| Date | May 2014 | Marks available | 1 | Reference code | 14M.3.HL.TZ1.18 |
| Level | Higher level | Paper | Paper 3 | Time zone | Time zone 1 |
| Command term | State | Question number | 18 | Adapted from | N/A |
Question
This question is about general relativity.
State the principle of equivalence.
An observer in a spaceship moving at constant speed measures the frequency f0 of light emitted by a source. The spaceship now accelerates to the right.
The observed frequency changes to f.
(i) Outline why, during the acceleration, f is less than f0.
(ii) Explain how the result outlined in (b)(i) leads to the deduction that time dilates near a planet.
Markscheme
a frame of reference accelerating in outer space is equivalent to a frame of reference at rest in a gravitational field / an inertial frame of reference in outer space is equivalent to a freely falling frame of reference in a (uniform) gravitational field;
Award [0] for only “gravitational and inertial mass are equivalent”.
(i) light source appears to be moving away from the observer;
so there is a red-shift (according to the Doppler effect);
or
spaceship (by equivalence) can be regarded as (at rest) in a gravitational field;
photons lose energy in reaching observer (so frequency must be reduced);
(ii) the planet has a gravitational field;
so (by equivalence) the situation is as though light source is near a planet;
f is still observed to be less than f0 / period of the light can be taken as unit of time;
this can be interpreted as an increase in the time for emission of one wavelength / increase in the period (ie time is dilated);
Examiners report
The principle of equivalence is generally well understood by the candidates. However, the majority of candidates wrote general statements (not wrong) but not in a sufficiently clear sequence. There were many vague statements about gravity and inertia in (a), which was not in response to the question of “state the principle...”.
In (b)(ii), some candidates did not realize that the question remained focused on the principle of equivalence. Good answers to this question required a deep understanding of the principle.
