The tiny deviation of the orbit of Mercury from a pure ellipse might seem to be of no consequence. Yet the minute precession of this planet was one of the factors leading to a revolution in our world view. Attempts to explain the anomaly in the context of Newtonian mechanics were unsatisfactory. It was only with the emergence of general relativity that we were able to understand the observed phenomenon.
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Posts Tagged 'Relativity'
Mercury’s Mercurial Orbit
Published November 10, 2022 Occasional ClosedTags: Astronomy, Mechanics, Relativity
The 3-sphere: Extrinsic and Intrinsic Forms
Published September 22, 2022 Occasional ClosedTags: Relativity, Topology
Figure 1. An extract from Einstein’s 1917 paper on cosmology.
The circle in two dimensions and the sphere in three are just two members of an infinite family of hyper-surfaces. By analogy with the circle 
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Dynamic Equations for Weather and Climate
Published September 8, 2022 Occasional ClosedTags: Analysis, Geometry, Relativity
“I could have done it in a much more complicated way”,
said the Red Queen, immensely proud. — Lewis Carroll.
Books on dynamic meteorology and oceanography usually have a full chapter devoted to the basic dynamical equations. Since the Earth’s fluid envelop is approximately a thin spherical shell, spherical coordinates 
Fig 1. The momentum equations, as in Lorenz (1967). The metric terms are boxed.
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Poincare’s Square and Unbounded Gomoku
Published July 28, 2022 Occasional ClosedTags: Games, Geometry, Relativity
Poincare’s hyperbolic disk model.
Henri Poincar’e was masterful in presenting scientific concepts and ideas in an accessible way. To explain that the Universe might be bounded and yet infinite, he imagined that the temperature of space decreased from the centre to the periphery in such a way that everything contracted with the distance from the centre. As travellers moved outward from the centre, everything got smaller in such a way that it would take an infinite time to reach the boundary.
Cornelius Lanczos – Inspired by Hamilton’s Quaternions
Published July 16, 2020 Irish Times ClosedTags: Analysis, Applied Maths, Mechanics, Relativity
In May 1954, Cornelius Lanczos took up a position as senior professor in the School of Theoretical Physics at the Dublin Institute for Advanced Studies (DIAS). The institute had been established in 1940 by Eamon de Valera, with a School of Theoretical Physics and a School of Celtic Studies, reflecting de Valera’s keen interest in mathematics and in the Irish language. Later, a School of Cosmic Physics was added. DIAS remains a significant international centre of research today [TM191 or search for “thatsmaths” at irishtimes.com].
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Gravitational Waves & Ringing Teacups
Published November 22, 2018 Occasional ClosedTags: Astronomy, Relativity, Wave Motion
Newton’s law of gravitation describes how two celestial bodies orbit one another, each tracing out an elliptical path. But this is imprecise: the theory of general relativity shows that two such bodies radiate energy away in the form of gravitational waves (GWs), and spiral inwards until they eventually collide.
Warning sign, described by Thomas Moore as a “geeky insider GR joke” [image from Moore, 2013].
The motto of the Pythagoreans was “All is Number” and Pythagoras may have been the first person to imagine that the workings of the world might be understood in mathematical terms. This idea has now brought us to the point where, at a fundamental level, mathematics is the primary means of describing the physical world. Galileo put it this way: the book of nature is written in the language of mathematics [TM102, or search for “thatsmaths” at irishtimes.com].
Visualization of gravitational waves. Image credit MPI/Gravitational Physics/ITP Frankfurt/ZI Berlin.
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