- #1
yuiop
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This relates to another thread about trains and manhole covers at relativistic speeds falling (or not) down gaps that would be normally be too small.
Consider two hollow cylinders aligned with each other along their long axes with a short gap between the hollow cylinders. They are designed so that a solid bar sliding along the inside of one cylinder can smoothly slide from one cylinder to the next and the bar is long enough that when it is at rest with cylinders, it can comfortably span the gap and complete an electrical circuit and turn on a light bulb.
Now when the bar is moving at relativistic speeds, length contraction makes the bar shorter than the gap and so when making the transition from one cylinder to the next it is never in electrical contact with both cylinders at the same time in the rest frame of the cylinders. The cylinders are alligned vertically so that we do not need to worry about the bar falling out sideways. In this frame the light bulb never comes on.
In the rest frame of the sliding bar, the gap is length contracted so when the bar passes the gap it easily completes the circuit and the light bulb comes on in this reference frame.
Of course there is resolution to this paradox and I suspect I know the answer, but I am interested in what others think of it too
Consider two hollow cylinders aligned with each other along their long axes with a short gap between the hollow cylinders. They are designed so that a solid bar sliding along the inside of one cylinder can smoothly slide from one cylinder to the next and the bar is long enough that when it is at rest with cylinders, it can comfortably span the gap and complete an electrical circuit and turn on a light bulb.
Now when the bar is moving at relativistic speeds, length contraction makes the bar shorter than the gap and so when making the transition from one cylinder to the next it is never in electrical contact with both cylinders at the same time in the rest frame of the cylinders. The cylinders are alligned vertically so that we do not need to worry about the bar falling out sideways. In this frame the light bulb never comes on.
In the rest frame of the sliding bar, the gap is length contracted so when the bar passes the gap it easily completes the circuit and the light bulb comes on in this reference frame.
Of course there is resolution to this paradox and I suspect I know the answer, but I am interested in what others think of it too