- #36
Karl Coryat
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Thanks, guys. That was very enlightening.
The Simultaneity Paradox: Investigating Net Rotation of a Balanced Beam
- I
- Thread starter e2m2a
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- Paradox Simultaneity
In summary, the two lightning bolts strike the ends of the beam simultaneously, but the moving frame sees one bolt strike one end first and another bolt strike the other end. This causes the beam to flex, and the waves of distortion propagate along the rod at the speed of sound. However, the speed of sound is direction dependent in the moving frame, and this conspires with the time between the strikes in this frame and the motion of the fulcrum so that the waves arrive at the fulcrum simultaneously. This means that there is no net rotation at the fulcrum.
- #37
Ibix
Science Advisor
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Not to scale, but here's a quick sketch of @Karl Coryat's two fibers connected to a black box detector, made at three different times in a frame where the apparatus is moving. The fibers are of equal length.
In the top diagram a pulse of light (coloured red) enters one end of the apparatus. In the second diagram the red pulse has traveled some way along the fiber, and the other pulse (coloured blue) enters the other end of the apparatus. In the final diagram both pulses arrive at the detector simultaneously. I've added vertical grey lines showing the points in space where the light pulses entered the fibers and where they meet at the detector. You can see that the distances are very different, although the distances from detector to fiber end are equal at all times. The point is that, in a frame where the apparatus is moving, "where the light entered the fiber" and "where the fiber end is now" are two different things in general.
Since this isn't drawn to scale, the same diagram works just as well for the "light moving in free space" variant.
In the top diagram a pulse of light (coloured red) enters one end of the apparatus. In the second diagram the red pulse has traveled some way along the fiber, and the other pulse (coloured blue) enters the other end of the apparatus. In the final diagram both pulses arrive at the detector simultaneously. I've added vertical grey lines showing the points in space where the light pulses entered the fibers and where they meet at the detector. You can see that the distances are very different, although the distances from detector to fiber end are equal at all times. The point is that, in a frame where the apparatus is moving, "where the light entered the fiber" and "where the fiber end is now" are two different things in general.
Since this isn't drawn to scale, the same diagram works just as well for the "light moving in free space" variant.