2 9 2 D O C U M E N T 3 7 0 C O M M E N T O N S E L E T Y case according to the general theory of relativity if the mean density of the matter is finite and the universe is spatially closed. I would like to attempt to illustrate this with a more simple, fictitious—if imperfect—case.[5] It is assumed that one could only know gravitation through a close study of the mechanics of masses that are available to us in laboratory experiments. The spher- ical shape of the Earth is unknown to us. Then the following theory could be pos- tulated. A vertical “cosmic” gravitational field primarily exists that extends everywhere into infinity. The Earth extends downwards into infinity. Its gravita- tional influence is negligible against the cosmic gravitational field.(1) The cosmic gravitational field is modified by gravitational effects from masses empirically accessible to experience on the Earth’s surface. Although the assumed cosmic gravitational field agrees with Poisson’s equation just as do the gravitational fields of the experimentally accessible masses on the Earth’s surface, this interpretation would be unsatisfactory because the cosmic field itself had been assumed to be without any material cause. The idea that the gravi- tational field, which mainly determines the fall of bodies on the Earth’s surface, did not exist independently but was caused by the Earth’s body, would certainly be received as a major advance. Today the need to attribute the world’s metric and inertial field to physical causes is not being demanded with similar intensity only because this latter field is not being perceived so clearly as a physical reality as was the physical reality of the “cosmic gravitational field” in the above example. To a later generation, however, this contentedness will seem incomprehensible. Mach’s postulate, according to which the inertial effect of an individual body should be determined by the totality of all the others in the same way as its gravi- tational force, is as little satisfied by the “molecular-hierarchical universe” as by the “island world.” I find it hard to understand how Mr. Selety could have allowed this fault in his system to escape him. This fault is particularly serious as, even without considerations of a cosmological nature, the general theory of relativity can show to first approximation that the bodies behave as should be expected according to Mach’s thought. In this regard I refer to the fourth of my “Four Lectures on the The- ory of Relativity” (delivered in May 1921 at Princeton University).[6] Finally, one more point is mentioned that causes confusion not just in Selety’s article but in many relevant publications. The theory of relativity states: The natural laws should be formulated independent of any special choice of coordinates, as the system of coordinates does not correspond to anything real the simplicity of a hypothetical law is only assessed by its generally covariant formulation. From this (1) Please excuse that this hypothesis does not fit with Newton’s law. [p. 437] [p. 437] [p. 438]
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