On Mar 21, 11:08*pm, "Jay R. Yablon" wrote:
"EdwardGreen" wrote in message

...
. . .

Finally, I thought of cirularly polarized light, which carries
intrinsic angular momentum: when you move to classical fields, you
don't have far to look. *But is cicularly polarized light described by
an anti-symmetric stress tensor? *I'm not sure. *Maybe the formalism
is better (necessarily?) to just introduce another vector density --
the density of intrinsic angular momentum.

[start Jay]

I thought about exactly the same question. *Is there a covariant
formulation for circularly polarized light this essentially adds one or
more terms to the Maxwell tensor and renders it non-symmetric?

Comment: if the formulation added terms to the Maxwell tensor,
wouldn't that necessarily be something other than the Maxwell tensor?
I guess it depends in what sense we mean "added terms". You possibly
mean "add an anti-symmetric part", as opposed to an algebraic sense
where we compose vector spaces.

*If so, where might I find it?

I don't know, but here is a possibly related thought:

Given a finite cylinder of circularly polarized light (possibly
smoothed off at the edges a bit, to make a continuous vacuum
solution), I'm going to take an educated guess that all the angular
momemtum in the field will turn out to have been translated off to the
edges of the beam -- formally -- much like a region of uniform
magnetization which is equivalent to a surface current density.

I'm (long) bemused by this idea in general: spinning little things
right next to eachother tend to cancel out until we meet a boundary --
or a non-uniform concentration of spinning things -- where the edges
hang out, so to speak.

Sorry to be so half-baked.

On Mar 21, 6:47 am, "Jay R. Yablon" wrote:
Can someone please explain or provide some links which explain how the
physics of a non-symmetric energy tensor would be different from that of
a symmetric energy tensor.

Especially, with the Poynting components

T^0k T^k0, k=1,2,3,

how would one interpret T^0k versus T^k0 and the physics of the energy
flux associated with each?

Thanks,

Jay,
____________________________
Jay R. Yablon
Email:
co-moderator: sci.physics.foundations
Weblog:http://jayryablon.wordpress.com/
Web Site:http://home.nycap.rr.com/jry/FermionMass.htm

++++++++++++++++++++++++++++++++++++++++
From SPF.

Consider an Induction Motor (IM).
http://hyperphysics.phy-astr.gsu.edu...ic/indmot.html

The only significant connection causing the rotator
to spin relatively to the stator is propagated via
the "spacetime" field. The IM's are quite efficient,
and more to the point the direction of IM rotation is
propagated strictly as a field effect, that is caused
by the relative geometries.

So the question becomes: How does the spacetime
field propagate the direction of relative spins between
the IM rotator and stator?

As far as I can see the issue could
only be resolved in full unification.

Ok, the EFE's applied to gravitation (IMHO) would be
unchanged, however the Poynting Vector

ExB=C = - (BxE = -C)

reverses the direction of rotation, (spin), of the IM,
and is an example of T_i0 = - T_0i , similiar to
F_i0 = F_0i.

Regards
Charles Francis
http://www.teleconnection.info/rqg/MainIndex

Regards
Ken S. Tucker

Edward Green wrote on Sat, 22 Mar 2008 07:45:27 -0700:

On Mar 22, 7:33Â*am, "Juan R." González-Ã�lvarez
wrote:

One of conditions of GR *connections* is precisely g_ab = g_ba, which

Let me shoot for the moon and hit my foot.

Can we describe the meaning of "g_ab" in words?

E.g., it is the number which tells us, in terms of a coordinate x^a and
a coordinate x^b, exactly what happens to first order when we....

http://en.wikipedia.org/wiki/Metric_tensor

First bonus question: what would it mean, operationally if g_ab /= g_ba
?

http://en.wikipedia.org/wiki/Torsion_tensor

http://en.wikipedia.org/wiki/Stress-energy_tensor

http://en.wikipedia.org/wiki/Spin_tensor

http://en.wikipedia.org/wiki/Einstein-
Cartan_theory#Geometric_insights_from_Einstein.E2. 80.93Cartan_theory

http://en.wikipedia.org/wiki/Einstein-
Cartan_theory#General_relativity_plus_matter_with_ spin_implies_Einstein.E2.80.93Cartan_theory

--
http://canonicalscience.org/en/misce...guidelines.txt

On Mar 22, 5:45 am, Edward Green wrote:
On Mar 22, 7:33 am, "Juan R." González-Álvarez

wrote:
One of conditions of GR *connections* is precisely g_ab = g_ba, which

Let me shoot for the moon and hit my foot.

Can we describe the meaning of "g_ab" in words?

The components of g_ab are the direction cosines between the a'th and
b'th component.


E.g., it is the number which tells us, in terms of a coordinate x^a
and a coordinate x^b, exactly what happens to first order when we....

The metric also defines distance. Take an arbitrary vector x^a and dot
it against itself using the metric - g_ab x^a x^b - and you find the
squared norm of the vector.


First bonus question: what would it mean, operationally if g_ab /=
g_ba ?

Things become nonsense. Is a.b different than b.a?


Second bonus question: rephrase both answers for the remaining
permutations of raised and lowered indices.

Extra-extra credit: I am handed a ruler, and told that it measures a
coordinate x. How can I tell, on operational grounds, whether I am
measuring a coordinate with a raised or lowered index?

You don't - a vector x^u and a covector x_u obey the relation x^u x_u
= delta^u_u.

I remember it like this - forces, distances, and velocities are
vectors A^u. Gradients, partial derivatives, covariant derivatives,
etc are covectors A_u.

Explaining tangent space won't mean much if you are going for an
operational definition imho.

On Mar 22, 10:11 am, "Juan R." González-Álvarez
wrote:

[...]

No. The metric tensor is still symmetric in Einstein-Cartan theory.

On Mar 22, 6:21*pm, Eric Gisse wrote:
On Mar 22, 5:45 am, wrote:

On Mar 22, 7:33 am, "Juan R." González-Álvarez

wrote:
One of conditions of GR *connections* is precisely g_ab = g_ba, which

Let me shoot for the moon and hit my foot.

Can we describe the meaning of "g_ab" in words?

The components of g_ab are the direction cosines between the a'th and
b'th component.



E.g., it is the number which tells us, in terms of a coordinate x^a
and a coordinate x^b, exactly what happens to first order when we....

The metric also defines distance. Take an arbitrary vector x^a and dot
it against itself using the metric - g_ab x^a x^b - and you find the
squared norm of the vector.



First bonus question: what would it mean, operationally if g_ab /=
g_ba ?

Things become nonsense. Is a.b different than b.a?



Second bonus question: rephrase both answers for the remaining
permutations of raised and lowered indices.

Extra-extra credit: I am handed a ruler, and told that it measures a
coordinate x. *How can I tell, on operational grounds, whether I am
measuring a coordinate with a raised or lowered index?

You don't - a vector x^u and a covector x_u obey the relation x^u x_u
= delta^u_u.

I remember it like this - forces, distances, and velocities are
vectors A^u. Gradients, partial derivatives, covariant derivatives,
etc are covectors A_u.

Explaining tangent space won't mean much if you are going for an
operational definition imho.

On Mar 22, 3:11*pm, "Juan R." González-Álvarez
wrote:
EdwardGreenwrote on Sat, 22 Mar 2008 07:45:27 -0700:

On Mar 22, 7:33*am, "Juan R." González-Álvarez
wrote:

One of conditions of GR *connections* is precisely g_ab = g_ba, which

Let me shoot for the moon and hit my foot.

Can we describe the meaning of "g_ab" in words?

E.g., it is the number which tells us, in terms of a coordinate x^a and
a coordinate x^b, exactly what happens to first order when we....

http://en.wikipedia.org/wiki/Metric_tensor

Hmmm... my feeling about this kind of answer, is that I was looking
for someone who might find it mutually stimulating to feed me a tiny
bit. I'm not sure about the motivation of someone who does not find
it so stimulating, and simply repeats "RTFM", without irony. If I
felt that way, I would prefer silence to effort probably wasted on the
ungrateful.

Ah well, I am lurking on the threshhold here, anyway, and will soon
cross over, whether you unbar the door, or not... the bar slowly
creeps out, while the hair on your arms stands up electrically.

I've lost some confidence in Wikipedia recently... some of their hard
articles seem to be standard pablum, in my very extremely humble
opinion and etc.,...

First bonus question: what would it mean, operationally if g_ab /= g_ba
?

http://en.wikipedia.org/wiki/Torsion_tensor

http://en.wikipedia.org/wiki/Stress-energy_tensor

http://en.wikipedia.org/wiki/Spin_tensor

http://en.wikipedia.org/wiki/Einstein-
Cartan_theory#Geometric_insights_from_Einstein.E2. 80.93Cartan_theory

http://en.wikipedia.org/wiki/Einstein-
Cartan_theory#General_relativity_plus_matter_with_ spin_implies_Einstein.E2..*80.93Cartan_theory

--http://canonicalscience.org/en/miscellaneouszone/guidelines.txt

Thanks for the pointers, anyway.

On Mar 22, 6:12 pm, Edward Green wrote:
On Mar 22, 3:11 pm, "Juan R." González-Álvarez



wrote:
EdwardGreenwrote on Sat, 22 Mar 2008 07:45:27 -0700:

On Mar 22, 7:33 am, "Juan R." González-Álvarez
wrote:

One of conditions of GR *connections* is precisely g_ab = g_ba, which

Let me shoot for the moon and hit my foot.

Can we describe the meaning of "g_ab" in words?

E.g., it is the number which tells us, in terms of a coordinate x^a and
a coordinate x^b, exactly what happens to first order when we....

http://en.wikipedia.org/wiki/Metric_tensor

Hmmm... my feeling about this kind of answer, is that I was looking
for someone who might find it mutually stimulating to feed me a tiny
bit. I'm not sure about the motivation of someone who does not find
it so stimulating, and simply repeats "RTFM", without irony. If I
felt that way, I would prefer silence to effort probably wasted on the
ungrateful.

Ah well, I am lurking on the threshhold here, anyway, and will soon
cross over, whether you unbar the door, or not... the bar slowly
creeps out, while the hair on your arms stands up electrically.

I've lost some confidence in Wikipedia recently... some of their hard
articles seem to be standard pablum, in my very extremely humble
opinion and etc.,...



First bonus question: what would it mean, operationally if g_ab /= g_ba
?

http://en.wikipedia.org/wiki/Torsion_tensor

http://en.wikipedia.org/wiki/Stress-energy_tensor

http://en.wikipedia.org/wiki/Spin_tensor

http://en.wikipedia.org/wiki/Einstein-
Cartan_theory#Geometric_insights_from_Einstein.E2. 80.93Cartan_theory

http://en.wikipedia.org/wiki/Einstein-
Cartan_theory#General_relativity_plus_matter_with_ spin_implies_Einstein.E2.*80.93Cartan_theory

--http://canonicalscience.org/en/miscellaneouszone/guidelines.txt

Thanks for the pointers, anyway.

Does the measurement of time require a length?
Ken

Edward Green wrote on Sat, 22 Mar 2008 19:12:07 -0700:

On Mar 22, 3:11Â*pm, "Juan R." González-Ã�lvarez
wrote:
EdwardGreenwrote on Sat, 22 Mar 2008 07:45:27 -0700:

On Mar 22, 7:33Â*am, "Juan R." González-Ã�lvarez
wrote:

One of conditions of GR *connections* is precisely g_ab = g_ba,
which

Let me shoot for the moon and hit my foot.

Can we describe the meaning of "g_ab" in words?

E.g., it is the number which tells us, in terms of a coordinate x^a
and a coordinate x^b, exactly what happens to first order when we....

http://en.wikipedia.org/wiki/Metric_tensor

Hmmm... my feeling about this kind of answer, is that I was looking for
someone who might find it mutually stimulating to feed me a tiny bit.
I'm not sure about the motivation of someone who does not find it so
stimulating, and simply repeats "RTFM", without irony. If I felt that
way, I would prefer silence to effort probably wasted on the ungrateful.

Ah well, I am lurking on the threshhold here, anyway, and will soon
cross over, whether you unbar the door, or not... the bar slowly creeps
out, while the hair on your arms stands up electrically.

I've lost some confidence in Wikipedia recently... some of their hard
articles seem to be standard pablum, in my very extremely humble opinion
and etc.,...

Use another sources then,

http://mathworld.wolfram.com/MetricTensor.html

First bonus question: what would it mean, operationally if g_ab /=
g_ba ?

http://en.wikipedia.org/wiki/Torsion_tensor

http://en.wikipedia.org/wiki/Stress-energy_tensor

http://en.wikipedia.org/wiki/Spin_tensor

http://en.wikipedia.org/wiki/Einstein-
Cartan_theory#Geometric_insights_from_Einstein.E2. 80.93Cartan_theory

http://en.wikipedia.org/wiki/Einstein-

Cartan_theory#General_relativity_plus_matter_with_ spin_implies_Einstein.E2.Â*
80.93Cartan_theory

--http://canonicalscience.org/en/miscellaneouszone/guidelines.txt

Thanks for the pointers, anyway.

Sorry, I made a mistake they are not about asymmetric metric but about
asymmetric conections coefficients gamma_ab =/= gamma_ba.

For non symmetric metrics {g_ab =/= g_ba} see

http://en.wikipedia.org/wiki/Nonsymm...ational_theory

and also its possible relation with string theory

http://motls.blogspot.com/2007/03/st...hysicists.html


--
http://canonicalscience.org/en/misce...guidelines.txt

"Juan R." González-�lvarez wrote on Sat, 22 Mar 2008 12:33:32 +0100:

One of conditions of GR *connections* is precisely g_ab = g_ba, which
does not hold for particles rotating around.

The connection is not g obviously, correct it like

"One of conditions of GR *connections* is precisely gamma_ab = gamma_ba,
which does not hold for particles rotating around."

--
http://canonicalscience.org/en/misce...guidelines.txt