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Homework Help: Question regarding GR and the cylinder condition

  1. Apr 30, 2010 #1
    Question regarding GR and the "cylinder condition"

    Im reading that in Kaluza-Klein theory, the derivatives (of the metric [tex] g_{\mu\nu}[/tex] with respect to the 5th dimension, [tex] X^4 [/tex], were chosen to be zero, to explain why we do not "feel", or detect, the existence of [tex] X^4 [/tex] i.e. the Cylinder Condition (a few different sources including http://arxiv.org/abs/gr-qc/9805018 page 4, 1st paragraph.
    But thinking about minkowski space it seems to me that derivatives of the minkowski metric with respect to all the spatial coordinates [tex] X^1, X^2, X^3 [/tex] are zero, but obviously we do detect [tex] X^1, X^2, X^3 [/tex], thus my confusion.

    I realize that zero derivatives implies that the geodesic becomes an equation that describes flat space. But not why it would mean that we don't detect those dimensions.


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  2. jcsd
  3. Apr 30, 2010 #2


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    Re: Question regarding GR and the "cylinder condition"

    How do you detect the 3 familiar space dimensions without any massive particles to do experiments with? If there is mass in your spacetime, the metric will not be the flat Minkowski one.
  4. May 1, 2010 #3
    Re: Question regarding GR and the "cylinder condition"

    Thanks. I need to look further into the 5-D metric proposed by Klein for the unification of EM and gravity and how that worked - any ideas for a good source for that? a review article or something of the sort...

    thanks again.
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