Abstract
We discuss how light acquired a velocity through history, from the ancient Greeks to the early modern era. Combining abstract debates, models of light, practical needs, planned research and chance, this history illustrates several key points that should be brought out in science education.
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Notes
For example, from our teaching experience, it is not uncommon to encounter undergraduate students who have no idea of the famous mean speed theorem for the uniformly accelerated motion and mistake the instant velocity for the mean one.
‘Wizards of Light’ (Les magiciens de la lumière), a film produced by the Faculty of Sciences of Orsay. Directors: Christine Azémar & Serge Guyon. Scientific writers: Pierre Lauginie & Alain Sarfati. Dialogues: Laurent Baraton. Contact: christine.azemar@u-psud.fr.
Hero (or Heron) from Alexandria (10–70 AD). This argument will be later reinterpreted by Ibn al-Haytham in the framework of his intromission theory against the visual ray model.
Since there is no transport of matter, this concept looks nearer to the future wave model of Huygens than to any corpuscular theory. However, this ‘tendency to motion’ is supposed to obey the laws of mechanics, particularly the law of conservation of momentum. Thanks to this, Descartes has sometimes been considered ‘father’ of corpuscular models of light. But Descartes cannot be considered father of either of the principal models—corpuscles or waves—which appeared as complete and competing theories only half a century later with Huygens and Newton.
Remember that the famous mean speed theorem for the uniformly accelerated motion was discovered in Merton College. A geometrical proof was given by Nicole Oresme around 1350 (Grant 1977, pp. 75–77).
In Römer’s original text, the letter K is used here in place of L, maybe due to a copyist error (Römer 1676). The mistake was corrected in the English version (Römer 1677). However, the error might originally have been in the drawing, rather than in the text. Indeed, the fact that EFGHLK are not in alphabetical order may have given rise to some confusion.
The diameter of the orbit is twice the mean Earth-Sun distance. This distance had been determined in 1671–1672 by Cassini and Richer from the parallax (and thus the distance) of the planet Mars and further use of Kepler’s laws. The parallax of Mars was determined from simultaneous observations by Cassini in Paris and Richer in Cayenne (Cassini 1672). Knowledge of the Earth’s radius was necessary to convert planetary parallaxes into measurements of distances. Thus all astronomical distances of the time relied on the size and figure of the Earth, and this remained the case at least up until Foucault’s terrestrial speed-of-light measurement (Foucault 1862).
The stellar parallax of a star is the angle subtended by the astronomical unit—or mean Earth-Sun distance—as viewed from the centre of the star. Stellar parallaxes are all below one arc-second. They are determined from the Earth by two observations of the star taken at 6 month intervals, i.e. from a baseline of ca. 300 million km. From this, the distance of the star can be deduced.
Some other astronomers, including Cassini and Picard, had reported, but not understood, the phenomenon that remained unexplained. Bradley was the first to give the right interpretation.
The phenomenon can be viewed, in a corpuscular model of light, as similar to the apparent deviation of rain from the vertical when viewed from a moving vehicle. Measuring this deviation α and knowing your own velocity v you get the velocity c of the falling drops from the equation tanα = v/c. In the case of the light ‘falling’ from a star, the moving vehicle is our Earth orbiting the Sun at a speed of ca. 30 km/s, or 1/10,000 of the speed of light. Thus, roughly, a star, supposed for simplicity to be at the ecliptic pole, is viewed in a direction slightly deviated in the direction of the Earth’s motion by an angle α = 10−4 radian, or 20 arc-second. Over 1 year, the star will describe a small ellipse in the sky, an image of the Earth’s orbit, with a size independent of the star’s distance (in contrast to stellar parallax). In this calculation, to get an explicit value of the speed of light, the orbital velocity v of the Earth is needed. It is easily deduced from the Earth-Sun distance and the time to cover the full orbit, which is just 1 year. The Sun-Earth distance was determined, at the time, from planetary parallaxes (see Cassini 1672, and note 7). A rigorous interpretation of stellar aberration actually requires the use of the Special Theory of Relativity, but the above treatment remains an excellent approximation, and anyway, it was in such a manner that things were understood at the time.
We specify here ‘sidereal year’ since Bradley took the precession of the equinoxes into account very accurately.
Emphasized by us.
The method of Venus transits, also in use in the eighteenth and nineteenth centuries (1761, 1769, 1874, 1882) can be considered a variant of the parallax method.
A typical example from as late as 1862 is given by Léon Foucault (Foucault 1862). Following orders from the French astronomer Le Verrier, Foucault performed the first accurate terrestrial measurement of the speed of light. His result yielded directly the astronomical unit, or Earth-Sun distance, independently of the size and shape of the Earth, for example by reversing the above aberration formula in which α and c are known. This constituted major progress. However, the title of Foucault’s article is: ‘Experimental Determination of the Speed of Light; Parallax of the Sun’ (title translated by us). Foucault does not write ‘distance to the Sun’, which is a length, but ‘parallax of the Sun’ which is an angle, evidently to conform to astronomical usage. And this in spite of the fact that he had to re-introduce the size of the Earth in order to deduce the solar parallax from the Earth-Sun distance he had independently determined!
In fact, Römer compared the length of 40 revolutions in the vicinity of a quadrature on the side F of the Earth’s orbit (cf. Fig. 1) to the corresponding 40 revolutions on the other side. Their difference is twice the integrated delay of 40 revolutions as compared with their intrinsic value and corresponds to twice the “600 s” of our example.
The apparent change in the period of Io follows a sinusoidal-like curve, being zero at the conjunctions and oppositions and reaching + or −15 s at the quadratures (Fig. 2a). The integrated change, called the ‘delay’, is represented by a bell-shaped curve peaking at a maximum of 16 min after a 6-months time interval (Fig. 2b). Around the inflexions, corresponding to quadratures, the curve is well approximated by a straight line over 40 revolutions, i.e. 70 days: the error in the total delay is ca. 5 %. This means that the apparent period of Io can be considered as approximately constant over 40 revolutions near a quadrature, i.e. increased by ca. 15 s over its intrinsic value.
The prominent role of Cassini in the discovery of the finite speed of light has been carefully re-examined in a recent paper by L. Bobis and J. Lequeux (Bobis and Lequeux 2008). However, three centuries after the discovery, the name of Römer had become synonymous with the discovery of the finite speed of light, just as on the commemorative plaque on the north frontage of Paris Observatory.
See ‘Wizards of Light’, note 2.
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The reviewers are gratefully acknowledged for their scrupulous reviews of the manuscript and for many relevant proposals of improvements.
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Lauginie, P. How did Light Acquire a Velocity?. Sci & Educ 22, 1537–1554 (2013). https://doi.org/10.1007/s11191-012-9487-z
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DOI: https://doi.org/10.1007/s11191-012-9487-z