The Generalization
Not content with all this, Einstein proceeded, a few years ago, to develop a “general” theory of relativity, which includes the effects of gravitation.
To make this idea clear, let us imagine two observers, each, with his measuring instruments, in a large and perfectly impervious box, which forms his “closed system.”
The first observer, with his box and its contents, alone in space, is entirely at rest.
The second observer, with his box and its contents, is, it may be imagined, near the earth or the sun or some star, and falling freely under the influence of its gravitation.
This second box and its contents, including the observer, will then fall under the gravitational force, that is, get up an ever-increasing speed, but at exactly the same rate, so that there will be no tendency for their relative positions to be altered.
According to Newton’s principles, this will make not the slightest difference in the motions of the physical objects comprising the system or their attractions on one another, so that no dynamical experiment can distinguish between the condition of the freely falling observer in the second box and the observer at rest in the first.
But once more the question arises: What could be done by an optical experiment?
Einstein assumed that the principle of relativity still applied in this case, so that it would be impossible to distinguish between the conditions of the observers in the two boxes by any optical experiment.
It can easily be seen that it follows from this new generalized relativity that light cannot travel in a straight line in a gravitational field.
Imagine that the first observer sets up three slits, all in a straight line. A ray of light which passes through the first and second will obviously pass exactly through the third.
Suppose the observer in the freely falling system attempts the same experiment, having his slits P, Q, R, equally spaced, and placing them at right angles to the direction in which he is falling. When the light passes through P, the slits will be in certain position
(Figure). By the time it reaches Q, they will have fallen to a lower level,
, and when it reaches R, they will be still lower,
. The times which the light takes to move from P to Q and Q to R will be the same: but, since the system is falling ever faster and faster the distance
will be greater than
. Hence, if the light which has passed through P and Q moves in a straight line, it will strike above R, as is illustrated by the straight line in the figure. But, on Einstein’s assumption, the light must go through the third slit, as it would do in the system at rest, and must therefore move in a curved line, like the curved line in the figure, and bend downward in the direction of the gravitational force.