Localizable energy

[William Beaty <billb@ESKIMO.COM>]

On Mon, 13 Sep 1999, Leigh Palmer wrote:

> I did not mean to suggest that the energy of an isolated system is not
> localized to the extent that it is contained within the boundary of the
> system. Though a truly isolated nontrivial system does not exist because
> gravity exists, I certainly use the concept myself. Please see my two
> automobile system example.
>
> > I would assert that the statement that "energy is not localizable" is too
> > restrictive.  I would, rather, support the statement that energy is not
> > always UNIQUELY localizable.

Here's an aspect that I suddenly see...  suppose we have a coil/capacitor
oscillator with some trapped EM energy at 1MHz, and suppose the coil is
unshielded so that the vibrating 1MHz b-field surrounds the circuit.

The circuit behaves as a dipole.  Will it radiate?  Will there be a weak
field at a great distance from the dipole?  Well, if the total energy in
the circuit is fairly low, then in the region far outside the nearfield,
there will not be enough total energy to comprise a single photon at 1MHz.

This goes back to the characteristics of dipoles.  At great distances, can
we ever say that the field of a dipole is zero?  But if the dipole exists,
the field is NEVER zero, it is just very weak at a distance.  It is far
weaker than 1/R^2 fields.  Yet below a certain range of frequency/energy,
it is too weak to produce any photon interactions.  To me this looks like
QM raising its head, and saying that a weak dipole produces *ZERO* field
in the region outside of 1/2 wavelength from the dipole.  Perhaps there is
a virtual photon flux out there, but it cannot be absorbed by another
distant dipole, because the total energy out there is less than a single
photon's worth.  The fields are so weak that they are below the minimum
threshold where Quantum Mechanics allows "real" energy interactions.

By including QM in our discussions of localized energy, it appears that
there is a situation where energy is genuinely localized in every sense of
the word.  When an atom absorbs a photon, that EM energy must remain
within 1/2 wavelength of the atom, and it can only escape if the photon is
again emitted.  In the time between absorbtion and emission, that quantum
of energy is stuck inside the atom, and is not available to the rest of
the universe anymore.  The same would apply to stars whose nucleii absorb
gammas.  The dipole field of the gamma "waves" is zero as long as the
photon remains stuck inside the nucleus.  (But perhaps I'm violating
"quantum weirdness" in thinking that the photon can have "location"  as
above?  If the photon can be many places at once, including being trapped
within a nucleus, then perhaps the wave nature of EM is preserved even at
incredibly low values of field strength.  Yet single-atom-trap experiments
have shown that humans can directly see an argon ion receive and later
lose a single photon.  While Wigner's Friend is watching the friend who
watches the watcher, does the photon behave nice, and stay stuck to the
single atom?)



> > God knows I learn a lot from PHYS-L, but I am at a complete loss to
> > understand the prodigal fecundity of these writers. I just spent two
> > hours reading and digesting today's mail, so I must ask, "How long does
> > it take you chaps to write all that stuff, and where in hell do you get
> > the time?"

LOL!

When I get on a roll, I get up reeeeeeally early in the morning, otherwise
I'll be gnashing my teeth as I read and delete huge amounts of email
during lunch.



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