[Fis] Limited info

 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.

But all that is handwaving.

Hans Christian von Baeyer
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Received on Tue Jun 13 17:35:23 2006