Lester Zick (lesterzick@earthlink.net)
Wed, 05 May 1999 11:24:11 -0400
If it seems strange to think in terms of energy quanta, it seems doubly
odd to consider the prospect of quantized angular momentum, as is
suggested by Planck's constant. (By the way, in the first posting on
this topic, Planck's discovery should have been described as arising
from his attempt to correlate the distribution of frequencies in
blackbody radiation as a function of temperature.) Angular momentum is
equal to a=mvr, or the product of some mass, its velocity, and the
distance between paths. And even if we allow the possibility of
quantized mass, there is nothing to suggest that v or r may quantized in
mechanical terms.
What, then, are to make of the whole concept? The correct interpretation
of quantum phenomena can only be approached from another direction.
First we must consider exactly what it is that is being quantized and
how and with what results. If we ignore the mechanical implausibility of
quantized angular momentum in general, what we find is that energy
arises from changes in angular momentum and that Planck's constant
simply represents the gradient on which this must occur.
Thus we are not technically dealing with quantum angular momentum at
all, rather a quantum gradient on which changes in angular momentum must
occur. In actuality, therefore, it is changes to angular momentum rather
than angular momentum in absolute terms which is quantized. And it is
the rate of such changes which are described by Planck's constant.
Now let us look at the mechanical rationale for this. A body with mass
and ordinary linear or longitudinal velocity has constant angular
momentum with respect to all points in space. Not necessarily the same
angular momentum, just some constant angular momentum with respect to
each point. This is because the product a=mvr remains constant with
respect to every point in space since the area swept in a unit of time
with respect to each point remains the same however far apart they may
be or become provided m, v, and r remain unchanged. This situation of
motion in a straight line at constant velocity I call constant angular
momentum in universal terms and the system has zero energy in angular
terms because there is no change in angular momentum.
However, if v changes direction then angular momentum also changes even
if the absolute magnitude of v does not. Thus the system acquires energy
resulting from the rate of change in angular momentum. And it is this
change which can only occur on a gradient defined by Planck's constant.
In the absence of change, there is no energy in angular terms, and in
the presence of change it is the rate of change, in effect the
frequency, which is quantized.
Thus in dealing with quantum phenomena in the context of particle
properties such as mass, energy, angular momentum, and uncertainty in
location, it is critical to understand that the underlying mechanical
property described by Planck's relation is not angular momentum in
general terms at all: it is changes in angular momentum. Therefore, we
must regard rotational motion in the context of particle and atomic
structure to reflect the gradient of change permitted according to
Planck's constant.
And if we correctly define a particle's frequency in terms of changes in
angular momentum, we can determine that particle mass and energy are
directly related to Planck's constant as well as its size and even the
origin of Planck's constant itself as a multiple of more fundamental
constants.
Regards - Lester
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