Posted: Oct 06, 2011 8:41 pm
by twistor59
Teuton wrote:
twistor59 wrote:
Teuton wrote:
What is the essential physical difference between "classical" fields and quantum fields?

A classical field assigns a value of some measurable quantity to each point in spacetime.
A quantum field assigns an operator to each point in spacetime (this is the heuristic version - the more mathematically rigorous version involves operator valued distributions as I alluded to earlier). This operator acts on "states" which live in an abstract (Hilbert) space and does stuff like changing the number of quanta.

Operators are mathematical entities which aren't part of physical reality. So the question is what is that which is part of physical reality and corresponds to or is represented by them.

The operators are the basic ingredients which are used to construct observables. An observable is a physical quantity whose value can be measured. The measured value obtained in a given instance depends, probabilistically, on the system state.