532 
Rotation is thus relative in Einstein's theory. Does this mean 
that it is physically equivalent to translation, which is also relative 
(and was relative in classical mechanics)? Evidently not. The fun- 
damental difference between a uniform translation and a rotation 
is that the former is an orthogonal transformation (LORENTz-trans- 
formation) of the four coordinates, or world-parameters, and the 
latter is not. Now orthogonal transformations are the only ones that 
leave the line-element invariant im the coordinates, i.e. that do not 
affect the gj, and are therefore without influence on the gravitational 
field. Consequently we can by a Lorentz-transformation “transform 
away” linear velocity. We can always find a system of reference 
relatively to which a given body has no rotation, as we can finda 
system in which the acceleration produced by a given body at a 
given point is zero, but we cannot transform away rotation, no 
more than mass. This is a fact, independent of all theories. Of 
course the fact is differently represented in different theories. NEwTon 
“explains” it by his law of inertia and the absolute space. For 
Eisrew, who makes no difference between inertia and gravitation, 
and knows no absolute space, the accelerations which the classical 
mechanies ascribed to centrifugal forces are of exactly the same 
nature and require no more and no less explanation, than those 
which in classical mechanics are due to gravitational attraction. 
of an entirely material origin of inertia. But practically it makes no difference 
whether we explain a thing by an uncontrollable hypothesis invented for the 
purpose, or not explain it at all. The hypothesis implies the finiteness of the 
physical world, it assigns to it a priori a limit, however large, beyond which 
there is nothing but the field of the gij which at infinity degenerate into the values 
(z). This field, in which also the fourdimensional time space is separated into a 
threedimensional space and a onedimensional time, undoubtedly has some of 
the characteristics of the old absolute space and absolute time. The hypothesis can 
thus be said to make space and time absolute at infinity, although arbitrary trans- 
formations of three-dimensional space are still allowed. If we wish to have com- 
plete four-dimensional relativity for the actual world, this world must of necessity 
be finite [Note added (29 Sept.) after a conversation with Prof. EINSTEIN]. 
