Let me summarize some of the points of the recent
discussion, and them move on.
1) The previous Subject: line "idealism vs materialism"
started things off on the wrong foot. Idealism and
materialism are merely two not-very-special points in
a multi-dimensional space of ideas. There are many
shades of gray between those two points, and (more
importantly) lots of orthogonal directions to pursue.
Only the lamest of philosphers limit themselves to
one-dimensional thinking with no shades of gray.
2) Materialism (by definition) claims that only
material things are significant. Physics does have a
notion of "material", namely mass/energy. But we do
not limit ourselves to that. As a first example,
consider things like
-- electric charge,
-- lepton number, and
-- angular momentum.
In my book, each of those has a reality unto itself,
transcending its embodiment in any particular piece
of matter. Conservation of each of those is independent
of, and on an equal footing with, the conservation of
mass/energy.
In particular, a RCP (right-circularly polarized) photon
has angular momentum, even though it has zero rest mass
and can have arbitrarily small total energy.
At the opposite extreme, idealism is quite disconnected
from real physics. Ideas are not constrained by reality.
Physics is.
3) The place where physics most dramatically parts
company with those simplistic/extremist ideas is
quantum mechanics.
A quantum wavefunction (probability amplitude) is at
least two steps removed from "material". At the
second step, it describes the universe in terms of
probabilities. The definite classical predictions
are seen as an extreme/simplified view of a much
subtler reality. And before we even get to that
step, the amplitude isn't even a probability.
To repeat: the stock-in-trade of real physics is
something that is "real" but not "material". (Here,
as always, I am using the word "real" to denote the
opposite of "fictional", in accordance with ordinary
usage as attested by standard dictionaries.)
4) Back in the bad old days, before we really
understood quantum mechanics, all sorts of silly
things were said about the role of consciousness
in the "quantum measurement" process. For example,
there is the oft-quoted requirement that Wigner
measures something, and then shows it to Wigner's
friend -- and that's how you know that it has
been well and truly and permanently measured.
And Schrödinger did non-PC things with cats.
But we're a lot smarter now. We understand that
the quantum measurement process revolves around
_dissipation_. Wigner and Schrödinger weren't
totally wrong: it turns out that friends and
cats are indeed sufficiently dissipative to well
and truly destroy quantum coherence and produce
the classical result. But lesser amounts of
dissipation will suffice, and shed more light on
the process.
In previous notes somebody quoted something about
"sufficiently energetic" and I mumbled something
about signal-to-noise ratios. Neither of those is
exactly right. The cardinal issue is dissipation.
Without dissipation you cannot get classical
behavior.
(The alert reader may have noticed that QM revolves
around Hamiltonians and Lagrangians and suchlike,
which describe energy, and may be wondering how
you can write down the Hamiltonian for a system
that doesn't conserve energy. Well, it _can_ be
done. In an RLC circuit, if you consider all the
internal modes of the resistor, and the heatsink
to which it is bolted, and the sky into which it
radiates, it conserves energy. But if you choose
to summarize the resistor as a two-terminal black
box, then it is dissipative. The properties of
such a resistor have been worked out in great
detail. You can go on from there to get a fully
quantum-mechanical description of amplifiers and
other interesting objects.)
Let me be more specific about the transition from
quantum behavior to classical behavior. As an
example of quantum behavior, consider the ammonia
molecule as described in _The Feynman Lectures on
Physics_ volume III chapter 9. It has two basis
states, which we can call |up> and |down>, but
you are not likely to find any particular molecule
in such a state. We can form other states by
taking linear combinations. The ground state
is the symmetric (gerade) combination of |up>
and |down>, while the higher-energy state is
the antisymmetric (ungerade) combination.
You can contrast this with the behavior of almost
all larger molecules. Alanine, for instance,
is larger but not outrageously larger, and its
behavior is completely different. It is chiral.
You can buy D-alanine (dextro-rotatory) separately
from L-alanine (levo-rotatory). You can buy
classical mixtures of the two, but nobody has
ever observed the gerade or ungerade quantum
superpositions of the two.
At this point you may be tempted to explain the
difference in terms of tunneling rates. It is
true (but !!not!! the whole story) that the
tunneling rate whereby D-alanine would convert
to L-alanine is much smaller than the rate of
the umbrella inversion in ammonia. But rates
are not the whole story. The |D> and |L> states
are just two points on the SU(2) sphere. To
say that the sphere twists slowly doesn't
explain what's special about those two points.
Even if we say that (to a first approximation)
the sphere isn't twisting, you need to explain
why it froze right at the point where every
molecule is |D> or |L> and not some other point.
Almost every point on the sphere is a combination
of |D> plus |L>.
The answer has to do with dissipation. The
alanine molecule couples to whatever solvent
its in, and even in the absence of a solvent
it couples to the electromagnetic field. This
couplings are highly dissipative. They couple
to the dipole moment of the molecule. It
is this dissipation that forces the molecule
into states of definite dipole moment.
Ammonia molecules including the isotopes ND3 and
NT3 (and even the chiral version NHDT) behave the
way Feynman described. But almost all other
molecules are gnarly enough to be classical.
So the ball-and-stick models that chemists
use are more-or-less OK for almost all molecules.
Molecules are, of course, not the only two-state
systems. A coin has two states |heads> and
|tails> which are classical by a wide margin.
You will never see the gerade or ungerade
combinations thereof. More interesting is a
SQUID (superconducting quantum interference
device) such as the following:
XXXXXXXXXXXXXXXXXXXXXX
X XX X
X \/ X
X /\ X
X XX X
XXXXXXXXXXXXXXXXXXXXXX
where everything is thick solid superconductor
except at the place where it necks down to a
"weak link" in the middle. There is one flux-
line trapped in the device, and it can either
be on the |left> side or the |right> side. You
can adjust the tunneling rate (the rate of rotation
of the SU(2) sphere) by adjusting the weakness
of the weak link. You can control the dissipation
by coupling to an antenna, or by depositing a
resistive metal film, or otherwise. Theory says
that tunneling will stop completely at a
non-extremal value of the resistance, namely
about 2 kOhms. (That's hbar in the appropriate
units.) This is the transition from quantum
behavior to classical behavior. You can treat
it as a symmetry-breaking phase transition.
AFAIK nobody has actually done the experiment.
But they have done similar things, since this
has ramifications for quantum computing. For a
snapshot of current thinking, see