On 4/11/2015 11:33 am, Russell Standish wrote:
On Wed, Nov 04, 2015 at 10:55:56AM +1100, Bruce Kellett wrote:
On 4/11/2015 4:49 am, Brent Meeker wrote:
I think that would have been better expressed if you had noted
that the robust basis is not necessarily the position basis. As
Schlosshauer notes, for atomic size things it is often the energy
eigenvalues that are robust. But we didn't predict that; we have
discovered it empirically.
This is the mistake made by both Zurek and Schlosshauer: Position
and energy are variables, not bases, and for both you have the same
basis problem (both are operators in infinite dimensional Hilbert
spaces, but *different* spaces). The question as to whether a
Not different spaces - unless you're talking about completely
different experiments.
Generally one is talking about different experiments.
The basis problem is that position and energy
do not commute, so along which basis has reality decohered to? Why
does it seem to depend on what we're interested in measuring?
The position operator does not generally commute with the full
Hamiltonian, though it may commute with the specific interaction
Hamiltonian. It depends on what we are measuring precisely because the
interaction Hamiltonian depends on the experimental set up. In some
cases the interaction will be independent of the energy and momentum, in
which case the interaction Hamiltonian commutes with the position
operator. If the interaction is energy dependent, then generally only
the Hamiltonian will commute with the interaction Hamiltonian (an energy
measurement).
As I continue to stress, this is not the basis problem, this is a
problem of which variable might have a stable basis. A basis is not an
operator, it is a complete set of eigenvalues.
measurement is primarily one of position or of energy is depends on
the system under study and the experimental set up. But the basis in
either position or energy space still has to be chosen. Einselection
then turns out to be rather trivial because all the measurements and
interaction Hamiltonians are always expressed in terms of the
classical counterparts of the relevant variables.
So would it be a complete solution of the measurement problem if
we could predict which basis choice would provide robust
eigenvalues? Would this prediction start from a very complex
instrument/environment interaction Hamiltonian? It seems that if
it did we'd be in the position of having to do stat mech on the
interaction, which would again involve assumptions about chaos and
averaging? I think we might run into Chris'es "cat in the tree"
problem.
The argument that is made is that the 'classical' world emerges from
the quantum, in the sense that the quantum is more fundamental. But
when we look into it, we find that Bohr was quite perceptive with
his Correspondence Principle: since we are essentially 'classical'
beings, we have to start with classical concepts even to begin to
build a quantum theory. I doubt that it would be even possible to
construct a quantum theory /ab initio/, without reference to
classical ideas.
Quantum theory ab-initio is fine, but I strongly suspect you will
never get the classical world emerging out of it with some extra
ingredient (which I believe is your critique). That extra ingredient I
think has been identified as the subjective - and the subjective is
possibly constrained to having to implement classical computation
(Bruno's idea), which explains why it is the classical world that
emerges from the quantum, not something else.
I disagree. I do not think the quantum mechanics /ab initio/ is in any
way possible. Physics is done with respect to observations and
experiments. Without prior observations we would not even know what
variables we might want to write down, much less how they behave
dynamically. I know it is the belief of most on this list that the
subjective plays a central role in all of this, but I disagree. I do not
think you can do physics, or even understand consciousness (the
subjective) without reference to experience of the objective world.
Bruce
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