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re:Flow of energy



Brian Whatcott asked:

When a particle transfers momentum to another particle so that
'heating is done' the momentum is said to transfer by
electromagnetic force, at least at one level of explanation.
Feynman was fond of charting transactions of several kinds.
How would he have shown the transfer?

Dumb question; Is it by means of a photon?
If not, then what?

At the level of individual fundamental particle interactions it is not true
that 'heating is done'. Heating and heat are *macroscopic* concepts which
appear as a statistically emergent phenomenon in branches of physics which
deal with *macroscopic* systems such as in thermodynamics and statistical
mechanics. This is because a heating process is one for which the
statistical distribution for the occupation of the microstates for a given
macroscopic system (i.e. a system containing a huge number of degrees of
freedom) whose state is described an entropy-bearing classical probability
distribution on the phase space (or in the quantum case as a density matrix
on the Hilbert space) of microscopic states is shifted to a new distribution
which results in a shifted value for the macroscopic expectation value of the
energy due to interactions between the degrees of freedom of the system and
those of its environment. For a purely heating process the system's own
Hamiltonian is unaffected and its energy level spectrum is unaffected.

OTOH, for a macroscopic process which is characterized by adiabatic work the
system's energy level spectrum is disturbed because the Hamiltonian has been
changed by the working process which changed one or more of the macroscopic
defining parameters (such as the volume in the case of a fluid) on which the
Hamiltonian depends. The changed energy levels results in a changed
macroscopic statistical expectation of the total energy even though the
probability distribution for the microscopic states is unchanged (or at
worst, unitarily connected to its previous version). When macroscopic work
is done the system's expectation of the total energy shifts due to a change
in the energy levels that are averaged over. When heating is done the
system's expectation of the total energy shifts due to a change in the
statistical distribution for the probability of occupation of those energy
levels. When a general macroscopic change occurs which involves both heating
and (macro) work then *both* the energy levels' values and their statistical
distribution change.

Since heat is a concept that requires a change in the probability
distribution for the occupation of the microstates for a macroscopic system
we see that the very concept of heat is inapplicable to a system (such as a
couple of elementary particles) with a few degrees of freedom described by an
individual quantum state (i.e. wave function) which is governed by the
reversible unitary evolution of the Schroedinger equation. Systems which are
simple enough to be described by mechanics (or quantum mechanics as the case
may be) have no room for the heat concept. In order to have heat the exact
detailed microstate is not treated. Rather a positive entropy statistical
distribution for the microstates' occupation must be considered instead.

When an elementary particle interacts with another one a photon (either
virtual or real) may or may not be involved. Certainly if one of the
originally interacting particles is a photon, a photon is involved. Also if
both of the interacting particles carry an electric charge then the
interaction might be characterized by the exchange of a virtual photon. Such
an interaction is said to occur because the charged particles interact with
the electromagnetic (photon) field which mediates the interaction. Photons
(and electromagnetism) do not need to be involved in general, and cannot be
involved in a process for which the constituent particles do not carry an
electric charge. This is because the photon field can only interact via its
coupling to electric charges. For instance, In the process of the beta decay
of a neutron one of the (two) 'd' quarks in the neutron interacts with the
weak vector boson field causing the emission of a virtual W- boson. This
emission process changes the flavor of the emitting quark from 'd' to 'u'.
This results in the neutron (udd) changing into a proton (uud). The virtual
W- decays *very* rapidly (while it is still deep inside the nucleon) due to a
temporary violation of energy conservation which must be repaid immediately
(the mass of a W- is about 2 orders of magnitude greater than the entire
initial neutron). The W- decays into an electron and an (electron-type)
antineutrino. The total energy contained in the outgoing electron and the
antineutrino came from the mass reduction which occurred when the heavier 'd'
quark turned in to the slightly lighter 'u' quark. The overall process
conserves momentum and energy when the masses and the recoils of all of the
product particles are accounted for. Some other quantities which are
conserved in the process are angular momentum, charge, lepton number, bayron
number, strangeness, etc.

Feynman would have shown this process (as well as all other elementary
particle interactions) by means of a stylized pictoral representation called
a 'Feynman diagram'. Feynman diagrams can be thought of as representing
actual and virtual processes as well as representing individual terms
(containing complicated multi-dimensional integrals over various functions of
the single particle propagators for the involved particles) in a perturbative
expansion for the probability amplitude for the overall interaction process.

David Bowman
dbowman@gtc.georgetown.ky.us