Deriving 3+1 Metrics from General P+Q Metric

[amnoob]

Hi,

I've got the following question: were there any efforts to derive 3+1 metrics from the general p+q one? Any links?

Thanks in advance...

 

[hossi]

Hi amnoob,

I came across this paper some while ago

On the origin of the difference between time and space
Authors: C.Wetterich
http://xxx.lanl.gov/ps/hep-th/0405223

We suggest that the difference between time and space is due to spontaneous symmetry breaking. In a theory with spinors the signature of the metric is related to the signature of the Lorentz-group. We discuss a higher symmetry that contains pseudo-orthogonal groups with arbitrary signature as subgroups. The fundamental asymmetry between time and space arises then as a property of the ground state rather than being put into the formulation of the theory a priori. We show how the complex structure of quantum field theory as well as gravitational field equations arise from spinor gravity - a fundamental spinor theory without a metric.

My personal opinion (feel free to ignore it): I can't make sense out of it, and I can't say I like theories that reqiure groups with 3 digits -- like SO(128, C)



B.

PS: good question btw

 

[jarek]

Hi,

I've got the following question: were there any efforts to derive 3+1 metrics from the general p+q one? Any links?

Thanks in advance...

Doesn't it come from the simple fact that there exists the max speed, which module should be preserved in all inertial frames? Then a simple calculus shows what is the invariant element. Heuristically:

(dx/dt)^2=c^2=(dx'/dt')^2 <=> (cdt)^2-dx^2=(cdt')^2-dx'^2


best,
jarek

 

[Careful]

Hi,

I've got the following question: were there any efforts to derive 3+1 metrics from the general p+q one? Any links?

Thanks in advance...

Hi amnoob,

Two answers :
(a) suppose you would start out with a (2,2) metric, sure you get out a
(1,3) metric by Wick rotation of one of the time coordinates.
(b) the (1,3) (or in general (1,q)) metric is the only one compatible with a partial order - that is causality.

Cheers,

Careful

 

[Demystifier]

Hi amnoob,

I came across this paper some while ago

On the origin of the difference between time and space
Authors: C.Wetterich
http://xxx.lanl.gov/ps/hep-th/0405223

We suggest that the difference between time and space is due to spontaneous symmetry breaking. In a theory with spinors the signature of the metric is related to the signature of the Lorentz-group. We discuss a higher symmetry that contains pseudo-orthogonal groups with arbitrary signature as subgroups. The fundamental asymmetry between time and space arises then as a property of the ground state rather than being put into the formulation of the theory a priori. We show how the complex structure of quantum field theory as well as gravitational field equations arise from spinor gravity - a fundamental spinor theory without a metric.

For a work with a similar title attempting to answer a similar question see also
http://arxiv.org/abs/gr-qc/9901045