Stuart, I said determinate, not determinist. I was objecting to the notion of an objectively indeterminate property—as if it made sense to say of a particle that it has a position, but no particular position… You yourself say “there is no such thing as position, or momentum… the combination of the two is the actual property that exists.” I would be very surprised if that is anything more than a slogan. Can you explain to me the exact nature of this ‘combination’ that is the actual property? (Please don’t just say that the formalism provides the details, without doing so yourself. I want to see the propositions of quantum theory, such as assertions about observables taking particular values, cashed out in terms of your ontology.) Can you explain to me how, though neither A nor B exists, a combination of A and B exists? Is this done using logical conjunction, counterfactuals, perhaps algebraic means?
Eliezer, how does abandoning the notion of particles as individuals save you from the questions you mention? For that matter, what is your alternative to the notion of particles as individuals? I can see more or less how I would think about the matter. For particles of the same species, instead of any product state ab being possible, you can only have states like ab+ba or ab-ba; so I might conclude that particle species are the individuals, the things-with-states. But then particles of different species can also get entangled, and so you end up with just one thing, the universe itself, its state described by the universal wave function. On the other hand, if you allow yourself the notion of a relative state, I would think that the notion of particle individuality could be retained, and the symmetry conditions interpreted as being ‘trans-world’ properties, properties of the ensemble of all branches of the wavefunction.
Presumably the actual property is the state of the wavefunction.
So for instance we could have a Gaussian wavefunction… and that would be the determinate physical variable. It has no particular position or momentum, because there are nonzero amplitudes for various different positions and momenta. We could choose a different wavefunction to get a more determinate position, but then because it’s a Fourier transform the momentum would grow ever more indeterminate.
Stuart, I said determinate, not determinist. I was objecting to the notion of an objectively indeterminate property—as if it made sense to say of a particle that it has a position, but no particular position… You yourself say “there is no such thing as position, or momentum… the combination of the two is the actual property that exists.” I would be very surprised if that is anything more than a slogan. Can you explain to me the exact nature of this ‘combination’ that is the actual property? (Please don’t just say that the formalism provides the details, without doing so yourself. I want to see the propositions of quantum theory, such as assertions about observables taking particular values, cashed out in terms of your ontology.) Can you explain to me how, though neither A nor B exists, a combination of A and B exists? Is this done using logical conjunction, counterfactuals, perhaps algebraic means?
Eliezer, how does abandoning the notion of particles as individuals save you from the questions you mention? For that matter, what is your alternative to the notion of particles as individuals? I can see more or less how I would think about the matter. For particles of the same species, instead of any product state ab being possible, you can only have states like ab+ba or ab-ba; so I might conclude that particle species are the individuals, the things-with-states. But then particles of different species can also get entangled, and so you end up with just one thing, the universe itself, its state described by the universal wave function. On the other hand, if you allow yourself the notion of a relative state, I would think that the notion of particle individuality could be retained, and the symmetry conditions interpreted as being ‘trans-world’ properties, properties of the ensemble of all branches of the wavefunction.
Presumably the actual property is the state of the wavefunction.
So for instance we could have a Gaussian wavefunction… and that would be the determinate physical variable. It has no particular position or momentum, because there are nonzero amplitudes for various different positions and momenta. We could choose a different wavefunction to get a more determinate position, but then because it’s a Fourier transform the momentum would grow ever more indeterminate.
Interestingly, there are apparently ways of working around this, by carefully choosing your observables to be operators that commute. http://arstechnica.com/science/2010/08/quantum-memory-may-topple-heisenbergs-uncertainty-principle/