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On 3/27/19 2:04 AM, Antti Savinainen quoted the assertion:
if a discussion on entanglementof
thought experiments (like Schrödinger's cat) does not address the notion
coherence, one can quite safely ignore it as outdated.I was surprised to read that, not because I disagree with it, but
because it's the answer to a question I never heard anybody ask.
I read "outdated" as a polite euphemism for "impossible". The folks
I run around with have always used the two terms -- entanglement and
coherence -- interchangeably in this context. Six florins of one,
half-a-dozen guilders of the other.
I now realize that there is (or was) a school of thought that
defined the two terms differently, but I still can't imagine why
anybody would want to. The physics is the same either way. A
discussion of the definitions and the non-distinction can be
found here:
https://phys.org/news/2015-06-physicists-quantum-coherence-entanglement-sides.html
I would explain the issue more simply: In the classical approximation,
when you have two particles, you can describe them separately. If
position is the only abscissa that matters, you have two different
functions of three variables apiece (x, y, z). QM says that in general,
you have to write *one* function of *six* variables.
Sometimes you can factor the wavefunction so as to achieve separation
of variables ... but sometimes you can't. That's the key idea. You
can call it a cat state or inseparable or correlated or coherent or
entangled or uncollapsed. The essential physics is the same no matter
what you call it.
_._ _,-'""`-._
(,-.`._,'( |\`-/|
`-.-' \ )-`( , o o)
`- \`_`"'-
====================================
At the next level of detail:
In the classical limit, you get separation of variables. You can
factor the wavefunction. In a great many cases, the classical
approximation is valid, but that requires some physical process
to account for the separation, aka the disentanglement, aka the
decoherence. Something to scramble the phase. It doesn't take
much -- perhaps a single black-body photon from the environment
interacting with one of the particles -- but there has to be
something.
Most people get by with rules of thumb:
a) The moving parts inside an atom are correlated and fully
quantum-mechanical.
b) An entire molecule, and anything bigger than that, can
"usually" be treated as a classical particle.
c) The exceptions to rule (b) tend to be very interesting:
-- For starters, consider the ammonia maser that is the subject
of a magnificent discussion in the Feynman lectures. The
ammonia molecule tunnels between two conformations. That is
easy to explain in terms of QM ... but did you notice that
ammonia is essentially the *only* molecule that does that?
Larger molecules play by qualitatively different rules.
Why is that?
-- Another exception to the rules of thumb concerns superconductors
and superfluids. If you have a gallon of superfluid, the whole
superfluid component is governed by a single wavefunction, vastly
larger than a single atom.
===============================
Here's an even more abstruse detail:
Although QM would be logically consistent without decoherence, it
would be completely useless. There are roughly 3×10^27 electrons
on earth, and they are identical particles, so a strict application
of the principles of QM says every time you want to describe even
one electron you have to write down *one* function of 3×3×10^27
variables ... which would be insanely impractical. Your physical
intuition says it must be possible to ignore most of the world's
electrons, and that's correct, but explaining exactly how that
comes about requires some deep thinking. Not the sort of thing
you want to bother with in the introductory course.
================================
Also:
As previously mentioned, I have no idea how to understand quantum
mechanics without thermodynamics -- or vice versa. In particular,
to understand disentanglement requires taking an ensemble average.
There is no easy way AFAIK to describe this in terms of "the"
wavefunction. Density matrices make life much simpler.
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