| Explain what is meant by the principle of relativity. | [1] |
| The principle of relativity is the statement that the laws of physics appear the same for any observer in an inertial reference frame. | [1] |
| If we combine the Galilean transformation with Maxwell's theory of electromagnetism, we violate the principle of relativity. Explain why this is so. | [1] |
| In Maxwell's theory, electromagnetic radiation travels with a speed given by c = 1/(μ0ε0)1/2. This is not frame dependent. | [0.5] |
| But in the Galilean transformation the measured speed of light is frame dependent, so by comparing the measurement with the prediction the observe can determine the velocity of his or her inertial frame. This is contrary to the principle of relativity. | [0.5] |
| What is the equivalence principle? Explain why the equivalence principle implies that light should be deflected by a gravitational field. How was this effect first used to test general relativity? | [3] |
| The equivalence principle is the statement that acceleration is, on sufficiently small scales, indistinguishable from gravity, i.e. that the observer cannot tell the difference between accelerationg upwards and being stationary in a gravitational field. (The statement that gravitational mass is exactly proportional to inertial mass is also acceptable.) | [1] |
| If an observer in a box accelerates upwards through the path of a horizontal light beam, s/he will see the beam curve downwards relative to the walls of the upwardly accelerating box. Since this must be indistinguishable from the behaviour of light in a stationary box under the influence of a gravitational field, it follows that light must curve downwards under gravity. | [1] |
| Eddington measured the positions of stars in the vicinity of the Sun during a total eclipse. The bending of light should produce a small displacement of the stars compared to their positions when measured in the absence of the Sun. (The effect was observed, and claimed as evidence in favour of General Relativity, though re-analyses of the original plates suggest that really the experimental error was too large for the results to be a true test.) | [1] |
(2005 Q1.)