Die Grundlagen der Physik

Hilbert, David

doi:10.1007/bf01448427

Cited by 273 publications

(255 citation statements)

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“…It is interesting to point out here that in the specific context of (essentially radial) geodesic motion in the exterior Schwarzschild field, the critical speed was already discussed by Hilbert [23]. An examination of the early references to this subject is contained in Ref.…”

Section: Discussionmentioning

confidence: 86%

Explicit Fermi coordinates and tidal dynamics in de Sitter and Gödel spacetimes

2006

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Fermi coordinates are directly constructed in de Sitter and Gödel spacetimes and the corresponding exact coordinate transformations are given explicitly. The quasi-inertial Fermi coordinates are then employed to discuss the dynamics of a free test particle in these spacetimes and the results are compared to the corresponding generalized Jacobi equations that contain only the lowest-order tidal terms. The domain of validity of the generalized Jacobi equation is thus examined in these cases. Furthermore, the difficulty of constructing explicit Fermi coordinates in black hole spacetimes is demonstrated.

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Section: Discussionmentioning

confidence: 86%

Explicit Fermi coordinates and tidal dynamics in de Sitter and Gödel spacetimes

2006

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“…In this frame and on the foliation, the metric rather than the geometry becomes measurable. The concept of reference fluid goes back to Einstein [40], and to Hilbert [41] who formalized the idea that the coordinate system should be realized by a realistic fluid carrying clocks which keep a causal time. They imposed a set of inequalities ensuring that the worldlines of the reference fluid be timelike and the leaves of the time foliation be spacelike.…”

Section: The Problem Of Timementioning

confidence: 99%

Time Paradox in Quantum Gravity

Macı́as

Quevedo

Quantum Gravity

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Abstract. The aim of this work is to review the concepts of time in quantum mechanics and general relativity to show their incompatibility. We show that the absolute character of Newtonian time is present in quantum mechanics and also partially in quantum field theories which consider the Minkowski metric as the background spacetime. We discuss the problems which this nondynamical concept of time causes in general relativity that is characterized by a dynamical spacetime. Mathematics Subject Classification (2000). Primary 46N50; Secondary 85A99.

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“…He himself had contributed substantially to modern mathematical physics in the preceding years, most notably through his two Communications to the Göttingen Academy Proceedings on the Foundations of Physics of November 1915and December 1916, respectively [Hilbert 1915, Hilbert 1917. By the summer of 1917 at the latest, however, another problem was increasingly occupying Hilbert's mind, namely the problem of an absolute consistency proof of arithmetic that would provide a sound logical foundation for the whole body of mathematics.…”

Section: Hilbert's Lectures On Fundamental Questions Of Modern Physicmentioning

confidence: 99%

Hilbert’s “World Equations” and His Vision of a Unified Science

Majer¹,

Sauer

2005

The Universe of General Relativity

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In summer 1923, a year after his lectures on the 'New Foundation of Mathematics' and half a year before the republication of his two notes on the 'Foundations of Physics,' Hilbert delivered a trilogy of lectures in Hamburg. In these lectures, Hilbert expounds in an unusually explicit manner his epistemological perspective on science as a subdiscipline of an all embracing science of mathematics. The starting point of Hilbert's considerations is the claim that the class of gravitational and electromagnetic field equations implied by his original variational formulation of 1915 provides valid candidate 'world equations,' even in view of attempts at unified field theoriesá la Weyl and Eddington based on the concept of the affine connection. We give a discussion of Hilbert's lectures and, in particular, examine his claim that Einstein in his 1923 papers on affine unified field theory only arrived at Hilbert's original 1915 theory. We also briefly comment on Hilbert's philosophical viewpoints expressed in these lectures. IntroductionIn the history of unified field theory, many contributors may be identified [Goldstein and Ritter 2003, Goenner 2004], among them certainly, and perhaps foremost, Einstein. Hilbert's place in the history of the unified field * To appear in a forthcoming volume of Einstein Studies, eds.

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Die Grundlagen der Physik

Cited by 273 publications

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Explicit Fermi coordinates and tidal dynamics in de Sitter and Gödel spacetimes

Explicit Fermi coordinates and tidal dynamics in de Sitter and Gödel spacetimes

Time Paradox in Quantum Gravity

Hilbert’s “World Equations” and His Vision of a Unified Science

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