I was wondering what should be used as the criteria for a straight line? One suggestion would be the path that a beam of light would take. Another criteria would be that based on inertia. An object in motion that experiences no forces could be considered to be moving in a straight line. This almost seems too simple, but I had considered that if one were in a capsule in orbit around the earth, and did not have a window, force measuring devices, like an accelerometer, could not distinguish an orbit from motion between stars. Could a gyroscope help? Could an "inertial" straight line be what is meant by gravity being "bent" space. This is my first post. I like to think about fundamental questions and not take anything for granted. I hope this post makes sense. Mark
The path a beam of light takes isn't always a straight line. Gravitational lensing can bend a beam of light as can mirrors or prisms.
In flat space, a Euclidean "straight line" is quite reasonable and it is in fact the basis for our understanding that space-time is NOT Euclidean. The "straight lines" in space-time are more properly called "geodesics" and yes, they are the path that light follows due to what in Euclidean geometry would be considered "bent". We CALL space-time "bent" and similar phrases and that is in reference to Euclidean space. This was shown by the "bent light" around the sun that confirmed the theory of relativity about 100 years ago.
"What is a straight line?" Isn't this a mathematics question and not physics? Physics does not define the shape and geometry. Zz.
What level of mathematical training and subject area would be needed to understand non-Euclidian geometry and geodesics?
Calculus (including partial differential equations), Vector and Tensor Analysis, Differential Geometry