Thomas Lee Abshier, ND
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Angular Momentum
Conservation of Angular Momentum
& the Photon
By: Thomas Lee Abshier,
ND
- Angular momentum obviously arises when a force is applied perpendicular to the normal
linear motion of a mass. The linear force that maintains momentum comes from the
decaying magnetic field associated with mass-velocity. The force acting perpendicular
to normal momentum may be an inter-atomic or intra-atomic bond, such as between two
atoms or between electron and nucleus. The perpendicular force may be produced by
a field acting on a mass, such as: gravitational fields acting between neutral bodies,
electrostatic fields acting between charges, magnetic fields acting between magnets,
or EM fields absorbed by an electron. In other words, the perpendicular force may
arise from many different sources, but the common ingredient is the presence of force
acting perpendicular to momentum.
- But, the fact that forces connecting orbiting systems may decouple requires us to
expand our definition of angular momentum to declare “conservation of momentum” as
a law.
o An example of decoupling of an angular system includes skaters who twirl together
and then release, each then taking separate linear paths. For conservation of angular
momentum to occur there must have been an element of angularity to the skaters’ relationship
prior to their coupling. They both had a velocity which was slightly askew, and
thus tangential to a central point where they joined. Thus, prior to their joining
as a coupled angular system, they had a velocity that was angular around a certain
point. And likewise, as the skaters release their grasp, they continue on their
separate linear paths, but they do so around a common point which retains an element
of angular momentum.
- This now brings us to our most difficult scenario, the conservation of momentum in
the orbital electron and emitted-photon system. The photon has no mass, but it can
be considered to have momentum.
o Before the electron loses angular momentum to photon emission, the energy of the
electron-nucleus is angular and electrostatic potential energy. At the moment the
electron releases from the orbital electron, the electrostatic potential energy component
diminishes.
o The system is unusual in that a portion of an orbital system has left and for all
practical purposes, the track of the photon has little ongoing relationship with
the orbital path of the electron after it decays into the lower orbital.
o Thus, to make the concept of angular momentum useful, we must tighten down the
system boundaries for examination. At the moment of photon release, the electron
has been in some way disturbed, and is no longer able to maintain its activated state.
Thus, the polarized energy in the space around the orbital electron becomes dissociated
with it, leaving the orbital electron as a photon.
o The normal method of analyzing conservation of momentum is to note that two masses
depart around a common point of axis rotation. In this case there is no offset between
the activated orbital and the photon. But, there is a differential of distance between
the photon and the lower energy orbital. Thus, the photon as a unit of momentum,
in relationship to the nucleus, at the same time as the orbital electron is in relationship
the nucleus in its lower orbital, the two entities split in a moment, the electron
simply assuming the lower energy state of the energy-depleted orbital. Thus the
moment before decay, the angular momentum of the system was entirely contained within
the orbital electron. The moment after the decay the two entities were separated,
photon with its angular momentum, and orbital electron with its photon-deficient
orbital angular momentum.
o The photon carries angular momentum even though it has no rest mass. The concept
of p=mv is not relevant to the photon because there is no rest mass to put into the
equation. Instead, the photon’s organization of E&B fields oscillating normal to
the direction of travel as a packet contain the energy and momentum-type organization
(i.e. organized DPs in motion). Another confirmation of the conservation of the
angular momentum as the photon separates from the orbital electron comes as the photon
carries its energy in units of integer multiples of Planck’s constant, which has
units of angular momentum (joule-sec).
o Note that linear momentum and angular momentum are interconvertible simply by changing
the focus of the system. A snapshot of two masses without note of their interconnection
reveals a system with a given amount of linear momentum. If we could instantly place
a connecting force between the two (such as a hook catching at a particular moment),
we would have an actual forced angular relationship between the two masses. And
while there was only a potential angular relationship between the two prior to the
hook-connection, there was an actual bonded angular momentum afterwards with no angular
momentum. This type of analysis, looking at the potential bonded angular momentum
when two masses are in their unbonded state is the conventional method of considering
the conservation of angular momentum before and after bonding.
o The photon-orbital electron system falls into this same category with the hook,
in that the photon completely decouples from the orbital system at the moment of
orbital electron decay. The method of characterizing and partitioning the energy-type
and their relationship to the angular momentum before and after decay is different
than in the ball and hook system, but nevertheless, there is a way of connecting
the angular momentum before and after so as to declare conservation.
o The linear photon leaves a system that continues in its angular character. This
is different than the more macroscopic ball and hook world of masses decoupling.
Nevertheless, the photon’s angular momentum associated with its fields, and the
angular momentum of the orbital electron after decay have a connection in the time
sequence of the decay, and make a smooth conversion between the pre and post decay
configurations of angular momentum.
