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?

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.

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/teachin...es/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...

"Edward Green" wrote in message
oups.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.

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.


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

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?

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 (:-)).

[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:
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_ he 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" wrote in message
oups.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)/gu...s/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.blueyonde...ickeyLarge.gif

Androcles.

Tom Roberts wrote:
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/teachin...es/node28.html


[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...




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_ he 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

Bill Hobba wrote:

"Edward Green" wrote in message
oups.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 ".

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:

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

[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.

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.

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.

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.

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.

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.

--
Timo Nieminen - Home page: http://www.physics.uq.edu.au/people/nieminen/
E-prints: http://eprint.uq.edu.au/view/person/...,_Timo_A..html
Shrine to Spirits: http://www.users.bigpond.com/timo_nieminen/spirits.html

Sue... wrote:
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