Curvature from dark energy/dark matter ZPF torsion fields

http://www.shipov.com
In Einstein's 1915 GR prior to the introduction of the teleparallel
Kibble-Shipov torsion field with the 6 anholonomic angular
pre-Calabi-Yau coordinates for the orientation of the Einstein-Cartan
tetrad frame mobile {e^a}

(Riemann Curvature)uvwl = (Weyl Vacuum Curvature)uvwl + (1/2)[(curved
metric)uwT(non-gravity source)vl + (curved metric)vlT(non-gravity
source)uw - (curved metric)ulT(non-gravity source)vw - (curved
metric)vwT(non-gravity source)ul] - (1/3)[(curved metric)uw(curved
metric)vl - (curved metric)ul(curved metric)vw]T(non-gravity source)

Tuv(Dark Energy/Matter) = (String Tension)/\zpf(curved metric)uv

/\zpf = (Quantum of Area of World Hologram)^-1(1 - |Higgs Vacuum ODLRO
Order Parameter|^2)

/\zpf 0 is repulsive blue-shifting universal anti-gravity field (e.g.
cosmic voids & Type 1a supernovae)

/\zpf 0 is attractive red-shifting universal gravity field (e.g.
Galactic halos & filaments)

Dark regions are where /\zpf 0, bright filaments are where /\zpf 0.

http://heasarc.nasa.gov/docs/cosmic/sheets_voids.html

Problem is how to put Shipov's torsion field as a replacement for /\zpf,
which he does in one of his papers on dark energy and torsion.

11) Derek Wise, MacDowell-Mansouri gravity and Cartan geometry,
available as gr-qc/0611154.

Elie Cartan is one of the most influential of 20th-century geometers.
At one point he had an intense correspondence with Einstein on
general relativity. His "Cartan geometry" idea is an approach to
the concept of parallel transport that predates the widely used
Ehresmann approach (connections on principal bundles). It
simultaneously generalizes Riemannian geometry and Klein's Erlangen
program (see "week213"), in which geometries are described by their
symmetry groups:

EUCLIDEAN GEOMETRY -------------- KLEIN GEOMETRY

| |
| |
| |
| |
v v

RIEMANNIAN GEOMETRY -------------- CARTAN GEOMETRY

Given all this, it's somewhat surprising how few physicists know
about Cartan geometry!

Recognizing this, Derek explains Cartan geometry from scratch before
showing how it underlies the so-called MacDowell-Mansouri approach
to general relativity. This plays an important role both in
supergravity and Freidel and Starodubtsev's work on quantum gravity
(see "week235") - but until now, it's always seemed like a "trick".

What's the basic idea? Derek explains it all very clearly, so I'll
just provide a quick sketch. Cartan describes the geometry of a lumpy
bumpy space by saying what it would be like to roll a nice homogeneous
"model space" on it. Homogeneous spaces are what Klein studied; now
Cartan takes this idea and runs with it... or maybe we should say he
*rolls* with it!

For example, we could study the geometry of a lumpy bumpy surface by
rolling a *plane* on it. If our surface is itself a plane, this
rolling
motion is trivial, and we say the surface is "flat" in the sense of
Cartan geometry. But in general, the rolling motion is interesting
and serves to probe the geometry of the surface.

Alternatively, we could study the geometry of the same surface by
rolling a *sphere* on it. Derek illustrates this with a picture of
a hamster crawling around in a plastic "hamster ball", which is
something you can actually buy for your pet hamster to let it
explore your house without escaping or getting in trouble.

(I've read about falling cats in papers on gauge theory, but this
is the first mathematical physics paper I've read containing the
word "hamster".)

If our surface is itself a sphere of the same radius, this rolling
motion is trivial, and we say the surface is flat in the sense of
Cartan geometry - but now it's a different sense than when we used
a plane as our "model geometry"!

Which model geometry should we use in a given problem? It depends
on which one best approximates the lumpy bumpy space we're studying!

The ordinary formulation of general relativity fits into this
framework, with a little work. Two well-known mathematical gadgets
called the "Lorentz connection" and "coframe field" fit together to
describe what would happen if we rolled a copy of Minkowski spacetime
over the lumpy bumpy spacetime we live in.

That's great if Minkowski spacetime is the best homogeneous
approximation to the spacetime we live in. But nowadays we think
the cosmological constant is nonzero, so the Universe is expanding
in a roughly exponential way. This makes another model geometry,
"deSitter spacetime", the best one to use!

So, if we know Cartan geometry, we can use that... and we get something

called the MacDowell-Mansouri formulation of gravity. Or, if we don't
want our spacetime to have lumps and bumps - if we want it to look
locally just like the Klein model geometry - we can use a different
theory, a topological field theory called BF theory (see "week232").

In short, the passage from a topological field theory describing a
"locally homogeneous" spacetime to full-fledged gravity with all its
lumps and bumps is nicely understood in terms of how Cartan's approach
to geometry generalizes Klein's!

For more details, you'll just have to read Derek's paper. You might
also try these:

12) Michel Biesunski, Inside the coconut: the Einstein-Cartan
discussion on distant parallelism, in Einstein and the History
of General Relativity, eds. D. Howard and J. Stachel, Birkhauser,
Boston, 1989.

This describes the correspondence between Cartan and Einstein.
I believe this centered, not on Cartan geometry per se, but on
the "teleparallel" formulation of gravity (see "week176"). But,
they're somewhat related.

13) R. W. Sharp, Differential Geometry: Cartan's Generalization of
Klein's Erlangen Program, Springer-Verlag, New York, 1997.

This is the main textbook on Cartan geometry. But, it's probably
best to read a few chapters of Derek's paper first, since the
key ideas are presented more intuitively.

My friend the geometer and analyst Rafe Mazzeo, whom I recently saw
at Stanford, told me that Cartan geometry was all the rage these days.
I'm embarrassed to say I hadn't know this! I think the kinds of
Cartan geometry being intensively studied are related to conformal
geometry, CR structures and stuff like that...

Merry Christmas!
Quote of the Week:
"The Universe has as many different centers as there are living
beings in it." - Alexander Solzhenitsyn

http://www.shipov.com
In Einstein's 1915 GR prior to the introduction of the teleparallel
Kibble-Shipov torsion field with the 6 anholonomic angular
pre-Calabi-Yau coordinates for the orientation of the Einstein-Cartan
tetrad frame mobile {e^a}

http://heasarc.nasa.gov/docs/cosmic/sheets_voids.html

thus:
I only write about stuff that I know about or, at least,
have read about in the God-am newspapers. just note that,
in many instances, there really is only "one side
to the story" being reported, Darfur e.g.

Isn't there a better forum for your warped political perspective than
a news group on Buckminster Fuller?

thus:
so, how many proofs of pyhtagoras' theorem,
can't you comprehend?... as for Hales' proof of Kepler's C.,
it never actually worked,
as shown in one of the popularizing books on it, I think;
it's kinda hard to find any overt admission of this
on Hales' website, though ... and, he *did*
prove an important related theorem.... this may also apply
to the fourcolorconjecture, but several simplicifications
of the computerized one have been done, so ...

I believe Ribet on Wiles' "proof," although
I'd rather learn how Fermat did it; at least,
he made no other known mistakes. still,
the characterization of the Fermat primes is an open problem,
arguably more important than his "last."

as for the nonexistence of a proof of RH or Goldbach C.,
quelle ridicule!

And the bugs in the accepted proofs of the fundamental theorem of
algebra by Girard, D´´

thus:
completely interconsistent with your theory, two, since
you can, now, have "travelled back" to them,
at Langley or where ever, to tell them how to do it....
I'd call Art Bell;
you should not let Al Beliek and John V. Neumann try
to take the credit for it, based upon the Philedelphia Experiment,
which everyone knows was just to test *radar* "invisibility,"
if you hadn't already preempted that in your Delorean....
don't drive over all of your great-great granchildren!
you were referring to Normal CIA Remote Viewing,
the kind that was completely ineffective (or
completely hidden from sight, of course, because
there's all of this great theory to back it "up" .-)
"If we knew what it was we were doing, it would not just be called research;
it would be also known as The Rectal Display Unit!" --J.Sarfatti

thus:
Harry Potter-affiliated stuff,
in general -- like both Iraq wars).

this just in:
yesterday's (Tues,. Nov.15) *UCLA Daily Bruin* finally noted that
darfur is entirely Muslim, though downplaying it AMAP.

thus:
Dick Cheeny, Don Rumsfeld and Osama bin Latin form a mission
to Darfur, to prevent a war instead of to start one:
if Darfur is "100% Muslim," then
what's really going on, there?
is it just aother British Quag for USA soldiers to get bogged
into, with Iran, Iraq, Afghanistan et al ad vomitorium,
under auspices of the UN and NATO?
why won't the Bruin publish the fact of Islam on the ground,
therein?

thus:
Why doesn't the [UCLA Daily] Bruin report that
Darfur's populace is "100%" Muslim,
according to the DAC's sponsor,
Terry Saunders?...
"99%" was the figure given
by Brian Steidle, when I finally found
him at the Hammer, after everyone else
had left (he, his friend & I were the
very last to leave!)...
What could it possibly mean?

--The Other Side (if it exists)

Aluminium Holocene Holodeck Zoroaster wrote:
11) Derek Wise, MacDowell-Mansouri gravity and Cartan geometry,
available as gr-qc/0611154.

Elie Cartan is one of the most influential of 20th-century geometers.
At one point he had an intense correspondence with Einstein on
general relativity. His "Cartan geometry" idea is an approach to
the concept of parallel transport that predates the widely used
Ehresmann approach (connections on principal bundles). It
simultaneously generalizes Riemannian geometry and Klein's Erlangen
program (see "week213"), in which geometries are described by their
symmetry groups:

EUCLIDEAN GEOMETRY -------------- KLEIN GEOMETRY

| |
| |
| |
| |
v v

RIEMANNIAN GEOMETRY -------------- CARTAN GEOMETRY

Given all this, it's somewhat surprising how few physicists know
about Cartan geometry!

Recognizing this, Derek explains Cartan geometry from scratch before
showing how it underlies the so-called MacDowell-Mansouri approach
to general relativity. This plays an important role both in
supergravity and Freidel and Starodubtsev's work on quantum gravity
(see "week235") - but until now, it's always seemed like a "trick".

What's the basic idea? Derek explains it all very clearly, so I'll
just provide a quick sketch. Cartan describes the geometry of a lumpy
bumpy space by saying what it would be like to roll a nice homogeneous
"model space" on it. Homogeneous spaces are what Klein studied; now
Cartan takes this idea and runs with it... or maybe we should say he
*rolls* with it!

For example, we could study the geometry of a lumpy bumpy surface by
rolling a *plane* on it. If our surface is itself a plane, this
rolling
motion is trivial, and we say the surface is "flat" in the sense of
Cartan geometry. But in general, the rolling motion is interesting
and serves to probe the geometry of the surface.

Alternatively, we could study the geometry of the same surface by
rolling a *sphere* on it. Derek illustrates this with a picture of
a hamster crawling around in a plastic "hamster ball", which is
something you can actually buy for your pet hamster to let it
explore your house without escaping or getting in trouble.

(I've read about falling cats in papers on gauge theory, but this
is the first mathematical physics paper I've read containing the
word "hamster".)

If our surface is itself a sphere of the same radius, this rolling
motion is trivial, and we say the surface is flat in the sense of
Cartan geometry - but now it's a different sense than when we used
a plane as our "model geometry"!

Which model geometry should we use in a given problem? It depends
on which one best approximates the lumpy bumpy space we're studying!

The ordinary formulation of general relativity fits into this
framework, with a little work. Two well-known mathematical gadgets
called the "Lorentz connection" and "coframe field" fit together to
describe what would happen if we rolled a copy of Minkowski spacetime
over the lumpy bumpy spacetime we live in.

That's great if Minkowski spacetime is the best homogeneous
approximation to the spacetime we live in. But nowadays we think
the cosmological constant is nonzero, so the Universe is expanding
in a roughly exponential way. This makes another model geometry,
"deSitter spacetime", the best one to use!

So, if we know Cartan geometry, we can use that... and we get something

called the MacDowell-Mansouri formulation of gravity. Or, if we don't
want our spacetime to have lumps and bumps - if we want it to look
locally just like the Klein model geometry - we can use a different
theory, a topological field theory called BF theory (see "week232").

In short, the passage from a topological field theory describing a
"locally homogeneous" spacetime to full-fledged gravity with all its
lumps and bumps is nicely understood in terms of how Cartan's approach
to geometry generalizes Klein's!

Above was used a rolling sphere to interrogate
the "lumpy-bumpy" surface, fair enough, the
analogy is respected, however I couldn't find any
mention as to how the sphere diameter would affect
the result. A smaller sphere diameter would resolve
a "lumpy-bumpy" surface with more accuracy.
In that case, we could use the analogy of a higher
energy photon to improve surface resolution, common
in electron microscopes and X-rays, compared to
visual light, (I'm sneaking in a bit of quantum theory).

((IMO, the Cartan philosophy leads to asymmetrical
metrics, but that's just me)).
Regards
Ken S. Tucker


For more details, you'll just have to read Derek's paper. You might
also try these:

12) Michel Biesunski, Inside the coconut: the Einstein-Cartan
discussion on distant parallelism, in Einstein and the History
of General Relativity, eds. D. Howard and J. Stachel, Birkhauser,
Boston, 1989.

This describes the correspondence between Cartan and Einstein.
I believe this centered, not on Cartan geometry per se, but on
the "teleparallel" formulation of gravity (see "week176"). But,
they're somewhat related.

13) R. W. Sharp, Differential Geometry: Cartan's Generalization of
Klein's Erlangen Program, Springer-Verlag, New York, 1997.

This is the main textbook on Cartan geometry. But, it's probably
best to read a few chapters of Derek's paper first, since the
key ideas are presented more intuitively.

My friend the geometer and analyst Rafe Mazzeo, whom I recently saw
at Stanford, told me that Cartan geometry was all the rage these days.
I'm embarrassed to say I hadn't know this! I think the kinds of
Cartan geometry being intensively studied are related to conformal
geometry, CR structures and stuff like that...

Merry Christmas!
Quote of the Week:
"The Universe has as many different centers as there are living
beings in it." - Alexander Solzhenitsyn

http://www.shipov.com
In Einstein's 1915 GR prior to the introduction of the teleparallel
Kibble-Shipov torsion field with the 6 anholonomic angular
pre-Calabi-Yau coordinates for the orientation of the Einstein-Cartan
tetrad frame mobile {e^a}

http://heasarc.nasa.gov/docs/cosmic/sheets_voids.html

thus:
I only write about stuff that I know about or, at least,
have read about in the God-am newspapers. just note that,
in many instances, there really is only "one side
to the story" being reported, Darfur e.g.

Isn't there a better forum for your warped political perspective than
a news group on Buckminster Fuller?

thus:
so, how many proofs of pyhtagoras' theorem,
can't you comprehend?... as for Hales' proof of Kepler's C.,
it never actually worked,
as shown in one of the popularizing books on it, I think;
it's kinda hard to find any overt admission of this
on Hales' website, though ... and, he *did*
prove an important related theorem.... this may also apply
to the fourcolorconjecture, but several simplicifications
of the computerized one have been done, so ...

I believe Ribet on Wiles' "proof," although
I'd rather learn how Fermat did it; at least,
he made no other known mistakes. still,
the characterization of the Fermat primes is an open problem,
arguably more important than his "last."

as for the nonexistence of a proof of RH or Goldbach C.,
quelle ridicule!

And the bugs in the accepted proofs of the fundamental theorem of
algebra by Girard, D´´

thus:
completely interconsistent with your theory, two, since
you can, now, have "travelled back" to them,
at Langley or where ever, to tell them how to do it....
I'd call Art Bell;
you should not let Al Beliek and John V. Neumann try
to take the credit for it, based upon the Philedelphia Experiment,
which everyone knows was just to test *radar* "invisibility,"
if you hadn't already preempted that in your Delorean....
don't drive over all of your great-great granchildren!
you were referring to Normal CIA Remote Viewing,
the kind that was completely ineffective (or
completely hidden from sight, of course, because
there's all of this great theory to back it "up" .-)
"If we knew what it was we were doing, it would not just be called research;
it would be also known as The Rectal Display Unit!" --J.Sarfatti

thus:
Harry Potter-affiliated stuff,
in general -- like both Iraq wars).

this just in:
yesterday's (Tues,. Nov.15) *UCLA Daily Bruin* finally noted that
darfur is entirely Muslim, though downplaying it AMAP.

thus:
Dick Cheeny, Don Rumsfeld and Osama bin Latin form a mission
to Darfur, to prevent a war instead of to start one:
if Darfur is "100% Muslim," then
what's really going on, there?
is it just aother British Quag for USA soldiers to get bogged
into, with Iran, Iraq, Afghanistan et al ad vomitorium,
under auspices of the UN and NATO?
why won't the Bruin publish the fact of Islam on the ground,
therein?

thus:
Why doesn't the [UCLA Daily] Bruin report that
Darfur's populace is "100%" Muslim,
according to the DAC's sponsor,
Terry Saunders?...
"99%" was the figure given
by Brian Steidle, when I finally found
him at the Hammer, after everyone else
had left (he, his friend & I were the
very last to leave!)...
What could it possibly mean?

--The Other Side (if it exists)

Aluminium Holocene Holodeck Zoroaster wrote:
11) Derek Wise, MacDowell-Mansouri gravity and Cartan geometry,
available as gr-qc/0611154.

Elie Cartan is one of the most influential of 20th-century geometers.
At one point he had an intense correspondence with Einstein on
general relativity. His "Cartan geometry" idea is an approach to
the concept of parallel transport that predates the widely used
Ehresmann approach (connections on principal bundles). It
simultaneously generalizes Riemannian geometry and Klein's Erlangen
program (see "week213"), in which geometries are described by their
symmetry groups:

EUCLIDEAN GEOMETRY -------------- KLEIN GEOMETRY

| |
| |
| |
| |
v v

RIEMANNIAN GEOMETRY -------------- CARTAN GEOMETRY

Given all this, it's somewhat surprising how few physicists know
about Cartan geometry!

That's probably because Cartan's connection can be also phrased in
terms of an Ehresmann connection on an adjusted bundle. So at the end
of the day it's just a question of preference for a type of
"packaging".

--
Jan Bielawski

JanPB wrote:
Aluminium Holocene Holodeck Zoroaster wrote:
11) Derek Wise, MacDowell-Mansouri gravity and Cartan geometry,
available as gr-qc/0611154.

Elie Cartan is one of the most influential of 20th-century geometers.
At one point he had an intense correspondence with Einstein on
general relativity. His "Cartan geometry" idea is an approach to
the concept of parallel transport that predates the widely used
Ehresmann approach (connections on principal bundles). It
simultaneously generalizes Riemannian geometry and Klein's Erlangen
program (see "week213"), in which geometries are described by their
symmetry groups:

EUCLIDEAN GEOMETRY -------------- KLEIN GEOMETRY

| |
| |
| |
| |
v v

RIEMANNIAN GEOMETRY -------------- CARTAN GEOMETRY

Given all this, it's somewhat surprising how few physicists know
about Cartan geometry!

That's probably because Cartan's connection can be also phrased in
terms of an Ehresmann connection on an adjusted bundle. So at the end
of the day it's just a question of preference for a type of
"packaging".
Jan Bielawski

OK, Jan, using that so-called "packaging", can you
provide a means to relate how EM and gravitation
are unified at some level, for example, I find that
gravitation is a 2nd order effect of EM caused by
matter, just as magnetism is a 2nd order effect of
electrostatic's relatively to moving frame.
Regards
Ken S. Tucker

"Ken S. Tucker" wrote in message
ps.com...


Hi Ken

Please e-mail me at peter102560NOSPAM at comcast DOT com. I once again lost
your e-mail address due to the need to wipe my system clean and reinstall
windows xp from scratch. This time I'll put your e-mail address in my
hotmail contacts list. Thanks.

Best regards

Pete

Pmb wrote:
"Ken S. Tucker" wrote in message
ps.com...


Hi Ken

Please e-mail me at peter102560NOSPAM at comcast DOT com.

I once again lost
your e-mail address due to the need to wipe my system clean and reinstall
windows xp from scratch. This time I'll put your e-mail address in my
hotmail contacts list. Thanks.

Best regards

Pete

Hi Pete, I've been slacking my course studies lately,
we lost a bit contact on our mutual study of Shultz sp
mainly cuz of holidays etc. and the chemo baby.

My email is
dynamics (at) uniserve.com
Best Regards
Ken

"Ken S. Tucker" wrote in message
ups.com...

Pmb wrote:
"Ken S. Tucker" wrote in message
ps.com...


Hi Ken

Please e-mail me at peter102560NOSPAM at comcast DOT com.

I once again lost
your e-mail address due to the need to wipe my system clean and reinstall
windows xp from scratch. This time I'll put your e-mail address in my
hotmail contacts list. Thanks.

Best regards

Pete

Hi Pete, I've been slacking my course studies lately,
we lost a bit contact on our mutual study of Shultz sp
mainly cuz of holidays etc. and the chemo baby.

My email is
dynamics (at) uniserve.com
Best Regards
Ken

Do you still want to do Schutz?

What else are you studying?

Pete

Pmb wrote:
"Ken S. Tucker" wrote in message
ps.com...


Hi Ken

Please e-mail me at peter102560NOSPAM at comcast DOT com. I once again lost
your e-mail address due to the need to wipe my system clean and reinstall
windows xp from scratch. This time I'll put your e-mail address in my
hotmail contacts list. Thanks.

Just switch to Linux and forget Hotmail. I haven't seen a virus since
1999 and this without any antivirus protection besides the standard
Linux firewall settings.

--
Jan Bielawski

On 2006-12-28 02:00:03 +0000, "JanPB" said:

Pmb wrote:
"Ken S. Tucker" wrote in message
ps.com...


Hi Ken

Please e-mail me at peter102560NOSPAM at comcast DOT com. I once again lost
your e-mail address due to the need to wipe my system clean and reinstall
windows xp from scratch. This time I'll put your e-mail address in my
hotmail contacts list. Thanks.

Just switch to Linux and forget Hotmail. I haven't seen a virus since
1999 and this without any antivirus protection besides the standard
Linux firewall settings.

Or do what I did and buy a Mac ;-) Admittedly also behind my own linux
firewall ;-)
--

For me, it is far better to grasp the Universe as it really is than to
persist in delusion, however satisfying and reassuring.

Carl Sagan


--
Posted via a free Usenet account from http://www.teranews.com