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Comptes Rendus Physique
Volume 15, n° 10
pages 789-840 (décembre 2014)
Doi : 10.1016/j.crhy.2014.09.007
Georges Sagnac: A life for optics
Georges Sagnac : Une vie pour l'optique

Olivier Darrigol
 Laboratoire SPHERE, UMR 7219, CNRS/Université Paris-Diderot, bâtiment Condorcet, case 7093, 5, rue Thomas-Mann, 75205 Paris cedex 13, France 


Georges Sagnac is mostly known for the optical effect in rotating frames that he demonstrated in 1913. His scientific interests were quite diverse: they included photography, optical illusions, X-ray physics, radioactivity, the blue of the sky, anomalous wave propagation, interferometry, strioscopy, and acoustics. An optical theme nonetheless pervaded his entire œuvre. Within optics, an original theory of the propagation of light motivated most of his investigations, from an ingenious explanation of the Fresnel drag, through the discovery of the Sagnac effect, to his quixotic defense of an alternative to relativity theory. Optical analogies efficiently guided his work in other domains. Optics indeed was his true passion. He saw himself as carrying the torch of the two great masters of French optics, Augustin Fresnel and Hippolyte Fizeau. In this mission he overcame his poor health and labored against the modernist tide, with much success originally and bitter isolation in the end.

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Georges Sagnac est principalement connu pour l'effet optique des faisceaux tournants, qu'il démontra en 1913. Ses intérêts scientifiques étaient très divers, incluant la photographie, les illusions d'optique, la physique des rayons X, le bleu du ciel, la propagation anormale des ondes, l'interférométrie, la strioscopie et l'acoustique. Le thème de l'optique habite néanmoins son œuvre toute entière. Dans le domaine de l'optique, une théorie originale de la propagation de la lumière a motivé la plupart de ses recherches, depuis une explication ingénieuse de l'entraînement de Fresnel, en passant par la découverte de l'effet Sagnac, jusqu'à son combat de Don Quichotte en faveur d'une alternative à la théorie de la relativité. Les analogies optiques ont efficacement guidé son travail dans d'autres domaines. En effet, l'optique était sa vraie passion. Il se voyait comme porte-flambeau de deux grands maîtres de l'optique française, Augustin Fresnel et Hippolyte Fizeau. Dans cet apostolat, il surmonta sa faible santé pour travailler à contre courant du modernisme, rencontrant d'abord beaucoup de succès, puis un isolement amer à la fin.

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Keywords : Sagnac, Sagnac effect, X-rays, Optics, Fluorescence, Interferometry

Mots-clés : Sagnac, Effet Sagnac, Rayons X, Optique, Fluorescence, Interférométrie

1  The plis cachetés , introduced by the Academy in 1735, have often been used by physicists who wished to protect their priority without publication. In relatively rare cases, after some time the author of the pli judges its contents to be ripe for publication, and he or she requests its opening. In most cases the pli remains sealed. In 1976, the Academy created a commission in charge of opening the plis that had remained sealed hundred years after being deposited. Cf. Berthon [[1]], Carosella and Buser [[2]]. My report on Sagnac's two plis is in the Sagnac folder in the archive of the Académie des sciences.
2  Cf. Quentin [[3]].
3  Ollivier [[4]] for a first textbook account; Pauli [[5]] for a review. On relativistic interpretation and on variants, cf. Martinez-Chavanz [[6]]. On recent, laser-based developments, cf. MacKenzie [[7]].
4  Sagnac [[10], [11], [12], [13], [14]].
5  The archive of the Wellcome Library in London holds a few Sagnac manuscripts under the reference MSS. 4332–4334. I have not been able to consult them.
6  Cf. P. Sagnac [[19]]; Sagnac to Lorentz, 6 January 1901, Archive for the history of quantum physics (AHQP). Sagnac's brother Philippe, a renowned historian of the French revolution, was his best biographer. Most biographical information in this paper comes from him. Further institutional information is found in Sagnac [[20]] and in Archives nationales, “Dossier professionnel de Georges Sagnac,” AJ/16/6149 (see Lalli [[15]]).
7  Sagnac [[21], [22]]; Lippmann [[23]]. Sagnac borrowed the vector representation of vibrations from Fresnel and Alfred Cornu.
8  Sagnac [[24], [25]].
9  Röntgen [[26], [27], [28]]; Sagnac to Poincaré, 15 Sep 1900, in Walter [[29]]. In conformity with French usage, I capitalize the X in X-rays (the most common old English spelling was “x rays”).
10  Sagnac [[30]]; [[31]]. On early interpretations of X-rays, cf. Wheaton [[32]].
11  Sagnac [[33]]; [[34]].
12  Sagnac [[35], [36]].
13  Sagnac [[31]]; Röntgen [[26]] (reflection–diffusion by metals); Röntgen [[28]] (diffusion by the air).
14  Sagnac [[31]]; [[37]].
15  Wiedemann [[38]]; Sagnac [[39]]. On Stokes's “fluorescence”, cf. Darrigol [[40]].
16  Quentin [[3]]; Röntgen [[28]]; Sagnac [[41]].
17  Sagnac [[42], [43]].
18  Sagnac [[43]]; [[45]]; [[46]].
19  Sagnac [[47], [48], [49], [50]] (heterogeneity of the secondary rays), [[51], [52], [53]] (on p. 208 of [[53]], Sagnac speculates that the transforming power might be related to the size of atoms).
20  Sagnac [[45], [54]]; [[55]]; Malagoli and Bonacini [[56], [57]].
21  Cf. Quentin [[3]].
22  Perrin [[58]]. On the earlier works, cf. Lelong [[17]].
23  Sagnac [[59]]; Perrin to Langevin, undated, cited in Lelong [[17]].
24  Langevin [[60]]. Cf. Lelong [[17]].
25  Lelong [[17]].
26  Becquerel [[61]]; Poincaré [[62]]; Becquerel [[63], [64], [65]]. There is no textual evidence for the traditional view that the conjecture of a relation between X-ray and phosphorescence emanated from Poincaré. And there is no reason to distrust Becquerel's account (cited above). However, Poincaré was plausibly the first to entertain the possibility of X-ray emission without cathode-ray excitation (the emphasis is his in the citation from [[62]]).
27  M. Curie [[66]]; Sagnac [[39]n]. Cf. Martins [[18]]. The closeness of the friendship between Sagnac and the Curie is well illustrated in the moving letter that Sagnac, wrote to Pierre Curie on 23 Apr 1903 to alarm him about his wife's physical condition and to press the frenetic couple to adopt a healthier lifestyle: cf. Reid [[67]].
28  P. and M. Curie [[68]]. Cf. Martins [[18]].
29  P. and M. Curie [[69]]; Sagnac, plis cachetés of 28 March and 18 July 1898, Archives de l'Académie des sciences; Curie and Sagnac [[70], [71], [72]]. Cf. Martins [[18]].
30  Sagnac, plis cacheté of 18 July 1898; Sagnac [[73]].
31  Curie and Sagnac [[72]].
32  Sagnac [[74]].
33  Sagnac [[75]]. Sagnac's pli cacheté of 23 Feb 1902 propounds a simpler pendulum experiment, with the additional conjecture that the ratio of the (inertial) atomic mass to the atomic number was the same for barium and radium, which gives a 20% relative difference in the pendulum frequencies. On Lesage's theory, cf. Chabot [[76], [77], [78]].
34  Sagnac [[79]]; [[80]] (J.J. Thomson's X-ray concept). On the French approach, cf. Lelong [[17]]. On contemporary debates on the nature of X-rays, cf. Wheaton [[32]]. The dominant hypothesis was the electromagnetic impulse hypothesis, which did not much differ from Sagnac's wave packet hypothesis for practical purposes.
35  Sagnac was also aware of Helmholtz's theory of dispersion, based on the coupling between ether waves and material oscillators, and leading to the same result in the limit of vanishing wavelength (Sagnac [[80]]).
36  Sagnac [[39]]; [[49]]; [[81]].
37  Sagnac to Lorentz, 6 Jan 1901, AHQP. On the development of X-ray physics after Sagnac, cf. Wheaton [[32]], Heilbron [[82]].
38  Boussinesq [[83]]. Cf. Darrigol [[84]]. On the first ether theories of the nineteenth century, cf. Buchwald [[85]].
39  Lorentz [[86], [87], [88]]. Cf. Buchwald [[89]]; Darrigol [[90]].
40  Sagnac to Lorentz, 6 Jan 1901, AHQP; Sagnac to Poincaré, 15 Sep 1900, in Walter [[29]].
41  On late nineteenth-century French molecular theories, cf. Principe [[91]].
42  Sagnac [[92]]. On this theory, cf. Martinez-Chavanz [[6]].
43  Sagnac [[92]].
44  Fresnel [[93]]; Fizeau [[94]]. Cf. Whittaker [[95]]; Darrigol [[40]]. As Mascart and Lorentz later realized, in Fizeau's setup the Doppler frequency-shift in the running water slightly modifies the Fresnel drag.
45  If the slower velocity of the waves in a medium of higher optical index is traced to a higher density of the ether in this medium, then the conservation of the ether flux at the interface between two different media implies the Fresnel drag.
46  Boussinesq [[83]]; Lorentz [[87], [88]]; Sagnac [[96]]. Cf. Janssen annd Stachel [[97]]; Darrigol [[40]].
47  Sagnac [[96]].
48  Sagnac [[98]]. As we will see in a moment, Sagnac later became aware of the connection with Lorentz's local time.
49  Sagnac [[98]].
50  Sagnac [[98]]; [[99]]. Cf. Lalli [[15]].
51  Sagnac [[100]n]; [[101]]. Retrospectively, Lorentz's local time is the first-order approximation of the Lorentz-transformed time. Lorentz used the local time in a formal manner, as a way to retrieve the electromagnetic equations for a body at rest in the ether. The interpretation of the local time as the time given by optical synchronization was first given by Poincaré in his own contribution to the Lorentz jubilee. See Darrigol [[90]].
52  Sagnac [[100]].
53  Natanson [[102]], for example.
54  Sagnac to Lorentz, 6 Jan 1901, AHQP.
55  Sagnac [[103]]. On the history, cf. Rayleigh [[104]], Lilienfeld [[105]].
56  Sagnac [[103]]; [[106]].
57  Rayleigh [[104]]; Lorentz [[107]]. For a modern approach, cf. Jackson [[108]]. I thank Jean-Michel Raimond for an illuminating discussion on this subject.
58  Gouy [[109]].
59  Sagnac [[110], [111], [112]].
60  The optical axis of the crystal must of course coincide with the optical axis of the lens.
61  Sagnac [[114], [115], [116]].
62  Sagnac [[117], [118], [119]]; Blondlot to Poincaré, 23 Dec 1903, in Walter [[29]], on p. 70. On N rays, cf. Nye [[120]].
63  On this laboratory, cf. P. Sagnac [[19]].
64  P. Curie to Gouy, 31 Jan 1905, cited in Barbo [[121]].
65  Sagnac [[80]]. Sagnac also conceived a spatial diffusion of the negative reaction. On Sagnac's visit to Lorentz, see Lorentz to Sagnac, 18 Apr 1905, Archives nationales.
66  Sagnac [[80]n]; Lorentz to Sagnac, 11 Aug 1905, Archives nationales; Sagnac to Lorentz, undated reply to the former, AHQP.
67  Veltmann [[122]]; Sagnac [[123]]. The date 1908 is from Sagnac [[124]].
68  Sagnac [[125]] for the reference to Kelvin and Bjerknes. In 1910, Sagnac [[124], [126]] described two versions of his interferometer before giving the motivation. On the relevance of Bjerknes's theorem, cf. Lalli [[15]].
69  Sagnac [[124]].
70  Sagnac [[125], [127], [128]]. Sagnac operated with white light, so that his central fringe had the “teinte sensible” for which the brightest spectral component is extinguished.
71  Sagnac [[127]] for the reference to Mascart, Poincaré, and Einstein. On this experiment, cf. Martinez-Chavanz [[6]].
72  On the earlier history of strioscopy, cf. Sagnac [[129]].
73  Sagnac [[129], [130], [131], [132]]. About odd/even number of mirrors, see Sagnac [[129]].
74  Sagnac [[133], [134]].
75  Sagnac suggests so much in Sagnac [[135]]. In a letter to Lucien Poincaré of 20 Jan 1919, Sagnac mentioned that in 1914 Brillouin had come to see his experiments “on the motion of the earth,” presumably meaning that his experiments of 1910 and 1913 had to do with his early idea to detect an effect of the rotation of the earth: cf. Lalli [[15]].
76  Sagnac confided this idea to Lippmann in 1909. At that time, he regarded a negative outcome of the experiment as possible in a proper emission theory (Walther Ritz had published his theory the preceding year). Cf. Sagnac [[136]].
77  Sagnac [[135], [137]]. On this experiment, cf. Martinez-Chavanz [[6]].
78  Sagnac [[135], [136], [137]]. Although Sagnac does not explicitly state the precision of his fringe-shift measurement, it must have been about 10% judging from the photographs and the numbers he gave.
79  Sagnac [[135]].
80  Sagnac [[136]], p. 191 (ship rolling), 185n (citation); Sagnac [[125]] (angular effect). On the angular effect, cf. Martinez-Chavanz [[6]].
81  Sagnac [[125]]; [[136]]. At first order in  , special relativity gives the same result since it is optically equivalent to Sagnac's principle.
82  Sagnac [[136]].
83  Houllevigue [[138]]. On the anticipations of Sagnac's ether-wind experiments, cf. Post [[139]]; Martinez-Chavanz [[6]]; Anderson, Bidger, and Stedman [[140]].
84  On the history of the optics of moving bodies, cf. Whittaker [[95]]; Janssen and Stachel [[97]]; Darrigol [[90]]; [[84]].
85  Michelson [[141]]; Michelson and Morley [[142]]. On Michelson's ether-drift experiments, cf. Swenson [[143]].
86  Michelson and Morley [[144]]. On Michelson's interferometry and silvered plates, cf. Staley [[145]].
87  The irrotational motion of an incompressible fluid is completely determined by the Neumann boundary condition of zero normal velocity on the surface of the earth, and the resulting motion has a non-zero tangential velocity.
88  Cf. Hunt [[146]]; Darrigol [[90]].
89  Lodge [[147]]. Cf. Martinez-Chavanz [[6]]; Hunt [[148]].
90  Lodge [[147]].
91  Lodge [[8]]. Lodge discussed these issues in contemporary correspondence with Joseph Larmor. At the end of murky reasoning and discussion, they privately arrived at Sagnac's phase-shift formula for a circuit of arbitrary shape. Cf. Anderson, Bilger, and Stedman [[140]].
92  Michelson [[149]] (after this remark, Michelson deplores that any theory that takes all experimental results into account, including Lorentz's, has to make fantastic assumptions about the relation between ether and matter). Cf. Martinez-Chavanz [[6]]; Lalli [[15]].
93  Cf. Sagnac [[127]]. Despite the rectangular geometry of Michelson's circuit, the number of mirrors is even, because the reflection at the corners of the rectangle is produced by pairs of mirrors. It is not clear why Michelson used pairs instead of single mirrors. He did not relate the parity of the number of mirrors with lower sensitivity to thermal fluctuations. As Jacques Vigué explained to me, Sagnac's success in air may have to do with better mechanical stability of his setup and perhaps also with the smaller number and better quality of his mirrors.
94  Wien [[150]]; Cohn [[151]]. Cf. Darrigol [[90]].
95  Michelson [[9]n]; Michelson, Gale, and Pearson [[152]]. Cf. Martinez-Chavanz [[6]]; Anderson, Bilger, and Stedman [[140]].
96  Born-rigidity, introduced by Max Born in 1909, means constant distance between two neighboring material points in the tangent inertial frame.
97  Kaluza [[153]]. Cf. Walter [[154]]. The formulas in Kaluza's article seem to be given for  .
98  Langevin starts with the Minkowskian metric formula   in polar coordinates and for observers at rest. The coordinate change   gives  . With respect to these coordinates the propagation of light is anisotropic because of the rectangular term in  . In order to restore the isotropy of light propagation with respect to the disk, Langevin introduces the proper time   for which  . The synchronization of neighboring clock obtains for  , which is equivalent to the condition   derived from the local Minkowskian structure.
99  Langevin [[155], [156]]. Cf. Dieks [[157]]. For a modern argument, cf. Gourgoulhon [[158]]. For the argument in general relativity, cf. Landau and Lifshitz [[159]].
100  See footnote 73 above.
101  Harress [[160]]. On the precision, cf. Knopf [[161]].
102  Harress [[160]], pp. 3–4 (Fresnel), 6 (Lorentz), 7–13 (relativistic), 59 (total time shift), 70 (results).
103  Harress [[160]]; Harzer [[162]]; Einstein [[163]]. Einstein's paper triggered a small polemic with Harzer: see Harzer [[164]], Einstein [[165]].
104  Knopf [[161]]; Laue [[166], [167]].
105  Laue [[166]]; Puccianti [[168]]; Witte [[169]]. On relativistic derivations of the Sagnac effect, cf. Post [[139]]; Martinez-Chavanz [[6]]; Malykin [[170], [171]]; Rizzi and Ruggiero [[172]]; Gourgoulhon [[158]].
106  Pogány [[173]].
107  Pogány [[173]].
108  Cf. P. Sagnac [[19]]; Berthelot [[174]]; Sagnac [[20]].
109  Sagnac [[175], [176], [177], [178], [179], [180], [181]]. On this theory, cf. Martinez-Chavanz [[6]].
110  Sagnac [[175]].
111  Sagnac [[175]], pp. 471 (group velocity), 531 (Eq. ((3))). The derivations of Eqs. ((2)) and ((3)) are mine. Even in his most detailed accounts [[176], [182]], Sagnac remained allusive.
112  Sagnac [[177]], pp. 783 (Michelson), 784 (canal rays), 785 (Sagnac effect); [[180]].
113  Sagnac [[178]].
114  Sagnac [[179]]; [[181]]; Jackson [[183]] (observed anomaly). Captain Jackson's explanation of the anomaly, based on wavelength differences in the successive wave trains from the emitter, seems reasonable to me.
115  G. Sagnac to P. Sagnac, undated, Archives nationales.
116  Sagnac [[184], [185], [186], [187], [188]]. Cf. Martinez-Chavanz [[6]]. Sagnac did not mention that in 1913 Willem de Sitter had failed to observe a prediction of emission theories: the distortion of the orbits of double stars.
117  Cf. Paty [[189]]; Biézunsky [[190]]; Borella [[191]]; Moatti [[192]].
118  Berthelot [[174]]; Berthelot's report of 1923 in the Sagnac folder of the archive of the Académie des sciences.
119  Fabre [[193]]. On Poincaré's views, see Darrigol [[194]].
120  Pomey [[195]].
121  Berthelot [[196]]. For instance Berthelot confused the dilation of time with the Doppler effect (p. 28). He portrayed relativity theory as the work of a wandering Jew who did not need the home of Newtonian space and time: cf. Lalli [[15]].
122  Alliaume [[197]]. I have consulted the Science abstracts, section A: Physics , the Physikalische Berichte , and the Jahrbuch über die Fortschritte in der Mathematik . Most reviews summarize Sagnac's results without judging them. In his review of Sagnac [[181]] for the Jahrbuch , Herman Müntz writes “Die Ausführung wird nur ganz flüchtig angedeutet…. Es wird nicht gesagt, welches Verhalten der von einer bewegten Quelle ausgehenden Wellen jenen Hypothesen entsprechen muss, wodurch die Grundlagen der Theorie erst geklärt werden würden.”
123  On the early alternatives to Einstein's theory, cf. Darrigol [[90]].
124  Cf. Martínez [[198]]. For contestations of Sitter's conclusion, see Alliaume [[197]].
125  On Cohn's theory, cf. Darrigol [[199]]; On Ritz's, cf. Martínez [[198]], Darrigol [[40]].
126  On Berthelot, cf. Moatti [[192]]. On Curie's friendship, cf. P. Sagnac [[19]]. On the relation with Poincaré, cf. Walter [[29]]. The letters on unipolar induction and the reaction principle are ibid., pp. 324–327.
127  Bjerknes to Sagnac, 1 Feb 1914, Archives nationales.
128  For Sagnac's Sorbonne career, cf. Maurain and Pacaud [[200]]. On the prizes, cf. the reports in the Comptes rendus and the Sagnac folder at the archive of the Académie des sciences. More biographical information is in Sagnac [[20]] and in Dostrovsky [[201]].
129  Cf. Lenard to Sagnac, 19 Dec 1905, Archives nationales.
130  Bénard [[202]S]; Lenard to Sagnac, 19 Dec 1905, Archives nationales.

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