Marshall, T. (2006). Wave particle duality in the seventeenth century. PHILICA.COM Article number 44.
Wave particle duality in the seventeenth century

Trevor Marshallunconfirmed user (Mathematics, University of Manchester)

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I argue that Newton’s theory of Optics - as presented in his “Opticks” of 1704 - does not differ greatly from modern Quantum Optics. If we apply any of the modern theories of how science progresses, for example Popper’s, we should judge that some of his contemporaries had a better description of interference, diffraction and double refraction than had Newton, and that evidence already available at the end of the seventeenth century confirmed their superiority. This indicates that ideological, rather than scientific criteria were brought to bear during the subsequent century, to bar progress in the understanding of Light.

Wave-particle duality in the 17th century
Trevor W. Marshall
Dept. of Mathematics, Univ. of Manchester, Manchester M13 9PL, UK

Newton's Opticks

    Isaac Newton published his Opticks in 1704. Between then and 1830 its conclusions, about the nature of light as a stream of particles, were accepted as correct by just about everybody. Maybe the mood was captured in Alexander Pope's epitaph to Newton God said, "Let Newton be", and all was light. In the early decades of the nineteenth century, with enormous difficulty and against the determined opposition of the scientific authorities, Thomas Young and Augustin Fresnel established the superiority of the wave theory of light. They were hardly recognized in their lifetimes — Young died in 1829 and Fresnel in 1827 — but by 1830 their correctness was conceded, and as a result the Opticks was considered as of purely antiquarian interest from then up to about 1920. The attitude was then reversed as a result of the growing popularity of the photon, a concept which Albert Einstein had introduced in 1905 to explain the photoelectric effect, and which today is widely considered to be a particle of light. In 1952 a modern edition of the Opticks was published with a Preface  by Einstein which hailed Newton's ideas as a forerunner of the Wave-particle duality of the twentieth century. However, Einstein had himself seriously challenged this concept in a critical article he published along with Boris Podolsky and Nathan Rosen in 1935, and in the very year he wrote the Preface he said, in a letter to Michel Besso, Nowadays every Tom Dick and Harry thinks he knows what a photon is, but he is wrong.
    At the beginning of the seventeenth century there were only two areas of optics, reflection and refraction, both of which became the basis of an important technology, that is mirror and lens grinding. The basic law of reflection, that a ray of light is reflected from a plane surface so as to produce an image, of an object in front of a mirror, which is symmetrically behind the mirror (hence "mirror image", see Fig.1), had been known from ancient times.


    Refraction is the bending of a light ray at an obtuse angle as it goes from a rarefied medium like air into a denser medium like water or glass. It results in the optical illusion that a straight stick appears bent at the point that it enters a pool of water (see Fig.2).

 [Refraction of a ray going from air to water. Snell's Law relates the sine of the angle i to the sine of r. Fermat's Principle describes the path from air to water as the one which makes the total optical path length a minimum.]

The law of refraction, corresponding to the mirror-image law of reflection, was first determined by Willebrord Snell around 1620. It states that the ratio of the sine of the incident angle to the sine of the refracted angle is a constant n, known as the refractive index, of the dense material - more accurately the ratio of the latter to the refractive index of air, but for most purposes that is one.
    In the new scientific spirit of the seventeenth century a phenomenological law like Snell's was not enough. Rather like Kepler's laws describing the orbits of the planets, it was descriptive rather than explanatory - the how rather than the why. Natural philosophers began to look for laws which incorporated the notion of causality, and at the same time mathematicians sought for unification, whereby two different but related phenomena could be linked. These two desirabilia have persisted right up to the present day, and their demands are not always respected in equal measure by today's physicists, who are, as always, natural philosophers and mathematicians in varying proportions.
    It was a mathematician, Pierre Fermat, who made the first contribution after Snell. He observed that a ray of light, going directly from an object to the observer's eye, travels in a straight line, that is by the shortest route, and that a ray reflected from a mirror, as in Fig.1, travels along that pair of straight lines which together gives the shortest route — the sum of the lengths AB and BC is less than the sum of AD and DC. Fermat now extended this idea to refraction. He introduced the notion of an optical path length which is the normal geometrical length multiplied by n. A ray going from air into water has a trajectory which minimises the total optical path along the two straight lines, just as in the case of reflection. Referring to Fig.2, a ray whose end points are specified by the three distances (a,b,d), crosses the interface at x which satisfies the condition that the function


    should be a minimum. Nowadays a reasonably gifted sixteen year old can do this sum; all he or she has to do is calculate the derivative dy/dx and make it equal zero — and that gives us Snell's Law. That Fermat was able to do it in the 1640s, round about the time Newton and Leibniz, the inventors of the Differential Calculus, were born, is remarkable, and qualifies him for a substantial part of the credit which Newton and Leibniz were later to argue over between themselves.
    But Fermat was not without philosophical instinct, because he gave his minimization the title Principle of Least Time. He made the hypothesis that light travels in air at speed c, and in water at c/n, so that the time to travel from A to C via B is


Since this gives t(x)=y(x)/c, Fermat's principle is simply the minimization of t with respect to x. This was a daring hypothesis indeed; the speed of light in air was first measured in the 1670s, and in water not until the 1850s.
    Even the notion that light "travels" from A to C had some novelty at that time; it raised some new questions — what is the nature of the travelling object, and what causes it to travel in straight lines at varying speeds? Almost from the beginning, two answers were presented, and they led to a great debate during the latter half of the seventeenth century. One school of thought supposed that light is some sort of wave motion, and the other that it is a stream of particles.
    The wave theorists made the initial running. Two prominent among them were Robert Hooke, who observed that thin films of soap solution or oil exhibited colours, and Francesco Grimaldi, who found that the image of a rectangular aperture cast on a distant screen was somewhat wider than the aperture itself, and also that the shadow had, on the illuminated side, coloured fringes close to its edges. They gave the phenomena they had observed their modern names, that is interference and diffraction respectively, and both of them published their findings in 1665 — Hooke's Micrographia and Grimaldi's Physico Mathesis de Lumine. That was also the year in which Newton, who became the champion of the corpuscular theory, began his researches in optics. A few years later, in 1669, Erasmus Bartholin made the new discovery of double refraction, which was to present the greatest challenge to the corpuscular theory in the hands of Christian Huygens, who published what is in effect the complete modern theory of that effect in 1690, that is fourteen years before the Opticks.
    Newton's responses to these three challenges were of varying qualities. On interference he carried out a formidable sequence of experiments, which told us an immense amount about light, and which prepared the ground for the vast discipline of spectroscopy. The theoretical structure he laid in that area, though it was discredited in the nineteenth century, came back in the twentieth. I do not myself believe that it will survive long into the twenty first, but even then it will not have done too badly! On diffraction some of his experiments were not at all accurate, and some of his measurements were just plain wrong. While quite a few present-day physicists will come forward to defend his replacement of Hooke's interference by his own Theory of Fits (see the next section) the same could not be said for his substitution of "inflexion" of particles for Grimaldi's wave diffraction. And on double refraction his experimental input is zero, while he nevertheless propounds, in Query 25  of the Opticks, a "law" of double refraction which contradicts completely the data gathered by everybody else.
    We really should address the question "Why did Newton prevail?". One obvious explanation is his immense prestige following the publication of his theory of gravitation in the Principia in 1687. A more cynical response is to echo the statement of Max Planck, who said that no theories die; only their proposers do, and indeed Grimaldi (1663), Hooke (1703) and Huygens (1695) were all dead by 1704. Neither of these explanations is entirely satisfactory, so I shall attempt an answer after considering the above three challenges in more detail.


    Hooke had proposed that the various colours of a thin film arise because light can reach the eye either by reflection from the top surface, or by refraction into the film followed by reflection from the lower surface (see Fig.3).


 [Interference or fits? Hooke's explanation for the colours of thin films is that the signals ABCDE and A?B?C? interfere constructively, leading to a bright fringe, if the optical path lengths differ by a whole number of wavelengths. Newton's is that refraction occurs at C, leading to a dark fringe, if BC is an even number of fit lengths.]

 Because light is a wave motion, the two waves are phase related and they may either reinforce each other or cancel each other out; that is the Principle of Interference, and Hooke was the first to propose it, albeit in a somewhat vague and incomplete form. To make it more precise would require knowledge of the wave length of the light; if t is the thickness of the film, n its refractive index and λ the wave length of the light, and if the angle of refraction is r, then the reflected and refracted waves reinforce if the difference in path lengths for the two interfering waves contains a whole number of waves, that is, for some whole number N,

 2ntcos r=Nλ .

This, we may reasonably suppose, would have been Hooke's condition for a bright interference fringe, the dark ones being obtained by replacement of N by (N+1/2).
    Paradoxically Newton, who refused to accept the wave concept, would be the first to supply the missing information. He was able to make amazingly accurate measurements of the wave lengths, because he studied the thin layer of air between a convex and a plane piece of glass; the thickness of such a layer could be controlled and measured with far greater accuracy than in Hooke's films of soap solution. The colours of the rainbow repeat themselves many times as a pattern of concentric rings, nowadays called Newton's rings, and the size of the air gap is found indirectly from the diameters of these. Newton deduced the wave lengths of the whole of the visible spectrum, from red light at about 670nm to violet at about 420nm, only he did not acknowledge that these were wave lengths. Instead he claimed to have "proved" that a particle of light which was refracted at the upper face went on to be preferentially reflected or refracted at the lower face, depending on some internal phase within the particle. He gave this new property of light particles the name fits of easy reflection and refraction. The particle is reflected at the lower surface if the optical path BC contains an odd number of "fit lengths", which we may denote f, so Newton's condition for a bright ring was, since he had an air film for which n=1,

 tsec r=(2N+1)f ,

a dark ring being obtained by replacing 2N+1 by 2N.
    We may say that Newton counterposed a form of internal oscillation within his light particles to Hooke's wave interference. His first presentation both of the theory of colours and of the theory of fits, following his election to the Royal Society in 1672, was attacked by Hooke. The data on wave lengths was all gathered before 1690, and by that time Hooke had conceded that Newton had been correct about colours. It is fascinating to speculate on how he would have received Newton's new evidence, especially since it contained just the information he needed to complete his own description. Putting n=1 would have been the first step, and then the identification λ=4f might have led him to modify his original formula to

 tcos r=2Nf .

Now Newton's and the modified Hooke formulae differ in two respects. Firstly their criteria for dark and light fringes are precisely the reverse of each other; in this respect Newton would have been able to show the superiority of his own formula, using his own data on the ring diameters; the full wave explanation for this part of the phenomenon would have to wait until after 1800. But the other difference is the r dependence of the two formulae. It would have been particularly interesting to see Newton's formidable experimental technique used to test these latter two formulae against each other for nonzero r; they agree for r=0 which is the only situation observed by Newton, but their behaviour is different for nonzero r. As it turned out, questions of personal animosity between these two very substantial scientists intervened, as well as Newton's health, so publication of the new material had to wait until 1704, which was a year after the death of Hooke.


    Grimaldi found that a beam of light, falling on a rectangular slit, casts an image on a screen some metres away which is somewhat wider than the slit, and that the shadow has coloured light and dark fringes close to its edges. A modern repetition of the experiment confirms his findings. In Fig.4 we depict the intensity in the image of a slit of width 9mm on a screen placed 1.08m behind the slit.

 [The diffraction pattern of a  9mm slit. This is a modern realization of the experiment reported by Grimaldi in 1665. The geometric shadow is the region outside the boundaries A?A?. Defining the shadow as the region in which the intensity is less than 10 percent of the incident intensity, that leaves an illuminated region about 1mm  wider than the geometric shadow, in agreement with Grimaldi.]

 If we define the shadow as the region in which the intensity is less than one tenth of the intensity at the middle of the image, then the width of the image is about 10mm, and the first bright fringe is about 1mm from the edge of the shadow. This figure represents the diffraction pattern with yellow sodium light at wave length 589nm. The fringes are in different positions if the colour of the light is changed, and with the white light used by Grimaldi it would not have been possible to observe more than the three fringes on each side that he reported.
    Newton's experiments on interference are the subject of Book Two of the Opticks, and in Book Three he directs his attention to Grimaldi's discovery. On the first page he makes the most cursory reference to Grimaldi, and he gives an incorrect account of that author's findings, stating that

Grimaldi has informed us, that if a beam of the Sun's light be let into a dark room through a very small hole, the shadows of things in this light will be larger than they ought to be if the rays went on by the bodies in straight lines…

    We see from Fig.4 that it would be more accurate to say that the shadow is made smaller, which is the way Grimaldi described his finding; he went on to infer that this was evidence for the wave nature of light, since it had bent slightly around the edge of the slit and into the shadow. Newton, on the other hand, consistently fails to see such evidence in any of his Observations, insisting very strongly that the rays of light are always bent away from the edge. For Grimaldi's diffraction of waves Newton substitutes inflexion of rays. Grimaldi, just like Hooke, was able to give only a qualitative account of his theory, but in this case Newton is no different. In Fig.2 of Opticks, Book Three he draws a diagram of a stream of inflected particles going past a narrow rectangular object, but he does not attempt to calculate the pattern which such a stream would make on a distant screen. In Observations 1-11 he goes on to make accurate measurements of the positions of the light and dark diffraction fringes, but, in the absence of the kind of theory he has constructed for the interference fringes of Book Two, he is unable to draw anything other than qualitative conclusions, based on that figure. These conclusions were not only incorrect, as was revealed by experiments made after 1830; they also caused him to claim he saw shadows where in fact he should have observed illuminated areas. His most spectacular failure is in Observation 6, where he observes the diffraction by a narrow slit, whose width is .06mm. Such slits fall in the region of what we now call Fraunhofer diffraction, named after Joseph Fraunhofer (1787-1826), the inventor of the diffraction grating, for which the complicated behaviour of Fig.4 is replaced by the simple formula for the intensity

 I(x)=I(0)(((λd)/(2πax)))²sin²(((2πax)/(λd))) ,

which is depicted, for the case λ=589nm, d=1.08m, 2a=.06mm, in Fig.5.

 [Fraunhofer diffraction pattern of a slit of width 0.06mm on a distant screen. Newton measured very accurately the position of all the outer fringes, but was unable to see the central peak.]

 Newton mapped very accurately the position of the first three fringes on either side of the central one, but failed to see the central peak — this in spite of the area under the central peak being more than nine times the total area under all of the other peaks put together!
    At the end of the Observations Newton states

When I made the foregoing observations, I designed to repeat most of them with more care and exactness, and to make some new ones for determining the manner how the rays of light are bent in their passage by bodies, for making the fringes of colours with the dark lines between them. But I was then interrupted, and cannot now think of taking these things into farther consideration. And since I have not finished this part of my design, I shall conclude with proposing only some Queries, in order to a farther search to be made by others.
    From this statement we may reasonably infer that the Observations of Book Three were made in the late 1680s or early 1690s, and that they therefore coincide, more or less, with the publication of Huygens's Treatise on Light, and also with the beginning of Newton's parliamentary and public service activities. We know that in 1692 Newton suffered a nervous breakdown which "interrupted" (as in the above quote) his intellectual activities for two years. By the time he came to write the Opticks he had lost his zeal for precise experimentation, and was interested only in establishing a kind of ideological hegemony over his rivals in the wave camp. While one can appreciate that Einstein's very generous comments, made in his Preface  to the 1952 edition of the Opticks, may have been in recognition of the experiments and analysis Newton reports in Book Two, it seems inconceivable that he intended to make the same assessment of these Observations in Book Three.

Double refraction

    Starting from the Fermat Principle of Least Time, Christian Huygens set out to provide a causal description of reflection and refraction. For Huygens it was the wave front of a light beam, rather than the rays considered by Newton, which were fundamental. There is a simple connection; the rays are perpendicular to the wave front (see Fig.6).

 [The Huygens construction for a wave reflected from a plane surface. The incident and reflected wave fronts are depicted by thick lines.]

 The wave front travels through air at a speed c, and when it falls upon a reflecting surface it sends out spherical wavelets also travelling at speed c. But the wave front reaches the surface at different times, so at some later time the set of all these wavelets has varying radii. Huygens constructs the reflected wave front by drawing the tangent plane to all of these wavelets, and the reflected rays are simply the perpendiculars to this wave front. It is then a matter of simple geometry to prove that the reflected rays make the same angle as the incident rays with the reflecting surface.
    According to Huygens's construction, when such a wave falls upon the plane surface of a refracting medium it sends out spherical wavelets into the medium travelling at speed c/n which is what Fermat had supposed. This again produces a set of wavelets of varying radii, and again the refracted wave front is constructed by drawing the tangent plane to these wavelets (see Fig.7).

 [Huygens's construction for ordinary refraction, obeying Snell's Law.]

 It is then a matter of simple geometry to prove that the direction of the refracted rays is in accord with Snell's Law. The optical lengths of the paths A?B?C?, A?B?C?, A?B?C? and A?B? are all equal, and in modern terminology we say that the Huygens construction interprets Fermat's Principle as stating that the wave front is a surface of constant phase.
    Huygens's main achievement was his treatment of double refraction. In 1669 Bartholin had discovered that a crystal of Iceland spar (modern name calcite) produces a double image of, for example, a cross on a horizontal piece of paper when viewed.from vertically above through the crystal. He also observed the orientation of the line which connects these two images. The calcite crystal is a parallelopiped whose faces are parallelograms with angles of 101.92deg. and 78.08deg. If two of the six faces are horizontal, then the other four faces are slanting, and only two of them are visible when viewed from vertically above (see Fig.8).

 [Double refraction in the calcite crystal. The planes of perpendicular refraction are parallel to the vertical plane through OC, and the two images lie in such a plane. Huygens's optic axis makes equal angles with each of the three planes OAB, OBC, OCA.]

 Now draw the vertical plane through the edge common to these two faces; it bisects the obtuse angle of the parallelogram on the top face of the crystal, and any plane parallel to it is known as a plane of perpendicular refraction (PPR). The line connecting the two images lies in a PPR, and in the ray description this means that a vertical incident ray (that is one with i=0), is split into an ordinary ray which is vertical (r=0) and an extraordinary ray with an angle r', measured to be between 6 and 7 degrees, lying in the PPR. Further observation had shown, by the time Huygens wrote his Treatise on Light in 1690, that, for any angle of incidence the ordinary ray satisfies Snell's Law. The extraordinary ray, however, completely violates it. Indeed, if the incident ray is not in the PPR, then the refracted ray is not even in the same vertical plane as the incident ray.
    Huygens proposed that there is a special axis in the PPR, whose modern name is the optic axis. For the extraordinary wave the spherical wavelets of Fig.7 are replaced by spheroidal wavelets (see Fig.9; for simplicity we consider only the case of the incident ray lying in the PPR), which spread at a velocity c/n (that is the same as the speed of the ordinary wave) along the optic axis, and with a different velocity c/n' perpendicular to it.

 [Huygens's construction for double refraction.]

 The wave front of the refracted wave is, as before, the common tangent of all these wavelets, but now the ray direction, which is the vector from the centre of the spheroid to the point of contact with this wave front, is no longer perpendicular to it. In modern terminology we use the term walkoff angle for the angle between the ray vector of the extraordinary ray and its wave vector. By considerations of symmetry Huygens was able to infer that the optic axis makes an equal angle of p=45.38 deg. with each of the three crystal planes meeting at O in Fig.8. He, or anyone else taking his theory seriously, could therefore translate his Fig.9 into a mathematical relation between the ordinary and extraordinary angles r and r', namely, putting tanr=x, and tanr'=y,

 y=x(1+ttan p)√(((1-tcot p)/(1-tx²tan p)))+t .

The only unknown quantity in this formula is the parameter t, which is the value of tanr' when r is zero. This quantity must be measured; Newton gave it as the tangent of 6.67 deg., which is quite close to the modern value of 6.23 deg. Since p is extremely close to 45 deg., we observe that the above formula may be adequately approximated by

 y=x(1+t)√(((1-t)/(1-tx²)))+t .

    Because of the existence of such a simple diagram, readily translated into a simple formula, the challenge posed by Huygens to Newton's corpuscular theory was more serious than had been posed by either Hooke's interference or Grimaldi's diffraction. Newton's response had to wait until the second edition of the Opticks in 1717, where he stated, in Query 28,

Are  not all hypotheses erroneous, in which light is supposed to consist in pression or motion, propagated through a fluid medium?… The waves on the surface of stagnating water, passing by the sides of a broad obstacle which stops part of them, bend afterwards and dilate themselves gradually into the quiet water behind the obstacle… But light is never known to follow crooked passages nor to bend into the shadow… To explain the unusual refraction of Iceland crystal by pression or motion has not hitherto been attempted… except by Huygens, who for that end supposed two several vibrating mediums within that crystal… But how two aethers can be diffused through all space, one of which acts upon the other, and by consequence is reacted upon, without retarding, shattering, dispersing and confounding one anothers motions, is inconceivable.

    Note the curious way Newton has of posing a "Query". This is not the response of the scientist, but rather of the ideologue. After restating what was, as we saw in the last section, an incorrect description of the diffraction phenomenon, he goes on to say it is "inconceivable" that two kinds of light wave coexist within the same medium. This seems a wholly inadequate reason for him, or anyone else, to refuse further consideration of Huygens's explicit proposal contained in Fig.9. His willful blindness in this matter was to hold up recognition of the correct wave description of light for more than a hundred years.
    This does not exhaust what Newton had to say, in the later Queries, about double refraction. Apologists for Newton, including, as I have already noted, Albert Einstein, have praised his assessment, also contained in Query 28, of experiments, already reported by Huygens, with two calcite crystals. His comment, that a ray which is extraordinary for the first crystal becomes ordinary for the second, which has been rotated about a common axis by ninety degrees, leads him to the idea that the light particles have a certain "sidedness". Ironically this idea, in the hands of Fresnel in the 1820s, turned out to be precisely what was needed to explain the two kinds of wave in Huygens's theory, and thence the modern understanding of light as a transverse wave, rather than the somewhat caricatured pressure wave referred to by Newton. What a pity that someone who, at age 75, was still so creative, should fail to acknowledge the equal creativity Huygens had shown in constructing Fig.9!
    Newton's other contribution, in Query 25, has no such qualities. In Book Two, he had constructed a makeshift theory of ordinary refraction, now mercifully dead and buried, in which the particles of light are accelerated at the air-water interface, so that, in contradiction with both Fermat and Huygens, the speed of light in water is greater than in air. Although it was more complicated than Huygens's theory of refraction, which preceded it by 14 years, it was accompanied by a disarmingly simple diagram, and nobody could refute it until the speed of light in water was measured in the 1850s. But Newton's attempt to extend the theory to double refraction in Query 25 was carrying such shift making to a new low level. He supposed that, in addition to the vertical acceleration suffered by his light particles at the interface, there was a horizontal component of acceleration in the PPR. This led him to propose, as an alternative to Huygens's formula connecting r and r', the relation

 y=x+t ,

for the extraordinary, or "unusually sided" particles. This, to be sure, is mathematically simple, even though the mechanical model leading up to it was extremely convoluted. What is amazing is that neither Newton nor any of his disciples during the next century thought to test this formula against Huygens's Fig.9. If they had done so, they would surely have found Huygens to be correct, because the difference between them (see Fig.10) is something the painstaking experimenter of Opticks Book Two would have easily detected.

 [Comparison of Huygens and Newton theories of double refraction. ]

Why did Newton prevail?

    There is a substantial difference between Newton's treatment of interference and his treatment of the other two phenomena we have considered here. Only his description of interference may be said to anticipate the wave-particle duality of the twentieth century, while his descriptions of both diffraction and double refraction are simply corpuscular. Both of the latter parts of his theory can be, and should have been, disproved using nothing more than the experimental technology already available during Newton's life time.
    In many contexts, both in the Principia and in the Opticks, Newton would insist that he was going directly and unequivocally from data, such as the diameter of his rings, to mathematical concepts, like the fits which he counterposed to Hooke's theory of interference. It is as though this superb experimentalist and mathematician felt that the intervention of the philosopher, whose tools he dismissed as "hypotheses" was unwelcome. Hence his frequently repeated dictum I do not feign hypotheses. He was very loth to admit that he himself made as many hypotheses as his opponents, still less that they could be wrong. The attack, by Hooke, on his first presentation of the fits theory, following his election to the Royal Society in 1672, may well have been the reason why he published no more on optics until a year after the death of Hooke, when he had been elected President of that body. Certainly he exacted a terrible revenge, because under his direction all records of Hooke's extensive services to the society were then destroyed. Had Hooke been able to comment on Newton's new material in 1690, he may well have been in a position to suggest ways to test the theory of fits against his own theory of interference, thereby advancing our understanding of light by about 100 years!
    On the subject of hypotheses, Newton had a double standard. Not only did he not acknowledge that he himself made hypotheses. He also denied his opponents the luxury, which he himself indulged in, of avoiding hypotheses when their state of knowledge was inadequate. Thus, in Query 28, he quotes a passage from Huygens's Treatise concerning that author's inability to explain why two different kinds of wave, ordinary and extraordinary, should travel through calcite

But, as for how this occurs, I have found nothing until now which satisfies me.

    This modest statement is of the same quality as Newton's own, in respect of the possible causes of the gravitational interaction. Newton conceded, in a letter to Richard Bentley in the early 1690s, that something like the modern field theory of Einstein would be superior to his own hypothesis (Yes!) of instantaneous attraction, but indicated that the current state of knowledge did not allow him to make any further hypothesis.
    I. B. Cohen, in the Foreword to the 1952 edition of the Opticks, suggests that it was the underdeveloped state of the wave theory in the seventeenth century that prevented its being a real challenge to Newton. I have tried to show that the real balance of the argument was not like that. The inadequacies of the corpuscular theory were not at all far below the surface, and nearly all of the elements of the wave theory, later to be developed by Young and Fresnel, were already there by 1690. To be sure, Huygens's theory lacked the notions of periodicity and of interference, but both of these elements were present in Hooke's theory. The latter, in its turn, lacked the quantitative data which Newton kept to himself for at least 14 years. In 1704 there were gaps in both the corpuscular and wave theories, but the Opticks exaggerated the latter and ignored the former.
    Critics of a reigning theory are always told that Science is objective. All they must do to advance their cause is devise a suitable crucial experiment, which will decide the merit of their idea against the current favourite. I suggest that it was not like that, either in the seventeenth century or today. A simple experiment is suggested by my analysis of Fig.3, and another by Fig.9. It is not unreasonable to argue that Hooke's analysis, on which the one I presented (essentially that of Thomas Young) was based, was too vague. But such a plea of mitigation cannot be used in respect of Huygens's very explicit Fig.9, from which my analysis follows without any modern revisionism. There must be something else, embedded in the scientific community, which decides whether a challenging idea, even one which contains a clear experimental proposal, should be seriously examined, or simply ignored, by that community.
    Isaac Newton played a part in the dethronement of James II in 1688, when a large section of public opinion became convinced that there was a danger of the return of the absolute monarchical doctrine of Charles I, or even the Catholic bigotry of Mary Tudor. He helped to organize, in the University of Cambridge, the demand for a constitutional monarchy, and after the enthronement of William of Orange and Mary Stuart he was elected as a Member of Parliament for that constituency. From 1696 till 1712 he became a salaried servant of the Crown, first as warden and then as Master of the Royal Mint. Along with the new politics came a new theology, called latitudinarian, which set its face against Catholicism, but also against the sectarian Puritans, whom they termed Enthusiasts and who had tried to end the monarchy in 1649. The intellectuals of this latitudinarian movement grouped themselves around the series of Boyle Lectures, which ran from 1692 to 1714, and in this circle Newton reigned supreme. They declared their opposition to both the 'rude mechanicals', by which they designated the Deists who were said to believe in a 'clockwork universe', and the Cartesian rationalists, whom they caricatured as opponents of the Experimental Method — recall that Descartes had coined the phrase I think, therefore I am. This group may justly be considered to have lit the first torch of the Enlightenment, and it was destined to be taken up by Voltaire, thereby conquering also the Paris Academy of Science. And its victory entailed a diminution in the prestige, not only of Descartes himself, but of such doughty successors as Huygens and Leibniz. That, I think, is a substantial part of the reason why the wave theory of light was neglected in the eighteenth century. Light, perhaps, is the one area in which the Enlightenment failed to enlighten!
    No doubt other factors, of a more philosophical nature, also played a role in the evolution of this, as with other theories. The arguments about scientific methodology still go on, almost unchanged, up to the present day, and the debate about how interactions, electromagnetic and gravitational, are carried across space became a major theme, with Faraday and Maxwell, through the nineteenth century, and into the twentieth with Einstein. But that is another story.

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The full citation for this Article is:
Marshall, T. (2006). Wave particle duality in the seventeenth century. PHILICA.COM Article number 44.

Author comment added 2nd November, 2006 at 10:26:51

My first attempt at posting this article was unsuccessful, because I was not able to send the figures. The editors are helping me with the IT and I hope to submit an improved version shortly. I am now writing aditional material because I was told by the automatic editor that my Comment was too short! You will appreciate that my IT skills are rather limited!

Peer review added 12th November, 2006 at 10:24:21

Despite saying that your IT skills are no good, I find that your article has many diagrams, which is good!

This article is also a combination of science and history, which is an original approach.

It is also interesting to note that a person as logical as Newton, could let his rivalry with Robert Hooke get in the way of truth and science.

To Quote:”, because under his direction all records of Hooke’s extensive services to the society were then destroyed. “

It is no wonder then, that today we associate Hooke only with Hooke’s law for springs, which is a rather trivial and minor scientific topic compared with gravity, light, and optics.

Peer review added 19th December, 2006 at 22:48:16

We now know that Newton did not destroy Hooke’s records, when he succeeded Hooke as Secretary of the Royal Society. The handwritten minutes of the Royal Society as recorded by Robert Hooke were discovered in an attic and purchased early in 2006 by the Society. The ~520 yellowing and stained pages are currently being restored and recorded (including the numerous comments in the margins) to be released for general study.

The article is useful, indeed important, in pointing out how far Newton was wrong in his optical theory - correcting the idea from school physics of Newton’s Rings (showing interferance) and the colours of light (via a prism) that Newton was pre-eminent on this topic. That Newton rejected Fermat’s idea on the speed of light differing in air, glass and water - replacing it to explain refraction as acceleration of light particles at the air-water/glass interface - should be taught at school, in order to show how wrong great scientists can be.

Why did Newton’s view prevail over Fermat, Huygens and Gremaldi is an important question. Marshall suggests that it was a group around Newton who were proselytising for the Enlightenment. But why choose to follow a religious (if non-conformist) Newton who espoused a science of “laws”, rather than of principles and relationships? Compare Newton’s ‘laws’ with Fermat’s principle of least time and Huygens’s energy conservation. Surely the explanation lies more in the difficulty in discarding religious (god-the-creator) concepts or in challenging the authority of the Church.

The article makes abundant use of diagrams, which is very appropriate. Mathematical techniques were being developed at the time, particularly the maths of infinitesimals, the precursor of calculus. Huygens’s alternative (correct) wave theory of light was developed as geometrical constructions, so the diagrams are necessary to appreciate his ingenuity. Much of maths is indeed algebra, but geometry has its place that is actually more important in mathematical creativeness than generally acknowledged.

Max Wallis, Cardiff University

Peer review added 20th August, 2011 at 20:34:28

In spite of the good graphical presentation of the article its main point about Newton’s theory of light ‘corpuscles’ assimilation with photons, or the classical waves with quantum wave function is both superficial and incorrect. The classical wave theories of light have been much improved in quantum physics. Thus, using the classical wave approach one cannot readily explain the photoelectric effect, nor can one explain the well-known blackbody radiation as Planck has done. The author may benefit from reading the contributed, general article on the History of Quantum Mechanics , that also has many of the references missing from this preprint.

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