On 11/15/2017 7:36 PM, [email protected] wrote:
On Wednesday, November 15, 2017 at 7:54:27 PM UTC-7, Brent wrote:
Interesting questions. Whenever we talk about a system being in a
quantum state, we're thinking of the "system" as some degrees of
freedom that are isolated, so they are not interacting with and
becoming entangled with other things. An SG experiment typically
uses silver atoms and refers to their state as UP or DOWN or LEFT
or RIGHT. But that's not a complete description of the silver
atom. It has other degrees of freedom, which we ignore as
irrelevant to the SG measurement. So a "system" which we describe
as having a state, isn't necessarily the same as an object, like a
baseball or even an atom. A classical object like a baseball has
lots of degrees of freedom and they are interacting with the
environment, so they are entangled with states of the
environment. Only certain collective variables, e.g. the
conserved ones like momentum, are stable in the stat mech sense.
These ones that are stable against interaction with the
environment are the einselected values we can measure classically.
So we could write a wave-function for the baseball as if it were
an isolated particle, like the silver atom, and ignore all the
internal dof which are not in any definite state because they're
entangled with atmospheric molecules and IR photons, etc.
Whether something is in a superposition of states isn't an
interesting question because the answer is always "Yes...relative
to some basis." The interesting point is that since constituents
in the baseball have interacted with and are now entangled with
air molecules, those constituents of the baseball are not in any
definite state. Only the constituent PLUS the molecules it is
entangled with has a definite state. In any basis we can imagine
measuring, they will be in a superposition relative to that
basis. But in theory there would some basis in which the isolated
baseball plus molecules would be an eigenstate; it's just so
complicated we could never measure in that basis. But if were to
consider a very simple system, like a few electrons then we might
be able to measure in the eigenbasis.
Brent
TY. That was very informative. Let's go on. How does a micro
constituent of a macro object get entangled with, say, an air
molecule? When I think of entanglement, I think of some special
process to it.create it. How does it happen spontaneously? Is it
stable or does it decay rapidly, and if so into what? TIA.
Don't think of the constituents as objects, think of them as degrees of
freedom or modes of excitations. So an N2 molecule collides with the
baseball and it excites a certain vibration mode of the ball. Now that
mode and the motion of the N2 molecule are entangled. If you're just
interested in the ball you can just average over, trace out, the N2
molecule modes and then you're left with a mixed density matrix for the
modes of the baseball. Of course all this changes very quickly,
spreading the entanglement to more modes of the baseball, radiating some
away as IR photons, more collisions of N2 and O2 molecules. That's
decoherence that washes out all the coherent interference that we can
observe with carefully isolated systems. It isn't decaying, it's
diffusing the information about the microscopic dof into the environment.
Brent
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