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Drakkith

Staff Emeritus

Science Advisor

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## Main Question or Discussion Point

Let's say you have a spaceship with an observer on it who has an experiment set up on the ship to measure the speed of light from a laser beam that is directed at the ship from behind. This experiment consists of two mirrors, one half silvered to only reflect part of the beam, that reflect the light down into two detectors. The half silvered mirror is place in the aft end of the ship while the other is placed in the forward end. The half-silvered mirror serves to reflect part of the light into the aft detector while letting the rest pass through to the forward detector. The laser sits in a stationary frame and the ship moves at 0.5c with respect to it.

Once the ship is accelerated up to 0.5c away from the laser the laser is then turned on and directed at the ship to hit both mirrors. The observer on board the ship measures when each photodetector goes off. Repeat the experiment as necessary to average out the shot noise and other effects.

What does the observer on the ship measure as the speed of the laser beam by measuring the time between the aft detector first detecting light and the forward detector first detecting light? I WANT to say c, but it doesn't make sense to me. At 0.5c you relativistic effects are only at a factor of 1.154, or about 15%, meaning that you would experience 1.154 seconds for every second of the stationary frame. It is my understanding that the light in the laser beam would take twice as long to catch up to the moving ship as it would if it were stationary since it is traveling at 0.5c. But if that is true, what is the observer measuring on the ship and does this particular experiment say anything about the speed of light or am I misunderstanding something, as accounting for time dilation and length contraction doesn't seem to be able to account for everything. I'm feel as if I've missed something horribly obvious but I can't seem to put my finger on it.

Thanks.

Once the ship is accelerated up to 0.5c away from the laser the laser is then turned on and directed at the ship to hit both mirrors. The observer on board the ship measures when each photodetector goes off. Repeat the experiment as necessary to average out the shot noise and other effects.

What does the observer on the ship measure as the speed of the laser beam by measuring the time between the aft detector first detecting light and the forward detector first detecting light? I WANT to say c, but it doesn't make sense to me. At 0.5c you relativistic effects are only at a factor of 1.154, or about 15%, meaning that you would experience 1.154 seconds for every second of the stationary frame. It is my understanding that the light in the laser beam would take twice as long to catch up to the moving ship as it would if it were stationary since it is traveling at 0.5c. But if that is true, what is the observer measuring on the ship and does this particular experiment say anything about the speed of light or am I misunderstanding something, as accounting for time dilation and length contraction doesn't seem to be able to account for everything. I'm feel as if I've missed something horribly obvious but I can't seem to put my finger on it.

Thanks.

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