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 _______________________________________________ fis mailing list fis@listas.unizar.es http://webmail.unizar.es/mailman/listinfo/fis