Posted: Oct 07, 2011 9:44 am
by mizvekov
hackenslash wrote:Still getting all your definitions from the dictionary of what colour is my lint.

What exactly is wrong with the definition of operator as pointed out in the link Teuton posted?

hackenslash wrote: ... _Operators

Do you think these definitions support the notion that operators are not mathematical abstract objects?

Teuton wrote:For every determinable physical property/quantity there is a range of possible determinate properties/quantities belonging to that determinable one; and there is certainly nothing "unacceptable" about assigning different probabilities to the various possible determinate ones. But physical reality cannot be reduced to mere possibilities or probabilities. The real properties of spacetime points or regions must be actual determinate properties. There may be a quick random oscillation between them such no spacetime point or region has the same determinate property for longer than some fraction of a second; but for every determinate time t there must be some determinate property had by the spacetime point or region in question. (I don't know what it means to say that there is an indeterminate property present at t. I don't know what an indeterminate or "vague" property is supposed to be.)

QM/QFT are theories about probabilities from the ground up. The most common way to interpret it is that these probabilities are what describe best the system even in principle, and that it is not just the case that those theories present an incomplete description. They leave almost no space left for determinism.
But even then, you can say that in QFT probability distributions are what is "exactly determined", and that gets me to my second point that the difference between stochastic and deterministic is often overplayed.

I agree that properties must be determinate, and you can still maintain this position but with one small change: Instead of these properties being best represented by the abstract objects that are the real numbers, they are best represented by the abstract objects that are probability distributions (PD).
And really, I don't think there is anything fantastic or mind blowing about that. Deterministic variables (ie numbers) are a special case of random variables (which are represented by PDs). You can have a PD which assigns probability 1 to just one value, and zero to all others. This can be done even for continuous PDs (see the dirac delta function, or the impulse function).