Note 1 — XIV NEW CONCEPTS FOR OLD

Einstein flatly denies Newton’s hypothesis that there is an absolute system (and, indeed, many others before him had found it difficult to admit that so insignificant a part of the universe as our fixed star system should have such a privileged position as that accorded to it in the Newtonian Mechanics). In any system, he says, we have no reason to distinguish between the so-called real gravitational force and the so-called fictitious centrifugal forces—if we wish so to express it gravitational force is fictitious force.1 A particle moving in the neighborhood of material bodies moves according to a law of inertia—a physical law expressible, therefore, in a manner quite independent of the choice of coordinates. The law of inertia is that a particle left to itself moves along the geodesics or shortest lines in the space. If the particle is remote from other bodies the space has the Euclidean character and we have Newton’s law of inertia; otherwise the particle is in a space of a non-Euclidean character (the space being always the four-dimensional space) and the path of the particle is along a geodesic in that space. Einstein, in order to make the theory more concrete, makes a certain stipulation as to the nature of the gravitational space which stipulation is expressed, as are all physical laws, by means of a tensor equation—and this is sometimes called his law of gravitation.