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FearlessFerret
science forum beginner
Joined: 03 May 2005
Posts: 17
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 Posted: Fri Jun 10, 2005 6:21 am Post subject:
Stringiness and curvature
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If String Theory is not background-free, and if it subsumes general relativity,
how can the theory 'explain' space-time curvature?
/ff |
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Guest
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| Posted: Mon Jun 13, 2005 10:36 am Post subject:
Re: Stringiness and curvature
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On Fri, 10 Jun 2005, FearlessFerret inquired:
| Quote: | If String Theory is not background-free, and if it subsumes general
relativity, how can the theory 'explain' space-time curvature?
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Look for a long discussion which appeared in this NG a year or more ago on
"local mimics of gtr" and the "local versus global" distinction. HTH,
"T. Essel" |
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Guest
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| Posted: Tue Jun 14, 2005 5:46 am Post subject:
Re: Stringiness and curvature
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Maybe spacetime is a large 3+1 brane. Or not. *Shrugs*
Also, gr is just sr plus the equivilence principle. Plus you don't need
a special background, just an acceleration. The curvature in a specific
area can be gravitons messing with the particles. At least, that's how
one of my friends rationalizes it. |
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Guest
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| Posted: Tue Jun 14, 2005 5:47 am Post subject:
Re: Stringiness and curvature
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In what sense do you mean explain? String theory replaces space-time
curvature with gravitons. I'm not sure how the rest works out, though. |
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Guest
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| Posted: Tue Jun 14, 2005 5:50 am Post subject:
Re: Stringiness and curvature
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FearlessFerret wrote:
| Quote: | If String Theory is not background-free, and if it subsumes general relativity,
how can the theory 'explain' space-time curvature?
|
The simplest way is this: all 4-dimensional Lorentzian manifolds are
representable as the limit of manifolds that are Minkowski except on a
submanifold of measure 0.
The measure 0 subset is where the curvature is concentrated at and --
for 4-dimensions -- the singularities are in the most general case
characterized as 2-dimensional. If timelike and compact, they will be
string singularities.
Associated with each singularity is a set of loop invariants that
essentially define the Riemannian tensor as a singular delta-like
function equal to 0 off the source, with loop integrals that give you
non-zero curvature when linking the source.
Thus, you can have your cake and eat it too -- a theory that is
simultaneously strings and loops; simultaneously background-free and
Minkowski background.
This appears the classical level in string theory, where the solution
to the classical 2-dimensional singularity in an otherwise Minkowski
background is a 2-surface closely associated with a lightlike helical
worldline -- i.e., the worldline of a relativistic particle.
This also appears on the classical level in a very closely related
vein, where fermions, themselves, are directly representable as string
singularities:
Kerr-Newman Solution as a Dirac Particle
hep-th/0210103v2
2004 January 19
Arcos and Pereira
(From the abstract)
"For [source mass m, angular momentum a, electric charge q, where m^2 <
a^2 + q^2], the Kerr-Newmann solution of Einstein's equatins reduces to
a naked singularity of circular shape, enclosing a disk across which
the metric components fail to be smooth [which the paper goes on to
describe as a 'looking glass' type wormhole entrance]. By considering
the Hawking and Ellis extended interpretation of the extended
Kerr-Newman spacetime [the looking glass], it is show that, similarly
to the electron-positron system, the solution represents four
inequivalent states. Next, it is shown that due to the topological
structure of the extended Kerr-Newman spacetime, it does admit states
with half-integral angular momentum. This last fact is corroborated by
the fact that, under a rotation of space coordinates, these states
transform into themselves only after a [720 degree] rotation [as is
characteristic of spin 1/2 particles]. As a consequence it becomes
possible to naturally represent them in a Lorentz spinor basis. The
state vector representing the whole Kerr-Newman solution is then
constructed [i.e. the Dirac spinor, itself], and the evolution is shown
to be governed by the Dirac equation. The Kerr-Newman solution can
thus be consistently interpreted as a model for the electron-positron
system, in which the concepts of mass, charge and angular momentum
becomes connected with the spacetime geometry. Some phenomenological
consequences of the model are explored. |
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FearlessFerret
science forum beginner
Joined: 03 May 2005
Posts: 17
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| Posted: Tue Jun 21, 2005 7:25 am Post subject:
Re: Stringiness and curvature
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markwh04@yahoo.com wrote:
| Quote: | FearlessFerret wrote:
If String Theory is not background-free, and if it subsumes general
relativity,
how can the theory 'explain' space-time curvature?
The simplest way is this: all 4-dimensional Lorentzian manifolds are
representable as the limit of manifolds that are Minkowski except on a
submanifold of measure 0.
|
"Wow, do I ever not understand this." You lost me halfway though the first
sentence. After I've made my millions in software I'm going to retire and go
learn all this stuff. Either that or train full time for a 6th degree Black
Belt in Tae Kwon Do, I haven't decided.
Thanks for trying, though.
/ff
(I probably have a better chance with the babes in post-grad physics, and
there's less attendant risk of grave physical impairment.)
| Quote: | The measure 0 subset is where the curvature is concentrated at and --
for 4-dimensions -- the singularities are in the most general case
characterized as 2-dimensional. If timelike and compact, they will be
string singularities.
Associated with each singularity is a set of loop invariants that
essentially define the Riemannian tensor as a singular delta-like
function equal to 0 off the source, with loop integrals that give you
non-zero curvature when linking the source.
Thus, you can have your cake and eat it too -- a theory that is
simultaneously strings and loops; simultaneously background-free and
Minkowski background.
This appears the classical level in string theory, where the solution
to the classical 2-dimensional singularity in an otherwise Minkowski
background is a 2-surface closely associated with a lightlike helical
worldline -- i.e., the worldline of a relativistic particle.
This also appears on the classical level in a very closely related
vein, where fermions, themselves, are directly representable as string
singularities:
Kerr-Newman Solution as a Dirac Particle
hep-th/0210103v2
2004 January 19
Arcos and Pereira
(From the abstract)
"For [source mass m, angular momentum a, electric charge q, where m^2
a^2 + q^2], the Kerr-Newmann solution of Einstein's equatins reduces to
a naked singularity of circular shape, enclosing a disk across which
the metric components fail to be smooth [which the paper goes on to
describe as a 'looking glass' type wormhole entrance]. By considering
the Hawking and Ellis extended interpretation of the extended
Kerr-Newman spacetime [the looking glass], it is show that, similarly
to the electron-positron system, the solution represents four
inequivalent states. Next, it is shown that due to the topological
structure of the extended Kerr-Newman spacetime, it does admit states
with half-integral angular momentum. This last fact is corroborated by
the fact that, under a rotation of space coordinates, these states
transform into themselves only after a [720 degree] rotation [as is
characteristic of spin 1/2 particles]. As a consequence it becomes
possible to naturally represent them in a Lorentz spinor basis. The
state vector representing the whole Kerr-Newman solution is then
constructed [i.e. the Dirac spinor, itself], and the evolution is shown
to be governed by the Dirac equation. The Kerr-Newman solution can
thus be consistently interpreted as a model for the electron-positron
system, in which the concepts of mass, charge and angular momentum
becomes connected with the spacetime geometry. Some phenomenological
consequences of the model are explored.
|
--
If virtual memory did not exist, it would be necessary for us to invent it. |
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Guest
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| Posted: Tue Jun 21, 2005 7:27 am Post subject:
Re: Stringiness and curvature
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On Tue, 14 Jun 2005 Rozmonth@Lycos.com wrote:
| Quote: | gr is just sr plus the equivilence principle.
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Those who don't know much about physics are not unwelcome here, but
-please- don't shoot your mouth off like this unless you have at least
thought about how confident you are that you know what you are talking
about. This is particularly important now that the moderators are too
overworked to try to catch such misstatements in at least very short posts
like this one.
Rozmonth, "STR+EP" could be said to describe (but not to define) "metric
theories of gravitation", but GTR is only one of many such theories which
are known. See for example
http://math.ucr.edu/home/baez/RelWWW/grad.html#tests
It would be better to say that GTR is defined by the EFE (or by the
Hilbert Lagrangian, from which the EFE may be obtained in the usual way).
[Pedantic note to serious students: yes, I and others have argued here
that the EFE alone cannot be a complete definition of "GTR", and I and
others have discussed here the fact that various ways of formulating GTR
may not be completely equivalent. See also a past thread here on "Will
the real GTR please stand up"? or something like that, dealing with issues
of allowed matter tensors, allowed smoothness, allowed topologies/causal
structure, etc. For the original question, the thread I previously cited
is still the most relevant, however.]
"T. Essel" |
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Guest
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| Posted: Tue Jun 21, 2005 7:27 am Post subject:
Re: Stringiness and curvature
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On Tue, 14 Jun 2005 Rozmonth@Lycos.com wrote:
| Quote: | String theory replaces space-time curvature with gravitons.
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That's not true either. (See my other post shooting down a second howler
you made in another short post which IMO should not have appeared.)
Rozmonth, in future, -please- think before you post, OK? Some of us here
take science seriously, and we care about the truth. The charter stands
behind us:
http://math.ucr.edu/home/baez/physics/Administrivia/Charters/research.txt
"T. Essel" |
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