Skip to main content
7 events
when toggle format what by license comment
Jan 7, 2019 at 16:01 comment added Martin C. @BenCrowell I'm afraid I still don't agree with you. I may of course be mistaken, but here is an(other) argument. See physics.stackexchange.com/questions/107928/… for an explicit example of the proper distance between two particles in the exterior Schwarzschild metric, that are separated by a coordinate distance $L$ in the radial direction. The proper distance is NOT $L$, while of course in a Newtonian picture it could not be anything else (the metric is Euclidean in that case).
Jan 2, 2019 at 3:52 comment added Tom B. @BenCrowell, Is there nothing special about a geodesic, like a radial, where particles of varying speeds released along it would all reach the same point on the surface? (neglecting the Earth's rotation). I can see the phenomenon in your example which would create wildly different values for A and r, but that phenomenon seems absent for radials.
Jan 2, 2019 at 3:52 comment added Tom B. @BenCrowell, Ah, I see, but why would one infer that the shape described by the test particles is a Euclidean cone in a test where they originate from anywhere but the center of the Earth, not to mention at speeds less than c? Indeed if the particles were released on the right side, in your example, and start off moving to the right, one might infer an r that is too big instead.
Jan 1, 2019 at 23:06 comment added user4552 @TomB.: but test particles released from the center of the earth would not bend like those in your example; they would fly straight, in the radial direction, wouldn't they? The lines in the diagram are straight. They're geodesics, which is the definition of straightness. They look curved in this representation only because of the way we visualize the two-dimensional projection of the four-dimensional spacetime.
Dec 31, 2018 at 9:20 comment added Martin C. @BenCrowell I have updated the question, you may want to review your answer. I do not think your example addresses the heart of my question.
Dec 29, 2018 at 0:40 comment added Tom B. but test particles released from the center of the earth would not bend like those in your example; they would fly straight, in the radial direction, wouldn't they?
Dec 28, 2018 at 18:27 history answered user4552 CC BY-SA 4.0