FAQFAQ   SearchSearch   MemberlistMemberlist   UsergroupsUsergroups 
 ProfileProfile   PreferencesPreferences   Log in to check your private messagesLog in to check your private messages   Log inLog in 
Forum index » Science and Technology » Physics » Relativity
Magnetic Idyll
Post new topic   Reply to topic Page 3 of 6 [81 Posts] View previous topic :: View next topic
Goto page:  Previous  1, 2, 3, 4, 5, 6 Next
Author Message
Bill Hobba
science forum Guru


Joined: 02 May 2005
Posts: 2138

PostPosted: Wed Jul 12, 2006 5:15 am    Post subject: Re: Magnetic Idyll Reply with quote

"Edward Green" <spamspamspam3@netzero.com> wrote in message
news:1152661495.629130.46200@m73g2000cwd.googlegroups.com...
Quote:

Bill Hobba wrote:

"Edward Green" <spamspamspam3@netzero.com> wrote in message...

Timo A. Nieminen wrote:

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
the whole deal.

Yes you can - check out
http://www.cse.secs.oakland.edu/haskell/SpecialRelativity.htm

Thanks very much for the reference.

The problem with discussing interesting topics with knowledgable people
is that they invariably come up with challenging follow on reading. ;-)

However some other assumptions are also used eg charge is not dependant
on
velocity and forces add linearly (it is a very interesting exercise to go
through the derivation and see exactly what the assumptions are). Bilge
correctly points out that Jackson notes it is not quite possible to do it
from SR and Coulombs law alone. However with the extra non stated
assumptions added it is derivable. It is interesting to see, for
example,
exactly what breaks down in gravity. Here, while rest mass certainly is
invariant, E=MC2 strongly suggests that for moving mass not only should
we
include mass as the source of gravitation but energy as well so the
source
of gravity being the invariant rest mass may not be true. The linear
adding
of forces looks doubtful with gravity as well.

I've started to think about how one would approach such a derivation.
I think I would have assumed the invariance and velocity independence
of charge without a qualm, also the linear addition of forces. Special
relativity has "linear" written all over it, anyway. I assume
classical EM is a linear limit of a more general classical theory of
the electromagnetic phenomenon.

Excepting quantum corrections (ie classically) EM is fully in accord with
all experimental evidence ie is linear, charge is invariant, and the source
of EM fields, Coulombs law holds etc. That is why Maxwell's equations are
so great - they are correct as far as we know.

Thanks
Bill
Back to top
Daryl McCullough
science forum Guru


Joined: 24 Mar 2005
Posts: 1167

PostPosted: Wed Jul 12, 2006 10:59 am    Post subject: Re: Magnetic Idyll Reply with quote

Tom Roberts says...
Quote:

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
Back to top
Sue...
science forum Guru


Joined: 08 May 2005
Posts: 2684

PostPosted: Wed Jul 12, 2006 11:20 am    Post subject: Re: Magnetic Idyll Reply with quote

Edward Green wrote:


Quote:

I've started to think about how one would approach such a derivation.
I think I would have assumed the invariance and velocity independence
of charge without a qualm, also the linear addition of forces. Special
relativity has "linear" written all over it, anyway.

That is an important point. So much so, that many like to re-label
the Theory of Relativity with a more functional description of
Theory of Invariants. This gives promenance to its goal of
showing equivalent physics in equivalent frames of reference.

I deliberatly avoided the term 'Inertial frame of reference' because
this is a separate set of postulates that don't draw much support
from SR's isotropy of light.

Quote:
I assume
classical EM is a linear limit of a more general classical theory of
the electromagnetic phenomenon.

That was Einstein's intent for GR. I am not at all convinced
he got very close to that goal. I feel the Nobel for photoelectric
effect pressured him into supporting a popular but flawed
particle light paradigm and all the abstraction required for
that crippled his vision for a field theory he sensed should
exist for gravity.

Sue...
Back to top
mmeron@cars3.uchicago.edu
science forum Guru


Joined: 14 Sep 2005
Posts: 434

PostPosted: Wed Jul 12, 2006 8:00 pm    Post subject: Re: Magnetic Idyll Reply with quote

In article <e92klk0v8e@drn.newsguy.com>, stevendaryl3016@yahoo.com (Daryl McCullough) writes:
Quote:
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"
Back to top
Igor
science forum Guru


Joined: 15 May 2005
Posts: 315

PostPosted: Wed Jul 12, 2006 8:44 pm    Post subject: Re: Magnetic Idyll Reply with quote

Edward Green wrote:
Quote:
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.
Back to top
Edward Green
science forum addict


Joined: 21 May 2005
Posts: 95

PostPosted: Wed Jul 12, 2006 9:39 pm    Post subject: Re: Magnetic Idyll Reply with quote

Daryl McCullough wrote:

Quote:
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.
Back to top
Daryl McCullough
science forum Guru


Joined: 24 Mar 2005
Posts: 1167

PostPosted: Wed Jul 12, 2006 9:49 pm    Post subject: Re: Magnetic Idyll Reply with quote

mmeron@cars3.uchicago.edu (Mati Meron) says...
Quote:

In article <e92klk0v8e@drn.newsguy.com>, stevendaryl3016@yahoo.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
Back to top
Edward Green
science forum addict


Joined: 21 May 2005
Posts: 95

PostPosted: Wed Jul 12, 2006 10:16 pm    Post subject: Re: Magnetic Idyll Reply with quote

Igor wrote:

Quote:
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.

Quote:
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. Wink
Back to top
Edward Green
science forum addict


Joined: 21 May 2005
Posts: 95

PostPosted: Wed Jul 12, 2006 10:34 pm    Post subject: Re: Magnetic Idyll Reply with quote

Bilge wrote:

<I beg your indulgence for postponing the parts of your post which
require close study, and asking a few simple questions>

Quote:
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?

Quote:
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?

Quote:
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.

Quote:
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?
Back to top
mmeron@cars3.uchicago.edu
science forum Guru


Joined: 14 Sep 2005
Posts: 434

PostPosted: Wed Jul 12, 2006 11:51 pm    Post subject: Re: Magnetic Idyll Reply with quote

In article <e93qpk010o8@drn.newsguy.com>, stevendaryl3016@yahoo.com (Daryl McCullough) writes:
Quote:
mmeron@cars3.uchicago.edu (Mati Meron) says...

In article <e92klk0v8e@drn.newsguy.com>, stevendaryl3016@yahoo.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"
Back to top
mmeron@cars3.uchicago.edu
science forum Guru


Joined: 14 Sep 2005
Posts: 434

PostPosted: Thu Jul 13, 2006 12:02 am    Post subject: Re: Magnetic Idyll Reply with quote

In article <1152742613.731366.126180@35g2000cwc.googlegroups.com>, "Edward Green" <spamspamspam3@netzero.com> writes:
Quote:
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. ;-)

Please carry on, this one is shaping up quite nicely.



Mati Meron | "When you argue with a fool,
meron@cars.uchicago.edu | chances are he is doing just the same"
Back to top
Bilge
science forum Guru


Joined: 30 Apr 2005
Posts: 2816

PostPosted: Thu Jul 13, 2006 7:24 am    Post subject: Re: Magnetic Idyll Reply with quote

Edward Green:
Quote:
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).

Quote:
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.

Quote:
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.

[...]

Quote:
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.
Back to top
tendon
science forum beginner


Joined: 13 Jul 2006
Posts: 18

PostPosted: Thu Jul 13, 2006 5:25 pm    Post subject: Re: Magnetic Idyll Reply with quote

Bilge wrote:
Quote:
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


Quote:

[...]

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.
Back to top
Jan Panteltje
science forum Guru Wannabe


Joined: 06 May 2005
Posts: 295

PostPosted: Thu Jul 13, 2006 5:50 pm    Post subject: Re: Magnetic Idyll Reply with quote

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>:
Quote:
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?
Back to top
tendon
science forum beginner


Joined: 13 Jul 2006
Posts: 18

PostPosted: Thu Jul 13, 2006 6:09 pm    Post subject: Re: Magnetic Idyll Reply with quote

Jan Panteltje wrote:
Quote:
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
Back to top
Google

Back to top
Display posts from previous:   
Post new topic   Reply to topic Page 3 of 6 [81 Posts] Goto page:  Previous  1, 2, 3, 4, 5, 6 Next
View previous topic :: View next topic
The time now is Sat Sep 20, 2014 2:24 pm | All times are GMT
Forum index » Science and Technology » Physics » Relativity
Jump to:  

Similar Topics
Topic Author Forum Replies Last Post
No new posts Computer Modelling of electro magnetic fields in Electros... bernard_stan@yahoo.com Physics 0 Sat Jun 24, 2006 8:34 pm
No new posts Tokomak and magnetic fields TQJDM Particle 1 Sat Jun 17, 2006 5:02 am
No new posts Magnetic Anyon Generators for Advanced Warp Propulsion? Jack Sarfatti Math 0 Wed Jun 14, 2006 3:18 pm
No new posts Neutrino magnetic moment absent David Jonsson Particle 0 Sat May 27, 2006 8:21 pm
No new posts Photo-electro-magnetic forces chemguy Electromagnetics 0 Wed May 17, 2006 12:20 am

Copyright © 2004-2005 DeniX Solutions SRL
Other DeniX Solutions sites: Electronics forum |  Medicine forum |  Unix/Linux blog |  Unix/Linux documentation |  Unix/Linux forums  |  send newsletters
 


Powered by phpBB © 2001, 2005 phpBB Group
[ Time: 0.1271s ][ Queries: 16 (0.0793s) ][ GZIP on - Debug on ]