Abstract
The principle of relativity states that in the laws of physics, only relative velocities occur, so that it is in particular meaningless to postulate a state of absolute rest.
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Notes
- 1.
In which he promoted the ‘Copernican World System’ and which led to his persecution by the church.
- 2.
Translation [M. W. Haskell, 1892]: “Given a manifoldness and a group of transformations of the same; to investigate the configurations belonging to the manifoldness with regard to such properties as are not altered by the transformations of the group.”
- 3.
Using the matrix exponential from (4.1.5).
- 4.
Named after the British mathematician and physicist Llewellyn Hilleth Thomas (1903–1992), who in 1926 predicted the relativistic precession of electrons in an atom that was then named after him.
- 5.
The assignment of the origin of \({\mathbb {R}}^4\) is not uniform over the literature.
- 6.
Which is not a norm on \({\mathbb {R}}^4\) !
- 7.
Frequently, the requirement of being timelike is assumed as part of the definition of a worldline.
- 8.
And more generally electromagnetic radiation to the extent that it doesn’t propagate in a medium, with speed below the speed of light 1.
- 9.
\({\mathrm {Z}}(V)\) is also called the center of \(\text {GL} (V)\), because it consists of those mappings that commute with all elements of the group.
- 10.
It can easily be determined by a consideration of physical dimensions (units) where the factors c for conversion between space and time need to be inserted.
- 11.
In contrast to the special theory of relativity!
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Knauf, A. (2018). Relativistic Mechanics. In: Mathematical Physics: Classical Mechanics. UNITEXT(), vol 109. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-662-55774-7_16
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DOI: https://doi.org/10.1007/978-3-662-55774-7_16
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