as if it made sense to say of a particle that it has a position, but no particular position
That might or might not make sense (mathematicians have been tearing their hair out about non-computable numbers, see Chaitin’s constant). But most quantum mechanists do not say that a particle has a position. In fact if you interpret Quantum mechanics in terms of “hidden variables” (there are underlying values for the objects, like spin and momentum, but we can’t get at them) then you will generally come unstuck.
Can you explain to me the exact nature of this ‘combination’ that is the actual property?
The property is exactly the one in the quantum formalism. I don’t really see why you object to the formalism. It gives specific predictions that have been confirmed, with high probability, in experiments.
If you want an ontological view, then my position is that science is only about making predictions about the results of experiments and then testing them. Properties such as position, energy, etc… are only valid in that they predict a lot of different experiments. In classical mechanics, it emerged that a mathematical concept called “position” led to great predictive power, giving universal laws. So classically, “position” existed.
In quantum mechanics, laws based on “position” don’t work, so the concept of position doesn’t make sense in a quantum framework (just as “colour” makes no sense in acoustics). Other concepts did make sense—they had to be expressed in certain formal mathematical ways, but they made sense.
So, to sum up, position doesn’t exist, momentum doesn’t exist, but certain other objects (such as the product of the uncertainties of momentum and position) do make sense.
Aha! But have I not defined “uncertainty of position”? How can I claim this exists if position doesn’t?
The problem is just the name (and this is going back to Elizer’s original point, and causing me to think I may have been a bit hasty in rejecting it). This is just the standard deviation of an observable. It’s only called “uncertainty of position” because of an analogy with the classical “position”—a wrong analogy (and an observable, like a classical “position”, is just a mathematical object that seems to make sense in experiments).
as if it made sense to say of a particle that it has a position, but no particular position
That might or might not make sense (mathematicians have been tearing their hair out about non-computable numbers, see Chaitin’s constant). But most quantum mechanists do not say that a particle has a position. In fact if you interpret Quantum mechanics in terms of “hidden variables” (there are underlying values for the objects, like spin and momentum, but we can’t get at them) then you will generally come unstuck.
Can you explain to me the exact nature of this ‘combination’ that is the actual property?
The property is exactly the one in the quantum formalism. I don’t really see why you object to the formalism. It gives specific predictions that have been confirmed, with high probability, in experiments.
If you want an ontological view, then my position is that science is only about making predictions about the results of experiments and then testing them. Properties such as position, energy, etc… are only valid in that they predict a lot of different experiments. In classical mechanics, it emerged that a mathematical concept called “position” led to great predictive power, giving universal laws. So classically, “position” existed.
In quantum mechanics, laws based on “position” don’t work, so the concept of position doesn’t make sense in a quantum framework (just as “colour” makes no sense in acoustics). Other concepts did make sense—they had to be expressed in certain formal mathematical ways, but they made sense.
So, to sum up, position doesn’t exist, momentum doesn’t exist, but certain other objects (such as the product of the uncertainties of momentum and position) do make sense.
Aha! But have I not defined “uncertainty of position”? How can I claim this exists if position doesn’t? The problem is just the name (and this is going back to Elizer’s original point, and causing me to think I may have been a bit hasty in rejecting it). This is just the standard deviation of an observable. It’s only called “uncertainty of position” because of an analogy with the classical “position”—a wrong analogy (and an observable, like a classical “position”, is just a mathematical object that seems to make sense in experiments).