🚀 go-pugleaf

snarfy@cruzio.santa-cruz.ca.us writes:

>   [...] In 
>   other  words  ,once  something  becomes  an  absorber  of electromagnetic
>   radiation it too becomes an emitter and what was at a previous  time  the
>   emitter  at  that point is now another absorber (from the reference frame
>   of the first absorber ,object B).

This is indeed how such calculations are usually done.  The argument
put forth here by others is that the steady-state situation corresponds
to a continuous series of transmitted waves from A to B and from B
to A; and that putting the load at point B changes its characteristics
as an emitter, causing a change in the emitted waves from B to propagate
back at c.

>    Any  symmetry  between an emitter and absorber ,as in resonance ,demands
>   that both  the  ``retarded''  and  ``advanced''  solutions  to  Maxwell's
>   equations  be put on equal footing . 

I'm not so sure about this.
If the scenario you've depicted with A and B is in one dimension,
so that there can be a standing wave in the box in between, I agree.
Such a wave can be modeled just as well with retarded or advanced
solutions, as long as the situation has been and remains 
forever in a steady state with no changes to the object at B.
In more dimensions, it might likewise be just as
easy to model the system either way if the whole setup is in a large
conducting box, or some such thing.  If A and B are in empty
space, though (and this is being considered as a method of
interstellar communication), waves will travel outward from A
and likewise outward from B, unless the boundary conditions at
large distances in the past have been set up in a very, very
special way (see below).  Both A and B can be considered both
emitters and absorbers, and if they're both supplied with power
so that they broadcast at equal strength, there is a symmetry
between them; but the system will clearly correspond to a
retarded solution.

>   The retarded solutions usually refer
>   to the sequence cause -> effect , while the advanced solutions are  often
>   referred  to  in  terms  of a backward sequence in time, effect -> cause;
>   which solutions, if applied, make it appear that the sequence in question
>   violates the law of causality. Again ,to avoid this apparent conflict  in
>   the  context of Maxwell's equations we must reverse the names emitter and
>   absorber.

Actually, it's a matter of boundary conditions.  When properly
considered, advanced solutions don't violate causality at all; they
just make assumptions about past boundary conditions rather than
future ones.  Emitters do become absorbers in the process, but
it's necessary to remember how the situation is set up.

Consider an antenna which emits a pulse of radio waves.  This
pulse travels away to infinity.  Electrodynamics is time-
symmetric, though, and we can just as easily imagine a wave
coming in from infinity to be absorbed-- like you say-- in the
antenna.  But that assumes that a very special boundary
condition has been set up in the past, with the incoming
wave approaching the antenna in just the right way.

Consider now that a situation like the experiment you describe
has been set up.  I described the situation in my first paragraph
in terms naturally described by retarded solutions; what happens
if we consider the advanced solutions?  It's the same as the antenna
situation.  Instead of the change in the field due to the added
load at B propagating outward from B, a change in the field
propagates *inward* to B and hits B just as the load is added,
in such a way that the field afterward is a steady-state,
continuous-wave situation.  But you need very special boundary
conditions set up in the past for that to happen; assuming
that they're there is like expecting eggs to unscramble.  The fact
that we don't expect such boundary conditions in the past is
a manifestation of the arrow of time, and opens up a whole
other can of worms-- though I suspect that most arrows of
time have something to do with *cosmological* boundary
conditions.

   Therefore  ,  it  is  the  elementary  interaction  that   is
>   fundamental , not the cause - effect relationship of emitter to absorber.

I have no argument with that, except that I'd add that the
boundary conditions necessary for a given solution are very
important.  I'd even say that the boundary conditions are what
determine the cause-effect relationships.

>    In  an  ideal  resonance  condition  most  of the energy between coupled
>   elements is contained in a standing wave field that can be quantitatively
>   represented in terms of E (joules) or, more accurately VARS*t (volt  amps
>   reactive*time).

Are you in fact proposing that the entire system of A and B be placed
in a box, so that the standing wave will occur?  Or are A and B
enormous plates, light-years wide in the case of interstellar
communication?  If they're small antennae placed on various planets,
most of the energy will be contained in *traveling* waves, unless
we introduce a boundary condition in which spherical wave fronts are
perpetually moving inward toward the antennae from parts unknown, to
interfere properly with the emitted waves.  But that's actually
irrelevant to what follows.
 
>   Changing  the value of one of the reactive elements will
>   have an effect on the E or VAR*T value of this entire field which must be
>   compensated for by some equal and opposite reaction on the  part  of  the
>   complementary  reactive  element  at  the  other end.  If energy is to be
>   conserved (according to the law of conservation of mass and energy)  then
>   any  delay  in  this  reaction  would  result  in  consequences  that are
>   mathematically unacceptable if the reactive elements continue to  operate
>   during  the  delay. In other words, depending on the nature of the change
>   at a reactive element ,you end up with + or - value of  VARS  *  T(delay)
>   which  is  either   incompatible  with conservation laws or ohm's law,(as
>   ohm's law is generically defined as Energy flow = Force /  impediment  to
>   force). On the other hand ,if the response at the other end is assumed to
>   be instantaneous , this conflict does NOT arise.

You *are*, then, abandoning Maxwell's equations here in favor of
something else.  Since nobody is conspiring to set up favorable past
boundary conditions to make the advanced solutions come out right,
the change in the system has to be described by retarded solutions.
The retarded solutions describe changes in the field propagating at
a speed of c from the changes in the sources.  There's no change from
the continuous-wave situation at A until the change in the field arrives
there.  Energy starts to flow out of the field near B before it
starts to flow into the field from A; conservation is ensured by
a loss in the energy content of the field.

Which of the myriad forms of the generalized Ohm's law are you
actually using?  If you're using V = I/z, keep in mind that the
(complex) voltage across the reactance at B is the one you should
use to compute the current through B.  That is not at all necessarily
the same as the voltage across A.  It may be that Ohm's law doesn't
explicitly include a time or distance allowance, but it obviously
doesn't allow you to calculate the current through some element in
a system by measuring the voltage across some totally different
element.  If you assume that the two voltages are always the same,
then that's where you're abandoning Maxwell.

If you then use the dot product of voltage and current phasors to
find the power turned to heat, keep in mind once again that the
voltage and current you should use are the voltage across and the
current through the reacting element at B.  To use anything else
is just as unwarranted as measuring the voltage across my 
terminal's electrical cord and the current through power
lines in Omaha and expecting the product to mean something.
 
>    Inasmuch as Maxwell's equations correctly predict phenomena , I have  no
>   argument  that they are not fundamental to that branch of electrodynamics
>   concerned with those phenomena. I am not aware of any  attempt  to  apply
>   Maxwell's  equations  to  resonance  conditions (where doing so would not
>   have the consequences outlined above). 

You might want to read volume 2 of the Feynman lectures; he applies
Maxwell's equations to cavity oscillations, albeit in a single,
very idealized situation.  It's clear in that case
that what I've described would happen if the absorber/emitter (in
this case, the wall of the cavity) were changed at some point, since
what I've said about boundary conditions and changes in the field
still applies there.

>   As far as Ohm's law is concerned ,
>   it  is  emphasized  that  we're generalizing the meaning to a fundamental
>   function that is applicable to many different phenomena, for example:

>       I=V/r , I=V/z , flow=pressure/restriction , work=force/load.. etc.

That's fine... see my concerns above.

>      I'm not sure by whose standards you are applying the term ``usual''.By
>   my own standards and others who work with actual electronic components it
>   would  be  unusual  to  do  design  calculations  starting with Maxwell's
>   equations on through  their  formulaic  derivations  (although  I'm  sure
>   that's possible) . It's simply that we've learned to get by with standard
>   formulas  that  may  be  (or  may not be , for all I know) derivable from
>   Maxwell.  I know of no derivation from Maxwell's equations  that  are  in
>   basic conflict with the generalized form of ohm's law, above.

Of course, it would be very difficult to work with electronic components
using nothing but Maxwell's equations; for active components using
quantum-mechanical effects, it wouldn't even be possible.

In this case, I'm not sure whether there really is a conflict between
Maxwell and generalized-Ohm, and I'm not sure whether the rules you 
used really imply the results you claim.  The AC version of Ohm's
law, in which the reactance appears, only applies to situations
in which the quantities all refer to the same circuit element,
and to elements small enough that the time scale on which events are
under consideration is much longer than the time it takes for transient
effects like those of a sudden change in the reactance to die
down.  In this case, the elements that satisfy those criteria
are the objects A and B, not the whole system.  If you apply
Ohm's law correctly, I think you'll find that it doesn't say
anything about instantaneous transfer of energy.

I *do* believe that Maxwell's equations don't
imply the results you claim.  At any rate, it's always good to be
aware of the limits of the assumptions used to derive formulae.
 
-- 
Matt McIrvin, professional gradgrind, amateur Usenet drifter