|San José State University|
& Tornado Alley
The Acceptance Speech of Louis V. de Broglie|
for the Nobel Prize in Physics for 1929
Louis de Broglie
Louis de Broglie (properly pronounced BROY) was born August 15th, 1892 in Dieppe, France and grew up living in the family manor house. His father was the 6th Duc de Broglie and Louis in the course of time became the 8th Duc de Broglie. He was a prince and as such was expected to pursue a gentlemanly career and uphold the family traditions. Louis did earn a degree in literary studies in 1910. But his older brother, Maurice, became a physicists and had the great good fortune of being able to attend the Solvay Conference where Albert Einstein and the other top physicists of the day debated the nature of reality in the formulation of Quantum Physics. Maurice related those debates to Louis and so inspired Louis that Louis pursued a degree in physics.
Louis began pondering the possibility that if the photon, the quantum of radiation, had a particle aspect as well as a wave apect then it might be that particles like electrons have a wave aspect. It was a proposition of comsmic symmetry. Louis completed a degree in physics but World War I intervened before he could devote himself to the pursuit of this bold idea. He volunteered for military service and spent the war years in Paris assisting in the development of wireless communication from the Eiffel Tower.
After the War he entered a doctoral program in physics at the University of Paris. In 1924 he presented the results of his thinking in the form of a thesis entitled "Recherches sur la Théorie des Quanta," (Research on Quantum Theory). His thesis was notable not only for the strangeness of the ideas but its shortness. Once he had examined the possible formulations for consistency he did not take much to space to present the final results. The equation he presented for the wave-length λ associated with a particle is
where h is Planck's constant and p is the momentum of the particle. De Broglie's derivation of this equation made use of concepts as the group velocity of a wave train and the Special Theory of Relativity.
His thesis was accepted and his doctoral degree granted. He soon began teaching physics first at the Sorbonne and later at the Henri Poincaré Institute. He received the Nobel Prize in Physics in 1929 after experiments by Clinton Davisson and Lester Germer published in 1927 proved his analysis to be correct. Louis de Broglie subsequently, in 1932, was made professor of theoretical physics at the University of Paris. He occupied this post the rest of his life. He died in 1962 at about 70 years of age. He never married.
Below is given the text of the speech Louis de Broglie delivered in Stockholm upon receiving the Nobel Prize in Physics in 1929,
The Undulatory Aspects of the Electron
When, in 1920, I resumed my investigations in theoretical Physics after a long interruption through circumstances out of my own control, I was far from imagining that this research would within a few years be rewarded by the lofty and coveted distinction given each year by the Swedish Academy of Sciences: the Nobel Prize in Physics. At that time what drew me towards theoretical Physics was not the hope that so high a distinction would ever crown my labours: what attracted me was the mystery which was coming to envelop more and more deeply the structure of Matter and of radiation in proportion as the strange concept of the quantum, introduced by Planck about 1900 during his research on black body radiation, came to extend over the entire field of Physics.
But to explain the way in which my research came to develop I must first outline the critical period through which Physics had for the last twenty years been passing.
Physicists had for long been wondering whether Light did not consist of minute corpuscles in rapid motion, an idea going back to the philosophers of antiquity, and sustained in the eighteenth century by Newton. After interference phenomena had been discovered by Thomas Young, however, and Augustin Fresnel had completed his important investigation, the assumption that Light had a granular structure was entirely disregarded, and the Wave Theory was unanimously adopted. In this way physicists of last century came to abandon completely the idea that Light had an atomic structure. But the Atomic Theory, being thus banished from optics, began to achieve great success, not only in Chemistry, where it provided a simple explanation of the laws of definite proportions also in pure Physics, where it enabled a fair number of the properties of solids, liquids and gases to be interpreted. Among other things it all the great kinetic theory of gases to be formulated, which, in the general form of Statistical Mechanics, has enabled clear significance to be given to the abstract concepts of thermodynamics. We have seen how decisive evidence in favour of the atomic structure of electricity was also provide experiments. Thanks to Sir J.J. Thomson, the notion of the corpuscle of electricity was introduced; and the way in which H. A. Lorentz has exploited this idea in his electron Theory is well known.
Some thirty years ago, then, Physics was divided into two camps. On the one hand there was the Physics of Matter, based on the concepts of corpuscles and atoms which were assumed to obey the classical laws of Newtonian Mechanics; on the other hand there was the Physics of radiation, based on the idea of wave propagation in a hypothetical continuous medium: the ether of Light and of electromagnetism. But these two systems of Physics could not remain alien to each other: an amalgamation had to be effected; and this was done by means of a theory of the exchange of energy between Matter and radiation. It was at this point, however the difficulties began; for in the attempt to render the two systems of Physics compatible with each other, incorrect and even impossible conclusions were reached with regard to the energy equilibrium between Matter and radiation in an enclosed and thermally isolated region: some investigators even going so far as to say that Matter would transfer all its energy to radiation, and hence tend towards the temperature of absolute zero. This absurd conclusion had to be avoided at all costs; and by a brilliant piece of intuition Planck succeeded in doing so. Instead of assuming, as did the classical Wave Theory, that a light-source emits its radiation continuously, he assumed that it emits it in equal and finite quantities -- in quanta. The energy of each quantum, still further, was supposed to be proportional to the frequency of the radiation, ν, and to be equal to hν, where h is the universal constant since known as Planck's Constant.
The success of Planck's ideas brought with it some serious consequencew, For if Light is emitted in quanta, then surely, once radiated, it ought to have a granular structure. Consequently the existence of quanta of radiation brings us back to the corpuscular conception of Light. On the hand, it can be shown--as has in fact been done by Jeans and H. Poincare--that if the motion of the material particles in a light-source obeyed the laws of classical Mechanics, we could never obtain the correct Law of black body radiation --Planck's Law. It must therefore be admitted that the older dynamics, even as modified by Einstein's Theory of Relativity cannot explain motion on a very minute scale.
The existence of a corpuscular structure of Light and of other types of radiation has been confirmed by the discovery of the photo-electric effect which, as I have already observed, is easily explained by the assumption that that the radiation consists of quanta-- hν --capable of transferring their entire energy to an electron in the irradiated, substance; and in this way we are brought to the theory of light-quanta which, as we have seen, was advanced in 1905 by Einstein--a theory which amounts to a return to Newton's corpuscular hypothesis, supplemented by the proportionality subsisting between the energy of the corpuscles and the frequency. A number of arguments were adduced by Einstein in support of his view, was confirmed by Compton's discovery in 1922 of the scattering of X-rays, a phenomenon named after him. At the same time it still remained necessary to retain the Wave Theory to explain the phenomena of diffraction and interference, and no means was apparent to reconcile this Theory with the existence of light-corpuscles.
I have pointed out that in the course of investigation some doubt been thrown on the validity of small-scale Mechanics. Let us imagine material point describing a small closed orbit--an orbit returning on itself; then according to classical dynamics there in an infinity of possible movements of this type in accordance with the initial conditions, possible values of the energy of the moving material point form a continuous series. Planck, on the other hand, was compelled to assume that only certain privileged movements--quantized motion--are possible, or at any rate stable, so that the available values of the energy form a discontinuous series. At first this seemed a very strange idea; soon, however, it had to be admitted, because it was by its means that Planck arrived at the correct Law of black body radiation and because its usefuli since been proved in many other spheres. Finally, Bohr founded his famous atomic Theory on this idea of the quantization of atomic motion--a theory so familiar to scientists that I will refrain from summing it up here.
Thus we see once again it had become necessary to assume two contradictory theories of Light, in terms of waves, and of corpuscles, respectively; while it was impossible to understand why, among the number of paths which an electron ought to be able to follow in the atom according to classical ideas, there was only a restricted number which it could pursue in fact. Such were the problems facing physicists at the when I returned to my studies.
When I began to consider these difficulties I was chiefly struck by facts. On the one hand the Quantum Theory of Light cannot be considered satisfactory, since it defines the energy of a light-corpuscle by the equation W = hν, containing the frequency ν. Now a purely corpuscular theory contains nothing that enables us to define a frequency; for this reason alone, therefore, we are compelled, in the case of Light, to introduce idea of a corpuscle and that of periodicity simultaneously.
On the other hand, determination of the stable motion of electrons in the atom introduces integers; and up to this point the only phenomena involving integers in Physics were those of interference and of normal modes of vibration. This fact suggested to me the idea that electrons too could not be regarded simply as corpuscles, but that periodicity must be assigned to them also.
In this way, then, I obtained the following general idea, in accordance with which I pursued my investigations:--that it is necessary in the case of Matter, as well as of radiation generally and of Light in particular, to introduce the idea of the corpuscle and of the wave simultaneously: or in other words, in the one case as well as in the other, we must assume existence of corpuscles accompanied by waves. But corpuscles and waves cannot be independent of each other: in Bohr's terms, they are two complementary aspects of Reality: and it must consequently be possible to establish a certain parallelism between the motion of a corpuscle am propagation of its associated wave. The first object at which to aim, therefore, was to establish the existence of this parallelism.
With this in view, I began by considering the simplest case: that of an isolated corpuscle, i.e. one removed from all external influence; with this we wish to associate a wave. Let us therefore consider first of all a refer system 0 x0y0z0 in which the corpuscle is at rest: this is the "proper" system for the corpuscle according to the Theory of Relativity. Within such a system the wave will be stationary, since the corpuscle is at rest; its phase will be the same at every point, and it will be represented by an expression of the form
0(t0−τ0), t0 being the "proper" time of the corpuscle, and τ0, a constant.
According to the principle of inertia the corpuscle will be in uniform rectilinear motion in every Galilean system. Let us consider such a Galilean system, and let v be the velocity of the corpuscle in this sy Without loss of generality, we may take the direction of motion to h axis of x. According to the Lorentz transformation, the time t employed by an observer in this new system is linked with the proper time t0 by the relation:
t0 = (t − βx/c)/(1−β²)½
where β = v/c.
Hence for such an observer the phase of the wave will be given by
sin (2π/(1−β²)½)(t − βx/c − τ0)).
Consequently the wave will have for him a frequency of
ν = ν0/(1−β²)½
and will move along the axis of x with the phase-velocity
V = c/β = c²/v
If we eliminate β from the two preceding formulae we shall easiy find the following relation, which gives the index of refraction of free space for the waves under consideration
n = (1−ν²0/ν²)½
To this "law of dispersion" there corresponds a "group velocity." You are aware that the group velocity is the velocity with which the resultant amplitude of a group of waves, with almost equal frequencies, is propagated. Lord Rayleigh has shown that this velocity U satisfies the equation
1/U = (1/c)(d(nν)/dν
Here we find that U = v, which means that the velocity of the waves in the system x y z t is equal to the velocity of the corpuscle system. This relation is of the greatest importance for the develoment of the Theory.
Accordingly, in the system x y z t the corpuscle is defined by the frequency ν and by the phase-velocity V of its associated wave. In order to establish the parallelism mentioned above, we must try to connect these magnitudes to the mechanical magnitudes--to energy and momentum. The ratio between energy and frequency is one of the most characteristic relations of the Quantum Theory; and since, still further, energy and frequency are transformed when the Galilean system of reference is changed, it is natural to establish the equation
Energy = h × frequency,
or W = hν
where h is Planck's constant. This relation must apply to all Galilean systems; and in the proper system of the corpuscle where, according to Einstein, the energy of the corpuscle is reduced to its internal energy (where m, is its proper mass) we have hν0 = m0c².
This relation gives the frequency ν0 as a function of the proper mass m0, or inversely. v
The momentum is a vector p equal to m0v/(1−β²)½, where |v|=v, and then we have
p = |p| = m0v/(1−β²)½ = Wv/c² = hν/V = h/λ
The quantity λ is the wave-length--the distance between two consecutive wave-crests, hence
λ = h/p
This is a fundamental relation of the Theory.
All that has been said refers to the very simple case where there is no field of force acting on the corpuscle. I shall now indicate very briefly how the Theory can be generalized for the case of a corpuscle moving in a field of force not varying with time derived from a potential energy function F(x,y,z). Arguments into which I shall not enter here lead us in such a case to assume that the propagation of the wave corresponds to an index of refraction varying from point to point in space in accordance with the formula
n(x,y,z) = [(1−F(x,y,z)/(hν))² − ν0²/ν²] ½
or, as a first approximation, if we neglect the corrections introduced by the Theory of Relativity
n(x,y,z) = [2(E−F)/(m0c²)]½ with E=W−m0c²
The constant energy W of the corpuscle is further connected with the constant frequency ν of the wave by the relation
W = hν
while the wave-length λ, which varies from one point to the other in the field of force, is connected with the momentum p (which is also variable) by the relation
λ(x,y,z) = h/p(x,y,z)
Here again we show that the velocity of the wave-group is equal to the velocity of the corpuscle. The parallelism thus established between the corpuscle and its wave enables us to identify Fermat's Principle in the case of waves and the Principle of Least Action in that of corpuscles, for constant fields. Fermat's Principle states that the ray in the optical sense ing between two points A and B in a medium whose index is n(x,y,z), variable from one point to the other but constant in time, is such that the integral ∫ABndl, taken along this ray, shall be an extremum. On the other hand, Maupertuis' Principle of Least Action asserts that the trajectory of a corpuscle passing through two points A and B is such that the integral ∫ABpdl taken along the trajectory shall be an extremum, it being understood that we are considering only the motion corresponding to a given value of energy. According to the relations already established between the mechanical and the wave magnitudes, we have
n = c/V = (c/ν)(1/λ)
= (c/hν)(h/λ) = (c/w)p = constant × p
since W is constant in a constant field. Hence it follows that Fermat' Principle and Maupertuis' Principle are each a rendering of the other: possible trajectories of the corpuscle are identical with the possible rays ofb its wave.
These ideas lead to an interpretation of the conditions of stability introduced by the Quantum Theory. If we consider a closed trajectory C [in] a constant field, it is quite natural to assume that the phase of the associated wave should be a uniform function along this trajectory. This leads us to write
∫Cdl/λ = ∫C(1/h)pdl
Now this is exactly the condition of the stability of atomic periodic motion, according to Planck. Thus the quantum conditions of stability appear as analogous to resonance phenomena, and the appearance of integers here becomes as natural as in the theory of vibrating cords and discs.
The general formulae establishing the parallelism between waves and corpuscles can be applied to light-corpuscles if we assume that in that case the rest-mass m, is infinitely small. If then for any given value of the energy W we make m0, tend to zero, we find that both v and V tend to c, and in the limit we obtain the two fundamental formulae on which Einstein erected his Theory of Light-quanta
W = hν
p = hν/c
Such were the principal ideas which wwwwwwwwwwwwwww developed during my earlier researches. They showed clearly that it was possible to establish a correspondence between waves and corpuscles of such a kind that the Laws of Mechanics correspond to those of geometrical optics. But we know that in the Wave Theory geometrical optics is only an approximation: there are limits to the validity of this approximation, and especially when the phenomena of interference and of diffraction are concerned it is wholly inadequate. This suggests the idea that the older Mechanics too may be no more than an approximation as compared with a more comprehensive Mechanics of an undulatory character. This was what I expressed at the beginning of my researches when I said that a new Mechanics must be formulated, standing in the same relation to the older Mechanics as that in which wave optics stands to geometrical optics. This new Mechanics has since been developed, thanks in particular to the fine work done by Schrodinger. It starts from the equations of wave propagation, which are taken as the basis, and rigorously determines the temporal changes of the wave associated with a corpuscle. More particularly, it has succeeded in giving a new and more satisfactory form to the conditions governing the quantization of intra-atomic motion: for, as we have seen, the older conditions of quantization are encountered again if we apply geometrical optics to the waves associated with intra-atomic corpuscles; and there is strictly no justification for this application.
I cannot here trace even briefly the development of the new Mechanics. All that I wish to say is that on examination it has shown itself to be identical with a Mechanics developed independently, first by Heisenberg and later by Born, Jordan, Pauli, Dirac and others. This latter Mechanics-- Quantum Mechanics--and Wave Mechanics are, from the mathematical point of view, equivalent to each other.
Here we must confine ourselves to a general consideration of the results obtained. To sum up the significance of Wave Mechanics, we can say that a wave must be associated with each particle, and that a study of the propagation of the wave alone can tell us anything about the successive localizations of the corpuscle in space. In the usual large-scale mechanical phenomena, the localizations predicted lie along a curve which is the trajectory in the classical sense of the term. What, however, happens if the wave is not propagated according to the laws of geometrical optics; if, for example, interference or diffraction occurs? In such a case we can no longer assign to the corpuscle motion in accordance with classical dynamics. So much is certain. But a further question arises: Can we suppose that at any given moment the corpuscle has an exactly deterrmined position within the wave, and that in the course of its propagation the wave carries the corpuscle with it, as a wave of water would carry a cork? These are difficult questions, and their discussion would carry us too far and actually to the borderland of Philosophy. All that I shall say he that the general modern tendency is to assume that it is not always possible to assign an exactly defined position within the wave to the corpuscle, that whenever an observation is made enabling us to localize the corpuscle, we are invariably led to attribute to it a position inside the wave, and that the probability that this position is at a given point, M, within the wave is proportional to the square of the amplitude, or the intensity, at M.
What has just been said can also be expressed in the following way. If we take a cloud of corpuscles all associated with the same wave, then the intensity of the wave at any given point is proportional to the density of the cloud of corpuscles at that point, i.e. to the number of corpuscle per unit of volume around that point. This assumption must be made in order to explain how it is that in the case of interference the luminous energy is found concentrated at those points where the intensity of the wave is at a maximum: if it is assumed that the luminous energy is transferred by light-corpuscles, or photons, then it follows that the density of the photons in the wave is proportional to this intensity.
This rule by itself enables us to understand the way in which the undulatory theory of the electron has been verified experimentally.
For let us imagine an indefinite cloud of electrons, all having the same velocity and moving in the same direction. According to the fundamental ideas of Wave Mechanics, we must associate with this cloud an infinite plane wave having the form
a·exp(2πi[(W/h)t − (αx+βy+γz )/λ])
where α, β, γ are the direction cosines of the direction of propagation, and where the wave-length λ is equal to (h/p).
where the wave-length λ is equal to (h/p). If the electrons have no extremely high velocity, we may say
p = m0v
λ = h/(m0ν)
m0 being the rest-mass of the electron.
In practice, to obtain electrons having the same velocity they are subjected to the same potential difference P. We then have
½m0v² = eP
λ = h/(2m0eP)½
Numerically, this gives
λ = (12·24/P½·10-8 cm.) (P in volts).
As we can only use electrons that have fallen through a potential difference of at least some tens of volts, it follows that the wave-length λ, assure by the Theory, is at most of the order of 10-8 cm., i.e. of the order of the Ångstrom unit. This is also the order of magnitude of the wave-lengths of X-rays.
The length of the electron wave being thus of the same order as that of X-rays, we may fairly expect to be able to obtain a scattering of this wave by crystals, in complete analogy to the Laue phenomenon in which, in a natural crystal like rock salt, the atoms of the substances composing the crystal are arranged at regular intervals of the order of one Angstrom, thus act as scattering centres for the waves. If a wave having a length of one Angstrom encounters the crystal, then the waves scattered agree in phase in certain definite directions. In these directions the total intensity scattered exhibits a strong maximum. The location of these maxima of scattering is given by the well known mathematical Theory elaborated by Laue and Bragg, which gives the position of the maxima in terms of the distance between the atomic arrangements in the crystal and of the length of the incident wave. For X-rays the Theory has been triumphantly substantiated by Laue, Friedrich and Knipping, and today the diffraction of X-rays by crystals has become a quite commonplace experiment. The exact measurement of the wave-lengths of X-rays is based on this diffraction, as I need hardly recall in a country where Siegbahn and his collaborators are pursuing their successful labours.
In the case of X-rays, the phenomenon of diffraction by crystals was a natural consequence of the idea that these rays are undulations analogous to Light, and differ from Light only by their shorter wave-length. But for electrons no such view could be entertained, so long as the latter were looked upon as being merely minute corpuscles. If, on the other hand, we assume that the electron is associated with a wave, and that the density of a cloud of electrons is measured by the intensity of the associated wave, we may then expect that there will be effects in the case of electrons similar to the Laue effect. In that event, the electron wave will be scattered with an intensity in certain directions which the Laue-Bragg Theory enables us to calculate, on the assumption that the wave-length is λ = h/(mv), a length corresponding to the known velocity v of the electrons falling on the crystal. According to our general principle, the intensity of the scattered wave measures the density of the cloud of scattered electrons, so that we may expect to find large numbers of scattered electrons in the directions of the maxima. If this effect actually occurs, it would provide a crucial experimental proof of the existence of a wave associated with the electron, its length being h/(mv). In this way the fundamental idea of Wave Mechanics would be provided with a firm experimental foundation.
Now experiment�which is the last Court of Appeal of theorie--has shown that the diffraction of electrons by crystals actually occurs, and that it follows the Laws of Wave Mechanics exactly and quantitatively. It is (as we have seen already) to Davisson and Germer, working at Bell Laboratories in New York, that the credit belongs of having been the first to observe this phenomenon by a method similar to that used by Laue for X-rays. Following up the same experiments, but substituting for the single crystal a crystalline powder, in accordance with the method introduced for X-rays by Debye and Scherrer, Professor G. P. Thomson, of Aberdeen, the son of the great Cambridge physicist, Sir J. J. Thomson, has discovered the same phenomena. At a later stage Rupp in Germany, Kikuchi in Japan and Ponte in France have also reproduced them under varying experimental conditions. Today the existence of the effect is no longer subject to doubt, and the minor difficulties of interpretation which Davisson's and Germer's earlier experiments had raised have been resolved in a satisfactory manner. Rupp has actually succeeded in obtaining the diffraction of electrons in a particularly striking form. A grating is employed--a metal or glass surface, either plane or slightly curved, on which equidistant lines have been mechanically drawn, the interval between them being of an order of magnitude comparable to that of the wave-lengths of Light. Between the waves diffracted by these lines there will be interference, and the interference will give rise to maxima of diffracted Light in certain directions depending on the distance between the lines, on the direction of the Light falling on the grating and on the wave-lengths. For a long time it remained impossible to obtain similar effects with gratings of this kind produced by human workmanship when X-rays were used instead of Light. The reason for this was that the wave-length of X-rays is a great deal shorter than that of Light, and that there is no instrument capable drawing lines on any surface at intervals of the order of X-ray wave-lengths lengths. InIngenious physicists, however (Compton and Thibaud), succeeded in overcoming the difficulty. Let us take an ordinary optical grating and let us look at it more or less at a tangent. The lines of the grating will then seem to be much closer together than they actually are. For X-rays falling on the grating at this grazing angle, the conditions will be the same as though the lines were extremely close together, and diffraction effects like those of Light will be produced. The physicists just mentioned have proved that such was in fact the case. But now--since the electron wave-lengths are of the same order as those of X-rays--we should also be able to obtain these diffraction phenomena by causing a beam of electrons, to fall on such an optical grating at a very small grazing angle. Rupp succeeded in doing this. He was thus enabled to measure the length of electron waves by comparing it directly with the distance between the lines drawn mechanically on the grating.
We thus find that in order to describe the properties of Matter, as well as those of Light, we must employ waves and corpuscles simultaneously We can no longer imagine the electron as being just a minute corpuscle of electricity: we must associate a wave with it. And this wave is not just a fiction: its length can be measured and its interferences calculated in advance. In fact, a whole group of phenomena was in this way predicted before being actually discovered. It is, therefore, on this idea of the dualism in Nature between waves and corpuscles, expressed in a more or less abstract form, that the entire recent development of theoretical Physics has been built up, and that its immediate future development appears likely to be erected.