On Jun 26, 1:55=A0pm, "Timo A. Nieminen" <t...@[EMAIL PROTECTED]
> wrote:
> On Wed, 25 Jun 2008, Bill Miller wrote:
>
> > "Timo A. Nieminen" <t...@[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" <t...@[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
electros=
taic
> >>> 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,
describin=
g
> >> gravitational forces as interactions between distant bodies, is
replac=
ed
> >> 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
partia=
l
> > credit for) =A0and 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
tha=
t
> 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-Heavisid=
e
> 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
charge=
d
> 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
n=
eed
> > to understand that if two events occur at the same time, neither can
ca=
use
> > 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
an=
d
> > 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) =3D 0, div(H) =3D 0) solutions of the
vec=
tor
> 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
teachi=
ng of
> > this is expeditious & that once one gets to the PG leve, the "true
fact=
s"
> > 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
fo=
r
> 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
man=
y
> 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
instructor=
s
> > don't know it!
>
> Likely enough.
>
> > Is there a single UG EM textbook that correctly categorizes the
relatio=
n****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
a=
nd
> >> 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
tha=
t
> 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
o=
ut.
>
> >>>> 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
objec=
ts
> >>>> each interacting with a field. Perhaps the interaction really is as
> >>>> described by field theory, a local interaction between field and
bod=
y,
> >>>> 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.
Th=
at'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
i=
n a
> >>> time-dependent environment.
>
> >> I think it is different conceptually. One is a conservation law, and
t=
he
> >> 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
objec=
ts,
> > 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
h=
ave
> > an interesting set of pre-made experiments already in process. Like,
ma=
ybe,
> > does our model explain why the rotational speed of the Sun at the
equat=
or 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
"missin=
g
> > mass of the universe" question? What might it say about gravitational
w=
aves?
> > Does it provide a definitive explanation of the process wherein
potenti=
al
> > energy is converted into kinetic energy by a falling body? Does it
expl=
ain
> > 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,
an=
d
> 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
Excellent response, Timo. It's thoughtful posts like this that make
trawling these groups worthwhile.
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