The LED puzzle makes one think hard about simultaneity in Special Relativity. The outcome looks paradoxical, but it is not.
Consider an inertial reference frame with two focused light emitting diodes (LEDs) that can illuminate two photo detectors (P/Ds), if the green plate is not in the way, as shown in Fig. 1. Situated halfway between the P/Ds is an ideal electronic NOR gate that will only give out a signal to the latching alarm if the moving green plate breaks both light beams. The dotted arrows represent signal flow in electrical wiring.
If the green plate, of length 10.5 ft is slowly (v<<0.4c) moving through the apparatus, then both light beams must be broken simultaneously at some stage and the alarm will latch and sound. If the green plate would pass through the apparatus at a speed of more than 0.4c, the Lorentz contracted plate will be too short to break two beams at the same time and hence no alarm will sound (Fig.2). All standard STR and nothing to it.
Now consider the situation with the green plate as the reference frame and the blue LED frame moving at a relative speed of more than 0.4c in the opposite direction. Relative to the green frame, the LED separation must now Lorentz contract and always be smaller than the green plate's length, so the plate should break two beams simultaneously and sound the alarm at any speed. However, the same experimental setup cannot have two different outcomes, depending on which inertial frame is used as reference.
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