# Re: [Fis] Probability Amplitudes

```       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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```