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Experiment --> 1 2 3 4 5 6 7 8 9 Experiment 6
Einstein's wife wants him to jump through hoops, but he wonders if anything
strange will happen with regard to lengths that are perpendicular to his
direction of motion.
Conclusion:
Let
us suppose that when an object moves that there is a contraction of length in
the direction that is perpendicular to its line of motion. Then the diagrams
below will show that this assumption leads to a contradiction.
By
this assumption, if the hoop considers itself as standing still, then Einstein
shrinks in the direction perpendicular to his motion and has no trouble going
through the hoop.
On
the other hand, if Einstein considers himself as standing still and the hoop as
moving toward him, then by our assumption he would see the hoop contract, and
conceivably, he might then be unable to pass through the hoop.
This
is a contradiction, though, since we can't have Einstein both passing through
and not passing through the hoop. The assumption that leads to this
contradiction is that lengths perpendicular to our line of motion will contract.
An assumption that these lengths would expand leads to a similar contradiction.
Thus, we can only conclude that there will be no change at all in lengths that
are perpendicular to our line of motion. The only lengths that change are those
that are parallel to our line of motion, as we showed in the previous
experiment. |