| Topic: |
Science > Physics |
| User: |
"Edward Green" |
| Date: |
08 Jul 2006 06:12:10 PM |
| Object: |
Magnetic Idyll |
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?
.
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| User: "Bilge" |
|
| Title: Re: Magnetic Idyll |
09 Jul 2006 09:04:58 PM |
|
|
Edward Green:
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.
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.
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.
.
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|
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| User: "Edward Green" |
|
| Title: Re: Magnetic Idyll |
10 Jul 2006 08:25:01 PM |
|
|
Bilge wrote:
Edward Green:
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.
Yes.
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...''
I think you meant "I'm not sure what you mean by 'formal simularity'.
That's similarity happening at the very same time. ;-)
I meant something like "term by term identity, after changing the
labels".
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.
True. As I mentioned, this seems to suggest that the rotational rest
frame seen by charge and that seen by mass are different. No don't ask
me to quantify this -- but it doesn't seem like such a very weird idea.
After all, cannot EM and gravity be put on the same footing by a
geometric theory called Kaluza-Klein? Possibly the extra dimensions
are exactly what is required to give this statement meaning.
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.
I'm not sure what you are getting at, but I rather think I just
answered you. Yes, this idea would imply that not all particles
behaved similarly under "geometry", but then, I think we are by
implication talking about a more complicated theory than one involving
gravity and mass alone. Different aspects of the particle may sample
different aspects of the environment -- like an ice skater feeling the
wind.
.
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| User: "Bilge" |
|
| Title: Re: Magnetic Idyll |
11 Jul 2006 05:24:23 AM |
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Edward Green:
Bilge wrote:
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.
True. As I mentioned, this seems to suggest that the rotational rest
frame seen by charge and that seen by mass are different. No don't ask
me to quantify this -- but it doesn't seem like such a very weird idea.
Depends upon one's notion of weird... But, I digress.
After all, cannot EM and gravity be put on the same footing by a
geometric theory called Kaluza-Klein?
``Seductively similar footing'' might be more accurate. Kaluza-Klein
theory died due to some problems which were not well understood. However,
the idea was resurrected, improved, expanded and lives on in what is
now known as string theory.
Possibly the extra dimensions are exactly what is required to give
this statement meaning.
If you allow another dimension, then it's not only relatively
straight-forward to create a (somewhat naive, but suggestive) theory,
but also to see how it relates to traditional E&M. In the kaluza-klein
theory, the fifth dimension was postulated to be intrinsically circular,
so that the metric had the form,
ds^2 = dt^2 - dx^2 - dy^2 - dz^2 - (Rdw)^2
A typical wavefunction for a charged particle would then be of the form,
\Psi(t,x,y,z,w) = \Psi(0)\exp[-i(Et - p.x - Rp_w w)]
where p.x means p_x x - p_y y - p_z z and p_w is the momentum in the
fifth dimension. So, we can write that as,
\Psi(t,x,y,z,w) = \Psi(t,x,y,z)\exp[-iR p_w w]
with \Psi(t,x,y,z) defined by \Psi(0)\exp[-i(Et - p.x)]
Now compare that with the standard theory in which we have some initial
wavefunction, \Psi(t,x,y,z) = \Psi(0)\exp[-i(Et - p.x)]. The standard
theory requires that the physics remain invariant under a change of
_phase_, i.e., a gauge transformation,
\Psi -> \Psi' = \Psi\exp(-iS)
must not result in any change of physics. (This requirement alone leads
to the existence of a globally conserved charge).
If you then make the identification: S = Rp_w w, you have some
basis for your claim. You can make that stronger by allowing S to
be a function of the coordinates (i.e., a local rather than
global gauge transformation). The goals of the kaluza-klein theory
were even more ambitious. Note that the mass-energy-momementum relation
(from which the earlier wave equation was obtained) now becomes,
E^2 - p.p - (p^4)^2 = 0
which suggests identifying p^4 with the usual mass, so that if you
redefine the mass as a five dimensional quantity, the electron is
massless. From there one can try to quantize the mass based on the
fact that the 5th dimension is intrinsically circular, so that one
might hope to explain the ratios of the charged particle masses
via a winding number, since \Psi(w) = \Psi(w + 2n\pi) must hold.
While that is suggestive, I don't think that sort of idea has lead
anywhere.
But, there are still more similarities. Note that in general
relativity, one defines a covariant derivative, such that when
operating on a four-vector, V^a, D_u V^a = d_u V^a + C^a_ub V^b,
where the C^a_ub are the connection coefficients (christoffel
symbols). The riemann (curvature) tensor is then obtained from
the commutator of the covariant derivatives:
[D_u, D_v] V^a = R^a_buv V^b
In qed, one obtains a gauge covariant derivative,
D_u == d_u + ieA_u
which suggests identifying iA_u as the ``electromagnetic connection
coeficients.'' (But note the factor of `i'.) By taking the commutator
of the covariant derivatives, we get:
[D_u, D_v] = (1/ie)F_vu
where F_vu is just the faraday tensor from classical E&M. Now, we
can take the partial to recover maxwell's (inhomogeneous)
equations, d_v F_vu = j^u. One then views the faraday tensor as
the electromagnetic ``curvature.''
As a final analogy, the homogeneous maxwell's equations
d^a F^bc + permutations = 0, are (in this language) a purely
geometric result, analogous to the bianchi identities.
(Look under ``fiber bundles,'' for more information on this
approach. This also analogizes to the weak and strong interactions,
and yang-mills theories, in general.)
However, the bottom line is that if you want to treat E&M
as some sort of space(time) rotation, you can't do it in
4-d. In 4-d, E&M corresponds to invariance under a change of
phase.
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.
I'm not sure what you are getting at, but I rather think I just
answered you.
Essentially, my point is that the traditional concept of space and
time applies to everything in the universe, so any adaptation of
the geometry to account for forces must apply in the _same_ way to
everything we can measure. That idea begat general relativity. By
simply eliminating one's preconceptions of how geometry has to be,
one find that gravity has a geometric origin and is not a real force,
in that it can be transformed away.
That is impossible for E&M (at least in 4-dimensions). To do what
you propose is equivalent to finding a coordinate transformation that
transforms away the electric charge.
Yes, this idea would imply that not all particles
behaved similarly under "geometry", but then, I think we are by
implication talking about a more complicated theory than one involving
gravity and mass alone. Different aspects of the particle may sample
different aspects of the environment -- like an ice skater feeling the
wind.
Well, it certainly is more complicated theory - it's called string
theiry (or M-theory), it requires 11 dimensions and it is so complicated
that nobody understands it. To the extent that some physicists understand
something about it, none have been able to suggest a realistic experiment
to test it. (This is not to say that it's wrong, but merely a fact). Once
you try to include E&M as a geometric artifact, you are stuck with having
to include the strong and weak interactions as well and start using
phrases like ``Calabi-Yau manifold'' when you speak of geometry.
Orthogonal rotations don't cut it.
.
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| User: "Edward Green" |
|
| Title: Re: Magnetic Idyll |
12 Jul 2006 05:34:27 PM |
|
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Bilge wrote:
<I beg your indulgence for postponing the parts of your post which
require close study, and asking a few simple questions>
I'm not sure what you are getting at, but I rather think I just
answered you.
Essentially, my point is that the traditional concept of space and
time applies to everything in the universe, so any adaptation of
the geometry to account for forces must apply in the _same_ way to
everything we can measure.
Why must it apply "the _same_ way"?
Are there not various charges and forces?
That idea begat general relativity. By
simply eliminating one's preconceptions of how geometry has to be,
one find that gravity has a geometric origin and is not a real force,
in that it can be transformed away.
That is impossible for E&M (at least in 4-dimensions). To do what
you propose is equivalent to finding a coordinate transformation that
transforms away the electric charge.
Electric_forces_, perhaps. Why would you expect to transform away
"charge". Do we transform away mass in GR?
Yes, this idea would imply that not all particles
behaved similarly under "geometry", but then, I think we are by
implication talking about a more complicated theory than one involving
gravity and mass alone. Different aspects of the particle may sample
different aspects of the environment -- like an ice skater feeling the
wind.
Well, it certainly is more complicated theory - it's called string
theiry (or M-theory), it requires 11 dimensions and it is so complicated
that nobody understands it.
That's encouraging.
Obviously the situation is complicated for the nuclear forces by the
necessity to consider quantization from the onset. With gravity a
classical theory covers much, and the same can presumably be said of
EM, although the border of "much" has shrunk.
To the extent that some physicists understand
something about it, none have been able to suggest a realistic experiment
to test it. (This is not to say that it's wrong, but merely a fact). Once
you try to include E&M as a geometric artifact, you are stuck with having
to include the strong and weak interactions as well and start using
phrases like ``Calabi-Yau manifold'' when you speak of geometry.
Orthogonal rotations don't cut it.
Are you certain it is impossible to devise an interally consistent
geometric theory covering merely gravity and EM?
.
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| User: "Bilge" |
|
| Title: Re: Magnetic Idyll |
13 Jul 2006 02:24:01 AM |
|
|
Edward Green:
Bilge wrote:
<I beg your indulgence for postponing the parts of your post which
require close study, and asking a few simple questions>
I'm not sure what you are getting at, but I rather think I just
answered you.
Essentially, my point is that the traditional concept of space and
time applies to everything in the universe, so any adaptation of
the geometry to account for forces must apply in the _same_ way to
everything we can measure.
Why must it apply "the _same_ way"?
Are there not various charges and forces?
Sure, but in order to define a force, you have to specify something
which differentiates it from a non-force or else the term force is
rather vacuous. Assuming you specify some quantities, A,B,C,... which
define a force and you specify some self-consistent means for measuring
those quantities, then you have a force if it is not possible to
make the quantities A,B,C,... vanish by some transformation of your
measurements consistent with their definitions. Hopefully, that was
very general without being too obtuse. I did not want to restrict the
definition to any particular theory.
Since coordinates are just numbers you assign to things as a means
or ordering them, you certainly _could_ choose to define them any
way you like to serve whatever purpose you think is useful for some
reason. The down side is that you are stuck with your definitions
and you need to explain how those coordinates translate into things
which can be measured. So, if you want to make your comparison between
the lorentz force and the coriolis force meaningful, you have to
explain what you mean by a spatial rotation, since it's not a spatial
rotation in terms of any standard definition of space.
The lorentz force actually corresponds to a spacetime rotation.
If you have a force F = qE in some frame, then under a lorentz
boost, the electric field transforms into an electric and a
magnetic field. (A change in velocity is a hyperbolic rotation).
That idea begat general relativity. By
simply eliminating one's preconceptions of how geometry has to be,
one find that gravity has a geometric origin and is not a real force,
in that it can be transformed away.
That is impossible for E&M (at least in 4-dimensions). To do what
you propose is equivalent to finding a coordinate transformation that
transforms away the electric charge.
Electric_forces_, perhaps. Why would you expect to transform away
"charge". Do we transform away mass in GR?
In effect, yes. The reason that gravity is not considered a force is
because it is possile to transform away the graviaional field at a point,
leaving a flat spacetime. In a flat spacetime, mass is a poincare invariant
but it doesn't couple to anything.
Yes, this idea would imply that not all particles
behaved similarly under "geometry", but then, I think we are by
implication talking about a more complicated theory than one involving
gravity and mass alone. Different aspects of the particle may sample
different aspects of the environment -- like an ice skater feeling the
wind.
Well, it certainly is more complicated theory - it's called string
theiry (or M-theory), it requires 11 dimensions and it is so complicated
that nobody understands it.
That's encouraging.
Obviously the situation is complicated for the nuclear forces by the
necessity to consider quantization from the onset.
Actually, it is not. One can write down a set of equations for
those forces which are exact analogues of maxwell's equations.
For example, the covariant derivative D_u = d_u + ieA_u from which E&M
follows via the commutation relations,
[D_u, D_v] = (1/ie)F_uv
( [d_u + ieA_u, d_v + ieA_v]
= [d_u, d_v] + ie [d_u,A_v] + ie [A_u, d_v] - e^2 [A_u,A_v]
The first term is zero, the second and third terms give d_u A_v - d_v A_u,
and the last term is zero because the transformation group is U(1) which
is the set of 1x1 unitariy matrices, i.e., multiplication by a phase
\exp(-iS) that depends on 1 parameter, S). (I can do this in more detail
or you can find it in any textbook on particle physics or field theory
under noether's theorem.) In any case, the eA_u comes from identifying
the field with the partial derivative of S and requiring the dirac
lagrangian to be invariant.
If the transformation is more complicated, i.e., S = M.l, where M
is some group of matricies and l are the vectors for those matrices,
you have a more complicated covariant derivative which may be written,
analogously to the one above, D_u = d_u + ig(b_u)^i. Then, you get the
general relation,
[D_u, D_v] = (1/ig)(G_uv)^k
(G_uv)^k = d_u (b_u)^k - d_u (b_u)^k - g^2 [(b_u)^i, (b_v)^j]
where the additional index comes from the fact that the phase in this
case is not a simple scalar. In fact, the index k for the strong force
corresponds to the gluon color field. There is a conserved current
obtained from taking the partial of the field strength tensor G and
that gives you the ``maxwell equations'' for the strong force (which
are more complex than in E&M, but derived in exacty the same way one
derives maxwell's equations from qed).
(A familiar analogy would be angular momentum, for which the
exponent of \exp(-i J.\Theta) defines a rotation in the direction
of the vector \Theta, with J being the rotation matrices. The
corresponding conserved current is the angular momentum if
the system is invariant under such a rotation.)
In the parlance of geometry, the field strength tensor is the
curvature tensor for the strong force. Note however, that the
curvature tensor for E&M, and the index k for the weak force and
stron force corresponds to some quantity other than the spacetime
variables, while for general relativity, the curvature is explicitly
in the spacetime itself. Loosely speaking, the basic idea behind
string theory is to increase the number of dimensions of spacetime
sufficiently to accomodate these forces as geometric quantities
in higher dimensions.
[...]
Are you certain it is impossible to devise an interally consistent
geometric theory covering merely gravity and EM?
In four dimensions? Yes. You can check this by counting the
degrees of freedom in the metric tensor. Since the metric is
a symmetric 4x4 matrix, the number of independent parameters
which characterize it is, at most 10: spatial rotations in
3 dimensions, boosts in 3 dimensions, translations in 3 spatial
directions and time translation: 3+3+3+1 = 10.
.
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| User: "tendon" |
|
| Title: Re: Magnetic Idyll |
13 Jul 2006 12:25:35 PM |
|
|
Bilge wrote:
Edward Green:
Bilge wrote:
Actually, it is not. One can write down a set of equations for
those forces which are exact analogues of maxwell's equations.
For example, the covariant derivative D_u = d_u + ieA_u from which E&M
follows via the commutation relations,
[D_u, D_v] = (1/ie)F_uv
( [d_u + ieA_u, d_v + ieA_v]
= [d_u, d_v] + ie [d_u,A_v] + ie [A_u, d_v] - e^2 [A_u,A_v]
The first term is zero, the second and third terms give d_u A_v - d_v A_u,
and the last term is zero because the transformation group is U(1) which
is the set of 1x1 unitariy matrices, i.e., multiplication by a phase
\exp(-iS) that depends on 1 parameter, S). (I can do this in more detail
or you can find it in any textbook on particle physics or field theory
under noether's theorem.) In any case, the eA_u comes from identifying
the field with the partial derivative of S and requiring the dirac
lagrangian to be invariant.
If the transformation is more complicated, i.e., S = M.l, where M
is some group of matricies and l are the vectors for those matrices,
you have a more complicated covariant derivative which may be written,
analogously to the one above, D_u = d_u + ig(b_u)^i. Then, you get the
general relation,
[D_u, D_v] = (1/ig)(G_uv)^k
(G_uv)^k = d_u (b_u)^k - d_u (b_u)^k - g^2 [(b_u)^i, (b_v)^j]
where the additional index comes from the fact that the phase in this
case is not a simple scalar. In fact, the index k for the strong force
corresponds to the gluon color field. There is a conserved current
obtained from taking the partial of the field strength tensor G and
that gives you the ``maxwell equations'' for the strong force (which
are more complex than in E&M, but derived in exacty the same way one
derives maxwell's equations from qed).
(A familiar analogy would be angular momentum, for which the
exponent of \exp(-i J.\Theta) defines a rotation in the direction
of the vector \Theta, with J being the rotation matrices. The
corresponding conserved current is the angular momentum if
the system is invariant under such a rotation.)
In the parlance of geometry, the field strength tensor is the
curvature tensor for the strong force. Note however, that the
curvature tensor for E&M, and the index k for the weak force and
stron force corresponds to some quantity other than the spacetime
variables, while for general relativity, the curvature is explicitly
in the spacetime itself. Loosely speaking, the basic idea behind
string theory is to increase the number of dimensions of spacetime
sufficiently to accomodate these forces as geometric quantities
in higher dimensions.
i can see yo kno material
we two wold make good partners
from now on yo do tha math, i do tha thinkin
just dont ask questions, i do tha thinkin, yo
do th math
[...]
Are you certain it is impossible to devise an interally consistent
geometric theory covering merely gravity and EM?
In four dimensions? Yes. You can check this by counting the
degrees of freedom in the metric tensor. Since the metric is
a symmetric 4x4 matrix, the number of independent parameters
which characterize it is, at most 10: spatial rotations in
3 dimensions, boosts in 3 dimensions, translations in 3 spatial
directions and time translation: 3+3+3+1 = 10.
.
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| User: "Jan Panteltje" |
|
| Title: Re: Magnetic Idyll |
13 Jul 2006 12:50:01 PM |
|
|
On a sunny day (13 Jul 2006 10:25:35 -0700) it happened "tendon"
<l3jklr94jt594j@comicmail.co.uk> wrote in
<1152811535.365504.172980@75g2000cwc.googlegroups.com>:
sufficiently to accomodate these forces as geometric quantities
in higher dimensions.
i can see yo kno material
we two wold make good partners
from now on yo do tha math, i do tha thinkin
just dont ask questions, i do tha thinkin, yo
do th math
But who do tha spelling?
.
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| User: "my mother" |
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| Title: Re: Magnetic Idyll |
13 Jul 2006 01:09:32 PM |
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Jan Panteltje wrote:
On a sunny day (13 Jul 2006 10:25:35 -0700) it happened "tendon"
<l3jklr94jt594j@comicmail.co.uk> wrote in
<1152811535.365504.172980@75g2000cwc.googlegroups.com>:
sufficiently to accomodate these forces as geometric quantities
in higher dimensions.
i can see yo kno material
we two wold make good partners
from now on yo do tha math, i do tha thinkin
just dont ask questions, i do tha thinkin, yo
do th math
But who do tha spelling?
yo too, just do tha math, i do tha thinkin
stop askin questions
.
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| User: "Sorcerer" |
|
| Title: Re: Magnetic Idyll |
11 Jul 2006 02:03:57 AM |
|
|
"Edward Green" <spamspamspam3@netzero.com> wrote in message
news:1152581101.395090.142470@h48g2000cwc.googlegroups.com...
| Bilge wrote:
|
| > Edward Green:
| > >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.
|
| Yes.
|
| > >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...''
|
| I think you meant "I'm not sure what you mean by 'formal simularity'.
| That's similarity happening at the very same time. ;-)
|
| I meant something like "term by term identity, after changing the
| labels".
|
| > 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.
|
| True. As I mentioned, this seems to suggest that the rotational rest
| frame seen by charge and that seen by mass are different. No don't ask
| me to quantify this -- but it doesn't seem like such a very weird idea.
| After all, cannot EM and gravity be put on the same footing by a
| geometric theory called Kaluza-Klein? Possibly the extra dimensions
| are exactly what is required to give this statement meaning.
|
| > 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.
|
| I'm not sure what you are getting at, but I rather think I just
| answered you. Yes, this idea would imply that not all particles
| behaved similarly under "geometry", but then, I think we are by
| implication talking about a more complicated theory than one involving
| gravity and mass alone. Different aspects of the particle may sample
| different aspects of the environment -- like an ice skater feeling the
| wind.
Not all particles behave similarly when viewed from different frames of
reference. This ball is disobeying Newton's first law, which it cannot do
and it doesn't:
http://ww2010.atmos.uiuc.edu/(Gh)/guides/mtr/fw/gifs/coriolis.mov
Androcles.
.
|
|
|
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|
| User: "Bill Hobba" |
|
| Title: Re: Magnetic Idyll |
08 Jul 2006 08:24:41 PM |
|
|
"Edward Green" <spamspamspam3@netzero.com> 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.
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?
.
|
|
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| User: "Sorcerer" |
|
| Title: Re: Magnetic Idyll |
09 Jul 2006 03:36:30 AM |
|
|
"Edward Green" <spamspamspam3@netzero.com> 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.
.
|
|
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|
| User: "Igor" |
|
| Title: Re: Magnetic Idyll |
09 Jul 2006 01:29:23 PM |
|
|
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.
.
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|
|
|
| User: "Igor" |
|
| Title: Re: Magnetic Idyll |
09 Jul 2006 02:56:30 PM |
|
|
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?
Here's a good link:
http://abacus.bates.edu/~msemon/Noteon.pdf
.
|
|
|
| User: "Tom Roberts" |
|
| Title: Re: Magnetic Idyll |
09 Jul 2006 07:19:55 PM |
|
|
Igor wrote:
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
.
|
|
|
| User: "Igor" |
|
| Title: Re: Magnetic Idyll |
10 Jul 2006 02:59:51 PM |
|
|
Tom Roberts wrote:
Igor wrote:
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
Yeah, I can see your point. Well, nobody called it a perfect analogy.
I think the paper that was referenced and the original paper by Coisson
from 1973 were just to point out the similarities. They were both
published in the American Journal of Physics, which tends to deal with
new ways of looking at old physics more often than not. Unfortunately,
the Coisson paper does not appear to be available online, although I
know I have a copy of it somewhere.
.
|
|
|
| User: "dda1" |
|
| Title: Re: Magnetic Idyll |
10 Jul 2006 03:08:04 PM |
|
|
Igor wrote:
Tom Roberts wrote:
Igor wrote:
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
Yeah, I can see your point. Well, nobody called it a perfect analogy.
I think the paper that was referenced and the original paper by Coisson
from 1973 were just to point out the similarities. They were both
published in the American Journal of Physics, which tends to deal with
new ways of looking at old physics more often than not. Unfortunately,
the Coisson paper does not appear to be available online, although I
know I have a copy of it somewhere.
American Journal of Physics is run by an imbecile (Jan Tobochnick) and
has as charter the publication of "no new reserach" (see the web page).
AmJPhys publishes regurgitations (as you well pointed out) of old
stuff, basically reinterpretations of older papers. Another junk
journal.
.
|
|
|
| User: "Bill Hobba" |
|
| Title: Re: Magnetic Idyll |
10 Jul 2006 08:12:05 PM |
|
|
"dda1" <rangeravenger@yahoo.com> wrote in message
news:1152562084.536415.122010@75g2000cwc.googlegroups.com...
Igor wrote:
Tom Roberts wrote:
Igor wrote:
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
Yeah, I can see your point. Well, nobody called it a perfect analogy.
I think the paper that was referenced and the original paper by Coisson
from 1973 were just to point out the similarities. They were both
published in the American Journal of Physics, which tends to deal with
new ways of looking at old physics more often than not. Unfortunately,
the Coisson paper does not appear to be available online, although I
know I have a copy of it somewhere.
American Journal of Physics is run by an imbecile (Jan Tobochnick) and
has as charter the publication of "no new reserach" (see the web page).
That characterization is silly. He is a well respected legitimate scientist
and teacher.
AmJPhys publishes regurgitations (as you well pointed out) of old
stuff, basically reinterpretations of older papers. Another junk
journal.
Isn't it the Journal of the American Association of Physics Teachers? That
its focus is not on research but understanding known physics looks quite
reasonable to me. In fact whenever I get to a library the AMJP is one
publication I always browse and learn a lot.
Bill
.
|
|
|
|
| User: "Timo A. Nieminen" |
|
| Title: Re: Magnetic Idyll |
10 Jul 2006 03:32:29 PM |
|
|
On Tue, 10 Jul 2006, dda1 wrote:
American Journal of Physics is run by an imbecile (Jan Tobochnick) and
has as charter the publication of "no new reserach" (see the web page).
AmJPhys publishes regurgitations (as you well pointed out) of old
stuff, basically reinterpretations of older papers. Another junk
journal.
AJP is a physics _education_ journal, not a _physics_ journal. Why should
they publish new physics research? They do publish new physics _education_
research.
AJP is far from being a junk journal; I find that I'm more likely to get
long term value out of an AJP paper that a paper in the physics research
journals (because so many research papers are out of my field, are badly
written, present research that's been salami-sliced into as many papers as
possible, are wrong, age rapidly, etc). It's not what you read to keep up
with cutting-edge research, but it isn't junk. All of the top 3 physics
education journals have lots of good stuff in them, and even if you're not
interested in teaching or teaching well, some of it is good physics,
explained well.
Your anonymous accusation of imbecility reflects badly on your character.
--
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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|
|
| User: "Sue..." |
|
| Title: Re: Magnetic Idyll |
08 Jul 2006 06:33:33 PM |
|
|
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/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. :o)
http://www.esa.int/SPECIALS/GSP/SEM0L6OVGJE_0.html
http://www.mypage.bluewin.ch/Bizarre/GRAV.htm
Sue...
.
|
|
|
|
| User: "Tom Roberts" |
|
| Title: Re: Magnetic Idyll |
09 Jul 2006 12:34:25 AM |
|
|
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_ 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
.
|
|
|
| User: "Edward Green" |
|
| Title: Re: Magnetic Idyll |
09 Jul 2006 01:01:42 PM |
|
|
Bill Hobba wrote:
"Edward Green" <spamspamspam3@netzero.com> 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 ".
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.
.
|
|
|
| User: "Tom Roberts" |
|
| Title: Re: Magnetic Idyll |
09 Jul 2006 03:01:56 PM |
|
|
Edward Green wrote:
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_.
I'm well aware that the Coriolis force is a so-called fictious force.
Then you should abide by the consequences.
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.
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.
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!
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
.
|
|
|
| User: "Daryl McCullough" |
|
| Title: Re: Magnetic Idyll |
12 Jul 2006 05:59:00 AM |
|
|
Tom Roberts says...
Edward Green wrote:
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_.
Well, the Kaluza-Klein approach to the unification of gravity
and electromagnetism interprets electromagnetic forces as a
manifestation of general relativity of 5-dimensional spacetime.
What this means is that the supposedly *physical* force of
electromagnetism can be explained in terms of *fictitious*
forces. So the distinction between "physical" and "fictitious"
may not be readily observable (the Kaluza-Klein
theory can be distinguished from E&M in 4-D spacetime, but
only if probed at high enough energies to detect spatial
variations of fields along the extra, curled-up dimension).
In a certain sense, it's the *theory* that tells you what is
physical and what is fictitious.
--
Daryl McCullough
Ithaca, NY
.
|
|
|
| User: "Edward Green" |
|
| Title: Re: Magnetic Idyll |
12 Jul 2006 04:39:42 PM |
|
|
Daryl McCullough wrote:
Tom Roberts says...
Edward Green wrote:
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_.
Well, the Kaluza-Klein approach to the unification of gravity
and electromagnetism interprets electromagnetic forces as a
manifestation of general relativity of 5-dimensional spacetime.
What this means is that the supposedly *physical* force of
electromagnetism can be explained in terms of *fictitious*
forces. So the distinction between "physical" and "fictitious"
may not be readily observable (the Kaluza-Klein
theory can be distinguished from E&M in 4-D spacetime, but
only if probed at high enough energies to detect spatial
variations of fields along the extra, curled-up dimension).
In a certain sense, it's the *theory* that tells you what is
physical and what is fictitious.
Yes, well put.
I would have added this same point if my last reply to Tom Roberts had
been longer; the example I would have used is Newtonian gravity vs.
General Relativity.
.
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| User: "" |
|
| Title: Re: Magnetic Idyll |
12 Jul 2006 03:00:47 PM |
|
|
In article <e92klk0v8e@drn.newsguy.com>, (Daryl McCullough) writes:
Tom Roberts says...
Edward Green wrote:
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_.
Well, the Kaluza-Klein approach to the unification of gravity
and electromagnetism interprets electromagnetic forces as a
manifestation of general relativity of 5-dimensional spacetime.
What this means is that the supposedly *physical* force of
electromagnetism can be explained in terms of *fictitious*
forces. So the distinction between "physical" and "fictitious"
may not be readily observable (the Kaluza-Klein
theory can be distinguished from E&M in 4-D spacetime, but
only if probed at high enough energies to detect spatial
variations of fields along the extra, curled-up dimension).
In a certain sense, it's the *theory* that tells you what is
physical and what is fictitious.
Aha, yes.
Mati Meron | "When you argue with a fool,
meron@cars.uchicago.edu | chances are he is doing just the same"
.
|
|
|
| User: "Daryl McCullough" |
|
| Title: Re: Magnetic Idyll |
12 Jul 2006 04:49:40 PM |
|
|
(Mati Meron) says...
In article <e92klk0v8e@drn.newsguy.com>, (Daryl
McCullough) writes:
In a certain sense, it's the *theory* that tells you what is
physical and what is fictitious.
Aha, yes.
Thanks for not rubbing it in that I'm arguing the opposite
side from our discussion of a year ago (or however long ago
that was).
--
Daryl McCullough
Ithaca, NY
.
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| User: "" |
|
| Title: Re: Magnetic Idyll |
12 Jul 2006 06:51:27 PM |
|
|
In article <e93qpk010o8@drn.newsguy.com>, (Daryl McCullough) writes:
mmeron@cars3.uchicago.edu (Mati Meron) says...
In article <e92klk0v8e@drn.newsguy.com>, (Daryl
McCullough) writes:
In a certain sense, it's the *theory* that tells you what is
physical and what is fictitious.
Aha, yes.
Thanks for not rubbing it in that I'm arguing the opposite
side from our discussion of a year ago (or however long ago
that was).
Has it been a year? Well, might be. Anyway, I wouldn't dream of
rubbing anything in, the discussion was most useful and I'm glad to
see that our positions are converging.
Mati Meron | "When you argue with a fool,
meron@cars.uchicago.edu | chances are he is doing just the same"
.
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| User: "Edward Green" |
|
| Title: Re: Magnetic Idyll |
11 Jul 2006 07:37:29 PM |
|
|
Tom Roberts wrote:
Edward Green wrote:
Tom Roberts wrote:
<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_.
I'm well aware that the Coriolis force is a so-called fictious force.
Then you should abide by the consequences.
You entirely missed the point.
Given that the Coriolis force is a fictious force -- one in particular
arising in a rotating reference frame -- and given that the Lorentz
force is formally identical to it -- changing labels but keeping
velocity as itself -- then the suggestion arises that in the presence
of a magnetic field charged particles, vis. a vis. their charge,
effectively see themselves in a frame rotating with respect to whatever
frame we would otherwise consider not to be rotating, when we use
massive neutral particles to establish the latter.
Whether these comments are deep or shallow, they do _not_ suffer from
ignorance of the meaning of the Coriolis force, nor its "fictitious"
origin. On the contrary, this awareness is at the heart of the thing.
<...>
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| User: "Igor" |
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| Title: Re: Magnetic Idyll |
12 Jul 2006 03:44:52 PM |
|
|
Edward Green wrote:
Tom Roberts wrote:
Edward Green wrote:
Tom Roberts wrote:
<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_.
I'm well aware that the Coriolis force is a so-called fictious force.
Then you should abide by the consequences.
You entirely missed the point.
Given that the Coriolis force is a fictious force -- one in particular
arising in a rotating reference frame -- and given that the Lorentz
force is formally identical to it -- changing labels but keeping
velocity as itself -- then the suggestion arises that in the presence
of a magnetic field charged particles, vis. a vis. their charge,
effectively see themselves in a frame rotating with respect to whatever
frame we would otherwise consider not to be rotating, when we use
massive neutral particles to establish the latter.
Whether these comments are deep or shallow, they do _not_ suffer from
ignorance of the meaning of the Coriolis force, nor its "fictitious"
origin. On the contrary, this awareness is at the heart of the thing.
Indeed, the Coriolis is somewhat analogous to the magnetic force. But
I think what Tom was saying had to do with how each of the forces
arise. The magnetic force will be present in all coordinate systems
since it occurs due to the presence of an external current, and hence
is tensorial. The Coriolis, on the other hand, while appearing to
mimic the magnetic force, disappears in rectangular coordinates, and
hence cannot be expressed as a tensor. It comes from the geodesic
equation for spherical coordinates in Euclidean space for Newtonian
dynamics. Interestingly enough, there a "force" that mimics the
magnetic force in GR, but is tensorial. It's the Kerr solution
relating to frame dragging due to a rotating mass source.
.
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| User: "Edward Green" |
|
| Title: Re: Magnetic Idyll |
12 Jul 2006 05:16:53 PM |
|
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Igor wrote:
Indeed, the Coriolis is somewhat analogous to the magnetic force. But
I think what Tom was saying had to do with how each of the forces
arise. The magnetic force will be present in all coordinate systems
since it occurs due to the presence of an external current, and hence
is tensorial. The Coriolis, on the other hand, while appearing to
mimic the magnetic force, disappears in rectangular coordinates, and
hence cannot be expressed as a tensor. It comes from the geodesic
equation for spherical coordinates in Euclidean space for Newtonian
dynamics.
There may be a simpler route.
Interestingly enough, there a "force" that mimics the
magnetic force in GR, but is tensorial. It's the Kerr solution
relating to frame dragging due to a rotating mass source.
Gratifyinger and gratifyinger! You and Daryl McCullough seem to be
thinking on my wavelength, as you bring up frame dragging and Daryl
brought up Kaluza-Klein, both of which I had already mentioned.
At first I idly noted a formal similarity between the Lorentz force and
the Coriolis force -- which is unimpeachable -- and then went on to add
some speculative tag about "charge seeing a coordinate frame rotating
in a different sense from the one seen by neutral mass" -- which may
just be wandering into the territory of the stained dress, unless we
take it as operationalized by the very identity already observed, and
hence tautological.
Now, however, I am ready to launch on a full flight of speculation, as
the pieces of a just-so-story fall into place! It has already been
objected that space can only harbor one rest frame for rotation -- one
set of geodesics -- so how can charge see a different one than sampled
by neutral mass? Qualitatively, a theory with a few odd extra
dimensions -- conveniently one in fact describing the EM phenomenon --
comes to the rescue. Further, one notices thinking of magnetic field
as a kind of rotation of space, that all magnetic sources involve the
circulation/angular momentum of charge. And one thinks of "frame
dragging". And behold, conveniently, a straight man comes in and tells
us that frame dragging describes a force that mimics the magnetic
force! Is it too much to speculate that frame dragging by charge -- in
the Kaluza Klein universe -- in fact corresponds to the production of a
magnetic field?
A few details remain to be worked out. ;-)
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