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On 05/17/2013 01:05 PM, Bob Sciamanda wrote:
It has been recently pointed out (on this list and elsewhere, eg.,
http://arxiv.org/ftp/arxiv/papers/1204/1204.4616.pdf) that Quantum
Field Theory (QFT) has dissolved the particle/field question in favor
of fields: "There are only fields."
I am hastening to the conclusion that there are not even fields!
The fields of QFT are OPERATORS. The system state is an abstract
vector in Hilbert (Fock?) space - not described by a field - only by
a "bra or ket", just a label. The field operators describe
INTERACTIONS by which the Hilbert states evolve.
IMHO all of this is a useful CALCULATIONAL MODEL, and does little or
nothing to identify a model for the ontological reality (particle,
field, wave or whatever) behind the entity being described. Perhaps
there is no useful CONCEPTUAL MODEL to describe ultimate reality in
human terms - and perhaps there is really no need for one.
I welcome comments.
I agree with most of that, although I might come at it from a
slightly different angle.
The fields of QFT are OPERATORS.
There's an important idea there, just slightly overstated.
Consider the photon-number states. Temporarily ignoring some
important normalization factors, we have
|0⟩ = |0⟩
|1⟩ ∝ a† |0⟩
|2⟩ ∝ a† a† |0⟩
|3⟩ ∝ a† a† a† |0⟩ [3]
and also the Glauber state
|G(α)⟩ ∝ exp(α a†) |0⟩
where |0⟩ is the ground state (vacuum state) and a† is a creation
operator.
Let's focus attention on line [3].
I claim that |3⟩ is a state whereas (a†)^3 is an operator. At this
level of detail, the distinction does not yet appear important, because
as you can see, there is a one-to-one relationship between a state and
the operator that creates that state from the vacuum. You can perfectly
well write an equation of motion for the states (Schrödinger picture)
or an equation of motion for the operators (Heisenberg picture).
Things get a lot more interesting when we stick the normalization
back in. Applying the creation operator to a state that is already
occupied by N bosons picks up a factor of √(1+N). This explains,
among other things, how lasers work: an atom is much more likely to
radiate into the mode that is already highly occupied.
Also: There is a factor of √(1-N) for fermions, which explains
exclusion.
Remember that quantum mechanics grew out of thermodynamics. In
statistical mechanics, the partition function is a sum over states.
It is conventionally denoted Z for Zustandssumme. The usual rule
is that all states are equally likely a_priori. However, that is
clearly not right in the laser; it works much better to say that
all /creation operators/ are equally likely.
At this point every person is probably saying to himself "This cannot
be right, because I know about quantum mechanics and I've never heard
of this before."
Well, fear not, because there are remarkably few situations where
this matters. Most of the time you can get the right answer without
worrying about this.
-- Suppose the system is highly degenerate, such as the electrons
in a metal, the electrons inside an atom, the neutrons in a
neutron star, the helium in a superfluid, et cetera. Everybody
knows in advance that the system is degenerate, and they tweak
the formalism to account for this. It's a zeroth-order effect,
and nobody is dumb enough to overlook it.
-- Suppose the system is highly non-degenerate, such as a classical
ideal gas. In this case every state is occupied at most once, so
the question of how to add something to a previously-occupied state
never arises.
++ If the system is just a little bit degenerate, it really helps
to think in terms of the operators.
So, all in all, I would say that the fields exist /and/ the operators
exist. The distinction is usually not important, but in tricky cases
the operators are half a step more fundamental.
Perhaps there is no useful CONCEPTUAL MODEL to describe ultimate
reality in human terms - and perhaps there is really no need for
one.
That point is well supported by tradition dating back to Day One
of modern science (Galileo). Newton summed it up by saying,
Hypotheses non fingo.
Just yesterday a professor of religion was telling me about a book
he was reading about the interpretation of quantum mechanics ...
and its connection to Hindu mysticism. I told him about Galileo
and Newton.
-- The laws of physics must say what happens.
-- They might or might not explain /how/ it happens.
-- They fundamental laws almost never say /why/ it happens.
For example, when we write F=ma, that does *not* mean there is
a cause-and-effect relationship. For details on this, see
http://www.av8n.com/physics/causation.htm
Humans, for various psychological reasons, always want to know
/why/ something happened ... and they are forever cooking up
ways of explaining why. Most of this is baloney. On the other
hand, there is such a thing as cause and effect. The guys who
know the most about this aren't the physicists; they're the
epidemiologists.
http://www.ph.ucla.edu/epi/snow.html
http://en.wikipedia.org/wiki/John_Snow_%28physician%29
If you want a book about the interpretation of quantum mechanics,
I can write you a reeeeally short book. It says "the equations
are right". If you turn the crank on the equations, you get the
right answer. When it comes to "interpretations" of QM, that
which interprets least interprets best. Hypotheses non fingo.
If you insist on a mechanistic model, I've got one of those,
too. It says there are little invisible angels who know the
rules. They fly around and push on stuff in such a way as to
make the outcome agree with the quantum mechanical equations.
Of course this is just a ridiculously overcomplicated way of
restating the previous interpretation, without adding anything
useful. Bottom line: The equations are right. Hypotheses
non fingo.
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