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Sue...
science forum Guru

Joined: 08 May 2005
Posts: 2684

Posted: Sat Jul 08, 2006 11:33 pm    Post subject: Re: Magnetic Idyll

Edward Green wrote:
 Quote: The formal simularity of the Coriolis force and the Lorentz force law -2w x v vs. -qB x v suggests that the magnetic field may correspond to a local rotation of space (inertial coordinate system) as seen by charge vs. that seen by mass. On the pro-side, one can easily list more hints that magentic effects have to so with something or other rotating. On the con side, there doesn't seem to be an obvious way in incorporate the centrifugal force into this analogy -- for purposes of "magnetic rotation", the test particle is always on axis. Comments?

What rotates is an ensemble of electric charges.
"The origin of permanent magnetism"
http://farside.ph.utexas.edu/teaching/302l/lectures/node62.html
"Visualizations"
http://web.mit.edu/8.02t/www/802TEAL3D/teal_tour.htm

If you take a Machian view of inertia, the the dielectric propeties
of free space don't make too bad an analogy to the gravitational/
inertial field established by nearby matter.

There are numerous way to incorporate the
magnetic force into gravity/inertia. You are building bricks
with little houses. Try it the other way round. )

http://www.esa.int/SPECIALS/GSP/SEM0L6OVGJE_0.html
http://www.mypage.bluewin.ch/Bizarre/GRAV.htm

Sue...
Bill Hobba
science forum Guru

Joined: 02 May 2005
Posts: 2138

Posted: Sun Jul 09, 2006 1:24 am    Post subject: Re: Magnetic Idyll

"Edward Green" <spamspamspam3@netzero.com> wrote in message
 Quote: The formal simularity of the Coriolis force and the Lorentz force law -2w x v vs. -qB x v suggests that the magnetic field may correspond to a local rotation of space (inertial coordinate system) as seen by charge vs. that seen by mass.

Cross products appear all over the place in physics. That does not imply
they are related any more than bacteria growth and monetary growth with
interest being exponential implies bacteria are related to money.

 Quote: On the pro-side, one can easily list more hints that magentic effects have to so with something or other rotating.

Sure - usually electron spin or electrons 'rotating' around atoms. Of
course these are quantum effects but in a very crude way it is rotation.

Bill

 Quote: On the con side, there doesn't seem to be an obvious way in incorporate the centrifugal force into this analogy -- for purposes of "magnetic rotation", the test particle is always on axis. Comments?
Tom Roberts
science forum Guru

Joined: 24 Mar 2005
Posts: 1399

Posted: Sun Jul 09, 2006 5:34 am    Post subject: Re: Magnetic Idyll

Edward Green wrote:
 Quote: The formal simularity of the Coriolis force and the Lorentz force law -2w x v vs. -qB x v suggests that the magnetic field may correspond to a local rotation of space (inertial coordinate system) as seen by charge vs. that seen by mass.

Not really.

The Lorentz force law, written in terms of physical quantities in 4-d
spacetime using the language of tensors is:
f = q F.U
Where f is the covariant force 4-vector, F is the electromagnetic field
2-form (includes both B and E), and U is the 4-velocity of the particle
with charge q.

Using the same language, the "Coriolis force" is:
f = 0

I see no similarity here at all ().

[Note, please, that "Coriolis force' is fictitious -- merely
an artifact of one's coordinates (your formula applies only to
rotating coordinates). It is _not_ a tensor; Lorentz force is.]

Besides, if this were truly a good analogy there would be an
electromagnetic analog to "centrifugal force" (which is usually much
larger than the "Coriolis force"). With your identification above, the
EM analogy would be B x (B x r), which does not appear in any usual
formula of classical electrodynamics that I am aware of (one applies
"centrifugal force" to a particle sitting still on a carousel, but a
charge sitting still does not "feel" B at all).

Bill Hobba wrote:
 Quote: Cross products appear all over the place in physics. That does not imply they are related any more than bacteria growth and monetary growth with interest being exponential implies bacteria are related to money.

Lest anybody wonder why such different phenomena are described by
similar mathematics, let me point out that one makes similar
_approximations_ here: in the real world, the bacteria do not really
have exactly equal and constant reproduction rates, and the money does
not have exactly constant interest rate; by _approximating_ those as
constant one obtains similar differential equations with similar solutions.

Tom Roberts
Sorcerer1
science forum Guru

Joined: 09 Jun 2006
Posts: 410

 Posted: Sun Jul 09, 2006 8:36 am    Post subject: Re: Magnetic Idyll "Edward Green" wrote in message news:1152400330.145973.161020@s13g2000cwa.googlegroups.com... | The formal simularity of the Coriolis force and the Lorentz force law | | -2w x v vs. -qB x v | | suggests that the magnetic field may correspond to a local rotation of | space (inertial coordinate system) as seen by charge vs. that seen by | mass. | | On the pro-side, one can easily list more hints that magentic effects | have to so with something or other rotating. On the con side, there | doesn't seem to be an obvious way in incorporate the centrifugal force | into this analogy -- for purposes of "magnetic rotation", the test | particle is always on axis. | | Comments? 1) Coriolis is a change of reference frame, not a force. The laws of physics in this frame of reference say the ball curves without being accelerated: http://ww2010.atmos.uiuc.edu/(Gh)/guides/mtr/fw/gifs/coriolis.mov 2) Single phase induction motors normally rotate in either direction, they have a starting winding to determine which. The Lorentz force is nothing more than the equivalent of squeezing a dough ball so that it spreads out, or stretching it so that it spreads in. A pastry chef understands physics better than Lorentz, he knows what to do with a rolling pin. 3) This bottle is juggled from Mickey's left hand to his right and back again. No forces are involved. If there were friction between the bottle and the Mickey's frame then the bottle frame and Mickey frame would try to combine. Then you have force. http://www.androcles01.pwp.blueyonder.co.uk/Wilson/RotateMickeyLarge.gif Androcles.
Sue...
science forum Guru

Joined: 08 May 2005
Posts: 2684

Posted: Sun Jul 09, 2006 8:53 am    Post subject: Re: Magnetic Idyll

Tom Roberts wrote:
 Quote: Edward Green wrote: The formal simularity of the Coriolis force and the Lorentz force law -2w x v vs. -qB x v suggests that the magnetic field may correspond to a local rotation of space (inertial coordinate system) as seen by charge vs. that seen by mass. Not really. The Lorentz force law, written in terms of physical quantities in 4-d spacetime using the language of tensors is: f = q F.U Where f is the covariant force 4-vector, F is the electromagnetic field 2-form (includes both B and E), and U is the 4-velocity of the particle with charge q. Using the same language, the "Coriolis force" is: f = 0 I see no similarity here at all ().

Because you did your transformation wrong so why the
big grin ?

http://farside.ph.utexas.edu/teaching/jk1/lectures/node28.html

 Quote: [Note, please, that "Coriolis force' is fictitious -- merely an artifact of one's coordinates (your formula applies only to rotating coordinates). It is _not_ a tensor; Lorentz force is.] Besides, if this were truly a good analogy there would be an electromagnetic analog to "centrifugal force" (which is usually much larger than the "Coriolis force"). With your identification above, the EM analogy would be B x (B x r), which does not appear in any usual formula of classical electrodynamics that I am aware of (one applies "centrifugal force" to a particle sitting still on a carousel, but a charge sitting still does not "feel" B at all).

What in the world do you think moves the currents toward
surface in this experiment ?

http://www.esa.int/SPECIALS/GSP/SEM0L6OVGJE_0.html

Oh! ... I forgot. That is probably something you'd really
rather not see isn't it.

Sue...

 Quote: Bill Hobba wrote: Cross products appear all over the place in physics. That does not imply they are related any more than bacteria growth and monetary growth with interest being exponential implies bacteria are related to money. Lest anybody wonder why such different phenomena are described by similar mathematics, let me point out that one makes similar _approximations_ here: in the real world, the bacteria do not really have exactly equal and constant reproduction rates, and the money does not have exactly constant interest rate; by _approximating_ those as constant one obtains similar differential equations with similar solutions. Tom Roberts
Edward Green

Joined: 21 May 2005
Posts: 95

Posted: Sun Jul 09, 2006 6:01 pm    Post subject: Re: Magnetic Idyll

Bill Hobba wrote:

 Quote: "Edward Green" wrote in message news:1152400330.145973.161020@s13g2000cwa.googlegroups.com... The formal simularity of the Coriolis force and the Lorentz force law -2w x v vs. -qB x v

That should have been " -2mw x v ".

 Quote: suggests that the magnetic field may correspond to a local rotation of space (inertial coordinate system) as seen by charge vs. that seen by mass. Cross products appear all over the place in physics. That does not imply they are related any more than bacteria growth and monetary growth with interest being exponential implies bacteria are related to money.

It at least implies that bacterial growth and monetary growth share a
common structural feature -- namely the proportionality of increment to
the amont of stuff there already. And the points of simularity in the
present case go a little deeper than "both involve cross product".
Both forms describe a force as the cross product of velocity with a
given vector (w or B) and a scalar (m or q). So prima facie, the
Lorentz force law and the coriolis force share more common features
than bacteria and money. ;-)

Tom Roberts wrote:

 Quote: Not really.

<Snip profound argument that if we express the Coriolis force in such a
way that there is no Coriolis force, then there is no Coriolis force>

 Quote: [Note, please, that "Coriolis force' is fictitious -- merely an artifact of one's coordinates (your formula applies only to rotating coordinates). It is _not_ a tensor; Lorentz force is.]

I'm well aware that the Coriolis force is a so-called fictious force.
The suggestion was put on the table that the "the magnetic field may
correspond to a local rotation of space (inertial coordinate system) as
seen by charge vs. that seen by mass". In other words -- I propose
simply in interesting speculation -- inertial coordinates may undergo a
kind of split on charge and mass in the presence of magnetic fields, so
that it is not possible to null out fictitious forces applying to both
simultaneously.

 Quote: Besides, if this were truly a good analogy there would be an electromagnetic analog to "centrifugal force" (which is usually much larger than the "Coriolis force").

A stronger objection, though I anticipated it. If the idyll is not to
die an early death, than apparently effective "r" is always zero -- the
charged particle seens a spinning world, but always sees itself at the
center of that world.

You and Mr. Hobba may find it ultimately more constructive, not to
treat every idle speculation as an occasion for yet more satisfying
error -- as you imagine it -- bashing. Assuming that is that your goal
is constructive.
Igor
science forum Guru

Joined: 15 May 2005
Posts: 315

Posted: Sun Jul 09, 2006 6:29 pm    Post subject: Re: Magnetic Idyll

Edward Green wrote:
 Quote: The formal simularity of the Coriolis force and the Lorentz force law -2w x v vs. -qB x v suggests that the magnetic field may correspond to a local rotation of space (inertial coordinate system) as seen by charge vs. that seen by mass. On the pro-side, one can easily list more hints that magentic effects have to so with something or other rotating. On the con side, there doesn't seem to be an obvious way in incorporate the centrifugal force into this analogy -- for purposes of "magnetic rotation", the test particle is always on axis. Comments?

Basically the centrifugal force is equivalent to the electric field in
this analogy. Taken together, the combined coriolis and centrifugal
forces represent the inertial analog of the Lorentz force. One can
even derive vector and scalar potentials corresponding to these
inertial forces.
Timo Nieminen
science forum Guru Wannabe

Joined: 12 May 2005
Posts: 244

Posted: Sun Jul 09, 2006 7:34 pm    Post subject: Re: Magnetic Idyll

On Sun, 8 Jul 2006, Edward Green wrote:

 Quote: The formal simularity of the Coriolis force and the Lorentz force law -2w x v vs. -qB x v suggests that the magnetic field may correspond to a local rotation of space (inertial coordinate system) as seen by charge vs. that seen by mass.

Very Maxwellian. Have you read Maxwell's papers on this kind of thing?
(Although he would have said "local rotation of the (a)ether", not space.)

For some insight: one can obtain Maxwell's equations from Coulomb's law
and special relativity. What happens if you start from Newton's law of
universal gravitation and SR? Surely you must get a gravito-magnetic term.
Heaviside did this, and it's a nice exercise. It isn't necessarily easier
to follow Heaviside than to do it from scratch.

Consider that E and B are defined in terms of the Lorentz force,
F=q(E+vxB), while D and H are defined in terms of source densities (charge
and current densities) and are thus in different units. So, even in free
space, you need constitutive relations for unit conversion (unless you
choose a perverted set of units). What are the gravitational constitutive
relations?

When I set this as a P/F open-book exam, one student was cunning enough to
find it on www, so you can search for it rather than doing it, but I
recommend trying it for an hour or so first.

--
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
Tom Roberts
science forum Guru

Joined: 24 Mar 2005
Posts: 1399

Posted: Sun Jul 09, 2006 7:53 pm    Post subject: Re: Magnetic Idyll

Sue... wrote:
 Quote: Tom Roberts wrote: The Lorentz force law, written in terms of physical quantities in 4-d spacetime using the language of tensors is: f = q F.U Using the same language, the "Coriolis force" is: f = 0 I see no similarity here at all (). Because you did your transformation wrong so why the big grin ?

Those are all tensor equations, there is _NO_ transformation involved.
That is, those equations are completely independent of coordinates or
choice of frame.

Tom Roberts
Igor
science forum Guru

Joined: 15 May 2005
Posts: 315

Posted: Sun Jul 09, 2006 7:56 pm    Post subject: Re: Magnetic Idyll

Edward Green wrote:
 Quote: The formal simularity of the Coriolis force and the Lorentz force law -2w x v vs. -qB x v suggests that the magnetic field may correspond to a local rotation of space (inertial coordinate system) as seen by charge vs. that seen by mass. On the pro-side, one can easily list more hints that magentic effects have to so with something or other rotating. On the con side, there doesn't seem to be an obvious way in incorporate the centrifugal force into this analogy -- for purposes of "magnetic rotation", the test particle is always on axis. Comments?

http://abacus.bates.edu/~msemon/Noteon.pdf
Tom Roberts
science forum Guru

Joined: 24 Mar 2005
Posts: 1399

Posted: Sun Jul 09, 2006 8:01 pm    Post subject: Re: Magnetic Idyll

Edward Green wrote:
 Quote: Tom Roberts wrote: Not really. Snip profound argument that if we express the Coriolis force in such a way that there is no Coriolis force, then there is no Coriolis force

Not at all! You ignored the fact that my equations used
_physical_quantities_.

 Quote: I'm well aware that the Coriolis force is a so-called fictious force.

Then you should abide by the consequences.

 Quote: The suggestion was put on the table that the "the magnetic field may correspond to a local rotation of space (inertial coordinate system) as seen by charge vs. that seen by mass".

This does not make sense -- the rotation of a coordinate system can have
no physical effects; something _physical_ must be rotating for there to
be physical effects. Magnetism certainly has physical effects.

 Quote: In other words -- I propose simply in interesting speculation -- inertial coordinates may undergo a kind of split on charge and mass in the presence of magnetic fields,

This, too, makes no sense. Changes ("kind of split") in the
_coordinates_ can have no physical consequences.

 Quote: Besides, if this were truly a good analogy there would be an electromagnetic analog to "centrifugal force" (which is usually much larger than the "Coriolis force"). A stronger objection, though I anticipated it. If the idyll is not to die an early death, than apparently effective "r" is always zero -- the charged particle seens a spinning world, but always sees itself at the center of that world.

Hmmm. Stranger than even quantum mechanics.... Solipsists of the world
unite!

 Quote: You and Mr. Hobba may find it ultimately more constructive, not to treat every idle speculation as an occasion for yet more satisfying error -- as you imagine it -- bashing.

To bring this up to the level of "speculation", you need to find
something _physical_ that is rotating. Imagining effects on coordinates
is irrelevant.

If you consider my pointing out errors in your thoughts as "error
bashing", then why did you post in the first place???

Tom Roberts
Tom Roberts
science forum Guru

Joined: 24 Mar 2005
Posts: 1399

Posted: Mon Jul 10, 2006 12:19 am    Post subject: Re: Magnetic Idyll

Igor wrote:
 Quote: Here's a good link: http://abacus.bates.edu/~msemon/Noteon.pdf

The authors forgot to mention that the putative E field:
E = (m/q) w x (w x r) (eq. 5)
does not satisfy Maxwell's equations, because div E != 0 yet there are
no charges present.

Tom Roberts
Edward Green

Joined: 21 May 2005
Posts: 95

Posted: Mon Jul 10, 2006 1:27 am    Post subject: Re: Magnetic Idyll

Timo A. Nieminen wrote:

 Quote: On Sun, 8 Jul 2006, Edward Green wrote: The formal simularity of the Coriolis force and the Lorentz force law -2w x v vs. -qB x v suggests that the magnetic field may correspond to a local rotation of space (inertial coordinate system) as seen by charge vs. that seen by mass. Very Maxwellian. Have you read Maxwell's papers on this kind of thing? (Although he would have said "local rotation of the (a)ether", not space.)

No I haven't. As regards rotation of the "aether" vs. "space", that is
of course merely (rather emotionally loaded, for some) semantics;
though we could say that if one of the watermarks of the aether is
"preferred rest frame", then the rotational aether, so to speak, has
never gone away.

 Quote: For some insight: one can obtain Maxwell's equations from Coulomb's law and special relativity.

The whole package? I knew that we could get a magnetic effect from SR
+ electric field (well, so I've heard), but I didn't know we could get
derivations I've seen centered on length contraction, and charge
consequently appearing bunched up, and I've seen those dismissed as at
best heuristic (which I guess means plausibility results we don't
happen to like) and at worst nonsensical -- i.e., as an example of a
failed oolie, like the infamous "flow above and below the wing must
meet up".

I suppose a proper relativistic derivation doesn't care how the distant
sources look to us, but focuses on the local properties of the field
and the requirements of Lorentz invariance. Something like?

 Quote: What happens if you start from Newton's law of universal gravitation and SR? Surely you must get a gravito-magnetic term. Heaviside did this, and it's a nice exercise. It isn't necessarily easier to follow Heaviside than to do it from scratch. Consider that E and B are defined in terms of the Lorentz force, F=q(E+vxB), while D and H are defined in terms of source densities (charge and current densities) and are thus in different units. So, even in free space, you need constitutive relations for unit conversion (unless you choose a perverted set of units). What are the gravitational constitutive relations? When I set this as a P/F open-book exam, one student was cunning enough to find it on www, so you can search for it rather than doing it, but I recommend trying it for an hour or so first.

Thanks for the constructive comments. One knows one should not be
sucked into profitless "no, what I said wasn't totally stupid"
arguments, but in the absence of positive feedback, one sometimes
falters. (Was it Pauli who said "You know, what professor Einstein says
is not so stupid...")?

I was just about prepared to stubbornly stand my ground: if we adopt as
the operational _meaning_ of "in the presence of a magnetic field
charged particles seem to see themselves at the center of a different
rotational rest frame than neutral massive particles" as "they obey an
appropriate Coriolis law analogue", then my musuing is a tautology.
And if one thinks about the geometric meaning of the cross product --
rotating the force relative to the velocity around a fixed axis in a
fixed sense, and proprotional in magnitude to the projection of the
velocity in a plane perpendicular to that axis -- the sense of having
something to do with rotation is inescapable. I also venture that
every static magnetic source (even an infinitely long straight wires)
involves effective circulation of charge.

Frame dragging?
Bilge
science forum Guru

Joined: 30 Apr 2005
Posts: 2816

Posted: Mon Jul 10, 2006 2:04 am    Post subject: Re: Magnetic Idyll

Edward Green:
 Quote: The formal simularity of the Coriolis force and the Lorentz force law -2w x v vs. -qB x v

Actually, you mean -2m w x v.

 Quote: suggests that the magnetic field may correspond to a local rotation of space (inertial coordinate system) as seen by charge vs. that seen by mass.

I'm not sure what you mean by the ``formal similarity...''
However, note that for a neutral particle, changing coordinates
to a rotating frame does not give it a charge and two different
particles with the same charge but different masses have different
radii of curvature in the same magnetic field.

What we call spacetime coordinates are numbers we can use to describe
all of the objects we observe in experiments in the same way. The
only reason that gravity can be described as spacetime curvature
(and hence transformed away locally by a suitable change of coordinates)
is that the equivalence principle, in which gravitational and inertial
masses are postulated to e equivalent, holds to the precision experiments
can so far test.

 Quote: On the pro-side, one can easily list more hints that magentic effects have to so with something or other rotating. On the con side, there doesn't seem to be an obvious way in incorporate the centrifugal force into this analogy -- for purposes of "magnetic rotation", the test particle is always on axis.
Bilge
science forum Guru

Joined: 30 Apr 2005
Posts: 2816

Posted: Mon Jul 10, 2006 4:34 am    Post subject: Re: Magnetic Idyll

Timo A. Nieminen:
 Quote: On Sun, 8 Jul 2006, Edward Green wrote: The formal simularity of the Coriolis force and the Lorentz force law -2w x v vs. -qB x v suggests that the magnetic field may correspond to a local rotation of space (inertial coordinate system) as seen by charge vs. that seen by mass. Very Maxwellian. Have you read Maxwell's papers on this kind of thing? (Although he would have said "local rotation of the (a)ether", not space.) For some insight: one can obtain Maxwell's equations from Coulomb's law and special relativity. What happens if you start from Newton's law of universal gravitation and SR? Surely you must get a gravito-magnetic term. Heaviside did this, and it's a nice exercise. It isn't necessarily easier to follow Heaviside than to do it from scratch.

Actually, jackson devotes several pages to explaining precisely why
one _cannot_ derive maxwell's equations from special relativity and
coulomb's law, giving gravitation as a counterexample as well a second
counterexample for a particle interacting with a scalar force.
(``Classical Electrodynamics,'' Jackson, J.D., 2nd ed. section 12.2).

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