Einstein, Tagore and the Nature of Reality
23 Jun 2016-pp 1-237
About: The article was published on 2016-06-23. It has received 4 citations till now. The article focuses on the topics: Einstein.
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TL;DR: The essence of the sixth problem is discussed and the content of this issue is introduced as part of the theme issue ‘Hilbert’s sixth problem’.
Abstract: In this introduction, the essence of the sixth problem is discussed and the content of this issue is introduced. This article is part of the theme issue Hilberts sixth problem.
19 citations
Cites background from "Einstein, Tagore and the Nature of ..."
...In his famous discussion with Tagore [42], Einstein formulated his point of view unambiguously:...
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TL;DR: In this paper, the authors examine two claims that arise in Brown's account of inertial motion in Physical Relativity (2005), and argue that there is nothing objectionable about inertia and that, while the theorems that motivate Brown's second claim can be said to figure in a deductive-nomological explanation, their main contribution lies in their explication rather than their explanation.
Abstract: I examine two claims that arise in Brown’s account of inertial motion in Physical Relativity (2005). Brown claims there is something objectionable about the way in which the motions of free particles in Newtonian theory and special relativity are coordinated. Brown also claims that since a geodesic principle can be derived in Einsteinian gravitation the objectionable feature is explained away. I argue that there is nothing objectionable about inertia and that, while the theorems that motivate Brown’s second claim can be said to figure in a deductive-nomological explanation, their main contribution lies in their explication rather than their explanation of inertial motion.
10 citations
TL;DR: Hilbert's Sixth Problem as mentioned in this paper has been studied in a wide range of domains, from quantum probability to fluid dynamics and machine learning, from solid mathematical and physical results to opinion pieces with new ambitious ideas.
Abstract: Introduction to the special issue of Phil. Trans. R. Soc. A 376, 2018, `Hilbert's Sixth Problem'. The essence of the Sixth Problem is discussed and the content of this issue is introduced.
In 1900, David Hilbert presented 23 problems for the advancement of mathematical science. Hilbert's Sixth Problem proposed the expansion of the axiomatic method outside of mathematics, in physics and beyond. Its title was shocking: "Mathematical Treatment of the Axioms of Physics." Axioms of physics did not exist and were not expected. During further explanation, Hilbert specified this problem with special focus on probability and "the limiting processes, ... which lead from the atomistic view to the laws of motion of continua". The programmatic call was formulated "to treat, by means of axioms, those physical sciences in which already today mathematics plays an important part." This issue presents a modern slice of the work on the Sixth Problem, from quantum probability to fluid dynamics and machine learning, and from review of solid mathematical and physical results to opinion pieces with new ambitious ideas. Some expectations were broken: The continuum limit of atomistic kinetics may differ from the classical fluid dynamics. The "curse of dimensionality" in machine learning turns into the "blessing of dimensionality" that is closely related to statistical physics. Quantum probability facilitates the modelling of geological uncertainty and hydrocarbon reservoirs. And many other findings are presented.
8 citations