The ArgumentBesides the well-known advocate of unified field theories, there was “another Einstein,” who was skeptical of the continuum as a foundational element in physics. This paper presents evidence for the existence of this “other Einstein,” and of the debate between the two Einsteins that lasted most of Einstein's life.

SynopsisThis essay concerns an aspect of the speculative contributions of J. J. Thomson to a field of physics somewhat removed from that upon which his popular fame and scientific eminence were alike founded. He published a number of statements in the period 1903–1910 advocating a discontinuous structure of the electromagnetic field. His unorthodox conception of the field was based upon the presumed discreteness of Faraday's physical lines of electric force. While his ideas led to significant experimental work, they were not (...) brought together in the form of a completed theory. It was at this same time that the quantum theory was independently evolving notions of a structure of the field, and Thomson's efforts at developing a theory of light were diverted into a protracted criticism of the hypothesis of quanta. In 1924–1936 he returned to the subject of the structure of light, but these latter speculations no longer had much relevance to contemporary physical thought. (shrink)

Mathematical continuity, in the technical sense, is a precisely definable mathematical notion which refers to certain properties of numbers and number sequences. The continuity of the physical world, on the other hand, is rather different from mathematical continuity, since it is a directly experienced attribute of nature and does not require, for being understood, any mathematical theory of properties of numbers.