The third test, the results of which are still in abeyance, is perhaps the most important of the three, inasmuch as it depends upon a very simple calculation from Einstein's Principle of Equivalence, which asserts that an observer cannot discriminate how much of his motion is due to a gravitational field and how much is due to an acceleration of his body of reference. Einstein illustrates his argument by supposing an observer situated in a closed box in free space. The observer has at first no sensation of weight, and need not support himself upon his feet. Now suppose an external agent to pull the box in a definite direction with constant force. The observer in the box performs experiments with masses of variable material, and as they all fall to the "floor" of the box at the same time, he concludes that he is in a gravitational field. He himself has acquired the sensation of weight. This result led Einstein to propound the equivalence of gravitational and accelerational fields. An immediate consequence of this principle is that the duration of an event depends upon the gravitational conditions at the place of the event.
If we consider the light (of frequency
) which is emitted by a distant star, and suppose it to traverse a practically invariable gravitational field in which bodies are assumed to fall with a constant acceleration
, then an observer at a distance
from the star will have attained a velocity
where