2 0 4 D O C . 4 9 R E P L Y T O R E I C H E N B Ä C H E R

I now turn to the objections against the relativistic theory of the gravitational

field. Here, Herr Reichenbächer first of all forgets the decisive argument, namely,

that the numerical equality of inertial and gravitational mass must be traced to an

equality of

essence.1

It is well known that the principle of equivalence

accomplishes just that. He (like Herr Kottler) raises the objection against the prin-

ciple of equivalence that gravitational fields for finite space-time domains in

general cannot be transformed away. He fails to see that this is of no importance

whatsoever. What is important is only that one is justified at any instant and at will

(depending upon the choice of a system of reference) to explain the mechanical be-

havior of a material point either by gravitation or by inertia. More is not needed; to

achieve the essential equivalence of inertia and gravitation it is not necessary that

the mechanical behavior of two or more masses must be explainable as a mere ef-

fect of inertia by the same choice of coordinates. After all, nobody denies, for

example, that the theory of special relativity does justice to the nature of uniform

motion, even though it cannot transform all acceleration-free bodies together to a

state of rest by one and the same choice of coordinates.

The gravitational fields that can be transformed away are important only as a

special case that must certainly satisfy the laws of nature we are after.

The second objection is that fields existing with respect to a coordinate system

rotating against an inertial system (such as centrifugal fields, Coriolis fields) are,

allegedly, only “fictitious” but not “real” fields. This is correct in Newton’s theory

because these fields do not satisfy Poisson’s differential law. But according to the

theory of general relativity, they satisfy the differential equations of the field and

are, consequently, with respect to the chosen coordinate system just as “real” as the

fields in the neighborhood of a ponderable body.

The adherents of the theory of relativity do not agree on whether these fields

should indirectly be traced to the effect of masses. I myself opt for the first opinion,

according to which all, even the most distant, masses of the universe take part in

establishing the gravitational field at every location. I do not have to go into the

details of this question, which is closely connected with the cosmological problem,

even though it is of fundamental significance. The justification or superiority,

respectively, of the theory of relativity can be judged without deciding these more

remote questions, which in the end can possibly only be answered by stellar astron-

omy.

1Instead

of “Since gravitation. . . shows its effect in acceleration,” Herr Reichenbächer

should have said, “Since the gravitational acceleration is independent of the material and

the state of the body influenced by the gravitational force.” The latter property only, and

alone, distinguishes the gravitational field from the other fields of force.

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