Hello all, I have a question that's been bothering me the last few days and wasn't sure where to turn.(adsbygoogle = window.adsbygoogle || []).push({});

Recall the original Special Relativity thought experiment: A spaceship travels at constant velocityv, moving in the positivexdirection. An observer on the spaceship emits a photon directly upwards, from the floor of his ship to the ceiling, and measures the time, call itT. To a stationary observer watching the ship fly by, the beam of light will travel in a diagonal path. If we denote the time measured by the stationary observert, then when the ship has traveled a distancev*t,the stationary observer will see the light travel a distancec*t. This situation can be modeled with a right triangle;

If we use Pythagoras we can solve for the ratio ofT/tand get the usual Lorentz Factor.

Now the question that has been bothering me: Imagine the same situation, however now we have two ships, each traveling in the same direction but with different speeds. Call the slower shipv1and the faster shipv2. In the same timet, as measured by a stationary observer, the slower ship will travel a distancev1*t, and the faster ship will travel a distancev2*t. If each ship emits a photon at the same time, the stationary observer will see two beams of light, with the one coming from the faster ship making a smaller angle. We can model this with a pair of triangles;

From this diagram it appears that the photons, as measured by everyone involved, travel different distances in the vertical direction.

Since the ships are identical, does this mean the photon on the second ship does not make it to the ceiling at the same time the first one does? How would this discrepancy be resolved if the two moving observers were watching each other? Since there is no length contraction in the vertical direction I would expect the two photons to reach the top in the same amount of time. Does this mean an observer on one ship would see the photon of the other ship traveling slower?

Maybe I'm missing something, any thoughts are much appreciated.

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# I Thought Experiment Contradiction

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