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
On 11/15/2017 5:56 PM, [email protected] wrote:
Consider a baseball. Is it in some kind of composite state, however
defined, of its constituents? Are all its constituents entangled with
the environment? If some are not, are they in a superposition of
states? I pose these questions because in my discussions with Clark on
another thread, it's unclear what state, if any, a macro object is in,
assuming that state fluctuates. TIA.
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