- #1
gerald V
- 67
- 3
- TL;DR
- Can variable devices living on a flat manifold create the impression of intrinsic curvature in sufficient generality?
A textbook (in German language: Sexl-Urbantke, Gravitation und Kosmologie) says that intrinsic curvature of spacetime is a definition. The alternative is to postulate a flat spacetime together with measuring devices that do not have constant length. These definitions are equivalent up to aspects of topology.
I am aware of Feynmans bug (hot plate), but had thought that this only works for special configurations. I have difficulties to understand the general case.
I assume that the specific nature of time can be left aside and spacetime be regarded as 4-dimensional Euclidean. This means, it is sufficient to have a single rod, which however changes in length as a function of its position and orientation inside this flat space.
My questions:
Is this behaviour of the rod actually sufficient to create the impression of an intrinsically curved spacetime in all necessary generality?
Is there literature where the respective calculations are done?
Thank you very much in advance.
I am aware of Feynmans bug (hot plate), but had thought that this only works for special configurations. I have difficulties to understand the general case.
I assume that the specific nature of time can be left aside and spacetime be regarded as 4-dimensional Euclidean. This means, it is sufficient to have a single rod, which however changes in length as a function of its position and orientation inside this flat space.
My questions:
Is this behaviour of the rod actually sufficient to create the impression of an intrinsically curved spacetime in all necessary generality?
Is there literature where the respective calculations are done?
Thank you very much in advance.