Structure Of Physical Space Research Articles

Peirce's Theory of the Geometrical Structure of Physical Space

JS PHYSICAL SPACE Euclidean or non-Euclidean? Charles S. Peirce's answer to Ithis question, primarily as found in his writings after 1890, is striking in its novelty. Among scientifically oriented philosophers writing in the second half of the nineteenth century, Peirce was alone in maintaining that space cannot be Euclidean. His arguments that physical space is necessarily non-Euclidean are intriguing (although at least one is flawed) and exemplary of the implications his general philosophy of science had for particular sciences. Furthermore, his conclusion that space is nonEuclidean led him in a curious effort to determine, by the examination of astronomical data, the approximate value of the curvature of space. I These researches resulted in Peirce's statement that his analysis of astronomical data seemed to indicate a hyperbolic space with a constant far from insignificant (8.93 n. 2).2 I shall first examine Peirce's arguments that space is necessarily non-Euclidean. I shall then give an inventory and criticize the methods Peirce employed to determine the curvature of space.

On isobaric spin space

The previously proposed treatment of reflexions as special cases of continous transformations is developed in detail by a method based on the introduction of 3-dimensional structures (triads). The requirement of Lorentz invariance of the definitions of an unreflected and a fully reflected state of a triad can be fulfilled only if from a relativistic point of view a triad has axial symmetry only. Rotations round the symmetry axis are Lorentz invariant processes. The development of the formalism leads to the introduction of a 4-dimensional space with (nearly) Euclidean properties. All its operations find interpretations in terms of local structures in physical space. Lorentz invariant operators are found which have exactly the properties of isospin operators and thus lead to an interpretation of isospace. One of its main characteristics is its axial symmetry which can be extended to spherical symmetry in a limited way only. The well known cases arise; they have only one common Lorentz invariant operator, corresponding to the electric charge operator.