Posted: Oct 09, 2011 11:44 am
Well, given the 'reality' of particles (ontological caveats aside for the moment, just for the sake of exploration), can we say that the property 'velocity' is real?
Of course, depending on which formulation of QM one is operating from, it's difficult to say whether or not a particle even has a definite velocity until such time as it is observed, but that aside, and given that some formulations insist that these properties are basic, then under those formulations, those operators are real things.
In the example you have given, the distance to the moon is, as you say, very real, but the number that describes it? This is the problem you run into when you speak of the number of fingers on your left hand. They have the real property of being fingers, but not the real property of 'fiveness', which would require support for Platonic realism.
I think the real problem here is that we're running into set-theoretic territory here, and while being a member of a set could be described as a property, it's problematic to insist that that membership has any 'reality'.
It's a thorny problem, to be sure.
Of course, depending on which formulation of QM one is operating from, it's difficult to say whether or not a particle even has a definite velocity until such time as it is observed, but that aside, and given that some formulations insist that these properties are basic, then under those formulations, those operators are real things.
In the example you have given, the distance to the moon is, as you say, very real, but the number that describes it? This is the problem you run into when you speak of the number of fingers on your left hand. They have the real property of being fingers, but not the real property of 'fiveness', which would require support for Platonic realism.
I think the real problem here is that we're running into set-theoretic territory here, and while being a member of a set could be described as a property, it's problematic to insist that that membership has any 'reality'.
It's a thorny problem, to be sure.