Even with these restrictions, Einstein was able to do the equivalent of finding an alteration of scales and clocks in the presence of matter which would account for our finding that the planetary motions take place very nearly in accordance with Newton’s law. The new law has accounted with surprising accuracy for certain astronomical irregularities for which Newton’s law failed to account, and has predicted at least one previously unknown phenomenon which was immediately verified.
In conclusion, it may be of interest to state how the new law describes the motion of a particle in the vicinity of a body like the earth. The law amounts to stating that, if we measure a short distance, radially as regards the earth’s center, we must allow for the peculiarity of our units by dividing by
where r is the distance from the earth’s center, m the mass of the earth, c the velocity of light, and G the Newtonian gravitational constant. Tangential measurements require no correction, but intervals of time as measured by our clocks must be multiplied, for each particular place, by the above factor. Then, in terms of the corrected measures so obtained, the particle will be found to describe a straight line with constant velocity although, in terms of our actual measures, it appears to fall with an acceleration.
XXI
THE EQUIVALENCE HYPOTHESIS
The Discussion of This, With Its Difficulties and the Manner in Which Einstein Has Resolved Them, from the Essay by
PROF. E. N. DA C. ANDRADE, ORDNANCE COLLEGE, WOOLWICH, ENGLAND
Having shown that, of several systems all moving with reference to one another with uniform motion, no one is entitled to any preference over the others, and having deduced the laws for such systems, Einstein was confronted with a difficulty which had long been felt. A body rotating, which is a special case of an accelerated body, can be distinguished from one at rest, without looking outside it, by the existence of the so-called centrifugal forces.