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Win Half of a Kingdom With a Fast Strudel!
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On the previous page we set up a competition between Albert the Smart and Arthur the Muscle for half the kingdom and the princess. On this page I explain Albert's thoughts how to win.
When you measure the length of a moving object, relativity theory dictates that the length is contracted. For example, suppose you have a strudel sitting on your table and you measure its length as 1 meter. If the strudel moves and passes a stationary observer, this observer will not measure 1 meter, but less, depending on the speed of the strudel. The higher the speed, the shorter the object. This contraction occurs only in the direction of motion: in any other direction, the dimensions of the object will not change.
So, Albert wins by making the strudel move with a very high speed. The strudel will contract, so its length, as measured by the people in the throne room, is 50 meters.
How does Albert prove that the strudel will fit to the throne room? (Please follow the picture)
Remember, Albert has installed two doors. Let's call them front door F and back door B.
(a) Albert first accelerates the strudel outside of the throne room to such a speed that its length as measured
from the stationary point of view is 50 meters.
(b) The strudel enters through the back door B.
(c) When the back of the strudel B_S is at the back door B, he orders someone to close the back door B. Since the
strudel appears to be 50 meters long, its front end F_S is precisely at the front door F.At this moment it is clear
that his strudel fits in the throne room.
(d) In order not to damage the strudel, he orders someone to open the front door F,
(e) catch the strudel and show that its length is 500 meter, which is 10 times bigger than Arthur the Muscle's
strudel.
Conclusion: Albert the Smart wins the competition.
Let's look at this issue also from the point of view of an observer tied to the moving strudel.
From his point of view, the throne room moves with a very high speed toward the strudel: therefore, the distance
between the front and back doors F and B contracts to 1/10 of its size, which means that the distance between F
and B is 5 meters. So, for the observer tied to the strudel, the strudel would not fit in the throne room.
Wait a minute: for one observer the strudel fits, and for the other one does not? This seems to be a paradox.
Please read the solution to this paradox on the next page.
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