many thanks,
Joseph
----- Original Message -----
From: Lars-Göran Johansson
To: fis@listas.unizar.es
Sent: Wednesday, January 22, 2014 12:45 PM
Subject: Re: [Fis] Probability Amplitudes
Dear Andrei, Hans and all
I agree with Andrei. And why make quantum theory more complex than it is? One
may use all kinds of mathematical tools in a scientific theory, and the more
these tools simplify calculations the better. I see no reason to avoid using
amplitudes or matrices in quantum theory. Using a mathematical concept for
making calculations doesn't entail that I accept that that concept represent a
physical property.
To Hans: Where exactly did Einstein wrote that one should avoid unmeasurable
concepts in the description of Nature? I can't remember having read that.
The issue is how we should interpret quantum theory, in particular the wave
function, i.e., probability amplitudes; are they just mathematical tools, or do
they describe real physical features of quantum systems? I believe the latter
alternative is true and so did Schrödinger. But there are formidable
difficulties to give a realistic interpretation of wave functions, and
Schrödinger didn't succeed. But I think the difficulties can be overcome and I
have published my views about these things (Lars-Göran Johansson: Interpreting
Quantum Mechanics. A realist view in Schrödinger's vein, Ashgate, Aldershot
2007).
Lars-Göran
22 jan 2014 kl. 10:59 skrev Andrei Khrennikov <andrei.khrenni...@lnu.se>:
Dear Hans,
I would like just to point that 99,99% of people working
in quantum theory would say that the complex amplitude of
quantum probability is the main its intrinsic property, so
if you try to exclude amplitudes from the model
you can in principle do this and this is well known
long ago in so called quantum tomographic approach of Vladimir
Manko, but in this way quantum theory loses its simplicity and
clarity, yours, andrei
Andrei Khrennikov, Professor of Applied Mathematics,
International Center for Mathematical Modeling
in Physics, Engineering, Economics, and Cognitive Science
Linnaeus University, Växjö-Kalmar, Sweden
________________________________________
From: fis-boun...@listas.unizar.es [fis-boun...@listas.unizar.es] on behalf
of Hans von Baeyer [henrikrit...@gmail.com]
Sent: Wednesday, January 22, 2014 12:21 AM
To: fis@listas.unizar.es
Subject: [Fis] Probability Amplitudes
Dear Dino and friends, thanks for bringing up the issue of probability
amplitudes. Since they are technical tools of physics, and since I didn't want
to go too far afield, I did not mention them in my lecture. The closest I came
was the wavefunction, which, indeed, is a probability amplitude. In order to
make contact with real, measurable quantities, it must be multiplied by its
complex conjugate. This recipe is called the Born rule, and it is an ad hoc
addition to the quantum theory. It lacks any motivation except that it works.
In keeping with Einstein's advice (which he himself often flouted) to try to
keep unmeasurable concepts out of our description of nature, physicists have
realized long ago that it must be possible to recast quantum mechanics entirely
in terms of probabilities, not even mentioning probability amplitudes or
wavefunctions. The question is only: How complicated would the resulting
formalism be? (To make a weak analogy, it must be possible to recast
arithmetic in the language of Roman numerals, but the result would surely look
much messier than what we learn in grade school.) Hitherto, nobody had come up
with an elegant solution to this problem.
To their happy surprise, QBists have made progress toward a "quantum theory
without probability amplitudes." Of course they have to pay a price. Instead
of "unmeasurable concepts" they introduce, for any experiment, a very special
set of standard probabilities (NOT AMPLITUDES) which are measurable, but not
actually measured. When they re-write the Born rule in terms of these, they
find that it looks almost, but not quite, like a fundamental axiom of
probability theory called Unitarity. Unitarity decrees that for any experiment
the sum of the probabilities for all possible outcomes must be one. (For a
coin, the probabilities of heads and tails are both 1/2. Unitarity states 1/2
+ 1/2 = 1.)
This unexpected outcome of QBism suggests a deep connection between the Born
rule and Unitarity. Since Unitarity is a logical concept unrelated to quantum
phenomena, this gives QBists the hope that they will eventually succeed in
explaining the significacne of the Born rule, and banishing probability
amplitudes from quantum mechanics, leaving only (Bayesian) probabilities.
So, I'm afraid dear Dino, that the current attitude of QBists is that
probability amplitudes are LESS fundamental than probabilities, not MORE. But
the story is far from finished!
Hans
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professor
filosofiska institutionen
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0701-679178
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