Utilisateur:Simon Villeneuve/Sur un point de vue heuristique concernant la production et la transformation de la lumière

On a Heuristic Point of View about the Creation and Conversion of Light by Albert Einstein, translated by Wikisource		D'un point de vue heuristique sur la création et la conversion de lumière par Albert Einstein en allemand (1905), traduit en anglais par la Wikisource en anglais (2011)
Maxwell's theory of electromagnetic processes in so-called empty space differs in a profound, essential way from the current theoretical models of gases and other matter. On the one hand, we consider the state of a material body to be determined completely by the positions and velocities of a finite number of atoms and electrons, albeit a very large number. By contrast, the electromagnetic state of a region of space is described by continuous functions and, hence, cannot be determined exactly by any finite number of variables. Thus, according to Maxwell's theory, the energy of purely electromagnetic phenomena (such as light) should be represented by a continuous function of space. By contrast, the energy of a material body should be represented by a discrete sum over the atoms and electrons; hence, the energy of a material body cannot be divided into arbitrarily many, arbitrarily small components. However, according to Maxwell's theory (or, indeed, any wave theory), the energy of a light wave emitted from a point source is distributed continuously over an ever larger volume.		La théorie de Maxwell des processus électromagnétiques dans le soi-disant vide diffère d'une façon profonde des modèles théoriques actuels des gaz et d'autre matière. D'un côté, nous considérons l'état d'un corps matériel comme étant entièrement déterminé par la position et la vélocité d'un nombre fini d'atomes et d'électrons, même s'il s'agit d'un nombre très grand. Au contraire, l'état électromagnétique d'une région de l'espace est décrite par des fonctions continues et, donc, ne peut être déterminée exactement par un nombre fini de variables. Donc, selon la théorie de Maxwell, l'énergie des phenomènes purement électromagnétiques (comme la lumière) devraient être représentée par une somme discrète sur les atomes et les électrons;donc, l'énergie d'un corps matériel ne peut être divisé en un nombre arbitraire de parties arbitrairement petites. Par contre, selon la théorie de Maxwell (ou, en fait, n'importe quelle théorie des ondes), l'énergie d'une onde lumineuse émise par une source ponctuelle est distribuée continuellement dans un volume grandissant.
The wave theory of light with its continuous spatial functions has proven to be an excellent model of purely optical phenomena and presumably will never be replaced by another theory. Nevertheless, we should consider that optical experiments observe only time-averaged values, rather than instantaneous values. Hence, despite the perfect agreement of Maxwell's theory with |[ 133 ] experiment, the use of continuous spatial functions to describe light may lead to contradictions with experiments, especially when applied to the generation and transformation of light.		La théorie ondulatoire de la lumière, avec ses fonctions continues dans l'espace s'est révélée être un excellent modèle pour les phénomènes purement optiques et ne sera vraisemblablement jamais remplacée par une autre théorie. Pourtant, nous devons considérer que les expériences d'optique n'observent que des valeurs moyennes dans le temps, plutôt que des valeurs instantanées. En conséquence, malgré un accord parfait de la théorie de Maxwell avec l'expérience, l'utilisation de fonctions continues pour décrire la lumière pourrait mener à des contradictions avec les expériences, en particulier lorsqu' appliquées à la génération et à la transformation de lumière.
Subsequently, I wish to explain the reasoning and supporting evidence that led me to this picture of light, in the hope that some researchers may find it useful for their experiments.		Subséquemment, je tiens à expliquer le raisonnement et les preuves qui m'ont conduit à cette image de lumière, avec l'espoir que des chercheurs puissent la trouver utile pour leurs expériences.
In particular, black body radiation, photoluminescence, generation of cathode rays from ultraviolet light and other phenomena associated with the generation and transformation of light seem better modeled by assuming that the energy of light is distributed discontinuously in space. According to this picture, the energy of a light wave emitted from a point source is not spread continuously over ever larger volumes, but consists of a finite number of energy quanta that are spatially localized at points of space, move without dividing and are absorbed or generated only as a whole.		En particulier, la radiation de corps noirs, la photoluminescence, la génération de rayons cathodiques provenant de lumière ultraviolette ainsi que d'autres phénomènes associés à la génération et la transformation de la lumière semble mieux lorsque combinés en assumant que l'énergie de la lumière est distribuée de façon discontinue dans l'espace. Selon cette image, l'énergie d'une onde lumineuse émise d'une source ponctuelle «n'est pas» distribuée continuellement dans un volume grandissant, mais est composée d'un nombre défini de quantas énergétiques qui sont spatialement localisés à des points de l'espace, bougent sans se diviser et sont absorbés ou générés seulement dans un ensemble.

Un problème particulier à propos de la théorie du rayonnement de corps noir

A certain problem concerning the theory of "black body radiation".		Un problème particulier à propos de la théorie du rayonnement de corps noir
We begin by applying Maxwell's theory of light and electrons to the following situation. Let there be a cavity with perfectly reflecting walls, filled with a number of freely moving electrons and gas molecules that interact via conservative forces whenever they come close, i.e., that collide with each other just as gas molecules in the kinetic theory of gases.[1] |[ 134 ] In addition, let there be a number of electrons bound to spatially well-separated points by restoring forces that increase linearly with separation. These electrons also interact with the free molecules and electrons by conservative potentials when they approach very closely. We denote these electrons, which are bound at points of space, as "resonators", since they absorb and emit electromagnetic waves of a particular period.		Commençons par appliquer la théorie de la lumière et des électrons de Maxwell à la situation suivante. Soit une cavité aux parois parfaitement réfléchissantes rempli d'un certain nombre d'électrons et de molécules gazeuses se déplaçant librement et qui interagissent par des forces statiques lorsqu'ils et qu'elles se rapprochent c'est-à-dire, qui entrent en collision les un(es) avec les autres tout comme dans la théorie cinétique des gaz. [2] |[ 134 ] De plus, soit un certain nombre d'électrons liés à des points bien séparés dans l'espace par des forces constructrices qui augmentent de façon linéaire lorsqu'on les séparent. Ces électrons interagissent aussi avec les électrons libres et les molécules libres par des potentiels statiques lorsqu'ils s'approchent de très près. On note ces électrons, lesquels sont reliés à des points de l'espace, comme étant des "résonateurs" puisqu'ils absorbent et émettent des ondes électromagnétiques durant une certaine période.
According to the present theory of the generation of light, the radiation in the cavity must be identical to black body radiation (which may be found by assuming Maxwell's theory and dynamic equilibrium), at least if one assumes that resonators exist for every frequency under consideration.		Selon la présente théorie de la production de la lumière, le rayonnement dans la cavité doit être identique au rayonnement d'un corps noir (lequel peut être trouvé en supposant la théorie de Maxwell et de l'équilibre dynamique), au moins si l'on suppose que les résonateurs existent pour chaque fréquence considérée.
Initially, let us neglect the radiation absorbed and emitted by the resonators and focus instead on the requirement of thermal equilibrium and its implications for the interaction (collisions) between molecules and electrons. According to the kinetic theory of gases, dynamic equilibrium requires that the average kinetic energy of a resonator equal the average kinetic energy of a freely moving gas molecule. Decomposing the motion of a resonator electron into three mutually perpendicular oscillations, we find that the average energy ${\bar {E}}$ of such a linear oscillation is		Initialement, négligeons la radiation absorbée et émise par les résonateurs et concentrons-nous au lieu sur les contraintes de l’équilibre thermal et de ses implications pour les interactions (collisions) entre molécules et électrons. Selon la théorie cinétique des gazes, l’équilibre dynamique requiert une moyenne d’énergie cinétique d’un résonateur égal à l’énergie cinétique d’une particule de gaz libre. En décomposant le mouvement d’un électron à résonateur en trois oscillations perpendiculaires, nous trouvons que la moyenne d’énergie${\bar {E}}$ d’une telle oscillation linéaire est
:${\bar {E}}={\frac {R}{N}}T,$		:${\bar {E}}={\frac {R}{N}}T,$
where R is the absolute gas constant, N is the number of "real molecules" in a gram equivalent and T is the absolute temperature. Because of the time averages of the kinetic and potential energy, the energy ${\bar {E}}$ is ⅔ as large as the kinetic energy of a single free gas molecule. Even if something (such as radiative processes) causes the time-averaged energy of a resonator to deviate from the value ${\bar {E}}$, collisions with the free electrons |[ 135 ] and gas molecules will return its average energy to ${\bar {E}}$ by absorbing or releasing energy. Hence, in this situation, dynamic equilibrium can only exist when every resonator has an average energy ${\bar {E}}$.		TRADUCTION ICI.
We apply a similar consideration now to the interaction between the resonators and the ambient radiation within the cavity. For this case, Planck has derived the necessary condition for dynamic equilibrium [3]; treating the radiation as a completely random process.[4]		On applique une considération similaire maintenant à l'interaction entre les résonateurs et la radiation ambiante à l'intérieur de la cavité. Pour ce cas, Plank a dérivé les conditions nécessaires à l'équilibre dynamique[5]; traitant la radiation comme un processus complètement aléatoire.[6]
:$Z=\sum \limits _{\nu =1}^{\nu =\infty }A_{\nu }sin\left(2\pi \nu {\frac {t}{T}}+\alpha _{\nu }\right)\ ,$		:$Z=\sum \limits _{\nu =1}^{\nu =\infty }A_{\nu }sin\left(2\pi \nu {\frac {t}{T}}+\alpha _{\nu }\right)\ ,$
where $A_{\nu }\geqq 0$ and $0\leqq a_{\nu }\leqq 2\pi$.		où $A_{\nu }\geqq 0$ et $0\leqq a_{\nu }\leqq 2\pi$.
Performing this expansion arbitrarily often with arbitrarily chosen initial times yields a range of different combinations for the quantities Aν and αν. Then for the frequencies of the different combinations of the quantities Aν and αν there are the (statistical) probabilities dW of the form:		L'execution de cette expansion se produit souvent arbitrairement et à des temps initiaux arbitraires eux aussi et cela donne une série de combinaisons différentes de la quantité de Aν et de αν.Donc pour les fréquences des différentes combinaisons des quantités Aν et αν il y a une probabilité (statistique) dW de la forme :
:$dW=f(A_{1}\ A_{2},\dots \alpha _{1}\ \alpha _{2}\dots )dA_{1}dA_{2},\dots d\alpha _{1}\ d\alpha _{2}\dots$		:$dW=f(A_{1}\ A_{2},\dots \alpha _{1}\ \alpha _{2}\dots )dA_{1}dA_{2},\dots d\alpha _{1}\ d\alpha _{2}\dots$
The radiation is then as unordered as imaginable, if		La radiation est ensuite aussi désordonnée qu'imaginable, si
:$f(A_{1},A_{2}\ \dots \alpha _{1},\alpha _{2}\dots )=F_{1}(A_{1})F_{2}(A_{2})\dots f_{1}(\alpha _{1}).f_{2}(\alpha _{2})\dots$		:$f(A_{1},A_{2}\ \dots \alpha _{1},\alpha _{2}\dots )=F_{1}(A_{1})F_{2}(A_{2})\dots f_{1}(\alpha _{1}).f_{2}(\alpha _{2})\dots$
That is if the probability of a particular value of A and α respectively is independent of the value of other values of A and x respectively. The more closely the demand is satisfied that the separate pairs of values Aν and αν depend on the emission and absorption process of separate resonators, the more closely will the examined case be one of being as unordered as imaginable.</ref>		Ça c'est seulement si la probabilité d'une valeur particulière de A et α sont indépendante des valeurs des autres valeurs de A et x. Le plus près les demandes sont satisfaites des paires séparé des valeurs Aν et αν dépendent de la procédure démission et de d’absorption de résonateur séparer, le plus près vont être les cas l'un de l'autre plus il vont être non ordonnée.
He found:		Il a trouvé:
:${\bar {E}}_{\nu }={\frac {L^{3}}{8\pi \nu ^{2}}}\rho _{\nu }.$		:${\bar {E}}_{\nu }={\frac {L^{3}}{8\pi \nu ^{2}}}\rho _{\nu }.$
Here, ${\bar {E}}_{\nu }$ is the average energy of a resonator of eigenfrequency ν (per oscillatory component), L is the speed of light, ν is the frequency, and ρνdν is the energy density of the cavity radiation of frequency between ν and ν + dν.		TRADUCTION ICI
|[ 136 ] If the net radiative energy of frequency ν is not to continually increase or decrease, the following equality must hold		Si l'énergie radiative nette de fréquence ν n'augmente ou ne diminue pas constamment, l'égalité suivante doit être tenue
:${\frac {R}{N}}T={\bar {E}}={\bar {E}}_{\nu }={\frac {L^{3}}{8\pi \nu ^{2}}}\rho _{\nu },$		:${\frac {R}{N}}T={\bar {E}}={\bar {E}}_{\nu }={\frac {L^{3}}{8\pi \nu ^{2}}}\rho _{\nu },$
or, equivalently,		ou, de façon équivalente,
:$\rho _{\nu }={\frac {R}{N}}{\frac {8\pi \nu ^{2}}{L^{3}}}T.$		:$\rho _{\nu }={\frac {R}{N}}{\frac {8\pi \nu ^{2}}{L^{3}}}T.$
This condition for dynamic equilibrium not only lacks agreement with experiment, it also eliminates any possibility for equilibrium between matter and aether. The wider the range of frequencies of the resonators is chosen the bigger the radiation energy in the space becomes, and in the limit we obtain:		Cette condition pour l'équilibre dynamique ne manque pas seulement de sens comparativement à l'expérience, elle élimine aussi toute possibilité d'atteindre l'équilibre en la matière et l'éther. Plus large est la gamme de fréquences des résonateurs choisie, plus grosse l'énergie de radiation dans l'espace devient, et à la limite on obtient:
:$\int _{0}^{\infty }\rho _{\nu }\,d\nu ={\frac {R}{N}}{\frac {8\pi }{L^{3}}}T\int _{0}^{\infty }\nu ^{2}\,d\nu =\infty \ .$		TRADUCTION ICI.

Description de Planck du quantum fondamental

Planck's Derivation of the Fundamental Quantum		Description de Planck du quantum fondamental
In the next section we want to show that the determination that Mr. Planck gave of the elementary quanta is to some extent independent of the "black body radiation" theory that he created.		Dans la prochaine section
The Formula by Planck [7] for ρν that suffices for all experiments so far goes		TRADUCTION ICI
:$\rho _{\nu }={\cfrac {\alpha \nu ^{3}}{e^{\cfrac {\beta \nu }{T}}-1}},$		TRADUCTION ICI
where		TRADUCTION ICI
: $\alpha =6.1\cdot 10^{-56},$ $\beta =4.866\cdot 10^{-11}.$		TRADUCTION ICI
In the limit of large values of T/ν, that is for large wavelengths and radiation densities this formula approaches the form:		Dans la limite des nombreuses valeurs de T/ν, qui est pour les grandes longueurs d'ondes et les densités de radiation, cette formule s'approche de la forme:
:$\rho _{\nu }={\frac {\alpha }{\beta }}\nu ^{2}T.$		:$\rho _{\nu }={\frac {\alpha }{\beta }}\nu ^{2}T.$
|[ 137 ] One recognizes that this formula is the same as the one that was derived from Maxwell theory and electron theory. Equating the coefficients of the formula's:		On reconnait que cette formule est la même que celle qui a été dérivée de Maxwell theory and electron theory. Équivalant les coefficients des formules:
:${\frac {R}{N}}{\frac {8\pi }{L^{3}}}={\frac {\alpha }{\beta }}$		${\frac {R}{N}}{\frac {8\pi }{L^{3}}}={\frac {\alpha }{\beta }}$
or		Ou
:$N={\frac {\beta }{\alpha }}{\frac {8\pi R}{L^{3}}}=6.17\cdot 10^{23},$		:$N={\frac {\beta }{\alpha }}{\frac {8\pi R}{L^{3}}}=6.17\cdot 10^{23},$
that is, a hydrogen atom weighs 1/N gram = 1.62·10-24g. This is precisely the value found by Mr. Planck, which is in satisfactory agreement with values obtained in other ways.		C'est à dire, qu'un atome d'hydrogène pèse 1/N gram = 1.62·10-24g.C'est précisément la valeur trouvée par Mr. Planck, ce qui est en accord satisfaisant avec les valeurs obtenues par différentes méthodes.
This brings us to the conclusion: the larger the energy density and the wavelength of radiation the more suitable the theoretical basis that we used; but for small wavelengths and low radiation densities the basis fails completely.		TRADUCTION ICI
In the following the "black body radiation" is to be considered in terms of what is experienced, without forming a picture of the creation and propagation of the radiation.		TRADUCTION ICI

The Entropy of Radiation		L'entropie du rayonnement
The following discussion is contained in a famous work of Mr. Wien, and is only included here for the sake of completeness.		TRADUCTION ICI
Let there be radiation taking up volume v. We assume that the observable properties of the radiation are determined completely when the radiation densities ρ(ν) are given for all frequencies. [8] Since we can regard radiations of different frequency as separable without doing work or transferring heat the entropy of the radiation can be expressed in the form		Attribuons le volume v à une radiation. Nous assumons que les propriétés observables de cette radiation sont complètement déterminées quand les densités de radiation ρ(ν) sont connues pour toutes les fréquences. [9] Depuis que nous pouvons considérer les radiations de différentes fréquences comme séparables sans effectuer de travail ou de transfert de chaleur, l'entropie de la radiation peut être exprimée sous la forme
:$S=v\int \limits _{0}^{\infty }\phi (\rho ,\nu )d\nu$		:$S=v\int \limits _{0}^{\infty }\phi (\rho ,\nu )d\nu$
where φ is a function of the variables ρ and ν. |[ 138 ] φ can be reduced to a function of only one variable by expressing that the entropy of radiation between reflecting walls is not changed by adiabatic compression. We won't go into that however, but investigate right away how the function φ can be obtained from the radiation law of the black body.		où φ est une fonction des variables ρ et ν.|[ 138 ] φ peut être réduit à une fonction d'une seule variable en exprimant que l'entropie de radiation entre des parois réfléchissantes n'est pas modifiée par la compression adiabatique. Par contre, nous n'allons pas approfondir cette notion, mais plutôt tout de suite rechercher comment la fonction φ peut être obtenue à partir de la loi de radiation des corps noirs.
In the case of "black body radiation" ρ is such a function of ν that for a given energy the entropy is a maximum, that is, that		TRADUCTION ICI
:$\delta \int \limits _{0}^{\infty }\phi (\rho ,\nu )d\nu =0,$		TRADUCTION ICI
When		TRADUCTION ICI
:$\delta \int \limits _{0}^{\infty }\rho d\nu =0.$		TRADUCTION ICI
From this it follows that for any choice of δρ as function of ν		TRADUCTION ICI
:$\int \limits _{0}^{\infty }\left({\frac {\partial \phi }{\partial \rho }}-\lambda \right)\delta \rho d\nu =0,$		TRADUCTION ICI
Where λ is independent of ν. Thus $\partial \phi /\partial \rho$ is independent of ν		TRADUCTION ICI
For the temperature increase of dT of a black body radiation of volume v = 1 the following equation is valid:		TRADUCTION ICI
:$dS=\int \limits _{\nu =0}^{\nu =\infty }{\frac {\partial \phi }{\partial \rho }}d\rho d\nu ,$		TRADUCTION ICI
or, since $\partial \phi /\partial \rho$ is independent of ν:		TRADUCTION ICI
:$dS={\frac {\partial \phi }{\partial \rho }}dE.$		TRADUCTION ICI
Since dE is equal to the transferred heat, and the process is reversible we also have:		TRADUCTION ICI
:$dS={\frac {1}{T}}dE.$		TRADUCTION ICI
Equating formulas gives:		TRADUCTION ICI
:${\frac {\partial \phi }{\partial \rho }}={\frac {1}{T}}.$		TRADUCTION ICI
This is the black body radiation law. So it's |[ 139 ] possible to determine the black body radiation from the function φ. Conversely, through integration one can obtain φ from the black body radiation law keeping in mind that φ vanishes for ρ = 0.		TRADUCTION ICI

Limiting law for the entropy of monochromatic radiation at low radiation density

Limiting law for the entropy of monochromatic radiation at low radiation density		?
Admittedly, the observations of "black body radiation" so far indicate that the law that Mr. Wien originally devised for the "black body radiation"		TRADUCTION ICI
:$\rho =\alpha \nu ^{3}e^{-\beta {\tfrac {\nu }{T}}}$		TRADUCTION ICI
is not exactly valid. However, for large values of ν/T experiment completely confirms the law. We shall base our calculations on this formula, keeping in mind that the results will be valid within certain limitations only.		TRADUCTION ICI
First, we get from this equation:		TRADUCTION ICI
:${\frac {1}{T}}=-{\frac {1}{\beta \nu }}\lg {\frac {\rho }{\alpha \nu ^{3}}}$		TRADUCTION ICI
and then, using the relation obtained in the preceding section:		TRADUCTION ICI
:$\phi (\rho ,\nu )=-{\frac {\rho }{\beta \nu }}\left\{\lg {\frac {\rho }{\alpha \nu ^{3}}}-1\right\}.$		TRADUCTION ICI
Let there be a radiation of energy E, with a frequency between ν and ν + dν. Let the radiation extend over volume v. The entropy of this radiation is:		TRADUCTION ICI
:$S=v\phi (\rho ,\nu )d\nu =-{\frac {E}{\beta \nu }}\left\{\lg {\frac {E}{v\alpha \nu ^{3}d\nu }}-1\right\}.$		TRADUCTION ICI
We will limit ourselves to investigating the dependency of the radiation's entropy on the volume that is occupied. Let the entropy of the radiation be called S0 when it occupies the volume v0, then we get:		TRADUCTION ICI
:$S-S_{0}={\frac {E}{\beta \nu }}\lg \left({\frac {v}{v_{0}}}\right).$		TRADUCTION ICI
This equation shows that the entropy of monochromatic radiation of sufficiently low density varies with volume according to the same law as the entropy of an ideal gas or that of a dilute solution. |[ 140 ] In the following the equation just found will be interpreted in terms of the principle introduced by Mr. Boltzmann that says that the entropy of a system is a function of the probability of its state.		Cette équation

Molecular Theoretical investigation of the Volume Dependence of the Entropy of Gases and Dilute Solutions

Molecular Theoretical investigation of the Volume Dependence of the Entropy of Gases and Dilute Solutions		??
In calculating Entropy on the grounds of molecular theory the word "probability" is often used in a meaning that isn't covered by the definition in probability theory. Especially the "cases of equal probability" are often set by hypothesis, where the applied theoretical representation is sufficiently definite to deduce probabilities without fixing them by hypothesis. I will show in a separate work that in considerations of thermal processes one obtains a complete result with the so-called "statistical probability". This way I hope to remove a logical difficulty that is in the way of fully implementing Boltzmann's principle. Here however only its general formulation and application in quite specific cases will be given.		TRADUCTION ICI
When it's meaningful to talk about the probability of a state of a system, and additionally every increase of entropy can be described as a transition to a more probable state, the entropy S1 of a system is a function of the probability W1 of its instantaneous state. In the case of two systems S1 and S2, one can state:		TRADUCTION ICI
:${\begin{aligned}S_{1}&=\phi _{1}(W_{1}),\\S_{2}&=\phi _{2}(W_{2}).\\\end{aligned}}$		TRADUCTION ICI
If one considers these systems as a single system with entropy S and probability W, then:		TRADUCTION ICI
:$S=S_{1}+S_{2}=\phi (W)$		TRADUCTION ICI
and		TRADUCTION ICI
:$W=W_{1}\cdot W_{2}.$		TRADUCTION ICI
|[ 141 ]The latter equation expresses that the states of the two systems are independent.		TRADUCTION ICI
From these equations it follows:		TRADUCTION ICI
:$\phi (W_{1}\cdot W_{2})=\phi _{1}(W_{1})+\phi _{2}(W_{2})$		TRADUCTION ICI
and hence finally		TRADUCTION ICI
:${\begin{aligned}\phi _{1}(W_{1})&=C\lg(W_{1})+const.\ ,\\\phi _{2}(W_{2})&=C\lg(W_{2})+const.\ ,\\\phi (W)&=C\lg(W)+const.\end{aligned}}$		TRADUCTION ICI
The quantity C is also a universal constant; it follows from kinetic gas theory, where the constants R and N have the same meaning as above. Denoting the entropy at a particular starting state as S0, and the relative probability of a state with entropy S as W we have in general:		TRADUCTION ICI
:$S-S_{0}={\frac {R}{N}}\lg W.$		TRADUCTION ICI
We now consider the following special case. Let a number (n) of movable points (for example molecules) be present in a volume v0, these points will be the subject of our considerations. Other than these, arbitrarily many other movable points can be present. As to the law that describes how the considered points move around in the space the only assumption is that no part of the space (and no direction) is favored over others. The number of the (first-mentioned) points that we are considering is so small that mutual interactions are negligible.		TRADUCTION ICI
The system considered, which can be for example an ideal gas or a diluted solution, has a certain entropy. We take a part of the volume v0 with a size of v and we think of all n movable points displaced to that volume v, with otherwise no change of the system. Clearly this state has another entropy (S), and here we want to determine that entropy difference with the help of Boltzmann's principle.		TRADUCTION ICI
|[ 142 ] We ask: how large is the probability of the last-mentioned state relative to the original state? Or, what is the probability that at some point in time all n independently moving points in a volume v0 have by chance ended up in the volume v?		TRADUCTION ICI
For this probability, which is a "statistical probability" one obtains the value:		TRADUCTION ICI
:$W=\left({\frac {v}{v_{0}}}\right)^{n}\ ;$		TRADUCTION ICI
one derives from this, applying Boltzmann's principle:		TRADUCTION ICI
:$S-S_{0}=R\left({\frac {n}{N}}\right)\lg \left({\frac {v}{v_{0}}}\right).$		TRADUCTION ICI
It's noteworthy that for this derivation, from which the Boyle-Gay-Lussac law and the identical law of osmotic pressure can be easily derived thermodynamically [10], there is no need to make any assumption regarding the way the molucules move.		TRADUCTION ICI

Interpretation of the Volume Dependence of the Entropy of Monochromatic Radiation using Boltzmann's Principle

Interpretation of the Volume Dependence of the Entropy of Monochromatic Radiation using Boltzmann's Principle		???
In paragraph 4 we found for the dependence of Entropy of the monochromatic radiation on volume the expression:		TRADUCTION ICI
:$S-S_{0}={\frac {E}{\beta \nu }}\lg \left({\frac {v}{v_{0}}}\right).$		TRADUCTION ICI
This formula can be recast as follows:		TRADUCTION ICI
:$S-S_{0}={\frac {R}{N}}\lg \left[{\left({\tfrac {v}{v_{0}}}\right)}^{{\tfrac {N}{R}}{\tfrac {E}{\beta \nu }}}\right]$		TRADUCTION ICI
|[ 143 ] Comparing this with the general formula that expresses Boltzmann's principle		TRADUCTION ICI
:$S-S_{0}={\frac {R}{N}}\lg W,$		TRADUCTION ICI
we arrive at the following conclusion:		TRADUCTION ICI
If monochromatic radiation of frequency ν and energy E is enclosed (by reflecting walls) in the volume v0, then the probability that at an arbitrary point in time all of the radiation energy located in a part v of the volume v0 is:		TRADUCTION ICI
:${\left({\tfrac {v}{v_{0}}}\right)}^{{\tfrac {N}{R}}{\tfrac {E}{\beta \nu }}}\ .$		TRADUCTION ICI
Subsequently we conclude:		Subséquemment, nous concluons:
In terms of heat theory monochromatic radiation of low density (within the realm of validity of Wien's radiation formula) behaves as if it consisted of independent energy quanta of the magnitude Rβν/N.		TRADUCTION ICI
We also want to compare the average magnitude of the energy quanta of the "black body radiation" with the mean average energy of the center-of-mass-motion of a molecule at the same temperature. The latter is 3/2(R/N)T, and for the average energy of the Energy quanta Wien's formula gives:		TRADUCTION ICI
:${\frac {\int \limits _{0}^{\infty }\alpha \nu ^{3}e^{-{\frac {\beta \nu }{T}}}d\nu }{\int \limits _{0}^{\infty }{\frac {N}{R\beta \nu }}\alpha \nu ^{3}e^{-{\tfrac {\beta \nu }{T}}}d\nu }}=3{\frac {R}{N}}T.$		TRADUCTION ICI
The fact that monochromatic radiation (of sufficiently low density) behaves as regards to dependency of entropy on volume like a discontinuous medium that consists of energy quanta of magnitude Rβν/N suggests we should investigate whether the laws of |[ 144 ] generation and transformation of light are what they must be if light consisted of such energy quanta. In the following we will address that question.		TRADUCTION ICI

Stokes's Rule

Stokes's Rule		????
Let monochromatic light be transformed by photoluminence into light of another frequency, and let it be assumed that according to the result just obtained the generating as well as the generated light consists of energy quanta of magnitude (R/N)βν, where ν is the corresponding frequency. The transformation process can then be interpreted as follows. Each generating energy quantum of frequency ν1 is absorbed and generates—at least with sufficiently small density of the generating energy quanta—by itself a light quantum of of frequency ν2; possibly other light quanta of frequency ν3, ν4 etc. as well as other form of energy (e.g heat) can be generated simultaneously. Through which intermedia processes the final result comes about is immaterial. If the photoluminescing substance isn't a continuous source of energy it follows from the energy principle that the energy of the generated energy quanta are not larger than the generating light quanta; therefore the following relation must hold:		TRADUCTION ICI
:${\frac {R}{N}}\beta \nu _{2}\leqq {\frac {R}{N}}\beta \nu _{1}$		TRADUCTION ICI
or		TRADUCTION ICI
:$\nu _{2}\leqq \nu _{1}.$		TRADUCTION ICI
As is well known this is Stokes' rule.		TRADUCTION ICI
Especially noteworthy is that with weak illumination the amount of generated light must, other circumstances being equal, be proportional to the amount of exciting light, since every incident energy quantum will cause one elementary process of the above indicated kind, independent of the action of other exciting energy quanta. In particular there will be no lower limit of the intensity of the exciting light below which the light would be incapable of exciting light.		TRADUCTION ICI
|[ 145 ] According to the way the understanding of the phenomena is laid down here deviations from Stokes' rule are conceivable in the following cases:		TRADUCTION ICI
# When the number of energy quanta per unit of volume that are simultaneously involved transformation is so large that the energy quantum of the generated light can receive the energy of several exciting energy quanta. When the generating (or generated) light does not have the energy characteristics of "black body radiation" that is in the realm of validity of Wien's law, when for instance the exciting light is generated by a body of such high temperature that for the wavelengths considered Wien's law is no longer valid.		TRADUCTION ICI
The last mentioned possibility merits special attention. According to the developed understanding it cannot be excluded that a "non-Wienian radiation" would behave energetically differently from Wien's law valid "black body radiation" even in high dilution.		TRADUCTION ICI

On the Generation of Cathode Rays by Illumination of Solid Bodies

On the Generation of Cathode Rays by Illumination of Solid Bodies		?????
The usual understanding, that the energy of light is distributed over the space through which it travels in a continuous way encounters extraordinarily large difficulties in attempts to explain photo-electric phenomena, as has been presented in the groundbreaking article by Mr. Lenard. [11].		La perception d'usage que l'énergie de la lumière est distribué dans l’espace à travers lequel elle voyage de façon continue rencontre d'immense difficultés lorsque vient le moment d'expliquer l'effet photo-électrique, comme cela a été montré Dans l'article révolutionnaire de Mr. Lenard.
According to the understanding that the exciting light consists of energy quanta of energy (R/N)βν the generation of cathode rays by light can be conceived as follows. Quanta of energy penetrate the surface layer of the solid, and their energy is transformed, at least partially, in kinetic energy of electrons. The simplest picture is one where the light quantum gives its entire energy to a single electron; we assume that this will occur. However, it must not be excluded that electrons accept the energy of light quanta only partially. An electron that has been loaded with kinetic energy |[ 146 ] will have lost some of its energy when it arrives at the surface. Other than that we must assume that on leaving the solid every electron must do an amount of work P (characteristic of that solid). Electrons residing right at the surface, excited at right angles to it, will leave the solid with the largest normal velocity. The kinetic energy of such electrons is		TRADUCTION ICI
:${\frac {R}{N}}\beta \nu -P.$		TRADUCTION ICI
If the body is charged to a positive potential Π and surrounded by conductors with potential zero and Π is just enough to prevent loss of electricity by the body, then we must have:		TRADUCTION ICI
:$\Pi \epsilon ={\frac {R}{N}}\beta \nu -P,$		TRADUCTION ICI
where ε is the electrical mass of the electron, or		TRADUCTION ICI
:$\Pi E=R\beta \nu -P^{\prime }\,\!,$		TRADUCTION ICI
where E is the charge of one gram equivalent of a single-valued ion and P' is the potentel of this amount of negative electricity with respect to this body. [12]		TRADUCTION ICI
If we set E = 9.6·103, then Π·10-8 is the potential in volts that the body will attain when it is irradiated in vacuum.		TRADUCTION ICI
To see now whether the derived relation agrees with experiment to within an order of magnitude we set P' = 0, ν = 1.03·1015 (corresponding to the ultraviolet limit of the solar spectrum), and β = 4.866·10-11. We obtain Π·107 = 4.3 Volt, which agrees to within an order of magnitude with the results of Mr. Lenard. [13]		TRADUCTION ICI
If the formula derived is correct, then Π, as a function of frequency of the excited light represented in Cartesian coordinates, must be a straight line, whose inclination is independent from the nature of the substance investigated.		TRADUCTION ICI
|[ 147 ] As far as I can see no contradiction exists between our understanding and the properties of photo-electric action observed by Mr. Lenard. If each energy quantum of the exciting light releases its energy independently from all others to the electrons, the distribution of velocities of the electrons, which means the quality of the generated cathode radiation, will be independent of the intensity of the exciting light; the number of electrons that exits the body, on the other hand, will, in otherwise equal circumstances, be proportional to the intensity of the exciting light. [14]		TRADUCTION ICI
We expect that limits of validity of these rules will be similar in nature to the expected deviations from Stokes' rule.		TRADUCTION ICI
In the preceding it has been assumed that the energy of at least some of the energy quanta of the generating light is transferred completely to a single electron. If one does not start with that natural supposition then instead of the above equation one obtains:		TRADUCTION ICI
:$\Pi E+P^{\prime }\leqq R\beta \nu .$		TRADUCTION ICI
For cathode-luminescence, which constitutes the inverse process of the one just examined, on obtains by way of analogous consideration:		TRADUCTION ICI
:$\Pi E+P^{\prime }\geqq R\beta \nu .$		TRADUCTION ICI
For the materials investigated by Mr. Lenard PE is always significantly larger than Rβν, as the voltage that the cathode rays have had to traverse to generate even visible light is in some cases several hundred, in other cases thousands of volts. [15]		TRADUCTION ICI

Ionisation de gaz par rayons ultraviolets

Ionization of Gases by Ultraviolet Light		Ionisation de gaz par rayons ultraviolets
We have to assume that in ionization of a gas by ultraviolet light always one absorbed light |[ 148 ] energy quantum is used for the ionization of just one gas molecule. Firstly it follows that the ionization energy (that is, the theoretically necessary energy to ionize) of a molecule cannot be larger than the energy of an absorbed light energy quantum. Taking J as the (theoretical) ionization energy per gram equivalent, we have:		Nous devons assumer que lors de l'ionisation d'un gaz par des rayons ultraviolets, seulement un quantum d'énergie lumineuse est absorbé et utilisé pour l'ionisation de juste une seule molécule de gaz. D'abord, il obéit que l'énergie d'ionisation (c'est-à-dire, la valeur énergétique théorique nécessaire pour ioniser) d'une molécule ne peut pas être supérieure à l'énergie d'un quantum d'énergie lumineuse absorbé. En prenant "J" comme l'énergie d'ionisation par gramme équivalent, nous avons:
:$R\beta \nu \geqq J.$		$R\beta \nu \geqq J.$
According to Lenard's measurements for air the largest wavelength that has an effect is about 1.9·1012, so:		Selon les mesures prises par Lenard, pour l'air, la plus grande longeur d'onde ayant un effet est d'environ 1.9·1012, alors:
:$R\beta \nu =6.4\cdot 10^{12}\ {\text{Erg}}\geqq J.$		$R\beta \nu =6.4\cdot 10^{12}\ {\text{Erg}}\geqq J.$
An upper limit for the ionization energy can also be obtained from the ionization voltage in rarefied gases. According to Stark [16] the smallest measured ionization voltage (for platinum anodes) is for air about 10 volt. [17] We have thus for J an upper limit 9.6·1012, which is nearly the same as the one just found. There is another consequence that in my mind is very important to verify. If every light energy quantum ionizes one molecule then the following relation must exist between the absorbed quantity of light L and the number j of thereby ionized gram molecules:		Une limite supérieure pour l'énergie d'ionisation peut aussi être obtenue par la tension d'ionisation dans un gaz raréfié. Selon Stark [18], la plus petite mesure de tension d'ionisation (pour des anodes en platine) est d'environ 10 Volt pour l'air[19]. Nous avons alors pour "J" une limite supérieure de 9.6·1012, ce qui est pratiquement le même valeur tout juste trouvée. Il y a une autre conséquence qui est, dans mon esprit, importante de vérifier. Si tous les quanta d'énergie lumineuse ionisent une molécule, alors la relation suivante doit exister entre la quantité d'énergie lumineuse absorbée "L" et le nombre "J" de grammes de molécule ainsi ionisée:
:$j={\frac {L}{R\beta \nu }}.$		$j={\frac {L}{R\beta \nu }}.$
If our understanding reflects reality this relation must hold for every gas that (at the particular frequency) has no absorption that isn't accompanied by ionization.		Si notre compréhension reflète la réalité, cette relation doit être pris en charge pour chaque gaz qui (à la fréquence particulière) n'a aucune absorption qui n'est pas accompagnée d’ionisation.
Bern, march 17, 1905		Bern, 17 mars, 1905

Notes et références

1. This assumption is equivalent to the condition that the mean kinetic energies of gas molecules and electrons are equal to each other when there is thermal equilibrium. As is known, using this condition Mr. Drude has theoretically derived the relation between thermal and electric conductivity of metals.
2. This assumption is equivalent to the condition that the mean kinetic energies of gas molecules and electrons are equal to each other when there is thermal equilibrium. As is known, using this condition Mr. Drude has theoretically derived the relation between thermal and electric conductivity of metals.
3. M. Planck, Ann. d. Phys. 1 p.99. 1900.
4. This condition can be formulated as follows. We expand the Z-component of the electric force (Z) in a given point in the space between the time coordinates of t=0 and t=T (where T is a large amount of time compared to all the vibration periods considered) in a Fourier series
5. M. Planck, Ann. d. Phys. 1 p.99. 1900.
6. This condition can be formulated as follows. We expand the Z-component of the electric force (Z) in a given point in the space between the time coordinates of t=0 and t=T (where T is a large amount of time compared to all the vibration periods considered) in a Fourier series
7. M. Planck, Ann. d. Phys. 4. p.561. 1901.
8. This is an arbitrary assumption. The natural course of action is to stay with this simplest assumption until experiment forces us to abandon it.
9. This is an arbitrary assumption. The natural course of action is to stay with this simplest assumption until experiment forces us to abandon it.
10. If E is the energy of the system, then one obtains:

    $-d(E-TS)=pdv=TdS=TR{\frac {n}{N}}{\frac {dv}{v}}$;

    therefore

    $pv=R{\frac {n}{N}}T.$

11. P. Lenard, Ann. d. Phys. 8. p.169 u. 170. 1902.
12. If one assumes that in order to release an electron from a neutral molecule light must do a certain amount of work then one doesn't have to change the derived relation; one only has to think of P' as the sum of two terms.
13. P. Lenard, Ann. d. Phys. 8. p165. u. 184 Taf. I, Fig.2 1902.
14. P. Lenard, l. c. p.150 und p. 166-168.
15. P. Lenard, Ann. d. Phys. 12. p.469. 1903.
16. J. Stark, Die Elektricität in Gasen p. 57. Leipzig 1902.
17. within the gas the ionization voltage for negative ions is nonetheless five times larger
18. J. Stark, Die Elektricität in Gasen p. 57. Leipzig 1902.
19. within the gas the ionization voltage for negative ions is nonetheless five times larger