> FearlessFerret wrote:
>> If String Theory is not background-free, and if it subsumes general
>> 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.
(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
> Kerr-Newman Solution as a Dirac Particle
> 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.