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Space--Time--Matter.
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This article is published in American Mathematical Monthly.The article was published on 1923-03-01. It has received 113 citations till now. The article focuses on the topics: Space time.read more
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The Mathematical Universe
TL;DR: In this paper, the authors explore the physics implications of the external reality hypothesis (ERH) that there exists an external physical reality completely independent of us humans and argue that with a sufficiently broad definition of mathematics, it implies the Mathematical Universe Hypothesis (MUH), that our physical world is an abstract mathematical structure.
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Towards a theory of spacetime structure at very short distances
TL;DR: In this article, a new locally scale-invariant extension of general relativity is proposed based on Weyl's conformally invariant geometry, and it is shown that if the theory contains a Higgs phase, then it reduces to Einstein's theory in the limit of large distances.
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A primer of infinitesimal analysis
TL;DR: In this article, the authors present a model for smooth infinitesimal analysis as an axiomatic system, based on the smooth worlds of the differential calculus and the definite integral.
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On the energy tensor of spinning massive matter in classical field theory and general relativity
TL;DR: In this article, a Lagrangian formalism in flat spacetime is used to derive the set of all possible energy-momentum and spin tensors compatible with the conservation laws.
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On the Advancements of Conformal Transformations and their Associated Symmetries in Geometry and Theoretical Physics
TL;DR: In this article, the historical development of conformal transformations and symmetries is sketched: their origin from stereographic projections of the globe, their blossoming in two dimensions within the eld of analytic complex functions, the generic role of transformations by reciprocal radii in dimensions higher than two and their linearization in terms of polyspherical coordinates by Darboux, Weyl's attempt to extend General Relativity.