Why is space 3-dimensional? The fi rst answer to this question, entirely based on Physics, was given by Ehrenfest, in 1917, who showed that the stability requirement for n-dimensional two-body planetary system very strongly constrains space dimensionality, favouring 3-d. This kind of approach will be generically called "stability postulate" throughout this paper and was shown by Tangherlini, in 1963, to be still valid in the framework of general relativity as well as for quantum mechanical hydrogen atom, giving the same constraint (...) for space{dimensionality. In the present work, before criticizing this methodology, a brief discussion has been introduced, aimed at stressing and clarifying some general physical aspects of the problem of how to determine the number of space dimensions. Then, the epistemological consequences of Ehrenfest's methodology are critically reviewed. An alternative procedure to get at the proper number of dimensions, in which the stability postulate - and the implicit singularities in three-dimensional physics - are not an essential part of the argument, is proposed. In this way, the main epistemological problems contained in Ehrenfest's original idea are avoided. The alternative methodology proposed in this paper is realized by obtaining and discussing the n-dimensional quantum theory as expressed in Planck's law, de Broglie relation and the Heisenberg uncertainty relation. As a consequence, it is possible to propose an experiment, based on thermal neutron di raction by crystals, to directly measure space dimensionality. Finally the distinguished role of Maxwell's electromagnetic theory in the determination of space dimensionality is stressed. (shrink)

Metascientific criteria used for explaining or constraining physical space dimensionality and their historical relationship to prevailing causal systems are discussed. The important contributions by Aristotle, Kant and Ehrenfest to the dimensionality of space problem are considered and shown to be grounded on different causal explanations: causa materialis for Aristotle, causa efficiens for young Kant and an ingenious combination of causa efficiens and causa formalis for Ehrenfest. The prominent and growing rôle played by causa formalis in modern physical approaches to this (...) problem is emphasized. (shrink)

Within the general discussion of space and its dimensionality, Aristotle's position is of the greatest relevance, as one will have the opportunity to argue and discuss in this article.

A general sketch on how the problem of space dimensionality depends on anthropic arguments is presented. Several examples of how life has been used to constraint space dimensionality (and vice-versa) are reviewed. In particular, the influences of three-dimensionality in the solar system stability and the origin of life on Earth are discussed. New constraints on space dimensionality and on its invariance in very large spatial and temporal scales are also stressed.

Space is one of the most fundamental concepts over which scientific knowledge has been constructed. But it is also true that space concepts extrapolate by far the scientific domain, and permeate many other branches of human knowledge. Those are fascinating aspects that could di per se justify the compilation of a long bibliography. Another one is the passion for books. My interest in some physical, historical and philosophical problems concerning the concept of space in Physics, and its properties, can be (...) traced back to the early 1980. Since that time, I have being studying, with several collaborators, the influence of space dimensionality in different physical phenomena, like the Casimir Effect, neutron diffraction, Cosmic Microwave Background Radiation and the stability of Schrödinger’s and Dirac’s hydrogen atom in arbitrary number of dimensions, as well as epistemological aspects of the works of Kant, Ehrenfest an others on this particular subject. Meanwhile, I gave lectures about the History of the Concepts of Space in Physics at the Centro Brasileiro de Pesquisas Físicas (CBPF), at the Program of History of Sciences, Technics and Epistemology of the Federal University of Rio the Janeiro (UFRJ) and also at the Physics Institute of the State University of Rio de Janeiro (UERJ). As a consequence of both this interest and my love for books, I continuously bought books on space for my personal library which contains now quite one half of all the books quoted here. In 1996, Roberto Moreira and I published the Sources for the History of Space concepts in Physics: From 1845 to 1995 in the series Notas de Física of the CBPF (NF # 084/96), which is still available online. This was a first initiative to share our bibliography on space. At that time, it contained 1075 references, including 414 books entirely devoted to space, 380 articles in periodical journals and proceedings and 281 miscellaneous citations. After fifteen years, I decided to focus my attention here to collect what in my opinion are the 601 essential books which could be useful for anyone interested on learning about space. An important restriction is imposed here by language: only texts written in English, French, German, Italian, Spanish, Portuguese and Latin were considered. References are given in chronological order covering the period between 1739 and 2010. For each year, the books are listed in alphabetical order of authors’ name. An onomastic index is included at the end of the book. -/- Francisco Caruso Rio de Janeiro, October 2011 . (shrink)