On Wed, 25 Jun 2008, Bill Miller wrote:
>
> "Timo A. Nieminen" <timo@[EMAIL PROTECTED]
> wrote in message
> news:Pine.WNT.4.64.0806240535450.1160@[EMAIL PROTECTED]
>> On Mon, 23 Jun 2008, Bill Miller wrote:
>>
>>>
>>> "Timo A. Nieminen" <timo@[EMAIL PROTECTED]
> wrote in message
>>> news:Pine.WNT.4.64.0806221102300.656@[EMAIL PROTECTED]
>>>> On Sat, 21 Jun 2008, Bill Miller wrote:
>
> <snip>
>
>>> Correct. And as long as the interaction is of a contact nature, then
>>> eveything is OK. But when there is a delay between the action and the
>>> reaction, then *for that delay period* momentum is not conserved. But
we
>>> know that momentum MUST be conserved, so we must look at Newton with
an
>>> eye
>>> to modifying it to deal with what amounts to a time dependency.
>>>
>>> This is not a new idea. We have long recognized, for EM that
electrostaic
>>> representations break down when time dependency is present.
>>>
>>> Heaviside suggested this in 1893 but never took it all the way to its
>>> logical conclusion.
>>
>> Heaviside's Maxwellian gravitation? There is no modification of
Newton's
>> laws of motion in it. Newton's law of universal gravitation, describing
>> gravitational forces as interactions between distant bodies, is
replaced
>> by a field theory, wherein all interactions are local - body interacts
>> with local field, not body with distant body.
>
> You must be looking at a different copy of Heaviside's 1893 article. In
it,
> he clearly (to me at least) understood concepts of time-dependancy, the
> gravitational equivalent of the Poynting Vector (that he claimed partial
> credit for) and others.
Of course he looks at time-dependent situations - otherwise his
finite-speed Maxwellian model of gravitation just reduces to Newton's law
of universal gravitation. But the whole essence of his approach is to
replace Newton's law of action at a distance with a local field theory,
starting firmly on this path right at equation (1).
> I agree that he did NOT deal with retardation.
> Neither did/does Maxwell!
Heaviside deals with retardation, but not so transparently. He introduces
a finite (constant, i.e., frequency independent) speed v of gravitation,
and goes from there.
Maxwell knew that his theory could be described in terms of retardation -
he recognises the mathematical equivalence between his theory and Lorenz's
in a footnote in his Treatise. I don't know when he realised this, or that
he had a retardation compatible theory. Perhaps when he gets the wave
equation with a constant speed?
Which brings me to a related, but not-so-related, point. Maxwell was, IMO,
a good enough mathematician so that he could have done the Hertz-Heaviside
simplification of his equations himself. Why didn't he? Since he
identifies the field quantities in his version as physically meaningful
(e.g., vector potential as momentum of the ether), there isn't any point
in getting rid of them. He's not just trying to describe forces on charged
bodies or currents (which Hertz and Heaviside seemed to be content with),
but wanted to know what the ether was up to. If you want an instantaneous
snapshot of the ether, you don't want a retarded formulation of the
theory. I don't know, but perhaps this influenced him.
> This "action at a distance" has always been an Achilles Heel.
>
> It is resolved, I believe by understanding and applying Causality. We
need
> to understand that if two events occur at the same time, neither can
cause
> the other. Instead, at least one must be caused by some other (hidden)
> event.
Shades of Aristotle.
> Recognition of this simple concept would, as one example, have stopped
> generations of instructors from teaching their students that E causes H
and
> H causes E. It would have also stopped generations of mathematical
> physicists from publi****ng articles in peer-reviewed publications that
> "proved" that E causes H or vice versa. And it would have stopped
> generations of experimental physicists from spending countless hours and
> dollars in building apparatus to measure the non-existent H between the
> plates of capacitors.
Not so many papers, hours, or dollars. The existence of electromagnetic
waves, transverse (i.e., div(E) = 0, div(H) = 0) solutions of the vector
Helmholtz equation, is pretty good evidence that the dD/dt term really
belongs in the Maxwell equations, so perhaps a more direct "proof" isn't
seen as essential.
> If I have understood your position on this, Timo, it is that the
teaching of
> this is expeditious & that once one gets to the PG leve, the "true
facts"
> are revealed and everything is fine.
Well, for better or for worse, what is taught is necessarily simplified.
Alas, while a small number of misconceptions might be corrected in later
undergrad or postgrad education, many are not. With limited time, and
limited initial knowledge, there are limits to what can be taught. I
woulnd't say that everything is fine, just that it isn't easy to do
much better. One particular problem is that many (most?) courses lead to
just cramming for an exam, followed by forgetting. Emphasis on techniques
and proofs over any real understanding. One problem is that understanding
comes with experience, and a 1 semester course allows very little time for
that.
I don't think that the current issue (E, H, and causality) is such a big
deal. It's mostly harmless as far as beliefs go, and only one of very many
various misconceptions that students pick up. They learn far worse ones
along the way. It also isn't enough to just tell them in lectures -
students don't learn from lectures, they learn from *****sment and
preparing for *****sment. It's hard to *****s understanding, so
understanding tends to not be *****sed strongly, so students don't get
really motivated to understand.
> That leaves hordes of non PG students still believing this rubbish. And
it
> begs the question of why, in UG cl*****, the instructors don't say
> *something* about how theses two parameters don't cause each other, but
that
> they always appear simultaneously. I suspect its because the instructors
> don't know it!
Likely enough.
> Is there a single UG EM textbook that correctly categorizes the
relation****p
> between E and H? Even ONE?
Probably. Very likely. But specialised EM texts are the stuff of advanced
(or at least intermediate) undergrad courses. Those who do just 1 or 2
physics courses ay uni, or only do high school physics never get to see
them. There might well even be generic introductory textbooks that don't
get it wrong, by not mentioning it at all. If I have time in the near
future, I will look.
>> Newton 1 and 2 are pretty much just definititions of inertial motion
and
>> force, while Newton 3 is (as above) conservation of momentum. How can
these
>> be modified sensibly?
>
> I'd say that looking at Causality and incor****ating what we learn into
new
> expressions that include factors tor time variation of position and for
> timevariation of mass would get the job done.
New expressions for what? My point is that it's easy enough to modify,
e.g., a force law (as Heaviside did Newton's law of universal
gravitation), or Coulomb's law (as per Maxwell), but a very different
thing to try to modify Newton's laws of motion, which are of a very
different fundamental nature.
> Naturally, any such additions
> must obey conservation of momentum AND must reduce to the original form
when
> time dependancy is absent.
Well, if you want conservation of momentum, then you're _not_ going to be
modifying Newton 3. Also, if you want retarded interaction at a distance
along with conservation of momentum, then you're going to need fields that
can carry the momentum from point A to point B (or some other "thing" to
have the momentum when the "interacting" objects don't have it).
Or we change our ideas about what conservation of momentum means.
>>>> Yes, if we consider two m***** as above (or two electric charges) to
be
>>>> interacting with each other, we have exactly the problem you point
out.
>>>>
>>>> Does this mean Newton 3 is wrong? Does this mean momentum is not
>>>> conserved? I would say that it means that we simply don't have a
>>>> situation
>>>> where there are two objects interacting at a distance, but two
objects
>>>> each interacting with a field. Perhaps the interaction really is as
>>>> described by field theory, a local interaction between field and
body,
>>>> and
>>>> we should throw away the classical mechanics idea of interaction at a
>>>> distance rather than Newton 3.
>>> That's one way of dealing with it. I believe that a better way would
be
>>> to
>>> recognize that Newton's work is not applicable to time dependency.
That's
>>> no
>>> different, conceptually, from Maxwell's expansion of Ampere's Law to
>>> include
>>> The rate of Change Of E field in order to deal with magnetic fields in
a
>>> time-dependent environment.
>>
>> I think it is different conceptually. One is a conservation law, and
the
>> other describes a limited set of experimental observations.
>
> It is true that gravity is a whole bunch of orders of magnitude more
> difficult to deal with experimentally than EM. Building planetary
objects,
> setting them rotating, and zapping them past one another is way beyond
our
> experimental capability.
>
> BUT, we have a handy set of "toys" in our own night sky. And there we
have
> an interesting set of pre-made experiments already in process. Like,
maybe,
> does our model explain why the rotational speed of the Sun at the
equator is
> different from the speed at the poles? Or does it provide some insights
into
> Mercury's (supposedly) residual precession? Does it sup****t or deny the
> existence of black holes? Does it provide some insight into the "missing
> mass of the universe" question? What might it say about gravitational
waves?
> Does it provide a definitive explanation of the process wherein
potential
> energy is converted into kinetic energy by a falling body? Does it
explain
> why EM beams are deflected by gravity?
>
> But that's a lotta work. Doing it wrong is a lot easier!
Apart from the rotational speed of the sun, which at first glance is more
a matter of fluid dynamics and plasma physics rather than gravitation, and
perhaps the missing mass stuff, yes, our best models of gravity do answer
these questions. Alas, they don't reduce to Heaviside's model in the
appropriate limit, There was a nice paper by Robert Forward in Proc. IEEE
(or Proc. IRE, if before the name change of the journal) in the 1960s
about the weak-field limit of GR.
--
Timo Nieminen - Home page: http://www.physics.uq.edu.au/people/nieminen/
E-prints: http://eprint.uq.edu.au/view/person/Nieminen,_Timo_A..html
Shrine to Spirits: http://www.users.bigpond.com/timo_nieminen/spirits.html
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