Relativity from Copernicus and Bruno to Leibniz

The problem of absolute and relative space does not begin with Newton. It begins with Copernicus and his assumption that the sun is at the center of our planetary system. In the theory of Copernicus we could discern a tendency toward making the sun the ontologi­cally real center of the system, but the predominant motivation was still the simplification of the mathematical description of planetary movements.

The problems of scientific description and of ontology were clearly distinguished. We have seen in an earlier part of this study that the issue was well understood in the sixteenth century and that it was carried to its systematic solution before the century's end.⁴³

Copernicus justified the revolutionary shift of his system of coordinates from the earth to the sun by explaining the relativity of movement. He made it clear that the "real" movement of two bodies that are moved relative to each other is in no way affected by the assumption that one or the other is the origin of the coor­dinates that are used for the description of the movement. Bodin, in his late work, saw the point with equal clearness and drew the conclusion that one might as well shift the coordinates back to the earth. Astronomers might prefer the sun as a center because the assumption allowed for a simpler mathematical description. He, as a philosopher of politics and nature, preferred the earth as a center for reasons of his own.

Relativity must be taken seriously. If the theory of space as an absolute extension around the earth is a fallacy, the theory of space as an absolute extension around the sun is no less a fallacy.

Giordano Bruno's Solution

Gior­dano Bruno had given the systematic elaboration of the problem. Space is phenomenally infinite because this infinity is a projection of the form of the human mind. Ontologically; in the mind of God, the universe is One and the celestial worlds are embraced by this Oneness. The celestial worlds are not embraced as by a space, but they in their turn embrace this Oneness as every part of the soul embraces the soul.

The empirical analysis of space, as well as the transcendental analysis in the Kantian sense, touches only certain aspects of the total problem. Cosmological specula­tion is the theoretical instrument for its complete formulation. This solution of Bruno needs elaboration and reformulation, but in principle it can hardly be improved.

On the level of empir­ical science it has been carried out and confirmed by the the­ory of relativity through the assumption of an unbounded, curved space that runs back into itself.⁴⁴ As far as the Copernican prob­lem is concerned, Bruno drew the conclusion that an infinitely closed space has no absolute center. Its center is everywhere and nowhere, and the choice of the place for the origin of coordinates is arbitrary.

Leibniz and the Logic of Physics

The correctness of the relativistic formulation impressed itself on the contemporaries of Newton. Leibniz developed the problem perhaps furthest in the course of his phoronomic studies. Geometry as the logic of mathematics should be supplemented by phoronomy, a general theory of motion, as the logic of physics.

The first principle of motion, however, is that the movement of a body can be observed only in relation to another body, which is assumed to be resting. Movement is a mutual and inevitable shift of position of material parts. In any system of bodies in relative movement with respect to each other we can chose one of the bodies as being at rest and refer the movement of the other to the coordinates originating in the "resting" body.

Such choice of a resting body for the purpose of description Leibniz calls a "hypothesis." One of these hypotheses may render a simpler description than the other, but its simplic­ity does not make the hypothesis "truer." On principle, all such hypotheses are "equivalent." The "general law of equivalence" is Leibniz's formulation of the problem of relativity.⁴⁵

The meaning Leibniz attached to this principle may be gathered from the fact that he wrote a memorandum on this question with the intention of inducing the Curia to admit the Copernican system. He argued that from the point of view of logic there is no opposition between the Copernican and the Ptolemaic systems. The choice of heliocentric or geocentric coordinates is equivalent, and the greater descriptive simplicity of the Copernican system does not imply the proposition that the movements as described by it are real in an ontological sense.⁴⁶