JEAN EISENSTAEDT

THE PREHISTORY OF RELATIVITY*

INTRODUCTION

Years ago, I wrote a paper on the prehistory of black holes (Eisenstaedt 1991). It dealtessentially with the history of the concept of dark bodies, so named by Simon deLaplace (1796, 2:304-306) who most probably took the idea from the work of JohnMichell. Actually, I showed.how John Michell constructed, essentially in his 1784 arti­cle (Michell 1784), the Newtonian theory of the action of gravitation on light. Else­where I showed how Michell's ideas are deeply rooted in Newton's theories : not onlyhis gravitation ofcourse but also his corpuscular theory of light. At the beginning of thenineteenth century, Arago was to use Michell 's ideas in order to think over and performhis well-known experiment on the velocity oflight. He was to show then that the veloc­ity of light was constant and his experiment, which was a predecessor of the Michelsonexperiment, drove him to support Fresnel's ideas. In this article , I will come back tothese trains of thought which concern light and gravitation from Newton to Arago.'

I. EINSTEIN ON THE BENDING OF LIGHT

How Einstein came to the conclusion that light could be subject to gravitation isfairly well known . Two of his 1905 articles were important in this context: his "elec­trodynamics of moving bodies" of course , but also the 1905 idea of a corpuscularview of light which was important in order to think over the action of a gravitationalfield on light. In 1907, Einstein was already working on what were to become his twofavorite concepts: light and gravitation . In 1911, his paper published in Annalen derPhysik was chiefly concerned with the question of the influence of gravitation on thepropagation of light. During the summer 1913 he wrote to Erwin Finlay-Freundlichwho aimed at observing the bending of light by different techniques,

that the idea of the bending of light rays appeared at the time of the theory of emission[wasl rather natural ... (Eisenstaedt 1991,378).

Actually it happens that the bending of light in a Newtonian context is explicitly dis­cussed in Bernstein, a popular handbook that Einstein read in his youth .

Thus to Einstein, such a train of thought was logical and coherent. At the end of1915, he predicted the precise formula of the relativistic deflection of light in a fieldof gravitation. In May 1919 the English astronomical expedition showed for the very

3

A. Ashtekar et al. (eds.), Revisiting the Foundations ofRelativistic Physics, 3-12.© 2003 Kluwer Academic Publishers .

4 JEAN E ISENSTAEDT

first time that light was actually influenced by gravitation, an essential confirmationof general relativity.

One year later, Sir Joseph Larmor publi shed a paper entitled "Gravitation andLight" where he quoted New ton's well-known Query on the bending of rays by bod­ies. But in the same line he also quoted "the physically-minded John Michell" who had

insisted that the Newtonian corpuscles of light must be subj ect to gravitation like otherbodie s, [and] that the velocities of the corpuscles shot out from one of the more massivestars would be sensibly diminished by the backward pull of its gravitation (Lannor 1920,324).

In 1921 Lenard partially republished an almost unknown paper on the grav itationalbending of light rays , an article that had been first published in 1801 by a Germanastronomer, Johann Georg von Soldner.? When general relativity was at a low ebb(Eisenstaedt 1989) , Lapl ace 's (actually Michell's!) dark bodies were ment ioned bynone other than Eddington in 1926.

In order to understand the emergence of this corpus and to put things moreclearl y, we must first come back to Newton 's corpuscular theory oflight.

2. NEWTON 'S BALLISTIC THEORY OF LIGHT

Newton 's corpuscular theory of light is essentially a dynamical theory of light , a bal­listic theory of a light-corpu scle.' In Section XIV, Book I of New ton's Principia,refraction is described as an attrac tive force-the refringent force-acting perpendi c­ularly to the surface separating the two media. Thus the incident corpuscles of lightare accelera ted and bent by this attrac tive force.

Fifty years after Principia, New ton's ballistic theory has been preciselyexpounded-in an algebraic way-by Clairaut (174 1). It shows up a mathematizedoptics which implies two different laws:

first of course Descarte s ' law of refrac tion that comes out with the conservation ofthe 'i mpulsion' parallel to the plane separating the two media:

sm tv r .- smr = n sin rVi

(where n is the relative index, i the angle of incidence , r that of refraction, Vi

the velocity of the incident corpuscle of light and vr the velocity of the refractedcorpuscle),and second, something like a conservation law of the energy of a light corpuscle ,implicit in Newton 's demonstration:

b

2 2 f 2vr - Vi = - 2 f(x )dx EVo

o

T HE PREHI STORY OF R ELATI VI TY 5

(where f is the refringent force per unity of mass and where v6 is the refr ingentenergy per uni ty of mass, E being equal to + or -1 depending on the path of thecorpuscle).From these equations it is clear that in Newto n's corpuscular theory of light

refrac tion was linked to the velocity of the incident light. As we will see later on, sucha dependence was to be used by Michell and Arago in order to try to show a differ­ence in the velocities of incident corpuscles of light. But Newton also used thisdependence as an attempt for a theory of chromatic dispersion.

3. FROM CHROMATIC DISPERSION TO THE THEO RY OF EMISSION

As we know, for Newton, white light consisted in a stream of corpuscles of differentcolors. In the year 1690, it seems that he hoped to explain chromatic dispersion byestablishing a connection between color and velocity, each corpuscle of differentcolor being endowed with a different velocity.Actually, velocity would be the param­eter of color.

Thus a particle with a greater velocity would be less deflected by the attractiveforce than a particle with a smaller velocity. The faster a corpuscle is, the less bentand less refracted it will be. The slower it is, the more bent and more refracted it willbe; just like a cannonball in the Earth 's gravitation field. As a consequence, a lessdeflected particle (like a "red-making" particle) is supposed to have a greater velocitythan the more deflected one (like the "violet-making" particle). At hand, we have apossible model for chromatic dispersion and an explanation of the spectrum.

Also, such a mechanical model of dispersion would imply that a moon of Jupiterwould have its color modified as it appeared (or disappeared) behind the planet: atemersion, over a short period of time, the colors of the spect rum would appear in tumbeginning with the fastest (red) rays.

On August 10th 169 I, Newton wrote to John Flamsteed, Royal Astronomer andlong-time correspondent, to ask if he had observe d any change of color in Jupi ter 'ssatellites before they disappeared. As Flamstee d had not observe d any change ofcolor in the light of the appeari ng or disappearing satellites of Jupit er, Newton as aconsequence abandon ed this hypothesis.

Actua lly, Newton was never rea lly involved in either his mechanica l model ofdis­persion nor in his corpuscular theory; after publ ishing Principia he never alluded to itin publ ic again. Nevertheless, in 1694 as Biot later showed, Newton used his corpus­cular theory as a model to compute his table of astronomical refraction.

Some fifty years later, in France and in Britain, Newton 's corpuscular theory stilldominated the field . Alexis-Claude Clairaut was certa inly one of the philosophersmost interested in it. The question of the color of Jupiter 's satellites at emersion wastaken very seriously by Jean-Jacques D'Ortous de Mairan, by the Marquis deCourtrivo n and Clairaut in France, by Thomas Melvill in Scotland, and finally byJames Short, the well-known London optician. After many interesti ng discussionsand a tentative observation by Short it became clear-as Newto n had understood longago-that it was no longer possible to deal with such a model.

In any case, New ton's corpuscular- ballistic-theory was to be used for quite a

6 JEAN E ISENSTAEDT

long time, but without any reference to colors; the angle of refraction was still relatedto the velocity of the incoming corpuscle but no longer to its color.

At the time, this reduced interpretation of Newton's corpuscular theory was themost valued theory in optics, in France it was called "La Theorie de l' Emission."Simon de Laplace, Jean-Baptiste Biot, Etienne-Louis Malus, Simeon-Denis Poisson,Francois Arago, all of the "Societe d'Arcueil" were all working in that way. Mean­while, it was still possible to use the emission theory in order to explain or predictphysical effects, for example, double refraction, astronomical refraction, or the Bos­covich effect.

4. JOHN MICHELL AND THE ACTION OF GRAVITATION ON LIGHT

For many a Newtonian, light was composed of corpuscles whose velocity was finite,and as James Bradley had shown through aberration, it seemed to be a constant. Butfrom a theoretical point of view there was at the time absolutely no reason for thevelocity of light to be a constant. More precisely, Galilee 's principle impeded thevelocity of light being shown as a constant. Here was one of the most important con­tradictions of the century.

Thus for John Michell" (1724-1793), a friend of Henry Cavendish and a mostconvinced Newtonian philosopher, there was no contradiction to suppose that lightwas subject to gravitation. In a context closely related to Newton's corpuscular theoryhe was to apply Newton's theory of gravitation to light. To him light was supposed tobe subject to gravitation in the very same way as an ordinary material corpuscle, butit was endowed with a greater (emission) velocity:

Let us now suppose the particle of light to be attracted in the same manner as all otherbodies with which we are acquainted; that is, by forces bearing the same proportion totheir vis inertiae, of which there can be no reasonable doubt, gravitation being, as far aswe know, or have any reason to believe, an universal law of nature (Eisenstaedt 1991,329).

Thus light could be slowed down or accelerated by gravitation. In his 1784article' Michell calculated in a geometical way the gravitational slowing down of acorpuscle of light. Fifteen years later the very same calculation was to be performedby Laplace (1799) but in an algebraic way: c( r) , the velocity ofl ight at a distance rof a star was to take the form:

c2(r ) c~ _ 2GM + 2GMro r

(where M is the mass of the star, ro its radius; Co is the emission velocity: actuallythe velocity of light at emission at ro) .

From his (geometrical) formulation Michell, followed by Laplace, inferred thepossible existence of "dark bodies"; simply that c

2(r) vanishes at infinity if

2 < 2G M .co- - - 'ro

T HE PREHISTORY OF R ELATIVIT Y 7

Hence [...] if the semi-dia meter of a sphaere of the same density with the sun were toexceed that ofthe sun in the proportion of 500 to I , a body falling from an infinite heighttowards it, would have acquired at its surface a greater velocity than that of light, andconseque ntly, supposing light to be attracted by the same force in proportion to its visinertiae, with other bodies , all light emitted from such a body wou ld be made to returntowards it, by its own proper gravity (ibid., 332 ).

Of course Michell's effect also allows for a diminution of the velocity of light , aslowing down of light by gravity:

But if the semi-diameter of a sphaere, of the same density with the sun, was of any othersize less than 497 times that of the sun, though the velocity of the light emitted from sucha body, whould never be wholly destroyed, yet would it always suffer some diminution ,more or less, according to the magnitude ofthe said sphaere (ibid ., 338) .

Even if Michell foresaw this, such an effect allows for an acceleration of light bygravity. In the same way, Michell stuck to the radial case and didn 't consider that agrazing ray of light could be deviated or bent by gravit ation . It was Soldner's aim(referrin g to Laplace but not to Michell) to work out this idea. His calculation can befound in his 180 I essay:

Thu s when a my of light passes by a celestial body, it will, instead of going on in astraight direction , be forced by its attrac tion to describe a hyperbola whose concave sideis directed against the attracted body."

This calculation was also independently performed (but never publi shed) by HenryCavendish at the beginning of the nineteenth century (Jungnickel and McCormmach1996, note 33, 303).

5. MICHELL'S EXPERIMENTS OF 1783

Michell was essenti ally interested in astronomy. From statistical considerations,applied to the distribution of stars in the sky, he predicted in 1767 the existence ofgroups of physically connected stars, of "double stars," long before William Hers chelcould obse rve their movements. Michell's aim was not so much to focus on the retar­dat ion of light ; he was primarily interested in measuring the distance of the stars.

Michell thought that in some double star systems, the mass of the central star hadto be much more important than that of its companion. Ifhe could observe such a sys­tem, he would (try to) collect at the same time the two beams of light , the first oneemitted by the central mass and the second one by its companion. He would then ana­lyze their lights with the help of a prism. The light of the massive star had to be grav ­itationally retarded in relation to that of the smaller star. Thus , due to Newton'scorpuscular theory of light it had to be differentially refracted on the prism: the anal­ysis of the observation would show a difference in the refraction of the beams due tothe difference in the velocities of the corpuscle of lights coming from the two stars.Such a measurement would have provided one more piece of data to help determinethe distanc e of the star system:

Now the means by which we may find what this diminution amounts to seems to be sup­plied by the difference which would be occasioned in conseq uence of it, in the refra ngi ­bility of the light, whose velocity should be so diminished (Eisenstaedt 1991, 343).

8 JEAN E ISENSTAE DT

/

Relative deviationof the two light-rays

Figure I, John Michell's Experiment, / 783.Light coming fro m the central star will be more deviated by the prism

than that coming from its less massive companion.

THE PR EHI STORY OF R ELATI VITY

But what kind of precision did Michell think he could obtain?

As a prism might be made use for this purpose, which should have a much larger refract­ing angle than that we have proposed, especially if it was constructed in the achromaticway, accordi ng to Mr. Dollond 's principles, not only such a diminution, as one part intwenty, might be made still more distinguishab le; but we might be able to discover con­siderably less diminut ions in the velocity of light , as perh aps a hundredth, a two-hun­dredth, a five-hundredt h, or even a thousandth part of the whole (ibid., 345).

9

The experiment was jointly performed by the Royal Astronomer Nevil Maskelyne andby William Herschel during the summer of 1783 in the direction of the Pleiades but

without success. Herschel even ground a prism for the occasion. Henry Cavendish wasalso involved in the experiment and had predicted that a reduction in the focal length of

an achromatic lens would be a further consequence ofMichell 's theory; Maskelyneperformed the new observation with the lens but he too failed to detect the effect.

6. ARAGO ON THE VELOCITY OF LIGHT

Arago began his experiments on the velocity of light as early as 1806. But it was onlyon his return from Africa in 1809- 1810 that these experiments were resumed. Theresults were made public at the time but were not published before 1853. To Arago,who took these ideas from Michell, a prism was a perfect tool for comparing thevelocities of light rays.

For Arago, there were many reasons for the velocity of light not to be constant,and consequently differences had to exist in the velocities of lights. He even thoughtthat the velocity oflight could double (2co! ) in certain circumstances. Such an effectmight be due to different causes, of course linked to the law of addition of velocities:the velocity of the Earth (rotation or translation) or the probable proper velocities ofthe stars themselves. But, of course, it might also be due to refraction (light beingaccelerated in a denser medium due to the emission theory), or even as he put it

one of the most powe rful eause ofehange in the velocity of light seems to be the unequalsize between the diameters of the stars (Arago 1853,47)

which is due to Michell 's effect of gravitation on light. Actually, Arago is well awareof Michell 's theory and even explains properly the dark body idea:

One finds actually, through calc ulations, that a star of the same density as the Sun andwhose diameter would be a little hundred times grea ter than that of this star, would ,through its attraction, annihi late totally the velocity of its rays , which consequently,could not reach us.?

Arago was to compare the prismatic deviation of a light-ray coming from a defi­nite star at twelve hours difference. The velocity of the Earth in relation to this star,v , will be - v twelve hours later; and as a consequence the velocity of a light corpus­cle coming from such a star will be respectively c + v and c - v in relation to a ter­restrial observer. The angles of refraction at the prism will have to be different.Actually, Arago is seeking for a Doppler-shift with Michell 's prism. A simple calcu­lation made in the context of Newton's emission theory relates the difference in the

10 J EAN E ISENSTAEDT

velocities as a function of the deviation of the ray. Arago was to perform this experi­ment a number of times from 1806 to 1810. At last he was convinced that no effectwas detectable.

But how can this very strange result be explained? Ofcourse it was not possible toquestion Galileo's principle of relativity. Was Newton's emission theory wrong?None of these conclusions were possible. At the time Arago assumed an ad-hochypothesis:

among the infinity of rays with every velocities that emanate from a lumin ous body. onlythose of a determined velocity are visible."

The reason is that the rays are seen and measured at last in the "vitreous humour ofthe eye" of the observer, where they will display-due to Newton's emission the­ory-the same velocity in the same medium; at least, if all the observers' vitreoushumour has the same refractive index. This is Arago's ultimate explanation that hemost probably picked up from de Mairan (Eisenstaedt 1996, 148).

As Arago put it in his paper:

this work [has] been the point of departure of experimental and theoretical researches(Arago 1853, 38).

A conclusion also made by Tetu Hirosige:

...in the first half of the century [00 '] Aragos experiment and the aberration of light wereconsidered the touchstone of [a legitimate theory of light] (Hirosige 1976. 12).

In the year 1815 Arago came to support Fresnel's ideas and the wave theory of light.Afterwards and due to the success of this line of thought it was no longer possible tothink in terms of Michell's influence of gravitation on light, probably because itproved to be quite complicated for gravitation to act on light waves. For a long timeMichell's theory was totally forgotten.

7. THE PREHISTORY OF RELATIVITY

To conclude, I will address the following question: is it justified to talk ofa prehistoryof relativity, as my title implies? First, the two main ingredients of genera l relativity,gravity and light, are also at the very basis of Michell's theory of the action ofgravi­tation on the propagation of light. And second, also at least two important predic­tions: that of the bending of light by Soldner and that of the dark bodies. As is wellknown, these predictions actually differ qualitatively and quantitatively, which showshow different the two theories of gravitation are. Light is not trapped in dark bodiesas it is in black holes, and the intensity of the bending of light rays, in the context ofNewton's theory, is only half of what it is in general relativity. But what is reallyimportant is that the effect of deviation is actually present.

I want to state clearly that this prediction is coherent with the vision that one hasthen of a corpuscle of light but also with Newton's theory of gravitation and also withGalilean kinematics. A grain of light, as it was often called then, might be acceleratedor slowed down without question. Actually, the idea of the constancy of the velocity oflight came to the fore at the end of the nineteenth century from numerous experiments

THE PREHISTORY OF RELATIVITY 11

and observations , but it was not ideologically coherent with the philosophy of the time.Moreover there is one additional link between Michell's theory and Einstein 's

theory of general relativity: more precisely, between Michell's 1783 experiment andthe 1925 experiment by Adams (1925) on the displacement of the spectral lines bythe Companion of Sirius. Both experiments aimed at the same physical prospect; theinfluence of gravity on light. Both observations relied on the same material , a binarysystem and on the same equipment, a telescope and a prism. Of course both observa­tions relied on completely different theories. Moreover, Michell was not waiting for aspectral shift but for a differential refraction-spectroscopy was not yet born. But theidea was almost the same. Michell's effect, the slowing down of light due to a gravi­tational field, is nearly parallel to the "Einstein effect," the displacement of the spec­tral lines of an atom due to a field of gravitation. But is that so astonishing? We havelong known that general relativity is not the only theory predicting such effects, atleast from a qualitative point of view. The theory of the influence of gravitation onlight, as it developed at the end of the eighteenth century, is without doubt an impor­tant part of the prehistory of Einstein's theory of gravitation.

Observatoire de Paris

ACKNOWLEDGEMENT

I would like to thank Raymond Fredette for revising the English of this text.

NOTES

*

I.

2.3.4.

5.

6.7.

8.

In hom age to John Stach el for his 70th birthday.

Much of this matter, references and quotations are to be found in (Eisenstaedt 1991, 1996, 1997 ). Thispaper is essentially a summary ofthese artic les, forthcomin g in an artic le on Arago and the veloc ity oflight.Concerning this point see (Jaki 1978).Concerning these sections see (Eisenstaedt 1996).There are few histori cal works on John Michell as an astronomer and a physicist; see (Mc Cormmach1968; Eisenstaedt 1991; Jungni ckel and McConnmach 1996; Vignolles 2000).Actually one finds early developm ents on this topic in Michell 's notes pub lished in Priestley 's Historyof Optic: see (Eisenstaedt 1991, 322).Soldner ( 180 I) translated in (Jaki 1978, 945) ."On trouve en cffet, par Ie calcul , qu 'une etoile de meme densite que Ie Soleil, et dont Ie diametre

scrait un petit nombre de centaines de fois plus considerable que celui de cet astre , aneantirait total e­ment par son attraction la vitesse de ses rayons, qui n'arrivcraient par consequent pas jusqu' a nous"(Arago 1853,47)."dans l'infinite des rayons de tout es les vitesses qui emanent d'un corps lumin eux, il n 'y a que ceuxd 'un e vitesse determinee qui so ient visibles" (Arago 1853,47).

12 J EAN EISENSTAEDT

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