Recent content by Bas73

Thanks. It's a strange world though ;-) For now, I am happy that I understand your answer at all and it seems logical. The line as second neighborhood for the cylinder is no good either (not open). Since parameters need to be open intervals, I guess you could simply pick (0 < x < 2pi, -oo <...

Hi vanhees71, Thanks. As I understand you, zero forms the second neighborhood, its chart being the identity. The same seems to happen with the Cylinder C2. In my book it is defined as (x,y) with (0 < x < 2pi, -oo < y < oo). Since x=0 is not included, this line needs a neighborhood as well. By...

In my introduction to manifolds the following is stated: Polar coordinates (r, phi) cover the coordinate neighborhood (r > 0, 0 < phi < 2pi); one needs at least two such coordinate neighborhoods to cover R2. I do not understand why two are needed. Any point in R2 can be described by polar...

Hi Nugatory, You are correct, I indeed meant a particle that is not subject to any external forces. My question however was, to put it in your own words: why are paths of extremal proper time always straight lines/the straightest lines possible? Bas

Hi vanhees71, I do not agree with "That's the action principle". The action principle only says you take an extreme (min or max) of the action. In optics this normally leads to the fastest path and often shortest path a photon/wave can propagate. Here it is said that the paths are those with...

Hi, I am working my way thought Hartle's Gravity. In Section 5.4 he states that "The straight lines along which free particles move in spacetime are paths of longest proper time" and proceeds to proof that "in flat space time the proper time is a curve of extremal proper time". Can someone...