On Friday, 5 October, I will stray from the PSA in Montreal to the adjacent History of Science Society conference and deliver a talk entitled “A giants’ singular struggle: Einstein, de Sitter, Weyl, and Klein’s debate on an alleged singularity”. Unfortunately, this will probably mean that I have to miss Fred Muller’s attack on my paper “Challenging the spacetime structuralist”. But I will be compensated with what promises to be insightful criticisms on my paper on this early episode in the history of GR!
This paper explores an early episode in the history of Albert Einstein’s general theory of relativity that turned on the interpretation of singularities. Einstein, in an attempt to restore stability to an otherwise imploding universe, introduced his infamous cosmological constant into his equations in 1917. Within a week, the Dutch astronomer Willem de Sitter produced a spacetime model of the modified equations. To Einstein’s dismay, de Sitter’s model violated his beloved “Mach’s principle”. Consequently, Einstein set out to nullify de Sitter’s model. The ensuing debate between Einstein and de Sitter, which also draws in, one by one, the mathematicians Hermann Weyl, Felix Klein and, from afar, David Hilbert quickly degenerates into what might uncharitably be depicted as a comedy of errors. For over a year, Einstein, de Sitter, and Weyl fail to recognize that the singularity–a mathematical pathology–they believe to have identified in de Sitter’s model is a mere artefact of an unfortunate choice of coordinates in a perfectly regular geometrical space, akin to the perfectly regular origin of a polar coordinate system. This paper seeks to explain this failure and its persistence over a surprisingly long period by offering an analysis of their correspondence, the mathematical traditions that they have been trained and operate in, and–paradoxically–their precipitant desire to endow the mathematical structure with physical meaning. A case will be made that Einstein simply lacked, due to his own negligence, the requisite mathematical training, while Weyl was led astray by Hilbert’s blatantly inadequate characterization of spacetime singularities.