S.P.E.A.K.

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# General relativity

Sophie

Posts : 56
Join date : 2017-12-02
The General Theory of Relativity was proposed by Albert Einstein in 1915 – ten years after the publication of his Special Theory of Relativity in the journal Annalen der Physik. The general theory incorporates gravity and accelerated frames of reference in the special theory, and may be summarized by the celebrated Einstein’s field equations:

$R_{\mu\nu}-\frac12Rg_{\mu\nu}+{\Lambda}g_{\mu\nu}\,\,=\,\,\frac{8{\pi}G}{c^4}T_{\mu\nu}$

where

Rμν is the Ricci curvature tensor,
R is the scalar curvature,
gμν is the metric tensor,
Λ is the cosmological constant,
G is the gravitational constant,
Tμν is the stress–energy–momentum tensor,

and μ, ν ∈ {0,1,2,3} refer to the four spacetime co-ordinates, one (0) for time and three (1, 2, 3) for space. Since μ and ν can each take on four values, there is not one but sixteen field equations. The left-hand side of each equation is an expression involving the curvature of spacetime while the right-hand side deals with energy and momentum. You could say that the equations are trying to tell us the following: “Space tells matter how to move, matter tells space how to curve.”

Sylvia

Posts : 122
Join date : 2017-12-02
Ruggiero Ricci (1918–2012) was an American violinist.

Michael

Posts : 54
Join date : 2018-01-16
Christina Ricci (b. 1980) is an American actress, who has played Wednesday Addams in The Addams Family.

Sophie

Posts : 56
Join date : 2017-12-02
And Gregorio Ricci-Curbastro (1853–1925) was an Italian mathematician – who along with Tullio Levi-Civita developed tensor calculus, a mathematical tool heavily made use of in general relativity.

Basically, tensors generalize scalars and vectors. A scalar may be regarded as a tensor of rank 0, and a vector a tensor of rank 1. Much of general relativity is about tensors of rank 2.

George

Posts : 354
Join date : 2017-11-26

There are covariant and contravariant tensors – as explained intuitively in the following YouTube video I have just watched.

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Vicky

Posts : 73
Join date : 2017-11-27
The music softly playing in the background is from the William Tell overture – or the overture to the opera Guillaume Tell, in French, by Gioachino Rossini.

Rossini was Italian but his last four operas are in French: Le siège de Corinthe, Moïse et Pharaon, Le comte Ory, Guillaume Tell.

Sylvia

Posts : 122
Join date : 2017-12-02
Giuseppe Verdi was another composer who wrote some of his operas in French. In particular, The Sicilian Vespers and Don Carlos were first written in French and later translated into Italian.

Sophie

Posts : 56
Join date : 2017-12-02
I have just read about Levi-Civita, Tullio (1873–1941) in The Penguin Dictionary of Mathematics.

Italian mathematician who was the first, in 1896, to apply to dynamics the work of Ricci-Curbastro on the absolute differential calculus, better known as tensor calculus. Further work with Ricci-Curbastro in 1900 led to their algorithm for the expression of physical laws in both Euclidean and Riemannian curved space, a result which later proved to be of value to Einstein.