Question regarding GR and the cylinder condition

[benbenny]

Question regarding GR and the "cylinder condition"

Im reading that in Kaluza-Klein theory, the derivatives (of the metric $$g_{\mu\nu}$$ with respect to the 5th dimension, $$X^4$$, were chosen to be zero, to explain why we do not "feel", or detect, the existence of $$X^4$$ 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 $$X^1, X^2, X^3$$ are zero, but obviously we do detect $$X^1, X^2, X^3$$, 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.

Thanks.

B

 

[gabbagabbahey]

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.

 

[benbenny]

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.

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.