| Date | November 2011 | Marks available | 2 | Reference code | 11N.3.HL.TZ0.14 |
| Level | Higher level | Paper | Paper 3 | Time zone | Time zone 0 |
| Command term | Outline | Question number | 14 | Adapted from | N/A |
Question
This question is about the principle of equivalence and red-shift.
Joe and Kim are travelling in a spaceship.
Joe is next to a light source L1 and Kim is next to an identical light source L2.
The acceleration of the spaceship is zero. Kim measures the frequency of the light from L1 to be the same as the frequency of the light from L2.
Outline why, if the spaceship now accelerates, Kim will measure the light from L1 to be red-shifted with respect to the light from L2.
Suggest, with reference to Einstein’s principle of equivalence, how your answer to (a) leads to the idea that a clock near a massive body runs more slowly than a clock in free space.
Markscheme
Look for an argument along these lines:
the speed of light is independent of speed of source;
because of the direction of acceleration;
to Kim it will appear as if L1 is moving away from her;
light from L1 will therefore be Doppler shifted toward the red end of the spectrum;
or
accelerating spaceship is equivalent to being at rest in a gravitational field / OWTTE;
photons leaving the source therefore gain potential energy and lose kinetic energy;
since E=hf;
Kim will measure a lower frequency;
according to the equivalence principle the accelerating spaceship is equivalent to a frame of reference at rest in a (uniform) gravitational field / can be regarded as being at rest on the surface of a planet/large mass / OWTTE;
if light is red shifted from L1 then this implies period of the light source is longer therefore time is slower / OWTTE;
