FearlessFerret

2005-06-10 06:21:52 UTC

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If String Theory is not background-free, and if it subsumes general relativity, Raw Message

how can the theory 'explain' space-time curvature?

/ff

Discussion:

(too old to reply)

FearlessFerret

2005-06-10 06:21:52 UTC

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If String Theory is not background-free, and if it subsumes general relativity, Raw Message

how can the theory 'explain' space-time curvature?

/ff

R***@Lycos.com

2005-06-14 07:47:32 UTC

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In what sense do you mean explain? String theory replaces space-timeRaw Message

curvature with gravitons. I'm not sure how the rest works out, though.

R***@Lycos.com

2005-06-14 07:46:42 UTC

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Maybe spacetime is a large 3+1 brane. Or not. *Shrugs*Raw Message

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.

m***@yahoo.com

2005-06-14 07:50:07 UTC

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FearlessFerret wrote:Raw Message

> 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.

FearlessFerret

2005-06-21 07:25:44 UTC

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***@yahoo.com wrote:Raw Message

> 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.)

> 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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