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Metrics signature

  1. May 5, 2006 #1

    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...
  2. jcsd
  3. May 5, 2006 #2
    Hi amnoob,

    I came across this paper some while ago

    On the origin of the difference between time and space
    Authors: C.Wetterich

    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) :eek:



    PS: good question btw
  4. May 5, 2006 #3
    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

    Last edited: May 5, 2006
  5. May 6, 2006 #4
    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.


  6. Nov 16, 2006 #5


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    For a work with a similar title attempting to answer a similar question see also
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