An interesting paradox has been suggested by R. Shaw that goes like this. A very thin steel plate with a circular hole 1 m in diameter centered on the y axis lies parallel to the xz plane in frame S and moves in the +y direction at constant speed v_y as illustrated in Figure 1-45. A meter stick lying on the x axis moves in the +x direction with β = v/c. The steel plate arrives at the y = 0 plane at the same instant that the center of the meter stick reaches the origin of S. Since the meter stick is observed by observers in S to be contracted, it passes through the 1 m hole in the plate with no problem. A paradox appears to arise when one considers that an observer in S', the rest system of the meter stick, measures the diameter of the hole in the plate to be contracted in the x dimension and, hence, becomes too small to pass the meter stick, resulting in a collision. Resolve the paradox. Will there be a collision?

Figure 1-45

Transcribed Image Text:

B=vic у