Lucien Poincaré

“ In chemical reactions, for example, the entropy increases without the substances borrowing any heat. When a perfect gas dilates in a vacuum its entropy increases, and yet the temperature does not change, and the gas has neither been able to give nor receive heat. We thus come to conceive that a physical phenomenon cannot be considered known to us if the variation of entropy is not given, as are the variations of temperature and of pressure or the exchanges of heat. The change of entropy is, properly speaking, the most characteristic fact of a thermal change. ”

“ A particular speed, for instance, is in reality nothing else but a speed, and it is only by the peculiar choice of unit that we can say that it is the space covered during the unit of time. In the same way, a quantity of electricity is a quantity of electricity; and there is nothing to prove that, in its essence, it is really reducible to a function of mass, of length, and of time. ”

“ The famous experiment of the blows with a stick by which it was demonstrated to a sceptical philosopher that an outer world existed, only proves, in reality, the existence of energy, and not that of matter. The stick in itself is inoffensive, as Professor Ostwald remarks, and it is its vis viva, its kinetic energy, which is painful to us; while if we possessed a speed equal to its own, moving in the same direction, it would no longer exist so far as our sense of touch is concerned. ”

“ Abandoning the search after mechanical models for all electrical phenomena, certain physicists reverse, so to speak, the conditions of the problem, and ask themselves whether, instead of giving a mechanical interpretation to electricity, they may not, on the contrary, give an electrical interpretation to the phenomena of matter and motion, and thus merge mechanics itself in electricity. One thus sees dawning afresh the eternal hope of co-ordinating all natural phenomena in one grandiose and imposing synthesis. ”

“ The discovery of the X rays—a discovery which physicists no doubt consider as the logical outcome of researches long pursued by a few scholars working in silence and obscurity on an otherwise much neglected subject—seemed to the public eye to have inaugurated a new era in the history of physics. If, as is the case, however, the extraordinary scientific movement provoked by Röntgen's sensational experiments has a very remote origin, it has, at least, been singularly quickened by the favourable conditions created by the interest aroused in its astonishing applications to radiography. ”

“ The conception of the atom of electricity, the foundation of the material atoms, evidently enables us to penetrate further into Nature's secrets than our predecessors; but we must not be satisfied with words, and the mystery is not solved when, by a legitimate artifice, the difficulty has simply been thrust further back. We have transferred to an element ever smaller and smaller those physical qualities which in antiquity were attributed to the whole of a substance; and then we shifted them later to those chemical atoms which, united together, constitute this whole. ”

“ When one looks at the phenomena of induction, would it not be just to remember that Arago foresaw them, and that Michael Faraday discovered them? It would be a delicate, and also a rather puerile task, to class men of genius in order of merit. The merit of an inventor like Edison and that of a theorist like Clerk Maxwell have no common measure, and mankind is indebted for its great progress to the one as much as to the other. ”

“ It is not the optics of Fresnel which absorbs the science of electricity, it is rather the optics which is swallowed up by a more general theory. The attempts of popularizers who endeavour to represent, in all their details, the mechanism of the electric phenomena, thus appear vain enough, and even puerile. It is useless to find out to what material body the ether may be compared, if we content ourselves with seeing in it a medium of which, at every point, two vectors define the properties. ”

“ The evolution of the different parts of physics does not, however, take place with equal speed, because the circumstances in which they are placed are not equally favourable. Sometimes a whole series of questions will appear forgotten, and will live only with a languishing existence; and then some accidental circumstance suddenly brings them new life, and they become the object of manifold labours, engross public attention, and invade nearly the whole domain of science. ”

“ The characteristic of a fluid is that its different parts can displace themselves with regard to one another without any reaction appearing so long as a variation of volume is not produced. There certainly may exist, as we have seen, certain traces of rigidity in a liquid, but we cannot conceive such a thing in a body infinitely more subtle than rarefied gas. Among material bodies, a solid alone really possesses the rigidity sufficient for the production within it of transverse vibrations and for their maintenance during their propagation. ”

“ The efforts of Helmholtz, Clausius, and Lord Kelvin to introduce the principle of the conservation of energy into mechanics, were far from useless. These illustrious physicists succeeded in giving a more precise form to its numerous applications; and their attempts thus contributed, by reaction, to give a fresh impulse to mechanics, and allowed it to be linked to a more general order of facts. If energetics has not been able to be included in mechanics, it seems indeed that the attempt to include mechanics in energetics was not in vain. ”

“ Absorbed in the contemplation of this new world, they succeed in persuading themselves that the old world of matter has no real existence and that energy is sufficient by itself to give us a complete comprehension of the Universe and of all the phenomena produced in it. They point out that all our sensations correspond to changes of energy, and that everything apparent to our senses is, in truth, energy. ”

“ Quite recently, Professor Rutherford has demonstrated in a fine series of experiments that the alpha particles of radium cease to ionize gases when they are made to lose their velocity, but that they do not on that account cease to exist. It may follow that many bodies emit similar particles without being easily perceived to do so; since the electric action, by which this phenomenon of radioactivity is generally manifested, would, in this case, be but very weak.
If we thus believe radioactivity to be an absolutely general phenomenon, we find ourselves face to face with a new problem. ”

“ At the present day we designate more peculiarly by the name of metrology that part of the science of measurements which devotes itself specially to the determining of the prototypes representing the fundamental units of dimension and mass, and of the standards of the first order which are derived from them. If all measurable quantities, as was long thought possible, could be reduced to the magnitudes of mechanics, metrology would thus be occupied with the essential elements entering into all phenomena, and might legitimately claim the highest rank in science. ”

“ They make up their minds not to see at once to the bottom of things; they no longer seek to suddenly strip the last veils from nature, and to divine her supreme secrets; but they work prudently and advance but slowly, while on the ground thus conquered foot by foot they endeavour to establish themselves firmly. They study the various magnitudes directly accessible to their observation without busying themselves as to their essence. They measure quantities of heat and of temperature, differences of potential, currents, and magnetic fields ”

“ Like an elastic and mobile object which, thrown into the air, attains by degrees the summit of its course, then possesses a zero velocity and is for a moment in equilibrium, and then falls on touching the ground to rebound, so the world should be subjected to huge oscillations which first bring it to a maximum of entropy till the moment when there should be produced a slow evolution in the contrary direction bringing it back to the state from which it started. ”

“ If we admit that this medium, the properties of which would explain the attraction, is the same as the luminous ether, we may first ask ourselves whether the action of gravitation is itself also due to oscillations. Some authors have endeavoured to found a theory on this hypothesis, but we are immediately brought face to face with very serious difficulties. Gravity appears, in fact, to present quite exceptional characteristics. No agent, not even those which depend upon the ether, such as light and electricity, has any influence on its action or its direction. ”

“ It is quite clear that such experiments do not prove that heat is work. We might just as well say that work is heat. It is making a gratuitous hypothesis to admit this reduction of heat to mechanism; but this hypothesis was so seductive, and so much in conformity with the desire of nearly all physicists to arrive at some sort of unity in nature, that they made it with eagerness and became unreservedly convinced that heat was an active internal force. ”

“ We may also address ourselves to a more noble form of energy, and ask ourselves whether we are not, for the first time, in presence of a transformation of gravitational energy. It may be singular, but it is not absurd, to suppose that the unit of mass of radium is not attached to the earth with the same intensity as an inert body. M. Sagnac has commenced some experiments, as yet unpublished, in order to study the laws of the fall of a fragment of radium. They are necessarily very delicate, and the energetic and ingenious physicist has not yet succeeded in finishing them. ”

“ We must, if we wish to penetrate deeper into details, particularize the hypothesis, and admit, for instance, with Gibbs that we are dealing with perfect gases; while, thanks to thermodynamics, we can constitute a complete theory of dissociation which leads to formulas in complete accord with the numerical results of the experiment. We can thus follow closely all questions concerning the displacements of the equilibrium, and find a relation of the first importance between the masses of the bodies which react in order to constitute a system in equilibrium. ”

“ It has now become possible to measure exactly the elements which enter into nearly all physical phenomena, and these measurements are taken with ever increasing precision. Every time a chapter in science progresses, science shows itself more exacting; it perfects its means of investigation, it demands more and more exactitude, and one of the most striking features of modern physics is this constant care for strictness and clearness in experimentation.
A veritable science of measurement has thus been constituted which extends over all parts of the domain of physics. ”

“ One difficulty, however, arises from the fact that the principle ought only to be applied to an isolated system. Whether we imagine actions at a distance or believe in intermediate media, we must always recognise that there exist no bodies in the world incapable of acting on each other, and we can never affirm that some modification in the energy of a given place may not have its echo in some unknown spot afar off. This difficulty may sometimes render the value of the principle rather illusory. ”

“ The molecular physics greatly in favour some fifty years ago leads to such complex representations and to solutions often so undetermined, that the most courageous are wearied with upholding it and it has fallen into some discredit. It rested on the fundamental principles of mechanics applied to molecular actions; and that was, no doubt, an extension legitimate enough, since mechanics is itself only an experimental science, and its principles, established for the movements of matter taken as a whole, should not be applied outside the domain which belongs to them. ”

“ This indestructibility, in truth, is an experimental fact, and the principle depends on experiment. It may even seem, at first sight, more singular than not that the weight of a bodily system in a given place, or the quotient of this weight by that of the standard mass—that is to say, the mass of these bodies—remains invariable, both when the temperature changes and when chemical reagents cause the original materials to disappear and to be replaced by new ones. We may certainly consider that in a chemical phenomenon annihilations and creations of matter are really produced ”

“ Noticing that entropy is a property added to matter, they admit that there is in the world a total amount of entropy; and as all real changes which are produced in any system correspond to an increase of entropy, it may be said that the entropy of the world is continually increasing. Thus the quantity of energy existing in the Universe remains constant, but transforms itself little by little into heat uniformly distributed at a temperature everywhere identical. In the end, therefore, there will be neither chemical phenomena nor manifestation of life ”

“ Finally, if we recollect that the phenomena of electric and calorific conductivity are perfectly interpreted by the hypothesis of electrons, it will no longer be possible to contest the importance of a theory which allows us to group together in one synthesis so many facts of such diverse origins.
If we study the conditions under which a wave excited by an electron's variations in speed can be transmitted, they again bring us face to face, and generally, with the results pointed out by the ordinary electromagnetic theory. ”

“ On this hypothesis, matter would only be the capacity for kinetic energy, its pretended impenetrability energy of volume, and its weight energy of position in the particular form which presents itself in universal gravitation; nay, space itself would only be known to us by the expenditure of energy necessary to penetrate it. Thus in all physical phenomena we should only have to regard the quantities of energy brought into play, and all the equations which link the phenomena to one another would have no meaning but when they apply to exchanges of energy. ”

“ But, as a matter of fact, no one has ever succeeded in giving an indisputable mechanical representation of the whole physical world. Even were we disposed to admit the strangest solutions of the problem; to consent, for example, to be satisfied with the hidden systems devised by Helmholtz, whereby we ought to divide variable things into two classes, some accessible, and the others now and for ever unknown, we should never manage to construct an edifice to contain all the known facts. ”

“ It is only by choosing our unit from those which at all times have seemed to all men the most invariable, that we are able in our experiments to note that the same causes acting under identical conditions always produce the same effects. The idea of absolute length is derived from the principle of causality; and our choice is forced upon us by the necessity of obeying this principle, which we cannot reject without declaring by that very act all science to be impossible. ”

“ If we keep to the simple idea at the bottom of this theory, we at once demonstrate that the gas ought to obey the laws of Mariotte and of Gay-Lussac, so that the characteristic equation would be obtained by the statement that the product of the number which is the measure of the volume by that which is the measure of the pressure is equal to a constant coefficient multiplied by the degree of the absolute temperature. But to get at this result we neglect two important factors.
We do not take into account, in fact, the attraction which the molecules must exercise on each other. ”

“ Persons are still to be met with who seem to have some illusions on this point, and who see in the doctrine of the dimensions of the units a doctrine of general physics, while it is, to say truth, only a doctrine of metrology. The knowledge of dimensions is valuable, since it allows us, for instance, to easily verify the homogeneity of a formula, but it can in no way give us any information on the actual nature of the quantity measured. ”

“ In the same way that, for the purpose of knowing the constitution of matter, it first occurred to us to investigate gases, which appear to be molecular edifices built on a more simple and uniform plan than solids, we ought naturally to think that an examination of the conditions in which emission and absorption are produced by gaseous bodies might be eminently profitable, and might perhaps reveal the mechanism by which the relations between the molecule of the ether and the molecule of matter might be established. ”

“ All the experiments effected on the conductivity of gases or metals, and on the radiations of active bodies, have induced us to regard the atom as being constituted by a positively charged centre having practically the same magnitude as the atom itself, round which the electrons gravitate; and it might evidently be supposed that this positive centre itself preserves the fundamental characteristics of matter, and that it is the electrons alone which no longer possess any but electromagnetic mass. ”

“ But even when we suppose that some magnitudes can never be connected with mass, length, and time, it still holds a preponderating place, and its progress finds an echo throughout the whole domain of the natural sciences. It is therefore well, in order to give an account of the general progress of physics, to examine at the outset the improvements which have been effected in these fundamental measurements, and to see what precision these improvements have allowed us to attain. ”

“ It might, no doubt, appear still more probable that the energy borrowed from the external medium by radium is one of those still unknown to us, but of which a vague instinct causes us to suspect the existence around us. It is indisputable, moreover, that the atmosphere in all directions is furrowed with active radiations; those of radium may be secondary radiations reflected by a kind of resonance phenomenon. ”