On Jan 9, 3:46*pm, Dave wrote:
On Jan 9, 9:27*pm, Art Unwin wrote:

and the other approaches offered are not accepted by you for
unspecified reasons.

i have been very specific about why they are not acceptable, there are
no specific equations that relate to something measurable, nor have
you made any predictions of things that aren't already well described
by existing laws and theories.

David, the acceptance that equilibrium must prevail for toatal
accountability states that one cannot use a 1/2 wave radiator as a
basis for the application of Maxwells equations. Why is this? Because
equilibrium is determined by a period. If each half wave that
constituted a period then one is saying that the half wave resonant
point is half way between the beginning and the end of a cycle. There
is a resonant point but that same point is NOT repeatable thus one
must refer to the "period point" for equilibrium.
Physics does not squable with this assertion,amature radio does by
ignoring equilibrium requirement.
Moving on with this revealment we can then say that a radiator can be
any shape ,size or elevation as long as it is in equilibrium when
Maxwell can be applied for accountability for all forces.
Thus a radiator can be deformed ,reshaped or condensed and still be
applicable to Maxwells laws as long as equilibrium is held to.
Imediately we can therefore deduce that lumped loads if provided must
be cancelled to retain equilibrium. Thus the application of
equilibrium as required in physics provide a path for the design of
compact radiators where all forces are accounted for as well as
maximum radiation.
To ask for mathematical proof of the requirement of equilibrium or
balance which is the root or datum line for all physics is patently
absurd and immediatly declares all prior physics laws supplied by the
masters as void and redundant as all are based on equilibrium.
The real problem here is that when Maxwell by the use of mathematical
rules with his equations showed that mathematics easily
supplanted past investigation by observation that all physicsts were
lead to believe that mathematics over rule observation. Thus we now
may use mathematical deductions such as probability to substitute for
observation knowing full well that a punter at the race course will
lose all by continuous betting on favorites and it doesn't happen that
way in real life. If my memory is correct "probability" was the path
taken in the double slit experiment in the face of tha absence of a
true mathematical or observed factor . Since the results matched
consensus among physicists the subject was considered "solved" never
to be questioned again. And worse, expanded beyond the limits applied
in the test. Imaginary answers provided! Don't worry, since
mathematics rules all so imaginary can be seen as factual. Same goes
for Newtons laws where he stated that every action has an equal and
opposite reaction where present day students now add "diametrically"
to further describe "opposite" which is not the intent of Newton
initial determination. Now we have CERN spending billions on
accellerating particles instead of the prior determined waves. O my!
Art