If you tell me that reality is one big wavefunction, and that observable reality is made of states of neurons, then you need to tell me how to get “state of neuron” from “wavefunction”. Which set of numbers do I use?
Is it the coefficients of the wavefunction, expressed in a global configuration basis? Is it the coefficients of the wavefunction, expressed in some other basis? Or should I be looking at the matrix elements of reduced density matrices?
Also, if we talk about the configuration basis, should I regard the numbers specifying a particular configuration as part of reality? From a Hilbert-space geometric perspective, a “wavefunction” is actually a state vector, so it’s just a ray in Hilbert space, and the associated configuration is just a label for that ray, like the “x” attached to a coordinate axis.
A basis function is a different object to a density matrix, and the coefficient of a basis vector is a different sort of quantity to the quantities appearing in the label of the basis vector (that is, the eigenvalues associated with the vector).
I need to know which of the various types of number that can be associated with a quantum state, are supposed to be related to observable reality.
No, you have this backwards. You’re looking for some words. I’m telling you there are just numbers. The numbers are all we need to be evaluating here.
Fine, let’s talk about numbers.
If you tell me that reality is one big wavefunction, and that observable reality is made of states of neurons, then you need to tell me how to get “state of neuron” from “wavefunction”. Which set of numbers do I use?
Is it the coefficients of the wavefunction, expressed in a global configuration basis? Is it the coefficients of the wavefunction, expressed in some other basis? Or should I be looking at the matrix elements of reduced density matrices?
Also, if we talk about the configuration basis, should I regard the numbers specifying a particular configuration as part of reality? From a Hilbert-space geometric perspective, a “wavefunction” is actually a state vector, so it’s just a ray in Hilbert space, and the associated configuration is just a label for that ray, like the “x” attached to a coordinate axis.
A basis function is a different object to a density matrix, and the coefficient of a basis vector is a different sort of quantity to the quantities appearing in the label of the basis vector (that is, the eigenvalues associated with the vector).
I need to know which of the various types of number that can be associated with a quantum state, are supposed to be related to observable reality.