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quantum "forces"



The following questions were asked off-list, but the answers may be of
general interest:

Should we really think of (some) quantum mechanical rules as forces?

That's a bit of a tricky question. See if this helps: Consider three
variations of the question:
a) think of (some) quantum mechanical rules as forces?
b) think of (some) quantum mechanical rules as being forces?
c) think of (some) quantum mechanical rules as giving rise to forces?

I would say that
a) is ambiguous, because of possible interpretations (b) and (c).
b) is mostly wrong; certainly they are not "just" forces.
c) is indubitably true. More on this below.

For example, does the Pauli exclusion principle describe a true "force"?

Truly the rules that give rise to the exclusion principle also give rise to
measurable forces.

Here is an example that may be slightly complicated, but I mention it
because it features prominently in my thinking about this.

Suppose we have a gas of monatomic hydrogen at low temperature. We apply a
strong magnetic field so that the atomic electrons are all lined up. They
stay lined up and we ignore them. (Electrons are like little bar magnets,
and if you pull on them hard enough they will line up.) We play some other
games (involving chemical reactions) that leave us with a sample where all
the nuclear spins are lined up, too.

Now we add one more atom. Its electron is lined up, but its nucleus might
be in the up state, the down state, or some superposition of the two.

If the atom has |up> nuclear polarization, it is indistinguishable from all
the other atoms. When it scatters off the others, it scatters according to
identical-particle rules. Its wavefunction picks up some scattering phase
shift.

If it has |down> polarization, it is distinguishable by its spin
label. When it scatters, it scatters according to distinguishable particle
rules. Its wavefunction picks up some scattering phase shift.

If it is in a superposition state, the |up> ket picks up a _different_
scattering phase shift than the |down> ket.

The difference in scattering phase shift is caused by the neighbors, but it
is not caused by magnetic dipole interactions or anything like that; the
nucleus is so well protected inside the atom that the neighbors cannot
significantly affect its energy. The phase shift is due to
identical-particle effects and nothing else.

Now, what else do we know of that causes a relative phase shift between
{up> and |down>????? Answer: The rotation
operator!!!! Interpretation: The spin orientation of the added atom will
_precess_ around an axis, namely the up-down axis of the surrounding
polarized gas.

Chemists call this a "molecular field effect". The molecular field is
proportional to the polarization of the local fluid. It has the same
vectorial character as a magnetic field. But it is not a magnetic field,
as we can check by putting in another atom such as deuterium. It sees
magnetic fields just like hydrogen would, but it isn't subject to hydrogen
identical-particle effects, so it does not see the molecular field.

Reference:
Johnson-B-R; Denker-J-S; Bigelow-N; Levy-L-P; Freed-J-H; Lee-D-M.
"Observation of nuclear spin waves in spin-polarized atomic hydrogen gas."
Phys-Rev-Lett 52, no.17, p.1508-121, 23 April 1984.

=================

Accordingly, when we speak of the four forces of nature, are we speaking
only of the non-quantum world?

1) What four forces?

1a) If you mean gravitation, electromagnetism, weak nuclear interaction,
and strong nuclear interaction..... Why unify electromagnetism without
unifying the electroweak interaction?
http://www.nobel.se/physics/laureates/1979/press.html
http://www.nobel.se/physics/laureates/1999/press.html


1b) If you are asking about "true" forces: I would not say gravitation
"is" truly a force. Certainly it _gives rise_ to forces, although it might
be better to say it gives rise to accelerations.

Similarly, the other fundamental interactions are not truly "forces".


2) There is no non-quantum mechanical world. The classical rules are
approximations that apply to the real (quantum mechanical) world in certain
limiting cases.

By way of analogy: In aerodynamics, we do not add the force of lift or
drag "plus" the force of air molecules hitting the wing; that would be
double-counting. The lift and drag _summarize_ the force resulting from
all those molecular impacts.

Similarly, we do not add the aforementioned molecular field "plus" the
identical-particle rules; that would be double-counting. So in some limit
we can, to a good approximation, describe the situation by calculating the
molecular field and then ignoring any (further) contribution from the
exclusion principle.