GRE Subject Test: Physics : Four Vectors
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Example Questions
Example Question #1 : Four Vectors
A reference frame S' is moving at 0.6c in the z direction with respect to a stationary frame S. An event occurs in S' with the coordinates (x', y', z', ct')=(1, 0, 2, 3). What are the coordinates (x, y, z, ct) of the event with respect to the stationary frame S?
(1, 0, 2.64, 3.3)
(1, 0, 5.25, 4.75)
(1, 0, 4.75, 5.25)
(1, 0, 3.3, 2.64)
(1, 0, 2, 3)
(1, 0, 4.75, 5.25)
To apply a Lorentz transformation, we need gamma and beta:
Then, apply the Lorentz transformation:
Example Question #2 : Four Vectors
A container of water is carried on a space ship traveling at 60% the speed of light relative to the Earth. From the perspective of an observer on Earth, what is the speed of the light in the water?
The speed of light through water in a stationary frame is found from the index of refraction of water, which is approximately
To find the relative speed, use the following equation:
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