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Relativistic - Solution to the Strudel Paradox

c and Einstein  |  c Top Speed  |  Speed & Speed  |  Faster than c?
Mass Gain  |  E=m*c^2  |  Age Slower  |  Time Dilation  |  Twin Paradox
Dopper Shift  |  Ticketed  |  Simultaneity  |  Competition  |  Fast Strudel
Paradox? No!  |  Confusions  | 
 
On the previous page I introduced a paradox: Suppose a room is 50 meters long and a strudel is 500 meters long. The strudel moves with a very high speed (let's say the strudel moves with such a speed that the strudel is Lorentz contracted 10 times). For a stationary observer tied sitting in the room, the strudel will fit inside, but for an observer tied to the strudel, the room moves and is Lorentz contracted 10 times; therefore; the strudel will never fit.

The solution to this paradox is hidden in the concept of "simultaneity of events," as witnessed by different observers. I have already discussed that two events that are simultaneous in one frame of reference are NOT simultaneous in moving frames of reference.

How do we apply this fact to our paradox?

Albert the Smart wins the contest because the Lorentz-contracted strudel fits between closed doors F and B. In other words, the front end of the strudel F_S coincides with the front door F, and, AT THE SAME TIME FOR ALBERT (and this is the key point), the back end of the strudel B_S coincides with the back door B.

This statement is not true for the observer tied to the strudel. (Please follow the picture.)

Since he is moving with a very high speed (remember, the room is very short for him), he sees that Albert's order to open the FRONT door came right in time, exactly when the front edge of the strudel touched the front door F; however, the BACK door was still wide open (c) for him. It remains open until the whole strudel moves across the throne room, and the order to shut the back door comes when the back end of the strudel is in the room.

No paradox whatsoever.

Notice: For an observer stationary in the throne room, at least one door is always closed, and both of the doors are never opened simultaneously. On the other hand, for the observer tied to the strudel, there is a time slot when both of the doors are open (giving him enough time to get through the room).

This page more or less concludes what I wanted to say about the light from the classical (non-quantum) point of view. Nevertheless, I will add the next page which describes the most common sources of mistakes when people think about relativity.
 

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last modified 1/5/2001   email Fermilab