Thats easy Hank,

Curvature can be measured entirely within a surface, and similarly
within a higher-dimensional manifold such as space or spacetime. On
earth, if you start at the North Pole, sail south for about 10,000 km
(to the Equator), turn left by 90 degrees, Sail for 10,000 more km, and
then do the same again (sail for 10,000 more km, turn left by 90
degrees, sail for 10,000 more km), you will be back where you started.
Such a triangle with three right angles is only possible because the
surface of the earth is curved. The curvature of spacetime can be
evaluated, and indeed given meaning, in a similar way. Spaces of only
two dimensions, however, require only one quantity, the Gaussian or
scalar curvature, to quantify their curvature. In more dimensions,
curvature is quantified by the Riemann tensor. This tensor describes
how a vector that is moved along a curve parallel to itself changes
when a round trip is made. In flat space the vector returns to the same
orientation, but in a curved space it generally does not.

Joe

So what instruments would you use to measure this?



"Joe" wrote in message
oups.com...
Thats easy Hank,

Curvature can be measured entirely within a surface, and similarly
within a higher-dimensional manifold such as space or spacetime. On
earth, if you start at the North Pole, sail south for about 10,000 km
(to the Equator), turn left by 90 degrees, Sail for 10,000 more km, and
then do the same again (sail for 10,000 more km, turn left by 90
degrees, sail for 10,000 more km), you will be back where you started.
Such a triangle with three right angles is only possible because the
surface of the earth is curved. The curvature of spacetime can be
evaluated, and indeed given meaning, in a similar way. Spaces of only
two dimensions, however, require only one quantity, the Gaussian or
scalar curvature, to quantify their curvature. In more dimensions,
curvature is quantified by the Riemann tensor. This tensor describes
how a vector that is moved along a curve parallel to itself changes
when a round trip is made. In flat space the vector returns to the same
orientation, but in a curved space it generally does not.

Joe

Light and mirrors

Joe