The discussion centers on the physical implications of Minkowski's spacetime model, specifically the metric tensor expressed as $$ds^2 = c^2dt^2 - (dx_1)^2 - (dx_2)^2 - (dx_3)^2$$. Participants agree that congruences of clocks can be synchronized using Einstein's synchronization method, ensuring that light propagation is isotropic and occurs at a constant speed, c. The conversation emphasizes the importance of associating mathematical concepts, such as proper acceleration, with physical measurements from accelerometers, thereby establishing a minimal interpretation that bridges theory and experimental physics.
PREREQUISITESPhysicists, students of relativity, and anyone interested in the foundational aspects of spacetime and its experimental validation.
That is correct. A light beam traversing clockwise or counterclockwise will give different times.cianfa72 said:Do you mean that for clocks at rest in a rotating frame a light beam traversing a closed path of length ##L## is not always ##L/c## (as measured by clocks at fixed points in rotating frame) ?
Which is the reason for this ?Dale said:That is correct. A light beam traversing clockwise or counterclockwise will give different times.
The second postulate.cianfa72 said:Which is the reason for this ?
Sorry, not sure to understand. The second postulate is about the invariance of speed of light as measured in inertial frames.Dale said:The second postulate.
Yes, from that you can derive the fact that in the rotating reference frame a light beam traversing clockwise or counterclockwise will give different times.cianfa72 said:Sorry, not sure to understand. The second postulate is about the invariance of speed of light as measured in inertial frame.
So analyse what happens to two light pulses going in opposite directions in a rotating closed (circular is easiest) path. Assuming the emitter is attached to the rotating apparatus do simultaneously emitted pulses return to the emitter simultaneously?cianfa72 said:Sorry, not sure to understand. The second postulate is about the invariance of speed of light as measured in inertial frame.
Ah ok, one can analyze it from the point of view of the inertial frame where the second postulate holds. No, the two emitted pulses do not return to the emitter simultaneously as measured in the inertial frame by Einstein's synchronized clocks in it. This latter fact is frame invariant (i.e. there is no coincidence of the two reception events), hence a light beam traversing clockwise or counterclockwise will give different times.Ibix said:So analyze what happens to two light pulses going in opposite directions in a rotating closed (circular is easiest) path. Assuming the emitter is attached to the rotating apparatus do simultaneously emitted pulses return to the emitter simultaneously?
No qualification about clocks or synchronization is needed.cianfa72 said:No, the two emitted pulses do not return to the emitter simultaneouslyas measured in the inertial frame by Einstein's synchronized clocks in it.
This because we are looking at the coincidence of events (whether they are the same spacetime point or not).Nugatory said:No qualification about clocks or synchronization is needed.
You can also analyze it in a rotating frame. The circumference with respect to this frame shall be called ##U'##.cianfa72 said:Ah ok, one can analyze it from the point of view of the inertial frame where the second postulate holds.