Dear Steven,

I was not able to reply you earlier. But I think that I should do this 
even so late after your Email. You posted problems which are very 
important (at least for me).
> 1. Quantum probability functions are either directly equivalent to 
> probability functions in Shannon\'s information theory or they are
> not.   
> Which is it?
Quantum probability functions are not equivalent probability functions 
in Shannon\'s information theory. They equivalent to quantum (von 
Neumann) information functions.

But we can generalize classical probability and consider contextual 
probability (I did this last years). I have never tried to proceed to 
contextual information theory, but it is possible. Such a classical 
probabilistic information theory will cover both CI and QI and some 
new information theories which are neither classical (noncontextual) 
nor quantum.

> 2. If there are new physical mechanisms discovered in quantum
> mechanics 
Personally I do not know. The common viewpoint is that QM is really 
about completely new physics, but if you ask people working in Bohmian
mechanics, SED and other random field models, they would reply that 
QM is a special representation of classical random fields, I am at the 
latter position.

> then I am with Penrose - recall my earlier report of his observation
> concerning cricket balls.  The mechanisms must exist independent of 
> scale. And that implies to me that a clear mechanistic integration
> with 
> information theory is possible and required.

I would like to say that mechanism is indepent of scale, but its 
representation, e.g., the QM-representation of laws of nature, is 
dependent on transition from one scale to another. Therefore I think 
that quantum-like descriptions can be useful not only in quantum 
physics, but everywhere we have a tarnsition from one scale to another.

> 3. It seems to me that the problem here is the parallel postulate and
> its equivalent by extension to computation.  This is the reason 
> probabilities come into it at all.  Perhaps we need to be reminded
> that 
> probabilities are the result of observations of the statistical
> behavior 
> of individuals.  Individuals have an ontological status while 
> probability functions only have epistemological status. 
But probability is just a special way of encoding of the onthological 
properties of individuals. In this sense probabilities (as well as 
information) are objective. This was the viewpoint of Richard von 

> 4. Recurring laws of probability do appear to be stable laws, but
> they 
> are founded upon the aggregation of individual behavior.  Their 
> ontological status is derived from the behavior of individuals, not
> by 
> their own account.

Well I agree, but probabilistic laws represent in a special way 
ontological laws. The Kolmogorov equation for probabilities represent 
Brownian motion as well. 

All the best, Andrei
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