Abstract
This chapter is devoted to the motion of a particle as perceived by a given observer. The focus is first set on a massive particle. The Lorentz factor is introduced as the ratio of the observer’s proper time to the particle’s one. Then the concepts of velocity and acceleration relative to an observer are discussed and expressed in terms of the 4-velocity and 4-acceleration of the particle and the 4-velocity, 4-acceleration and 4-rotation of the observer. All the chapter is illustrated with three simple uniform motions: the linear, accelerated and circular ones. The last part deals with massless particles (photons) and addresses the propagation of light with respect to a given observer. The invariance of the (locally measured) velocity of light is established, and experimental tests of it are presented.
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Notes
- 1.
Hendrik A. Lorentz (1853–1928): Dutch theoretical physicist, author of many works on electromagnetism, the electron theory and relativity; he received the 1902 Nobel Prize in Physics for the explanation of the Zeeman effect (cf. p. 146).
- 2.
Incidentally, the muon has been discovered in this manner in 1937; cf. the historical note below.
- 3.
Bruno Rossi (1905–1993): Italian physicist, who moved to United States in 1939 to escape from the fascist regime. Specialist of cosmic rays, he was also a pioneer of X-ray astronomy in the 1960s. The Rossi X-ray Timing Explorer (RXTE) satellite (1995–2012) was named after him.
- 4.
Actually, the muon selection has been performed from their penetration depth in iron plates, which provides their energy E and, in a second stage, their velocity, by assuming the relation \(E = m{c}^{2}/\sqrt{1 - {V }^{2 } /{c}^{2}}\); cf. Eq. (9.16).
- 5.
- 6.
Hideki Yukawa (1907–1981): Japanese theoretical physicist, pioneer of particle physics; he was awarded the Nobel Prize in Physics in 1949 (the first Japanese one!) for his prediction of the meson.
- 7.
The satellite BeppoSAX (1996–2003), dedicated to X-ray astronomy, has been named to honour him,Beppo being the nickname of Giuseppe.
- 8.
Jean-Dominique Cassini (1625–1712): Italian–French astronomer, first director of the newly built Paris Observatory in 1671, under the reign of Louis XIV. Apart from the study of Io’s eclipses, he discovered four Saturn’s moons and the famous “Cassini division” in Saturn’s rings. He also supervised the first measure of the size of the Solar System by means of the parallax of Mars.
- 9.
Ole C. Rømer (1644–1710): Danish astronomer who worked at Paris Observatory from 1672 to 1679, at the invitation of Jean Picard (cf. p. 157) and under the supervision of Cassini.
- 10.
James Bradley (1693–1762): British astronomer, famous for this explanation of stellar aberration (Sect. 5.6.3 ) and the discovery of Earth nutation.
- 11.
Hippolyte Fizeau (1819–1896): French physicist who authored many studies on light; in addition to the measurement of c, he notably discovered the Doppler effect on light waves (Sect. 5.5 ).
- 12.
Léon Foucault (1819–1868): French physicist and astronomer, famous for this works in optics (measure of c, Foucault test for telescope mirrors), electromagnetism (Foucault currents) and mechanics (Foucault pendulum).
- 13.
François Arago (1786–1853): French astronomer, well known for his works in optics. He was director of Paris Observatory and minister of the French Second Republic, where he acted for the abolition of slavery in French colonies (1848).
- 14.
Arago’s results have been presented to the French Academy of Sciences in 1810, but the corresponding article has been published only in 1853 because the original manuscript had been lost.
- 15.
Augustin Fresnel (1788–1827): French physicist, cofounder of the wave theory of light; he invented the lens bearing his name and that equips lighthouses.
- 16.
Albert A. Michelson (1852–1931): American physicist who devoted his life to precision optics and, in particular, to the measure of V light; he was awarded the Nobel Prize in Physics in 1907 (the first American!).
- 17.
Edward W. Morley (1838–1923): American chemist, mostly known for his work with Michelson.
- 18.
George F. FitzGerald (1851–1901): Irish physicist, who worked mostly on Maxwell theory and electromagnetism.
- 19.
Willem de Sitter (1872–1934): Dutch physicist and astronomer, famous for having introduced a cosmological model within general relativity, called de Sitter universe.
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Gourgoulhon, É. (2013). Kinematics 1: Motion with Respect to an Observer. In: Special Relativity in General Frames. Graduate Texts in Physics. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-37276-6_4
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