Dear Hans,

Thank you for your explanation about probability amplitudes,
that clarifies a lot.  My only worry was about the *epistemological*
implications of quantum mechanics in its standard formulation,
that in my opinion point to a paradigm shift, which is felt not only
in this domain, but in all fields where *emergent* phenomena are
accounted for—a process that I thought was hinted to by Wheeler's
famous words "It from Bit," that I remember reading for the first
time precisely in your book on information.  That's the ground for
expressing my worry that reverting to classical probability theory
might entail a drawback to this decisive epistemological turn.

But I might misunderstand the whole story, that is certainly not
over yet  :-)                              -dino

On 22 January 2014 00:21, Hans von Baeyer <> wrote:

> 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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