Abstract
In 1905, Einstein published three articles which dramatically changed our conception of physics. One of them introduced the special theory of relativity [8], a new vision of space and time. It became the general theory of relativity [9] ten years later, in 1915, with the inclusion of gravity in this new framework. Although it is not the reason why Einstein earned a Nobel Prize, relativity is certainly the greatest achievement of his scientific career and, in my opinion, the most remarkable theory of physics of all times.
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Change history
01 February 2020
The original version of the book was inadvertently published with incorrect equations in Chapters 3 and 4 that have been replaced with the correct equations in the updated version.
Notes
- 1.
The importance of this assumption will be clearer in the following.
- 2.
The symbol f stands for ‘flat’.
- 3.
They differ from \(\mathrm {SO}(4)\), which would generalise rotations to the four-dimensional Euclidean geometry, where we would replace \(\eta _{\alpha \beta }\) by \(\delta _{\alpha \beta }\).
- 4.
The Danish physicist Ludvig Lorenz [1829–1891] must be distinguished from the Dutch physicist Hendrik Lorentz [1853–1928]; they differed by one letter and a couple of decades.
- 5.
- 6.
In this section, for notational ease, we will use Greek indices of the beginning of the alphabet \((\alpha ,\beta ,\gamma ,\ldots )\) similarly to indices of middle of the alphabet \((\mu ,\nu ,\rho ,\ldots )\); they will also refer to arbitrary coordinates, and not necessarily to ICCs.
- 7.
Beware! An even permutation of four indices is not a circular permutation. In general, an even (resp. odd) permutation is a permutation made of an even (resp. odd) number of transpositions. A transposition is the exchange of two indices.
- 8.
The proof is not too hard, but a bit long. We will therefore admit this result here. The interested reader is referred to, e.g. the excellent A Relativist’s Toolkit [3], by Eric Poisson, for more details.
- 9.
We use \(X^0=t\), because we want to keep the notation T for the energy–momentum tensor.
- 10.
According to George Gamow in his autobiography [17].
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Fleury, P. (2019). Einstein’s Theory of Relativity. In: Gravitation. SpringerBriefs in Physics. Springer, Cham. https://doi.org/10.1007/978-3-030-32001-0_3
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DOI: https://doi.org/10.1007/978-3-030-32001-0_3
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