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Spin or, Actually: Spin and Quantum Statistics ∗

Séminaire Poincaré, Jürg Martin Fröhlich

Published May 17, 2011• 8 citations
OpenAlex

Abstract

“He who is deficient in the art of selection may, by showing nothing but the truth, produce all the effects of the grossest falsehoods. It perpetually happens that one writer tells less truth than another, merely because he tells more ‘truth’.” (T. Macauley, ‘History’, in Essays, Vol. 1, p 387, Sheldon, NY 1860) Dedicated to the memory of M. Fierz, R. Jost, L. Michel and V. Telegdi, teachers, colleagues, friends. 1 Introduction to ‘Spin ’ 1 It appears that the 21 st Century is witnessing a strong decline in Society’s (the public’s, the politicians’,...) interest in fundamental science, in particular in fundamental theoretical science based on precise mathematical reasoning. It is hard to imagine that a discovery like the deflection of light in the gravitational field of the sun, along with the underlying

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“He who is deficient in the art of selection may, by showing nothing but the truth, produce all the effects of the grossest falsehoods. It perpetually happens that one writer tells less truth than another, merely because he tells more ‘truth’.” (T. Macauley, ‘History’, in Essays, Vol. 1, p 387, Sheldon, NY 1860) Dedicated to the memory of M. Fierz, R. Jost, L. Michel and V. Telegdi, teachers, colleagues, friends. 1 Introduction to ‘Spin ’ 1 It appears that the 21 st Century is witnessing a strong decline in Society’s (the public’s, the politicians’,...) interest in fundamental science, in particular in fundamental theoretical science based on precise mathematical reasoning. It is hard to imagine that a discovery like the deflection of light in the gravitational field of the sun, along with the underlying
The history of the discovery of electron spin and the Pauli principle and the mathematics of spin and quantum statistics are reviewed. Pauli’s theory of the spinning electron and some of its many applications in mathematics and physics are considered in more detail. The role of the fact that the tree-level gyromagnetic factor of the electron has the value g e = 2 in an analysis of stability (and instability) of matter in arbitrary external magnetic fields is highlighted. Radiative corrections and precision measurements of g e are reviewed. The general connection between spin and statistics, the CPT theorem and the theory of braid statistics, relevant in the theory of the quantum Hall effect, are described. “He who is deficient in the art of selection may, by showing nothing but the truth, produce all the effects of the grossest falsehoods. It perpetually happens that one writer tells less truth than another, merely because he tells more ‘truth’.” (T. Macauley, ‘History’, in Essays, Vol. 1, p 387, Sheldon, NY 1860) These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.
Abstract ‘When all is said and done, physics is only a description, not an explanation’. I have uttered similar statements many times myself in informal discussions, when my interlocutor happened to slide into an excessive praise of experimental science and an excessive contempt of other forms of human knowledge. In the mouth of Jean-Paul Fragnière, a friend and philosophy teacher who lives in the small Swiss town of Fribourg, this sentence sounds, however, the expression of a different and distant line of thought of a rivalry between human and natural sciences that is still latent in the French-speaking world, a relic of the arrogance of Positivism. We are in the massive building of Saint-Michel College – a sixteenth century Jesuit establishment, a public school for several decades; and though Jean-Paul’s classroom is a modernization of what was the granary, history weighs heavily here. For the first generations of young people educated in this school, heliocentrism was one of the hot topics; now Jean-Paul has invited me to speak to his students about quantum physics.
Many researchers determine the question “Why anything rather than nothing?” as the most ancient and fundamental philosophical problem. Furthermore, it is very close to the idea of Creation shared by religion, science, and philosophy, e.g. as the “Big Bang”, the doctrine of “first cause” or “causa sui”, the Creation in six days in the Bible, etc.Thus, the solution of quantum mechanics, being scientific in fact, can be interpreted also philosophically, and even religiously. However, only the philosophical interpretation is the topic of the text.The essence of the answer of quantum mechanics is:1. The creation is necessary in a rigorous mathematical sense. Thus, it does not need any choice, free will, subject, God, etc. to appear. The world exists in virtue of mathematical necessity, e.g. as any mathematical truth such as 2+2=4.2. The being is less than nothing rather than more than nothing. So, the creation is not an increase of nothing, but the decrease of nothing: it is a deficiency in relation of nothing. Time and its “arrow” are the way of that diminishing or incompleteness to nothing.