Dear Hans,
Thank you very much for extremely interstring discussion on
Schrodinger\'s ideas (where can I read this?). I really like this point
that our mathematical model of space-time, namely the real continuum, is
heavily involved into foundations of QM. We took the space model of
classical physics into a new framework -- QM. Then we try to elaborate
discreteness.
I just point out that recent ten years there was an activity to create
new physical models which are not based on the real continuum, but on
the p-adic space (I have a few books in this domain). These
invetsigations were especially supported by research in cosmology and
string theory. But I cannot say that we did a revolution in physics.
P-adic space is also continuous (but in different way). The same problem
of the infinite amount of information in any domain of p-adic space
arises again.
> Dear all -- Pedro\'s pearls are, as always, inspiring.
>
> For me the biggest problem is the precise formulation of a principle
> that limits the information nature allows us to discover.
> Schroedinger related this question to the nature of space-time, and
> the use, in mathematics, of the continuum of numbers. If you could
> pinpoint the location of a particle
> on the line of real numbers from zero to one, as you do in classical
> physics, you would have an infinite amount of info about it,
> represented by an infinite string of decimals. Surely, Schroedinger
> felt, the information that is physically carried by a material system
> must DECREASE as the volume of the object gets smaller, not
> increase. So, he argued, real numbers should not be used at all. In
> his estimation his own equation is a trick, and a poor one at that,
> to solve this problem. His equation starts with a continuum, but
> ends with discrete integers (eigenvalues).
>
> Quantum mechanics is an elaboration of the idea that a box with
> volume h in six-dimensional phase space can SOMEHOW carry one bit of
> info.
The main question: really carry or that we are able to extract just
one bit of > info. If there is nothing more than this one bit, this
would be the end of the story. I expect that we just could not extract,
but there is essentially more information.
I again emphasize that for me QI is physical information. Therefore
there is no place to subjective probability. Look: what is qubit?
It is not at all our expectations, but this is a two level physical system.
All the best, Andrei
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Received on Wed Jun 14 18:15:47 2006
