diogenes500@gmail.com
Nov4-06, 03:32 PM
Hello,
I have a question concerning the radiative energy balance of particles
in a magnetic field.
For example, say I have a box of hydrogen atoms (or molecules; it
doesn't matter as long as the atom/molecule can have excited electron
states) at room temperature and I expose this box to a constant
magnetic field (via permanent magnets) in the z direction. Now, since
the particles are moving (from being at a non-zero temperature,
"bumping" in to other particles, the walls, etc) with respect to
the frame in which the magnetic field is constant the particles will
feel an electric field. It seems to me this electric field, since for
each particle it is nearly always changing in time due to the change in
motion of the particle, can be treated as a perturbation, similar to
varying an electric field on a stationary atom (somewhat like in
problem 5.28 in Sakurai). If this is true then there is a non-zero
probability that the particle will go into an excited state*. If a
particle does go into an excited state then, at some later point (maybe
it goes to an even high state next), it will return to the ground state
and to do so it must emit a photon. The particle can then repeat this
cycle ad infinitum.
It seems there must be something wrong with this explanation of events
because if it is correct it seems energy would not be conserved.
Let's keep track of the energy from the beginning. It took some
finite amount of energy to put the magnets near the box of particles,
but once they were in place no more energy is required to keep the
magnetic field there (i.e. no more energy is need to produced the
electric fields the particles see do to the magnetic field). Next,
atoms are perturbed, some go into excited states and eventually
radiate. But this exciting/emitting phase apparently has no time limit,
so one could wait some arbitrarily long time for an arbitrarily large
amount of energy to leave the magnet/box system (some, even most, of
the photons emitted will be reabsorbed by other particles but some
fraction of the emitted photons will make it out).
The "obvious" explanation is that the energy which the particles
radiated is taken from the electromagnetic field. But this must imply
that the strength of the field, the strength of the B field created by
the permanent magnets, decreases over time, which just doesn't seem
physical to me. You can't "drain" a permanent magnetic, can you?!
Another explanation might be that the atoms are taking the thermal
energy and turning it into radiation. But this would be spontaneous
cooling and other no-nos, which seems just as bad as violation of
energy.
So I'm guessing it must be the case that the atoms actually don't
emit photons (from atomic transitions). But I can't see how the
exciting/emitting is suppressed; after all, the particles do see an
electric field (and a changing one at that!) and that seems to point to
transitions. Pheeww! This is turning into a manifesto, anyone know what
is going on here?
* Of course the particles won't actually be in a particular state
until interactions with other particle, the environment in general,
force them to be in some particular state which with some non zero
probability is an excited state.
I have a question concerning the radiative energy balance of particles
in a magnetic field.
For example, say I have a box of hydrogen atoms (or molecules; it
doesn't matter as long as the atom/molecule can have excited electron
states) at room temperature and I expose this box to a constant
magnetic field (via permanent magnets) in the z direction. Now, since
the particles are moving (from being at a non-zero temperature,
"bumping" in to other particles, the walls, etc) with respect to
the frame in which the magnetic field is constant the particles will
feel an electric field. It seems to me this electric field, since for
each particle it is nearly always changing in time due to the change in
motion of the particle, can be treated as a perturbation, similar to
varying an electric field on a stationary atom (somewhat like in
problem 5.28 in Sakurai). If this is true then there is a non-zero
probability that the particle will go into an excited state*. If a
particle does go into an excited state then, at some later point (maybe
it goes to an even high state next), it will return to the ground state
and to do so it must emit a photon. The particle can then repeat this
cycle ad infinitum.
It seems there must be something wrong with this explanation of events
because if it is correct it seems energy would not be conserved.
Let's keep track of the energy from the beginning. It took some
finite amount of energy to put the magnets near the box of particles,
but once they were in place no more energy is required to keep the
magnetic field there (i.e. no more energy is need to produced the
electric fields the particles see do to the magnetic field). Next,
atoms are perturbed, some go into excited states and eventually
radiate. But this exciting/emitting phase apparently has no time limit,
so one could wait some arbitrarily long time for an arbitrarily large
amount of energy to leave the magnet/box system (some, even most, of
the photons emitted will be reabsorbed by other particles but some
fraction of the emitted photons will make it out).
The "obvious" explanation is that the energy which the particles
radiated is taken from the electromagnetic field. But this must imply
that the strength of the field, the strength of the B field created by
the permanent magnets, decreases over time, which just doesn't seem
physical to me. You can't "drain" a permanent magnetic, can you?!
Another explanation might be that the atoms are taking the thermal
energy and turning it into radiation. But this would be spontaneous
cooling and other no-nos, which seems just as bad as violation of
energy.
So I'm guessing it must be the case that the atoms actually don't
emit photons (from atomic transitions). But I can't see how the
exciting/emitting is suppressed; after all, the particles do see an
electric field (and a changing one at that!) and that seems to point to
transitions. Pheeww! This is turning into a manifesto, anyone know what
is going on here?
* Of course the particles won't actually be in a particular state
until interactions with other particle, the environment in general,
force them to be in some particular state which with some non zero
probability is an excited state.