The Idea of Structureless Points and Whitehead’s Critique of Einstein

Abstract

It is no exaggeration to say that since Euclid’s famous definition of points (as without parts and with no magnitude), this idea had been an almost unquestioned assumption at the basis of geometry and theoretical physics. The idea of structureless or extensionless points had been accepted as elementary. But elementarity may not be the same as logical simplicity or physical simplicity. There are at least two beautiful examples from recent History of Science to illustrate this. During the last two decades two age-old presumptions of science have been questioned and in some sense replaced. Firstly Fractal Geometry showed e.g. that the concept of dimensions is by no means necessarily connected with whole numbers like 1, 2, 3 or 4.¹ Algorithmic geometries became an immensely rich extension of the classical conception. But I’m not going to elaborate on this. Secondly during the development of physics in our century the elementarity of points became questionable. Within quantum theory and later due to the models of unification (especially string theories) it turned out that the theory of relativity is in some sense still classical. Super String Theory² is an actual candidate for a Unified Theory of elementary forces after the Grand Unified Theories or alternative candidates like Super Symmetry or Super Gravity had not been as successful as hoped for. One basic problem is still the incompatibility of Relativity and Quantum Theories. Relativity is geometrically a “classical” theory. But the Uncertainty Principle demands e.g. that points in quantummechanical description cannot be local objects. It is very interesting to see that basic structures of Relativity and Quantum Theories are pointing to such geometrical presumptions.