Dr. Gustave Le BON
The Evolution of Forces
The International Scientific Series
D. Appleton and Company ~ New York ~ 1908
Contents
Part I
The New Principles
Book I
The New Bases of the Physics of the Universe
Chapter I ~ The Present Anarchy of Science
Chapter II ~ The New Doctrines
Book II
The Irreducible Magnitudes of the Universe
Chapter I ~ Time, Space, Matter and Force
1. The Conception of the Irreducible Magnitudes of the
Universe
2. Measurement of the Same
Chapter II ~ The Great Constants of the
Universe: Resistance and Movement
1. Inertia or Resistance to Change
2. Mass
3. Movement and Force
Chapter III ~ The Building-Up of Forces
and the Mechanical Explanations of the Universe
1. The Cycle of Forces
2. The Mechanical Explanations of the Universe
Book III
The Dogma of the Indestructibility of Energy
Chapter I ~ The Monistic Conception of
Forces and the Theory of the Conservation of Energy
1. The Conservation of Energy
2. The Principles of Thermodynamics
Chapter II ~ The Energetical Explanation
of Phenomena
1. The Principles of Energetic Mechanics
2. Quantity and Tension of Energy
3. Transformation of Quantity into Tension, and Conversely
4. Part of Matter in Energetic Mechanics
Chapter III ~ The Degradation of Energy
and Potential Energy
1. The Theory of the Degradation of Energy
2. Potential Energy
Book IV
The New Conception of Forces
Chapter I ~ The Individuation of Forces
and the Supposed Transformations of Energy
1. The Transformations of Energy
2. Forms of Energy in Matter
Chapter II ~ The Changes of Equilibria of
Matter and the Ether Origin of Forces
1. Alterations of Level as Generators of Energy
2. Elements of Entity called Energy
Chapter III ~ The Evolution of the Cosmos
– Origin of Matter and Universal Forces
1. The Origin of Matter
2. Formation of a Solar System
3. Molecular and Intra-Atomic Energies
4. Intra-atomic Energy Source of Universal Forces
Chapter IV ~ The Vanishing of Energy and
End of Our Universe
1. The Old Age of Energy and Vanishing of Forces
2. Summary of Doctrine of Vanishing of Energy and Discussion
of Objections
3. Periods of Evolution of World
Part II ~ The Problems of Physics
In the following pages, Dr Gustave Le Bon develops further the strikingly novel and original theories put forward by him in The Evolution of Matter (Paris 1905). As in the last-named work, he enunciated the doctrine, which he was the first to deduce, that all matter is continually in a state of dissociation and decay, so in this he goes in detail into the corollary, there only briefly stated, that the atom is a great reservoir of energy, and itself the source of most of the forces of the universe. In support of this position, he calls in the aid of his earlier researches into the nature of invisible radiations, phosphorescence, and the Hertzian waves, all which, with several related phenomena, he declares to be explicable by the hypothesis that the atom, on dissociating, sets free, either wholly or in part, the energy stored up within it on its formation. Yet he is careful to declare that this is rather suggested than demonstrated by his researches, and that the conclusive proof of the validity of his assertion must be delayed for the result of further experiments by himself or others.
In the meantime, it is well to notice that both Dr Le Bon’s original thesis and its corollary have received approval from an unexpected quarter. Every new scientific theory, if sufficiently far-reaching, is received with disapproval by those brought up on the ideas it would supplant, and Dr Le Bon’s assertion of the universal dissociation of matter formed no exception to this rule. In France, as he reminds us in The Evolution of Matter, his first discovery of the phenomena which he classed together under the odd name of "Black Light", aroused a perfect storm of obloquy which has long since died away. In England, whither his theories penetrated only after they had been in great part accepted by the scientific world, this was not the case; but two members of the Cavendish Laboratory at Cambridge took upon themselves, upon the appearance of The Evolution of Matter, to assail its teaching as well as its novelty with ore virulence than force (See the Athenaeum of Feb 17 and 24 and of March 3, 10, 17, and 24, 1906; and the Jahrbuch fur Elektronik ii (1905), p. 459 et seq.). It is therefore pleasing to find Mr P. D. Innes, himself a member of the Cavendish Laboratory, writing, with the apparent approval of its Director, in the Proceedings of the Royal Society (A, vol. lxxix, No. 4 (Sept 1907), p. 442.), with regard to radioactive phenomena, that:
"The only theory which can satisfactorily account for the phenomena observed is that of atomic disintegration, a process that is apparently going on in several, if not all, of the elements";
and further (p. 443):
"That there is a great store of energy in the atom seems now beyond question, and if this reservoir could only become available, all our present conditions might be completely revolutionized."
This is exactly -- as any one can see for himself -- the position taken by Dr Le Bon in The Evolution of Matter, and further defined and emphasized by hi in the present work. There seems therefore good reason to suppose that Dr Le Bon’s later theories, as well as his earlier ones, are now widely accepted by men of science, and that before long this acceptance will be extended to all points of his doctrine.
It should be noted that the present work was written expressly for the International Science Series, and was intended to appear simultaneously in England and France. Difficulties connected with the reproduction of the illustrations have caused the appearance of this version to lag some months behind the French, of which 8 editions of 1000 copies apiece have been rapidly exhausted. The delay has not been useless, as it has enabled me to add a few corrections and notes, together with indexes, which are wanting in the French editions.
F. Legge
Royal Institute of Great Britain (February 1908)
Part I
The New Principles
Book I
The New Bases of the Physics of the
Universe
Chapter I
The Present Anarchy of Science
Every philosopher devoted to the study of subjects with rather vague outlines and uncertain conclusions, such as Psychology, Politics, or History; who had a few years ago to peruse a work on Physical Science, must have been struck by the clearness of the definitions, the exactness of the demonstrations, and the precision of the experiments. Everything was strictly linked together and interpreted. By the side of the most complicated phenomenon there was always figured its explanation.
If this same philosopher had the curiosity to look for the general principles on which these precise sciences were founded, he could not but be compelled to admire their marvelous simplicity and their imposing grandeur. Chemistry and mechanics had the indestructible atom for their foundation, physics the indestructible energy. Learned equations, produced either by experiments or by pure reasoning, united by rigid formulas the four fundamental elements of things -- i.e., time, space, matter and force. All the bodies in the universe, from the gigantic star describing its eternal revolutions in space down to the infinitesimal grain of dust which the wind seems to blow about at will, were subject to their laws.
We were right to be proud of such a science, the fruit of centuries of effort. To it was due the unity and simplicity which everywhere reigned. A few minds enamored of formulas thought it possible to simplify them further by taking into account only the mathematical relations between phenomena. These last appeared to them solely as manifestations of one great entity, viz.: energy. A few differential equations sufficed to explain all the facts discovered by observation. The principal researches of science consisted in discovering new formulas that from that moment became universal laws which nature was forced to obey.
Before such important results, the philosopher bent low, and acknowledged that if but little certainty existed in the surrounding in which he lived, at least it could be found in the domain of pure science. How could he doubt it? Did he not notice that the majority of learned men were so sure of their demonstrations that not even the shadow of a doubt ever crossed their minds?
Placed above the changing flux of things, above the chaos of unstable and contradictory opinions, the chaos of unstable and contradictory opinions, they dwelt in that serene region of the absolute where all uncertainty vanishes and where shines the dazzling light of pure truth.
Our great scientific theories are not all very ancient and great, since the cycle of precise experimental science hardly covers more than three centuries. This period, relatively so short, reveals two very distinct phases of evolution in the minds of scholars.
The first is the period of confidence and certainty to which I have just referred. In the face of the daily increase of discoveries, especially during the first half of the last century, the philosophical and religious dogmas on which our conception of the universe had for so long been based, faded and vanished completely. No complaint was raised. Were not absolute truths to replace the former uncertainties of ancient beliefs? The founders of each new science imagined that they had once for all built up for that science a framework which only needed filling in. This scientific edifice once built up, it would alone remain standing on the ruins of the vain imaginings and illusions of the past. The scientific creed was complete. No doubt it presented nature as regardless of mankind and the heavens as tenantless; but it was hoped to repeople the latter at an early date and to set up for adoration new idols, somewhat wooden perhaps, but which at least would never play us false.
This happy confidence in the great dogmas of modern science remained unaltered until the quite recent day when unforeseen discoveries condemned scientific thought to suffer doubts from which it imagined itself forever free. The edifice of which the fissures were only visible to a few superior intelligences has been suddenly and violently shaken. Contradictions and impossibilities, hardly perceptible at first, have become striking. The disillusion was so rapid that, in a short space of time, the question arose whether the principles which seemingly constituted the most certain foundations of our knowledge in physics were not simply fragile hypotheses which wrapped profound ignorance in a delusive veil. Then that befell scientific dogmas which formerly happened to religious dogmas so soon as any one dared discuss them. The hour of criticism was quickly followed by the hour of decadence, and then by that of disappearance and oblivion.
No doubt those great principles of which science was so proud have not yet perished entirely. For a long time they will continue to be positive truths to the multitude and will be propagated in elementary textbooks, but they have already lost their prestige in the eyes of real scholars. The discoveries just alluded to have simply accentuated the uncertainties which the latest works had already commenced to reveal; and it is thus that science herself has entered into a phase of anarchy from which she might have been thought forever safe. Principles which appeared to have a sure mathematical foundation are now contested by those whose profession it is to teach and defend them. Such profound books as La Science et l’Hypothese of M. Henri Poincare give proofs of this on nearly every page. Even in the domain of mathematics, this illustrious scholar has shown that we only subsist on hypotheses and conventions.
One of M. Poincare’s most eminent colleagues in the institute, the mathematician Emile Picard, has shown in one of his publications how "incoherent" are the present principles of another almost fundamental science -- mechanics. He says: “At the end of the 18th century, the principles of mechanics seemed to defy all criticism, and the work of the founders of the science of motion formed a block which seemed for ever safe against the lapse of time. Since that epoch, searching analysis has examined the foundations of the edifice with a magnifying glass. As a matter of fact, where learned men like Lagrange and Laplace deemed everything quite simple, we today meet with the most serious difficulties. Every one who has had to teach the first steps of mechanics, and who has troubled to think for himself, has experienced how incoherent are the more or less traditional explanations of its principles".
The principles of mechanics, which are apparently most simple, writes Prof. Mach in his History of Mechanics, "are of a very complicated nature. They are based on unrealized, and even on unrealizable, experiments. In no way can they be considered in themselves as demonstrated mathematical truths".
At the present time we possess three systems of mechanics, each of which declares the other two to be absurd. Even if none of them, perhaps, deserves this qualification, they may at least be considered very incoherent, and as furnishing no acceptable expantion of phenomena.
"There hardly now exist", writes M. Lucien Poincare, "any of those great theories once universally admitted, to which, by common consent, all searchers subscribed. A certain anarchy reigns in the domain of the natural sciences, all presumptions are allowed, and no law appears rigidly necessary... We are witnessing at this moment, rather a demolition than a definite work of construction... The ideas which to our predecessors seemed strongly established are now controverted... Today the idea that all phenomena are capable of mechanical explanations is generally abandoned... The very principles of mechanics are contests, and recent facts unsettle our belief in the absolute value of laws hitherto considered fundamental".
Assuredly the great theories which dominated the science of each epoch, and gave direction to its studies, did not remain forever undisputed. After an existence generally pretty long, they slowly vanished, but did not give place to new doctrines, until these last were strongly founded. Today the old principles are dead or dying, and those destined to replace them are only in course of formation. Modern man destroys faster than he builds. The legacies of the past are merely shadows. Gods, ideas, dogmas, and creeds vanish one after the other. Before new edifices capable of sheltering our thoughts can be built, many ruins will have crumbled into dust. We are still in an age of destruction, and therefore of anarchy.
Noting, fortunately, is more favorable to progress than this anarchy. The world is full of things we do not see, and it is of the erroneous or insufficient ideas imposed by the traditions of classic teachings that the bandage is woven which covers our sight. History shows to what degree scientific theories retard progress so soon as they have acquired a certain fixity. A fresh forward only becomes possible after a sufficient dissociation of the earlier ideas. To point out error and to follow up its consequences is at times as useful as discovering new facts. Perhaps the most dangerous thing to the progress of the human mind is to place before readers -- as is invariably the case with all educational works -- uncertainties as indisputable truths, and to presume to impose limits to science, or, as Auguste Comte wished to do, to the knowable. The celebrated philosopher even proposed the creation of an Areopagus of scholars with the mission of fixing limits to the researches which should be permitted. Such tribunals are, unfortunately, already too numerous, and no one can be unaware how baneful has been their influence.
There should therefore be no hesitation to examine closely the fundamental dogmas of science for the sole reason that they are venerated and at first sight appear indestructible. The great merit of Descartes lay in his viewing as doubtful what down to his time had been considered uncontested truth. Too often do we forget the scientific idols of the present day have no more right to invulnerability than those of the past.
The two dogmas of modern science formerly most respected were those of the indestructibility of matter and energy. The first was already 2000 years old, and all discoveries had only tended to confirm it. By a marvelous exception, the strangeness of which struck no one, while all things in the universe were condemned to perish, matter remained indestructible. The beings formed by the combinations of atoms had but an ephemeral existence; but they were composed of immortal elements. Created at the beginning of the ages, these elements defied the action of centuries and, like the gods of ancient legends, enjoyed eternal youth.
Matter was not, however, alone in possessing this privilege of immortality. The Forces -- which are now termed Energy -- were equally indestructible. This last might incessantly change its form, but the quantity of it in the world remained invariable. A form of energy could not disappear without being replaced by another equivalent one.
I have devoted nearly 10 years of the experimental researched summarized in my book, The Evolution of Matter, to proving that the first of the above-mentioned dogmas can no longer be maintained, and that matter also must enter into the cycle of things condemned to grow old and die. But if matter be perishable, can we suppose that energy alone enjoys the privilege of immortality? The dogma of the conservation of energy still retains so much prestige that no criticism seems to shake it. In this work we shall have to discuss its value, and this study will necessitate many others. My own experimental researches have lead me to explore somewhat different chapters of physics without much heeding what was taught regarding them. Notwithstanding the necessarily fragmentary character of these researches, they will perhaps interest those readers whose scientific beliefs are not yet settled.
What has finally given very great force to certain principles of physics and mechanics has been the very complicated mathematical apparatus in which they have been wrapped. Everything presented in an algebraic form at once acquires for certain minds the character of indisputable truth. The most perfect skeptic willingly attributes a mysterious virtue to equations and bows to their supposed power. They tend more and more to replace, in teaching, reason and experiments. These delusive veils which now surround the most simple principles only too often serve to mask uncertainties. It is by lifting them that I have succeeded more than once in showing the frailty of scientific beliefs which for many scholars possess the authority of revealed dogmas.
The New Doctrines
Newton, wrote Lagrange, was the greatest, and, at the same time, the most fortunate of geniuses, for one does not more than once in a way find a universe in want of a system.
In saying this, the illustrious mathematician was evidently persuaded that the system of the universe must be considered as established once and for all. This simple belief has no longer many adherents. It now appears pretty clearly that we know very little of the general laws of out universe. We can only dimly see in the far-off future the epoch when these laws will be established. It is, however, already felt that the actual mechanism of the world differs greatly from that constructed by the science of the past. We now feel ourselves surrounded by gigantic forces of which we can only get a glimpse, and which obey laws unknown to us.
Ideas necessarily follow one another in a chain. A new theory cannot be started without bringing with it a series of equally new consequences. After I had proved that the dissociation of atoms was a universal phenomenon, and that matter is an immense reservoir of an energy hitherto unsuspected in spite of its colossal grandeur, I was naturally led to ask myself whether all the forces of the universe -- notably solar heat and electricity -- did not proceed solely from this reservoir of energy, and therefore from the dissociation of matter.
As regards solar heat, the source of most terrestrial energies, dissociation appeared sufficient to explain the maintenance of the sun’s temperature on the hypothesis that the atoms of incandescent stars must have contained more intra-atomic energy than they possess when once grown cool. As regards electricity, I recall the result of my experiments: -- that the particles emitted by an electrified point are identical with those which come forth from a radioactive body such as radium. This fact proves that electricity also is a product of the dematerialization of matter.
The phenomenon of the dissociation of atoms presented therefore consequences of considerable importance, since it was possible to regard it as the origin of the forces of the universe. Matter became a simple reservoir of forces, and could itself be considered as a relatively stable form of energy. This conception caused the disappearance of the classic dichotomy between matter and energy, and between matter and the ether. It allowed us to connect the two worlds of the Ponderable and the Imponderable, once considered very distinct, which science believed she had definitely separated. Berthelot even asserted at the recent inauguration of the Lavoisier monument, that the distinction between ponderable matter and imponderable agencies is one of the greatest discoveries ever made".
It now seems, however, that physicists should have seen a long time ago -- that is, long before the recent discoveries -- that matter and the ether are intimately connected, that they are unceasingly interchanging energies, and are in no way separate worlds. Matter continuously emits luminous or calorific radiations, and can absorb them. Down to the absolute zero it radiates continuously -- that is to say, it emits ethereal vibrations. The agitations of matter propagate themselves in the ether, and those of the ether in matter, and without this propagation there would be neither heat nor light. The ether and matter are one thing under different forms, and we cannot put them asunder. If we had not taken as a starting point the narrow view that light and heat are imponderable agents because they appear to add nothing to the weight of bodies, the distinction between the ponderable and imponderable, to which scholars attach so much importance, would have long ago vanished.
The ether is doubtless a mysterious agent which we have not yet learnt to isolate, but its reality is manifest, since no phenomenon can be explained without it. Its existence now seems to several physicists more certain than even that of matter. It cannot be isolated, but it is impossible to say it cannot be seen or touched. It is, on the contrary, the substance we most often see and touch. When a body radiates the heat which warms or burns us, what constitutes this heat, if it be not the vibrations of the ether? When we see a green landscape on the ground glass of a camera obscura, what constitutes this image, if not the ether?
The theory of the dissociation of matter has not only served to clear away the two great dichotomies, force and matter, ponderable and imponderable, which seemed established forever. The doctrine of the vanishing of matter by its transformation into energy carries with it important consequences in regard to current ideas of energy.
According to the most fundamental principles of mechanics, when we communicate to a material body a determined quantity of energy, this energy may be transformed, but the body will never give back a quantity in excess of that received by it. This principle was considered too self-evident ever to have been disputed. In fact it was indisputable so long as it was admitted that matter could only give up the energy transmitted to it and was unable to create any. By showing that matter is an immense reservoir of energy, I at the same time proved that the quantity of energy it emits, under the influence of an outside force acting on it as a kind of excitant, may far exceed that which it has received.
With such a very slight excitement as that of a thin pencil of invisible ultraviolet radiations, -- or even with no excitement at all, we observe in the emission of spontaneously dissociating bodies such as radium, -- we can obtain considerable quantities of energy. No doubt, we do not create this liberated energy, since it already exists in matter, but we obtain it under conditions which the old laws of mechanics could never have imagined. The idea that matte cold be transformed into energy would have seemed absolutely absurd only a very few years ago.
It will be part of the science of the future to discover the means of freeing, in a practical form, the considerable forces which matter contains.
"Intra-atomic energy, scientifically brought into play", recently wrote M. Ferrand, "will create the totally new science of modern Energetics: it will give us the formula of the thermodynamic potential of energy freed from matter. Turned commercially to account, it is capable of turning upside down the productive activity of our old world".
The researches which I have set forth in numerous papers for the last 10 years have rapidly spread through the laboratories, and have been largely utilized, especially by those physicists who have not quoted them. Some of my propositions, considered very revolutionary when first formulated, are now beginning to be almost commonplace, although they are far from having yet produced all their consequences. When those last are unfolded, they will lead to the renewal of a great part of a scientific edifice the stability of which seemed eternal.
It is useful to prove that this edifice, so stable in appearance, is far from being so, and that things may be viewed from very different points from those to which our regular education has accustomed us. It is to the demonstration of this that a portion of this work will be devoted.
The fundamental principles which will guide us are those enumerated in my preceding work, which I repeat: --
1. Matter, hitherto deemed indestructible, slowly vanishes by the continuous dissociation of its component atoms.
2. The products of the dematerialization of matter constitute substances placed by their properties between ponderable bodies and the imponderable ether -- that is to say, between two worlds hitherto considered as widely separate.
3. Matter, formerly regarded as inert and only able to give back the energy originally supplied to it, is, on the other hand, a colossal reservoir of energy -- intra-atomic energy -- which it can expend without borrowing anything from without.
4. It is from the intra-atomic energy liberated during the dissociation of matter that most of the forces in the universe are derived, and notably electricity and solar heat.
5. Force and matter are two different forms of one and the same thing. Matter represents a stable form of intra-atomic energy: heat, light, electricity, etc., represent unstable forms of it.
6. By the dissociation of atoms -- that is to say by the materialization of matter, the stable form of energy termed matter is simply changed into those unstable forms known by the names of electricity, light, heat, etc., matter therefore is continuously transformed into energy.
7. The law of evolution applicable to living beings is also applicable to simple bodies; chemical species are no more invariable than are living species.
8. Energy is no more indestructible than the matter from which it emanates.
The Irreducible Magnitudes of the Universe
Chapter I
Time, Space, Matter and Force
1. The Conception of the Irreducible Magnitudes of the Universe
Time, space, matter and force form the elements of things, and the fundamental basis of all our knowledge.
Time and space are the two magnitudes in which we confine the universe. Force is the cause of phenomena, matter their web.
Three of these elements -- time, space, and force -- are quite irreducible. Matter may be reconverted into force, not only because it is, as I have proved, a particular form of energy, but also because it is only defined, in equations of mechanics, by the symbols fo force (1).
[(1) In the CGS system now generally adopted for the evaluation of the magnitudes of physical quantities, we take into consideration: (1) the fundamental quality, length, mass, and time; and (2) the derived quantities. These last, which are very numerous, comprise notably the derived quantities of geometry -- surface, volume, and angle; those of mechanics -- speed, acceleration, force, energy, work, power, etc.; and those of electricity and magnetism -- resistance, intensity, potential difference, etc.]
Time, space, and force being irreducible, cannot be compared with anything and are indefinable. We only know of them that which our common sense tells us. So soon as, in order to define these great entities, we endeavor to go beyond what is revealed by ordinary observation, we meet with inextricable difficulties and end by acknowledging, as do the philosophers, that they are simply creations of the mind, and cover completely unknown realities.
These realities are not knowable to us, because our senses ever remain interposed between them and us. What we perceive of the universe are only the impressions produced on our senses. The form we give to things is conditioned by the nature of our intelligence. Time and space are, then, subjective notions imposed by our senses on the representation of things, and this is why Kant considered time and space as forms of sensibility. To a superior intelligence, capable of grasping at the same time the order of succession and that of the co-existence of phenomena, our notions of space and time would have no meaning.
It is, moreover, not space and time only, but all phenomena, from matter which we think we know up to the divinities created by our dreams, which have to be considered as forms necessary for our understanding. The world constructed with the impressions of our senses is a summary translation, and necessarily a far from faithful one of the real world which we know not. Time is, for man, nothing but a relation between events. He measures it by the changes in position of a mobile body, such as a star or a clock. It is only by a change, that is to say, by movement, that the notion of time is accessible to us. "In a world void of all kind of movement", says Kant, "there would not be seen the slightest sequence in the internal state of substances. Hence, the abolition of the relation of substances to one another carries with it the annihilation of sequence and of time". If there are no events there is evidently no sequence, and consequently no time.
To immobilize the world and the beings which inhabit it would be to immobilize time -- that is to say, to cause it to vanish. If this fixedness were absolute, life would be impossible, since life implies change; but neither could anything grow old. The immortal gods who, according to the legends, never undergo change, cannot know time. For them the clock of heaven marks always the same hour. Change is therefore the true generator of time [** Ed.: -- see Kozyrev]. It is only conceivable, like forces and all phenomena, under the form of movement. This fundamental concept of movement will be found at the base of all phenomena. It serves to define the magnitudes of the universe, and can only be defined by them. It is not an irreducible concept, for it is formed by the combination of the notions of force, of matter, of space, and of time. It is evident that we require the intervention of all these in order to define the displacement of a body.
In physics the most variations of quantities are expressed by reference to the variations of time. When the curve expressing the relations of a phenomenon with time is known, science can go back from the present to the past and can know the future.
The notion of space is as little clear as that of time. Leibnitz defined it as the order of co-existence of phenomena, time being the order of their succession. Space and time are perhaps two forms of the same thing.
Space does not appear conceivable without the existence of bodies. A world entirely void could not give birth to the idea of space, and this is the reason philosophers refuse to space an objective reality. In their view, space being, like time, a quality, where there is neither phenomenon nor substance, there is neither space nor time.
The above brief expose’ suffices to show how inexact and limited are the ideas man can form as to the fundamental elements of the universe. Our knowledge being only relative, we only define with a known one. All knowledge therefore implies a comparison, but to what can we compare the irreducible elements of things? They condition phenomena, and remain hidden behind them.
If the irreducible magnitudes of the universe are not known in their essence, they at least produce measurable effects. We are situated with regard to them like the railway porter who can weigh with exactness parcels the content of which he is ignorant.
It is of these measurements alone that science is composed. By means of them are established the numerical relations which form to one web of our knowledge, since the realities which uphold them escape us. The properties of things are only properly definable by measurement. The qualitative represents a subjective appreciation which may vary from one individual to another. The quantitative represents a fixed magnitude which can be preserved, and which gives precision to our sensations. The substitution of the quantitative for the qualitative is the principle task of the scholar. "I often say", writes Lord Kelvin, "that if you measure that of which you speak, and can express it by a number, you know something of your subject; but if you cannot measure it, your knowledge is meager and unsatisfactory".
2. The Measurement of the Irreducible Magnitudes of the Universe
By measuring and placing one on the other the heterogeneous elements which form the web of things, science has managed to create certain concepts, such as those of mass, kinetic energy, etc., which we have to consider realities by reason of our incapacity to imagine others.
These concepts vary with the way in which we bring together the irreducible elements of things. Associate force with space, and we create the science of energy. Associate space and time, and we create the science of velocities -- that is to say, kinematics. Associate force, space and time, and we create the science of mechanical power. It is evident that, by thus acting, we must associate very heterogeneous elements.
Force ( F = MA ) is a coefficient of resistance multiplied by an acceleration. Work ( T = F x E ) is a force multiplied by a length. Velocity ( V = L/T ) is a space divided by a time. Mass (M = P/g) is a weight divided by a velocity, etc.) It is only by the combination of these very different magnitudes, that it has been possible to state precisely the concepts of mechanics on which the interpretation of the phenomena of the universe is still based.
To define completely a phenomenon there have to be associated the three great coordinates of things -- time, space, and force. If one or two of these only are measured, the phenomenon is only partially known. The formation of the modern notions of energy and of power furnishes excellent examples of this. They were no precisely stated until to the vague idea of force considered as the synonym of effort was added the notion of space, and then that of time.
In mechanics, force is defined as a cause of movement; the unit of force is represented by the acceleration produced on the unit of mass. When a force displaces its point of application it generates work. This last is the product of the force considered as a cause of movement. The kilogram-meter has been chosen as the unit of work. It is the work necessary to displace a kilogram for the length of a meter. This unit of mechanical energy is now used to measure all forms of energy.
Thus, by the sole fact that we have associated space with force, we can measure this last and comprise it in a formula. This enables us to understand how with an invariable quantity of energy we can produce forces of variable magnitude. If, in fact, we call the Force F, the Space E, and the work T, we obtain according to the preceding definitions T = F x E. In this formula, which defines the unit of work, the force F and the space E can evidently be inversely varied without changing their product -- that is to say, the work. We can therefore largely increase the force on condition that we proportionately reduce the space covered. It is this operation which is affected by certain machines, such as the lever, which multiplies the force but not the work. By the expenditure of one kilogram-meter, hundreds of kilogram-meters can be raised, but what is gained in force will be lost in the space covered, and the product F x E will never exceed a kilogram-meter. Force therefore can be multiplied, but not energy, of which the magnitude remains invariable.
Into the unit of work there enter only the elements force and space, but not the element time. One kilogram-meter may be expended in one second or in a thousand years, and the results will necessarily be very different I the two cases. This is very well illustrated in the case of radium, of which one gram contains thousands of kilogram-meters. Such a force appears immense, but its production is in each instant so slight that it would require thousands of years to liberate it entirely. It is the case of a reservoir containing an immense quantity of water which can escape by a drop at a time. Hence, by confining ourselves to the association force and space, we have already created a unit which permits us to evaluate in kilogram-meters the power of any machine moved by any motor, but it does not tell us if these kilogram-meters are produced in one minute or in a year. We know therefore very little of the power of the machine.
To ascertain this, it suffices to superimpose on the two elements force and space, which give us the unit of work, the element time. We shall then have what is called the unit of power, which is the quotient of the work by the time. It shows us the work produced in a given time. If we are told that a machine produces a kilogram-meter, we know nothing as to its power. If it be added that this kilogram-meter is produced in one second, we are fully informed.
The kilogram-meter per second being too small a unit from the commercial point of view, one 75 times larger has been adopted. This is the horsepower, which represents 75 kilograms raised one meter in one second (1).
[(1) In physics other units are often made use of, but we do not alter what has been said. If, instead of being evaluated in kilograms, the force is evaluated in dynes, and if the space, instead of being evaluated in meters, is measured in centimeters, the work, instead of being expressed in kilogram-meters, is expressed in ergs.]
In this last unit are found collected, as will be seen, the three irreducible elements of things -- time, space, and force. Matter likewise figures init indirectly, for that which is measured is the force employed to combat its inertia and to give it certain movements.
We have just seen how, by enclosing in space and time that mysterious Proteus called force, it is possible to grasp it and know it under its deceiving forms. On penetrating further into the inmost nature of phenomena, we shall see that space and time not only serve to measure force, but that they also condition its form and its magnitude.
The Great Constants of the Universe: Resistance and Movement
1. Inertia or Resistance to Change
Forces are known to us solely by the movements they generate. Mechanics, which claims to be the foundation of the other sciences and to explain the universe, is devoted to the study of these movements.
The notion of movement implies that of things to move. Observation sows that these things to move present a certain resistance. The resistance of matter to movement or to a change of movement is what is termed its inertia. It is from this property that is derived the notion of mass.
We thus find ourselves in the presence of two elements, not irreducible like those just studied, but fundamental. These are movement and resistance to movement, or, in other words, change and resistance to change. Inertia -- that is to say, the aptitude of matter to resist movement or a change in movement -- is the most important of its properties, and even the only one which allows us to follow it through all its modifications. While its other characteristics, solidity, color, etc., depend on several variable causes and consequently may change, inertia depends on no factor and is unchangeable. Whether it be liquid, solid or gaseous, whether it be isolated or in combination, the same body possesses an unvarying quantity of inertia. Measured indirectly by the balance, this allows us to follow it through all its changes.
On this notion of the invariability of inertia, or, in other words, of the mass, are based the edifices of chemistry and mechanics. The preponderant part played by inertia in phenomena is a matter of daily observation. It is by virtue of inertia that the worlds continue to circulate in space, that a ball hurled from a cannon by the explosion of gunpowder travels several thousand meters. Inertia being opposed to a change of movement, bodies would even continue their course indefinitely if different antagonistic forces, such as the resistance of the air, did not finally arrest them. A railway train would thus continue to advance with the same velocity without the help of any motor if its inertia did not unceasingly tend to be annulled by various resistances, friction, etc., which the locomotive only serves to overcome. The same inertia of matter forbids the train stopping abruptly. To effect this, very powerful brakes must be employed even if the engine has ceased working. Inertia being opposed to movement as well as to change of movement, it requires a very great force to start the train from its repose, and one equally great to stop it when once in motion.
It results therefore from the principle of inertia that, when a moving body tends to slacken speed from any cause whatsoever, inertia tends to maintain that speed, since, by its definition, it is opposed to change of movement. Conversely, when the speed of the moving body increases, inertia comes in to retard this acceleration for the same reason, viz., that it is opposed to change of movement.
Electricity, which possesses, or at least appears to possess, inertia, behaves like matter in motion. Its inertia acts in the phenomena of induction exactly, as has been said above, by opposing itself to change of movement -- that is to say, in the converse direction to the cause which tends to produce its slackening or acceleration. This is expressed by the law of Lenz, which governs the phenomena of induction. It would perhaps be possible to explain them on the principle of the equality of action and reaction without invoking inertia at all. To measure the inertia of matter is easy, to note its properties is likewise easy, but to explain its nature is as yet impossible.
Newton, who was the first to study inertia scientifically, considered it to be a force. "The force which dwells in matter", he says, "is its power of resistance, and it is by this force that every body perseveres of itself in its actual state of repose or of movement in a straight line".
At the present day, the tendency is to admit that matter is connected with the ether by lines of force, and that the whole of the inertia of matter should be that of the ether gripped by lines of force. But whether inertia be attributed to matter or to the medium in which it is plunged, this does not bring us any nearer to an explanation.
Perhaps the least improbable thing that may be said regarding inertia is that matter, being, as I have shown, an immense aggregate of forces, possesses certain relations of equilibrium with the ether surrounding it. The movement of a body must break up this equilibrium and create others, from which would result the continuation of the movement and its resistance to change of speed. In the internal equilibrium of a body in motion something is probably changed.
To the notion of inertia there should, doubtless, be attached the principle of the equality of action and reaction. Although this is a fundamental principle in mechanics, it, too, is very little explicable. It has been formulated by Newton as follows: --
"A body exercising on another a pressure or traction, receives from the latter an equal and opposite traction or pressure". This would signify that if you exercise a traction of 100 kilograms on an infinitely rigid wall it will exercise the same traction on you. The wall thus becomes, as M. Wickersheimer points out, a metaphysical person entering into antagonism with you. At bottom, mechanics, which seems to be the most precise of sciences, the one most foreign to metaphysics, is the one which contains most evident or hidden metaphysical notions. They evidently cover profound but entirely unknown causes. Perhaps we should explain the principle of equal reaction in the direction contrary to action by considering certain forces as couples -- that is to say, as acting like a spring stretched between two points. It is evidently impossible then to act on one without the other reacting immediately. Gravity and electricity would come under this head.
2. Mass
The mass which serves to characterize matter is only the measure of its inertia -- that is to say, of its resistance to movement. It is measured by seeking the magnitude of the force which must be opposed to inertia in order to annul it. Gravity has been chosen because it is easy to handle. We can by means of weights, each of which represents a certain quantity of attraction, measure the inertia of a certain portion of matter placed on one of the scales of a balance.
The notion of mass was slow in establishing itself. Mach, in his History of Mechanics, points out that Descartes, Newton and Leibnitz had only a very vague comprehension of it. Galileo confused mass with weight, which many people do even at the present time, although by reason of the units adopted, weight is represented by a figure about 10 times greater than that expressed by mass (1).
[(1) The distinction between weight and mass, formerly considered synonymous, only became manifest when the observation of the pendulum revealed that the same body may receive a different acceleration of gravity in different parts of the globe. It was in 1871 that it was noted for the first time in astronomical observations that a clock giving the exact time in Paris no longer did so in Guiana. To render its pace regular, it is necessary to shorten the length of the regulating pendulum.]
The term mass is, moreover, employed at the present day in two different senses. For physicists mass is a coefficient of inertia, and for astronomers a coefficient of attraction. If the attraction due to gravity were the same all over the globe, the mass of a body, that is to say, the quantity of inertia it possesses -- would be measured according to the force of attraction necessary to annul it. Chemists, who have only to compare the masses of bodies, proceed in no other way. For the calculations of mechanics it was necessary to find another element, because gravity alters with latitude and the height from the earth. This last variation even shows itself at the different stories of a house.
The weight of a body varies from one place to another, but the acceleration which this body may take undergoes the same variation. The ratio of these two magnitudes is therefore constant at all points of the globe. It is this relation P/g which always figures in the calculations of mechanics. Given the value of the number g, it follows that in numerical expressions the mass of a body hardly represents the tenth part of its weight. The equation M = P/g which defines mass, refers to the gravity; but as the weight may be replaced by any force F, which produces an acceleration A, we obtain as a general expression of mass M = F/A. This is the fundamental equation of mechanics. One must not look too closely into its meaning.
Mass has been considered as an invariable magnitude down to the recent researches mentioned in my last book. These last have shown that not only does the mass vary by the dissociation of atoms, but, further, that the products of this dissociation have a mass varying with their velocity. This mass can even increase to the point of becoming infinite -- that is to say, when the velocity approached that of light. Nothing proves, moreover, that it would not be the same with ordinary matter animated by a like velocity.
Not only does the mass vary with the velocity, but it has lately become a question whether it does not also vary with the temperature. The question has not yet been elucidated. However that may be, mass is not at all that invariable magnitude which chemistry and mechanics formerly supposed it to be. The element which science considered as the immovable pivot of phenomena, the starting point to which it endeavored to refer all things, has become a variable magnitude of which the apparent fixity was only due to the imperfection of our means of observation.
The inertia of matter is still, however, the most stable thing in the changing ocean of phenomena. This stability is not absolute, but as regards our ordinary requirements the inertia of matter can be considered as one of the great constants of the universe.
3. Movement and Force
For half a century science thought she had discovered a second constant element in the universe. This element is energy, of which forces would be simple manifestations.
We will now examine only the fundamental elements of forces. They are knowable to us by the movements they produce, and that is why, in the classic mechanics, force is simply defined as a cause of movement.
By virtue of their inertia alone, bodies would only assume a uniform and rectilinear movement. Directly this movement is accelerated, we recognize that a force has intervened. It is solely this acceleration which mechanics measures and which figures in its equations.
Force is therefore only known to mechanics through movement. Movement is not an irreducible magnitude, since it is derived from the four great elements of the universe -- time, space, matter and force -- which alone enable it to be defined.
We have seen previously how by associating force and space the unit of mechanical energy and of work has been constituted; we shall see in a later chapter the transformations which the modern notion of the conservation of energy has introduced into the conceptions of force.
What precedes shows us how notions of movement and of resistance are derived from those of force and mass, on which the principles of mechanics were built up. The equation F = MA defines force by the acceleration imparted to a body endowed with resistance to movement.
To sum up, movement -- that is to say, change -- and inertia -- that is to say, resistance to change -- constitute the fundamental elements accessible to mechanics. We will now see how, by associating them, this science has sought to interpret the phenomena of the universe.
The Building Up of Forces and the Mechanical Explanations of the Universe
1. The Cycle of Forces
We have just seen that on reducing to their essential elements the forces of the universe there still remain resistance and movement. Resistance is represented by the inertia of matter or of the ether, and movement by the displacement of these substances in space and time.
The magnitude of forces is determined by the velocity of movements that they produce, their form by the nature of these movements. The movements of matter are only apparent to us when it comes into contact with an antagonistic factor which annuls or diminishes its velocity. The earth, for instance, by reason of its movements of rotation and of translation in space, possesses an immense kinetic energy; but it is not noticed, because out globe meets no obstacles in its path. Yet its kinetic energy would be sufficient, perhaps, to reduce to vapor any planet it chanced to strike. All things living on the surface of our globe are carried along with it in its movement, and possess in consequence a considerable kinetic energy. This would appear if they were suddenly transported from on point on the globe’s surface to another endowed with a different velocity; for instance, from the pole to the equator. On arriving at the equator they would be hurled into space with a speed more than six times that of a railway train.
Independently of the movements of translation in a straight line like that of a cannon ball, or of rotation like that of the stars, matter and ether may show very different forms of movement. There result from this forces very different in aspect. We observe notably vibratory movements like those of a tuning fork, and circular disturbances such as those produced by casting a stone into the water, etc. Light and heat show exactly these last forms of movement. It is not only the kind of movements, but also the variations in velocity which condition the nature of forces. The recent theories on electricity put this last point well in evidence. They show, in fact, that forces differing from each other so widely as magnetism, the electric current, and light are generated by simple variations in the movements of electric particles.
An electrified body in repose produces effects of attraction and repulsion only, and possesses no magnetic property. Set it in motion, and it is immediately surrounded by magnetic lines of force, and produces all the effects of a current like that which traverses telegraph wires. Let us vary by a sudden acceleration the speed of the particles, and they immediately radiate through the ether. Hertzian waves, calorific waves, and lastly light. These forms of energy, although so different in kind, only appear therefore as the consequence of simple changes of movement.
The forces of nature probably contain other elements than movement. These elements do not affect our reagents, and we are therefore not cognizant of them. In the ocean of phenomena, science can only pick out what is accessible to it.
2. The Mechanical Explanations of the Universe
That which precedes makes us feel in advance how fragmentary, and consequently how insufficient, must be the final explanation of phenomena which the science of mechanics proposes.
Naturally this conclusion is not the one arrived at by the defenders of the doctrine which claims to explain everything by means of the equations of movement. In no way stopped by the excessive simplicity of their concepts, persuaded that all phenomena were wrapped up in their formulas, they have known neither mistrust nor uncertainty, and have imagined that they had for all eternity built up an edifice of imposing grandeur.
For the majority of scholars, this sublime confidence still endures. One of the most eminent among them, Cornu, the Academician, at the Congres de Physique in 1900, delivered himself as follows: --
"The spirit of Descartes soars over modern physics. What am I saying? He is its shining light! The more we penetrate into the knowledge of natural phenomena, the more developed and precise is the audacious Cartesian conception of the mechanism of the universe. There is in the physical world only matter and movement".
At the very moment these words were uttered, the classic edifice was furrowed by deep chasms. While the mathematicians were drawing up formulas, the physicists were making experiments, and these experiments fitted in less and less with the formulas. These discrepancies, however, did not greatly trouble the mathematicians. So soon as the equations no longer agreed with the experiments, they rectified the equations by imagining the intervention of "hidden movements" which completely baffled observation. The process was evidently ingenious, but evidently also a little childish. "Since", says M. Duhem, "no condition, no restriction, is imposed on these hidden movements, on what should we found the proof that a given difference may not find in them its raison d’etre?".
Notwithstanding such subterfuges, the insufficiency of the classical mechanics has every day become more manifest with the progress of physics. "There exists", writes the author I have just quoted, "a radical incompatibility between the mechanics of Lagrange", that is to say, the classical mechanics, "and the laws of physics; this incompatibility attacks not only the laws of these phenomena in which the reduction to movement is the object of hypothesis, but also the laws which govern perceptible movements".
It is not wholly in the great questions relating to the synthesis of the universe that the classical mechanics has shown itself very insufficient, but also in apparently much more modest problems like the theory of gases. It is by invoking the calculation of probabilities, by imagining a kind of statistics that it arrives at establishing extraordinarily complicated and also extraordinarily uncertain equations which elude all verification.
Professors who continue to teach the formulas of mechanics renounce more and more their belief in them. This fictitious universe, reduced to the points to which forces are applied, seems to them very chimerical. "There is not a single one of the principles of rational mechanics which is applicable to realities", recently wrote to me one of the scholars who have most deeply sounded the problems of mechanics, the eminent Prof. Dwelshauwers Dery.
In fact, mechanics has fallen into a state of anarchy from which it does not seem likely to emerge, notwithstanding the numerous attempts made to transform it. At the present time there exist three very different systems of mechanics: --
1. The classical mechanics, built up on the concepts of mass, force, space and time.
2. The mechanics of Hertz, which discards the notion of force and replaces it by hidden links, supposed to exist between bodies.
3. The energetic mechanics, founded on the principles of the conservation of energy, which we shall study later on. In this, matter and force disappear. There is not in the universe any other fundamental element but energy. This element is indestructible, while unceasingly changing its aspect. The various phenomena only represent mutations of energy.
We might, however, vary mechanical systems to infinity by replacing the concepts of time, space, and mass by arbitrary magnitudes and expressing phenomena as functions of these new magnitudes. This is sometimes done by introducing into the equations, instead of the coordinates of the classical mechanics, the physical magnitudes such as pressure, volume, temperature, electric charge, etc., which determine the state of the body. From the principles derived from the study of the dissociation of matter cited in a previous chapter, there might be deduced a new mechanics in which matter would figure as the source of the various forces of the universe. We should write in the equations that such and such a force is simply matter minus something, that inertia is a consequence of the relations of equilibrium between intra-atomic energy and the ether, etc. We should thus link force to matter, and we should express the former as a function of the latter conformably with the teachings of experiment.
But the moment has not arrived to translate into equations magnitudes of which the relations are not yet fixed. It is not very probable that this new mechanics would explain much better than the old one the mysteries of the universe.
The fact that we only perceive in the universe matter and movement does not authorize us to maintain that it is not composed of anything else. We can only say that by reason of the insufficiency of our senses and of our instruments we only perceive that which presents itself in the form of matter and movement. Twenty years ago, we might strictly have said that there was nothing else. But the very unforeseen phenomena revealed by the study of the dissociation of matter have proved that the universe is full of formidable powers hitherto unexpected, and has shown the existence of immense territories completely unexplored. The edifice built by science which has so long sheltered our uncertainty now appears like a fragile shelter, of which the entire foundations have to be set up anew.
The Dogma of the Indestructibility of Energy
Chapter I
The Monistic Concept of Forces and the
Theory of the Conservation of Energy
1. The Conservation of Energy
The various forces of the universe were considered by the old physicists as different from, and as exhibiting no connection with each other. Heat, electricity, light, etc., seemed unrelated phenomena.
The ideas which sprang up during the second half of the last century differ much from this. After having settled that the disappearance of one force was always followed by the appearance of another, it was soon recognized that they all depended on the transformation of one indestructible entity -- energy. Like matter it might change its form, but the quantity of it in the universe remained invariable. The various forces, light, heat, etc., were only different manifestations of energy.
The idea that forces might be indestructible is of fairly recent origin. The dogma of the conservation of energy only boasts, in fact, about half a century of existence. Up to the date of its discovery, science only possessed one permanent element -- matter. For the last 60 years it has possessed, or has thought it possessed, a second -- energy.
The principle of the conservation of energy presents itself in a form so imposing and so simple, and answers so completely to certain tendencies of the mind, that one would suppose that it must have attracted keen attention the very day it was promulgated. Quite other was its fate. For 10 years not a single scholar in the world could be found who would even consent to discuss it. In vain did its immortal author, Dr Mayer of Heilbronn, multiply his memoirs (1) and his experiments. Mayer died of despair and so unknown that when Helmholtz repeated the same discovery a few years later, taking as a basis only mathematical considerations, he did not even suspect the existence of his predecessor. The critical mind is so rare a gift that the most profound ideas and the most convincing experiments exercise no influence so long as they are not adopted by scholars enjoying the prestige of official authority.
[(1) The first paper of Mayer, "Remarks on the Forces of Inanimate Nature", was published in 1842. His last, "Remarks on the Mechanical Equivalent of Heat" was published in 1851.]
Nevertheless, it always happens in the long run that a new idea finds a champion in some scholar possessing this prestige, and then it rapidly makes its way. As soon as the grandeur of the idea of the conservation of energy was understood by one such, it had an immediate success.
It was especially the discussion of W. Thomson (Later Lord Kelvin) and the experiments of Joule, confirming the results of Mayer on the equivalence of heat and work, which attracted the attention of specialists. The whole army of laborers of science then pounced upon this subject, and in a few years the unity and the equivalence of physical forces came to be proclaimed, though on rather narrow grounds.
This generalization proceeded from experiments which in reality did not include it. It was, in fact, deduced from the researches made to determine the rise in temperature produced by the fall of a weight to a given height into a liquid. It was noted that in order to raise by 1 degree the temperature of a kilogram of water it was necessary to let drop from a height of one meter a weight of 425 kilograms. This number 425 was called the mechanical equivalent of heat.
In this experiment and other similar ones we simply establish that the different forms of energy can be transformed into mechanical work; but nothing indicates any relationship between them. We can, by making a machine to turn by human arms, steam, the wind, electricity, etc., produce the same amount of work, although its causes are perceptibly different. To speak of the mechanical equivalent of heat only signifies that with 425 kilograms falling from a height of one meter we raise the temperature of water by 1 degree. In reality, heat or any form of energy is equivalent to work rather as a piece of 20 sous is equivalent to the pound of beef one can buy with it.
Since the part of science is much more to measure things than to define them, the acquisition of a unit of measure always realizes for it an immense progress. Thanks to the creation of a unit of energy or work, we have succeeded in stating exactly notions which were formerly very vague. When, by means of any form of energy, it is possible to produce a determined number of calories or of kilogram-meters, our minds are made up as to its magnitude. Practically it is always by means of the heat they produce, measured by the elevation of the temperature of the water of a calorimeter, that most chemical, electrical, and other forces are calculated.
To the principle of the conservation of energy others have been successively added which have allowed the laws of distribution to be clearly established. Applied at first solely to heat -- that is to say, to that branch of physics called thermodynamics -- they were soon extended to all forms of energy. Thus was founded a particular science, Energetic Mechanics, which we will briefly examine later on.
2. The Principles of Thermodynamics
Thermodynamics and energetic mechanics which is only the extension of the first named, rest on the three principles (1) of the conservation of energy, (2) of its distribution, or the principle of Carnot, and (3) of the law of least action.
The first, already indicated above, is formulated as follows: The quantity of energy contained in the universe is invariable.
Generalizing a little less confidently at the present time, we limit ourselves to saying that, in an isolated system, the sum of the visible energy and of the potential energy is constant. In this form the principle evidently remains unassailable, because the potential energy not being always available, we can always attribute to it the value necessary to satisfy the required ratio.
The second principle of thermodynamics, or principle of Carnot, although it has become very complicated from the introduction into it of very different things in a purely mathematical form, is nevertheless completely contained in the following enunciation given by Clausius: Heat cannot pass from a cold body to a hot without work. This is now generalized thus: The transport of energy can only be effected by a fall in tension. This signifies that energy always goes from the point where the tension is highest to that where it is lowest. The importance of the principle of Carnot dwells in this generalization. It is applicable not only to heat but to all known modes of energy -- calorific, thermal, electrical, or otherwise.
This passage of energy from the point where its tension is highest to that where it is lowest is perfectly comparable to the flowing of a liquid contained in a vessel communicating by a tube with another vessel placed at a lower level. It may equally be compared to the flowing of the water of a river into the sea.
Heat foes from a heated to a cold body, and never from a cold to a heated body, by a law analogous to that which compels rivers to flow down to the sea and prevents them from flowing back to their source. To say that rivers flow down to the sea and do not retrace their course is a simple translation of the principle of Carnot.
Expressed in this way, it appears as a self-evident fact. Carnot put it into almost as simple a form, and yet physicists took nearly 25 years to grasp its full bearing. His genius-inspired idea was just to compare a fall of great heat to a fall of water, and all subsequent progress has consisted in recognizing that the various forms of energy, electricity in particular, obey, in their distribution, the laws which regulate the flow of liquids. Let us see, however, exactly what Carnot wrote: --
"The production of motive power is due, in steam engines, not to an actual consumption of calorific, but of its transport from a heated body to a cool body -- that is to say, to the restoration of its equilibrium which is supposed to be broken by one cause or another, by a chemical reaction such as combustion or by some other... The motive power of heat may be compared to that of a fall of water. Both have a maximum that cannot be passed, and this irrespective of the machine employed to receive the action of the water and the substance used to receive the action of the heat. The motive power of a fall of water depends on the height and the quantity of the liquid; the motive power of heat depends likewise on the quantity of calorific used, which we will call the height of its fall -- that is to say, the difference of temperature of the bodies between which is effected the exchange of calorific".
Carnot was not an experimenter. His brief memoir is based on simple arguments, and can, in its essence, be brought down to the short passage I have quoted. And yet, by the sole fact of his principle being understood, the theoretical and practical science of the last century was entirely overturned. No physicist or chemist now enunciates a new proposition without first verifying whether it is in contradiction to the principle of Carnot. It might be said that never did so simple an idea have such profound consequences. It will forever serve to show the preponderant role of directing ideas in scientific revolution, and also how slow is the acquisition of the most simple generalization.
The second principle of thermodynamics has, in reality, much greater importance than the first. Of which, moreover, it is almost independent. Even if energy were not preserved, its distribution would always take place, at least in the immense majority of cases, in accordance with the principle of Carnot.
The generality of this principle permits it to be extended to all the phenomena in the universe. It regulates their march, and forbids them to be reversible -- that is to say, it condemns them always to take the same direction, and consequently not to go backwards up the course of time. If some magic power greater than that of the demons of the mathematician Maxwell were to compel the molecular edifices to pass again into their former condition, it would slowly lead the world backward, and oblige it to retreat up the course of ages, and would thus force its inhabitants to assume successively the earlier forms in which they appeared during the chain of geological periods.
The principle of Carnot was completed by that called the principle of least action, or principle of Hamilton, which shows us the road which is follows by molecules constrained by superior force to transport themselves from one point to another. He tells us that these molecules can only take one direction, viz. the one which requires the least effort. This again is one of those principles of very great simplicity and yet immensely far-reaching. Reverting to the form given above to the principle of Carnot, that rivers descend to the sea and do not go back along their course, we may add that, by reason of the principle of least effort, rivers flow to the sea by the way which demands the least effort for the flow of water -- that is to say, by the greatest slope.
The Energetical Explanation of Phenomena
1. The Principles of Energetic Mechanics
It is one of the principles of thermodynamics, just briefly set forth, that the science of energetic mechanics, which claims to replace the classical mechanics, has been founded.
Energetic mechanics occupies itself solely with the measurement of phenomena, and never with their interpretation. Nothing inaccessible to calculation exists. Eliminating matter and force, it studies nothing but the transformations of energy, and only knows phenomena from their energetic actions. It measures quantities of heat, magnetic fields, differences of potential, etc., and confines itself to establishing the mathematical relations between these magnitudes.
A few brief indication will suffice to show how, in this theory, the forces of the universe are conceived. The energetic theory is rather a method than a doctrine. Still it has introduced into science certain important conceptions which I will briefly state.
In energetic mechanics, energy is considered under two forms -- the kinetic and the potential. The first represents energy in movement, the second energy at rest, but capable of acting when the repose ceases. Such, for instance, is the force of a coiled spring, of the weight of a wound-up clock, etc.
The potential and kinetic energy of a system may vary inversely, but their sum remains constant within the system. Kinetic energy depends on the position of the molecules and their velocities, and is proportioned to the square of these velocities. Potential energy depends solely on the position of the molecules. The principle of least action, explained above, permits the equations of movement to be established when the kinetic and potential energies are known.
2. The Quantity of Energy and Its Tension
Bringing precision into certain notions which are rather confused in the old mechanics, the energetic theory has shown that the energy of a body, whatever be the natural force to which it is related, is the product of two factors, the one tension or intensity, the other quantity. Tension regulates the direction of the transport of energy. According to the forms of energy, it is represented by a velocity, a pressure, a temperature, a height, an electromotive force, etc. By returning to the comparison of a force with the flow of a liquid which served Carnot to explain his principle, it is easy to understand the part played by these two factors -- quantity and tension. In a reservoir, quantity is represented by the mass of the liquid, tension by its height above the orifices through which it escapes.
All forms of energy being known only by the work they produce, and there being nothing to differentiate the work of the various forces -- electrical, mechanical, thermal, etc. -- it follows that they can all be expressed by the same unit of work, viz. the kilogram-meter. For the sake of convenience others are sometimes used, but they can always be reduced to kilogram-meters. It is thus, for instance, that the joule used in electricity as the unit of work represents about one-tenth of the kilogram-meter. In the language of modern physicists, energy has become synonymous with work reckoned in kilogram-meters.
The two factors quantity and tension are magnitudes to which we can give no other definitions that their measurement. In gravity, the quantity is represented by kilograms, the tension by the number of meters in the height of the drop. Their product represents the gravitic energy. In electricity, the quantity is represented by the output of the source in coulombs, the tension by the electric pressure in volts. In kinetic energy the quantity is represented by the mass and the tension by the velocity, etc.
In a general way, therefore, if we designate by E the energy expressed in units of work, by Q the quantity, and by T the tension, we have E = Q x T. It follows that Q = E/T. The quantity is therefore represented by the energy divided by the tension. (1)
[(1) In thermal energy the name of entropy is generally given to the quotient Q/T, in which Q represents the thermal energy and T the absolute temperature. This is expressed in a more general way by the integral M/T. When a certain quantity of thermal energy passes from a heated to a cold body, its entropy diminishes, and that of the cold body increases. The entropy can be varied without changing the temperature. It is therefore a variable which under certain conditions may change in an independent manner.
Out of this notion of entropy certain physicists seem desirous of making a special physical magnitude which can be generalized in the different forms of energy. We have seen that by the artifice of expressing the most varied forms of energy in work measured by kilogram-meters all energies are made equivalent, which allows them to be added up arithmetically. But there is no basis of equivalence for the factors of which they are composed. It is therefore not possible to add up the entropies of the different energies of a body to obtain one single total entropy. It is easy to see that the factors of the different energies express things very different in reality. In thermal energy, for example, the factor tension is represented by a temperature; in kinetic energy by a velocity; in gravitic energy by a height, etc.
One can be sure that a notion is obscure when it is understood in very different ways by the scholars who make use of it. Poincare regards entropy as "a prodigiously abstract concept", and it must be singularly so for the most celebrated physicists to comprehend it in such different fashions. This can be gathered from a long discussion published in the English journals Nature, The Electrical Review, and The Electrician, for 1900 and 1901. Eminent physicists published therein the most contradictory opinions, and seemed, moreover, astonished at their reciprocal ignorance of each other’s ideas. To engineers, the concept of entropy is a very simple matter calculable in figures because they have only applied it to the case of steam engines. To them the entropy of a body simply represents the variation (estimable in calories) of its thermal energy available for external work by degree of temperature and by kilogram of matter when heat is neither added nor taken away from it. The difficulties relative to entropy are derived from the impossibility of defining in what the different forms of energy consist. So far as electricity and heat, for instance, are concerned, one may remark with M. Lucien Poincare, "that it is impossible to establish a connection translatable into exact numerical ratios between a quantity of heat which is equivalent to a quantity of energy and a quantity of electricity which must be multiplied by a certain potential to express a certain quantity of work".]
One finds indeed things which seem analogous in the different forms of energy, but these analogies are often very superficial. In electricity the resistance almost corresponds to mass in kinetic energy, but to what does it correspond in thermal energy? Is it the heat necessary to change the state of a body without modifying its temperature, and to simply conquer the resistance of the molecules to change? On these important points the textbooks are silent. However that may be, in all forms of energy these two elements, quantity and tension, of which the product represents the work, are always found. Without tension there could be no transmission of energy. It is especially in electricity that the difference between the two factors quantity and tension is clearly seen. The static machines in our laboratories yield electricity under a very high tension since it may reach as high as 50,000 volts; but their output is insignificant, since it never amounts to more than a few thousandths of an ampere. A galvanic battery, on the contrary, has a high yield in amperes, while the electricity issues from it at a very feeble tension hardly exceeding two volts.
The old electricians, who knew not these distinctions, thought very erroneously that the static machines in our laboratories were, by reason of the loud sparks they produced, powerful generators of electricity. The tension is enormous, but the quantity infinitesimal, so that the product of these two magnitudes represents an insignificant amount of work. It is for this reason that the sparks from these noisy machines produce insignificant results, while with industrial machines where the tension hardly exceeds 100 volts or so, but which give a high output, the physiological, calorific, and luminescent effects are considerable.
In the study of heat, the difference between the two magnitudes tension and quantity can likewise be clearly shown. Tension is represented by the temperature of a body, quantity by the number of calories it can produce. A very simple example will show the difference between the two factors.
Let us burn a match of fir-wood or a whole forest of the same tree, and the thermometer thrust into the flame of the match or into that of the forest will indicate the same temperature. It is evident, however, that the quantity of heat generated in the two cases will be far different. With the heat produced by the combustion of the match we can only bring a few drops of water to boiling point, while with the quantity of heat resulting from the combustion of the forest, we could boil several tons of the same liquid.
3. Transformation of Quantity into Tension, and Conversely
The product of the quantity by the tension -- that is to say, the work -- is a constant magnitude; but it is possible, without altering that product, to increase one of the factors and to diminish the other. These are operation to which commerce has recourse daily.
The hydraulic analogies given above -- and to which we should always turn if we wish to thoroughly understand the distribution of energy -- enable us to conceive how quantity can be transformed into tension, or conversely, without varying their total product. As regard a reservoir of liquid, for example, we can see that without varying the weight of the liquid and by simply modifying the height and width of the receptacle, we can obtain at will a very great output with very feeble pressure, or, on the other hand, a very small output with a very great pressure.
The transformation of quantity into tension, and conversely, is inconstant use in electricity. With a battery having a tension of only a few volts, but an output in amperes fairly great, it is possible, by passing the current through an induction coil, to bring the electricity to a tension of more than 20,000 volts, while greatly reducing its output. The converse operation may likewise be effected. In certain industrial installations we succeed in producing electricity under a tension of 100,000 volts, and then this tension, much too great to be of practical use, is transformed so as to obtain a great output at a feeble voltage. In all these operation, the product of the quantity by the tension -- that is to say, of the coulombs by the volts -- remains invariable.
Judging by their effects, we might believe that quantity and tension constitute two very different elements. They are in reality but two forms of the same thing. The transformation of quantity into tension results simply from the mode of distribution of the same energy. The converse operation will transform, on the contrary, tension into quantity. A coulomb spread over a sphere of 10,000 kilometers radius will give only a pressure of one volt. Let us spread the same quantity of electricity over a sphere of a diameter 100,000 times less -- that is to say, of 100 meters, and this same quantity of electricity will produce a potential a hundred thousand times higher -- that is to say, a pressure of 100,000 volts.
It would be the same for any other form of energy -- for instance, light. If we possess a pencil of light, lighting feebly a surface of given extent, and wish to increase the light of a part of this surface, we have only to concentrate the pencil on a small space by means of a lens. The intensity of the part lighted will be considerably increased, but the illuminated surface will be notably reduced. By the same operation, we might increase the temperature produced by a pencil of radiant heat to the melting point of a metal. By a converse operation -- that is to say, by dispersing a pencil of radiations by a prism or diverging lens -- we increase the surface lighted or warmed, but reduce the intensity by the unit of surface. None of the above operations has varied the quantity of energy expended. Its distribution alone has altered.
4. The Part of Matter in Energetic Mechanics
In the above summary, we have had recourse to the principles of energetic mechanics especially. As a method of calculation they are above criticism, but we must not try to get from them an attempt at the explanation of phenomena. Moreover, the energetic theory utterly rejects such explanations. Confining its role to the measure of magnitudes subsequently connected together by equations, it denies the existence of force, ignores matter, and replaces them both by a single entity -- energy, the varieties of which it limits itself to measuring.
"But then, it will be said", writes on of the defenders of the doctrine (Prof Ostwald), "if we have to give up atoms and mechanics, what image of reality will remain to us? But we need no image and no symbol. The task of science is to establish the relations between realities -- that is to say, tangible and measurable magnitudes -- in such fashion that, some being given, the others are deduced from them... Hereafter there is no need to trouble ourselves about forces of which we cannot demonstrate the existence, acting between atoms of which we are not cognizant, but only to concern ourselves with the quantities of energy brought into play in the phenomena under study. These we can measure... All the equations which link together two or more phenomena of different species are necessarily equations between quantities of energy. There cannot be any other, for, besides time and space, energy is the only magnitude which is common to all orders of phenomena".
Nor did the classical mechanics bring matter into its equations, since it only dealt with its effects, but it did not deny its existence. Energetic mechanics, which finds it simpler to ignore it than to seek to explain it, will never lead to any very high philosophical conception. Science would hardly have progresses if it had declined to try to understand what at first seemed above its reach. Tendencies of the same nature formerly existed in zoology, at the time when it was purely descriptive, and refused to deal with the origin of beings and their transformation. So long as such ideas prevailed, that science made but trifling progress; but if this narrow conception had not reigned for a long enough period, philosophical minds like Lamarck’s and Darwin’s would not have found the materials for their synthesis. It would be impossible to multiply too extensively the number of specialists whose lives are spent in weighing or measuring something. From time to time an architect appears who raises an edifice with materials which have been patiently brought together by sleepless workmen. The disciples of energetic mechanics are today accumulating documents of this kind against the day when superior minds will appear who will make good use of them.
In treating matter as a negligible quantity, energetic mechanics has only taken on its shoulder a metaphysical inheritance centuries old. For a long time it was one of the regular recreations of philosophers to prove that matter and even the universe did not exist, and to expatiate at length on these negations. These inoffensive speculations lose all interest as soon as one enters a laboratory. We are then indeed compelled to act as if matter were a very real thing with which the universe was built, and which is in consequence the substratum of phenomena. We there have to distinguish very clearly also the matter which can be weighted, and the different forms of energy -- light, heat, etc. -- which cannot be weighed, and are consequently added to bodies without increasing their weight.
Notwithstanding therefore all the equations of energetics, the great duality between matter and energy continued to exist. Matter might be eliminated from calculations, but this elimination did not make it vanish from reality.
The readers of my last work know how I endeavored to make this classical dichotomy vanish by showing that matter was nothing else than energy in a form which had acquired fixity. We have taken from it none of the special properties which allow is to affirm its existence as matter, but have simply shown that it constitutes a form of energy capable of transforming itself into other forms, and that it is, through its dissociation, the origin of most of the forces of the universe, notably solar heat and electricity. Far, then, from deciding on its non-existence, we have been led to consider it as the principal element of things.
The Degradation of Energy and Potential Energy
1. The Theory of the Degradation of Energy
The dogma of the indestructibility of energy no longer rests on very safe arguments, but it is supported by some very strong beliefs which put it above discussion. Very scarce are the scholars who, following the example of the illustrious mathematician Henri Poincare, have discovered its weakness and pointed out its uncertainties.
From the time of the earliest researches into the relations of heat and work, it was recognized that if it were possible to transform a given quantity of work into heat, we possess no means of effecting the converse operation without loss. The best steam engines do not transform into work much more than one tenth of the heat expended. Observation indeed shows that the disappearance of any form of energy is always followed by the apparition of a different energy; but this evolution is accompanied by a degradation of the original energy, which becomes less utilizable. The sole exception is perhaps gravitic energy.
The indestructibility of energy did not, then, imply its invulnerability. There would have to be several qualities of energy, of which heat would be the lowest. The different energies having an invincible tendency to transform themselves into this low form of energy, it followed that all those in the universe would finally undergo this transformation. As differences of temperature equalize themselves by diffusion, and as heat is only utilizable as energy on condition of its being able to act on bodies of lower temperature, it follows that when all particles of matter contain energy at the same low degree of tension, no exchange could take place between them. This would be the end of out universe. From a highly differentiated state, it would have passed gradually to a non-differentiated state. Its energy would not be destroyed, since by definition it is supposed to be immortal. It would become simply unusable, and would remain unutilized until the day when our world would meet with another at a lower level of energy, with which it would in consequence exchange something. In the theory which we shall now deduce from our researches, things would have a little differently.
2. Potential Energy
The concept of potential energy is only the extension of facts of elementary observation. I have already said that in the theory of conservation of energy this latter presents itself in two forms, kinetic energy or energy of movement and potential energy. In an isolated system these two forms of energy may vary in opposite directions, but their sum remains constant. If therefore we call the kinetic energy of a system C, and the potential energy P, we obtain C + P = constant.
Evidently nothing is simpler and the classic example of the weight of the wound-ip clock well illustrates this apparent simplicity. So long as the weight does not act, the kinetic energy employed in winding it up remains stored up in the potential state. So soon as the weight commences to descend, this potential energy passes into the kinetic state, and at any moment of its course the sum of the kinetic energy expended and that of the potential energy not yet used is equal to the total energy primarily employed to raise the weight.
In such elementary cases as this, there is no difficulty in distinguishing the kinetic from the potential energy; but once we go beyond these very simple examples, it becomes possible, as Poincare has shown, to separate the two forms of energy, and consequently to ascertain the total energy (chemical, electrical, etc) of a system. The formulas end by including such heterogeneous things, that energy can no longer be defined.
"If we wish", he says in La Science et l’Hypothese, "to enunciate the principle of the conservation of energy in all its generality, and to apply it to the universe, we see it, so to speak, vanish, and there remains but this -- there is something which remains constant. But is there even any sense in this?".
Very fortunately for the progress of science, when the consequences of the principle of conservation of energy were developed, its champions did not look so closely into the matter. Disdaining objections, they established a principle which has rendered immense services by the researches of which it was the origin. What it has especially shown is that the work expended to produce a certain effect -- a new chemical equilibrium, for instance -- is not lost, but is recovered when the body returns to its primitive state. It is nearly thus, moreover, that the principle of the conservation of energy is now regarded. It brings us back, then, to saying that the work yielded by a spring when released is equal to the power absorbed in compressing it. And we thus stumble once more on one of those truths of commonplace obviousness which often form the web of the greatest scientific principles.
However this may be, the faculty which physicists have arrogated to themselves of considering the energy which appears to be lost as having passed into its potential state, will always remove the principle of the conservation of energy from experimental criticism. Latent potential energy plays the part of those "hidden forces" by the intervention of which the early mechanics succeeded in fitting into its equations the experiments which escaped them. The moment conservation of energy is admitted as a postulate, we must suppose that that which appears lost is to be found somewhere else, and the abyss of potential energy provides it with an inviolable shelter. But if we start from the contrary postulate, that energy can be used and lost, we are compelled to acknowledge that the second postulate would have in its favor at least as many facts as the first.
These are, moreover, barren discussions, since experiment is incapable of throwing light on this question. We had, therefore, to retain the principle of the conservation of energy until, after having penetrated further into the intra-atomic universe, it had benn clearly set forth in what way energy becomes lost. This is a point of which the solution can be dimly seen, and I will presently examine it.
It would be equally useless to dwell on facts which agree very badly or not at all with the principle of the permanence of energy, since it is enough to imagine any hypothesis whatever to make them fit in with this principle. Thus a way of explaining how the mass of a body can immensely increase with its velocity, as has been proven by experiments with radioactive particles, will certainly be found. It has indeed been explained how a permanent magnet may be for an indefinite space of time traversed by currents without its becoming heated by the friction, which would lead to the loss of its magnetism. It was enough to suppose that either it had no resistance -- that is to say, to confer on it a property that the non-instantaneous nature of the propagation of light proves not to exist.
These unverifiable hypotheses have always allowed a theory to be saved so long as it is a fertile one. Many hypotheses in physics, such as that of the kinetic theory of gases, would probably quickly vanish if the experiment could throw light on them. These molecules unceasingly bustling against each other with the velocity of a cannon ball, without becoming heated, thanks to an elasticity supposed to be infinite, having perhaps but a very remote resemblance to the reality. The theory is rightly retained because it is a fruitful one, and because no possible experiment enables us to prove its inaccuracy.
We have seen how the theory of the degradation of energy and its transformation into inaccessible potential energy allows us to withdraw the principle of the conservation of energy from the criticism of experiment. This theory has satisfied the immense majority of physicists, but not all. We know what Poincare thinks of it. He is not the only one to have stated doubts. Quite recently, M. Sabatier, Dean of the Faculty of Sciences at Montpellier, propounded in an interesting inaugural lecture with the title "Is the Material Universe Eternal?", the question whether it was quite certain that there was not a real and progressive loss of energy in the world; and more recently still, in a memoir on the degradation of energy, one of our most far-seeing physicists, M. Bernard Brunhas, expressed himself as follows: --
"What is our warrant for the statement that the universe is a limited system? If it be not so, what signify these expressions: ‘the total energy of the universe’, or the utilizable energy of the universe? To say that the total energy is preserved but that the utilizable energy diminishes, is this not formulating meaningless propositions?
"It would not be absurd to imagine a universe where, after the example of our solar system, the total internal energy might go on diminishing while the fraction remaining would constantly pass into an unusable form, where energy would be lost and at the same time degraded.
"The law of the conservation of energy is only a definition: the proof of this is that when a new phenomenon comes to establish a discord in the equation of energy, there is set up for it a new form of energy defined by the conditions of reestablishing the compromised inequality".
And in answer to a letter in which I set forth my ideas on this point, the same physicist wrote to me: --
"The ‘nothing is lost’ should be deleted from the exposition of the laws of physics, for the science of today teaches us that something is lost. It is certainly in the direction of the leakage, of the wearing away of the worlds, and not in the direction of their greater stability, that the science of tomorrow will modify the reigning ideas".
I have faithfully set forth, in this and the preceding chapters, the theories which rule science at present. My criticisms have not interfered with the faithfulness of my exposition. Their object was simply to show that the current theories contain some very weak points, and that consequently it is permissible to replace them, or at least to prepare for their replacement. No longer fettered by the weight of early principles now sufficiently shaken, we can proceed to examine whether, in place of being indestructible, energy does not vanish without return, like that matter of which it is only the transformation.
The New Conception of Forces
Chapter I
The Individualization of Forces and the
Supposed Transformation of Energy
1. The Transformations of Energy
No one at the present day is unaware -- and the first savages who succeeded in obtaining fire by rubbing together two bits of wood might have suspected the fact -- that with a given form of energy other forms may be produced. Yet the theory of the equivalence of forces and their transformations was only clearly formulated at the date of the discoveries relating to the conservation of energy.
The most elementary textbooks now teach that all the forces of nature are interchangeably transformable, and are only transformations of a single entity, viz.: energy.
In his work on The Evolution of Physics, Poincare has summed up the existing ideas as follows: --
"The physicists of the end of the 19th century were brought to consider that in all physical phenomena there occur apparitions and disappearances which are balanced by various energies. It is natural, however, to suppose that these equivalent apparitions and disappearances corresponding to transformations, and not to simultaneous creations and destructions. We thus represent energy to ourselves as taking different forms -- mechanical, electric, calorific, and chemical -- capable of changing one into the other, but in such a way that the quantitative value always remains the same".
It is easy to comprehend the origin of this theory, but when we go deeper into it we discover neither the necessity nor the exactness of it. All that can be said in its favor is, that it escapes the test of experiment. It is certain that the various forms of energy appear to transform themselves, or better, that from any form of energy others can be produced. But these are merely apparent transformations like the turning of money into goods. For a 5-franc piece we obtain a meter of silk; but nobody thinks that the silver of which the coin is made transforms itself into silk. Yet a like transformation is admitted when we are assured that the friction of a rod of resin with a strip of flannel has been turned into heat and electricity. The modern theory of the equivalence and the transformation of energies seems indeed to be only an illusion arising from the fact that in order to measure them, we have chosen the same unit, viz., that of work estimated in kilogram-meters or in calories.
Under its most dissimilar forms, energy is simply defined as equivalent to a certain amount of mechanical work, and to the modern physicist energy and work have always been synonymous, although they are in reality very distinct things. We should have a very poor idea f the comparative value of a horse, a Negro, and a white man, if we confined ourselves to measuring the number of kilogram-meters that each could produce. Little can be known of things from simply measuring one of their quantitative elements. We must indeed be satisfied with such indications when others cannot be obtained; but in that case we must resign ourselves to acknowledging the insufficiency of our knowledge.
Movement, electricity, heat, etc., being evidently very different things, its seems natural to say that the different forms of energy are too dissimilar to be transformed one into another, but that the same effect may come from different causes. A motor is set in movement by various agents such as steam, electricity, manual labor, or wind, which are not akin to each other, although they produce identical effects. When movement or any kind of force produces heat, does this signify anything else than that with dissimilar means we obtain the variations of molecular equilibrium from which heat results? A transmutation such as that of movement into electricity or light would assuredly be more marvelous than that of simple bodies -- of, for instance, lead into gold.
I will not dwell further on this theory, which is little in conformity with the teachings of the present day. I should even have judged it useless to formulate it if chance had not brought before my eyes a memoir by Prof Ostwald, who arrives by other roads at the same conclusion as myself. These are his words:--
"As is well known, we distinguish since Hamilton’s time two kinds of physical magnitudes -- scalars and vectors. These two kinds of magnitudes are essentially different in their nature, and the one can never be represented by the other. I am persuaded that there exist a greater number of magnitudes of different kinds, and I believe I am justified in admitting that the different forms of energy are all characterized by magnitudes possessing such an individuality. Let this be confirmed, and the fact that up to the present mechanics has been unable to give a complete image of nature will appear as a necessity. Such a notion would be as precious for science as was, in its time, the notion of the individuality of chemical elements, and the modern adepts of mechanical theories, by claiming to reduce all forms of energy to mechanical energy, would no more have done useful work than did the alchemists who sought to turn lead into gold. That, in the course of such labor, all kinds of discoveries, as interesting as they were unexpected were made, is only one likeness the more to the often fertile activity of these obstinate gold-seekers".
2. Under What Forms Energy Can Exist in Matter
I have already examined this question in my last work, and I arrived at the conclusion that the energies manifested by matter are the consequences of the movements of its elements. It must be thanks to their rapidity that matter contains a very great quantity of energy in a very small volume. It is known that the liberation of one gram of hydrogen in the decomposition of water corresponds to a production of electricity equal to 96,000 coulombs -- say, an output of nearly 27 amperes an hour.
It does not appear that chemists consider in this light the manifestations of energy of which matter may be the seat. While careful to affirm that energy is in no way anything material, they treat it exactly as if it were a kind of fluid absorbed and restored by bodies as a sponge imbibes a liquid and gives it out when being squeezed. They constantly speak, in fact, of heat being absorbed or given out by a combination, and all thermochemistry is founded on the measurement of these absorptions and liberations. In reality, bodies in their transformation absorb nothing at all. When we are told that a body absorbs heat to transform itself, this simply signifies that in order to compel its elements to modify their equilibria they have had to expend energy. This energy will be restored on their return to their primary equilibria, just as a spring produces when released an amount of work, equal to that expended in its compression.
This image of a spring, rude as it may be, makes us clearly understand that the absorptions or liberations of heat by chemical compounds during their transformation are only displacements of energy following on changes of equilibrium. It will be easily recognized that a spring on its release produces a power equal to that expended to set it. It is to this elementary fact that the whole science of thermochemistry and also the principle of the conservation of energy may be referred. Carbon, the combustion of which -- that is to say, its combination with oxygen -- generates a quantity of heat, offers us the type of those bodies supposed to be capable of absorbing energy and then of retaining it. Chemists tell us with regard to coal that "the heat of combustion represents stored-up solar energy". It would seem that the coal has stored heat as a reservoir stores water.
In reality, it has stored nothing during its formation; but, being a body with a strong affinity for the oxygen of the air, and producing, when in combination with it, equilibria which are accompanied by a great liberation of heat, we utilize this last to produce water-vapor, the elastic force of which sets in motion the pistons of our steam engines. If the air, instead of oxygen, had contained only nitrogen, coal would never have been considered as a storehouse of energy. It does not, in reality, contain it any more than a crowd of other bodies more abundant in nature, such as aluminum and magnesium. These metals, if not already engaged in certain combinations, would produce, by uniting with oxygen, heat as utilizable as that generated by the oxidation of carbon.
The reader who bears in mind my theory of intra-atomic energy, according to which all atoms are a colossal reservoir of energy, will no doubt object that, apart from any combination, any body whatever is thus a reservoir of forces. But these forces have not been utilized up to the present. Only molecular and not intra-atomic reactions are recognized by chemistry and commerce. They were thus the only ones we had to deal with in the preceding remarks.
The Changes of Equilibria of Matter and of the Ether as the Origin of Forces
1. Alterations of Level as Generators of Energy
Physicists measure forces and energy, but do not define them. For them force is simply the cause of a movement, and they evaluate its magnitude by the acceleration it produces. When a force displaces its point of application over a certain length, it gives a determined amount of work. This mechanical work being the unit with which all forms of energy are measured, the effect has finally become confused with the cause, and for many physicists work and energy have become, as has been said, synonymous. Forces form part of the irreducible elements of the universe. Not being, like time and space, comparable to anything, we cannot define them. We shall here only attempt to put in evidence a general condition of their manifestation.
All the forces of nature are generated by disturbances of equilibrium in either the ether or matter, and disappear when the disturbed equilibria are restored. Light, for instance, which is born with the vibrations of the ether, ceases with them.
Two bodies charged with heat, electricity, movement, etc., cannot, whatever be the difference of magnitude of these bodies, act on each other and produce energy, save when the elements with which they are charged are out of equilibrium. From this defect of equilibrium results what is called tension, or, again, potential. In heat, tension is represented by the difference of temperature; in electricity, by the electromotive force; in energy of movement, by the velocity; in gravity, by the drop, etc.
This break of equilibrium excites a sort of flow of energy. It takes place from the point where the tension is highest towards that where it is lowest, and continues till the equilibrium is reestablished -- that is to say, until there is an equality of level between the two bodies in question. We may therefore consider as generators of energy a liquid passing from a higher to a lower level; heat passing from a hot to a cold body; electricity flowing from a body with a high potential to one with a low potential; movement transmitted from a body animated by velocity to another with less velocity, etc. Thus energy depends on the state of the bodies in presence. There is only an exchange between them if they are out of equilibrium -- that is to say, if they possess different tensions. One of the bodies present then loses something which it yields to the other until their tensions are equalized. In order that they may then generate a new quantity of energy, they must be put in presence of a third body, which is out of equilibrium with them.
Generally speaking, that which substances yield up to each other during these exchanges are forms of movement. All the modes of energy are known and measured by these movements.
According to the media in which the disturbances of equilibrium manifest themselves, and according to their form, they are termed heat, electricity, light, etc.
The disturbances of equilibrium which generate forces are themselves the consequence of other disturbances. They follow, by substituting themselves for, on another, which is why a force only appears at the expense of another force, which is at the same time annulled.
Taking these facts as starting point, we could formulate in the following way the principle of the conservation of energy. In a closed system and equilibrium cannot be destroyed without being replaced by another equivalent form of equilibrium. These things happen as if all the elements of the universe were related to each other in such a way as to constitute a sort of articulate system. Nothing, however, indicates that the universe is a closed system, and the fact that energy is always degraded when transformed -- that is to say, becomes less and less utilizable -- seems to show that the springs of our supposed articulate system cannot work without losing something.
This essential notion of the disturbance of equilibrium as the origin of energy may be put in evidence by a few examples. Let us place on the same level two receptacles full of water and connected by a tube. Being in equilibrium they cannot produce any energy. Raise one of the receptacles above the other, and the equilibrium of their contents is at once disturbed, and part of the liquid flows from the higher to the lower receptacle until the equilibrium is again established. During this interruption, and only while it lasts, will the water be able to do work -- to lift a piston, for example.
It is exactly the same with heat, electricity, or any other energy. Two bodies heated to the same temperature represent two reservoirs on the same level, or two equal weights on the scale-pans of a balance, and there results from this no manifestation of energy. If, on the contrary, the temperature of one of the bodies is lower than that of the other, there will be a disturbance of equilibrium and a production of energy until the two bodies arrive at the same calorific level.
It is the same with electricity. There can be no production of electrical energy without an interruption of equilibrium. Whatever the quantity of electricity with which we charge a body, it will produce no energy if it be in relation with another at the same potential -- that is to say, at the same electrical level.
Our instruments of measurement -- thermometers, galvanometers, manometers, etc., simply indicate energetic differences of level, to which we give the names of temperature, pressure, voltage, etc., existing between some source of energy and an arbitrary zero taken as point of reference. If the bulb of a thermometer were at the temperature of the source to be measured -- that is to say, in equilibrium with it -- it is evident that the column of mercury would remain motionless. What a voltmeter measures is likewise the difference of level between a source of electricity and itself. Our instruments, like our senses, are only sensitive to differences.
Thus, then, without an alteration of level of the ether of matter there can be no possible manifestation of energy. If the sun possesses throughout its mass a uniform temperature of 6000 degrees, and there could exist in it beings capable of supporting that heat, it would represent to them no energy. Having no cold bodies at their disposal, they could produce no fall of heat, a condition indispensable for the production of thermal energy.
Let us now suppose that, instead of finding themselves at a uniform temperature of 6000 degrees, these imaginary beings live in a world of ice at the uniform temperature of zero, but possess in a corner of their world still colder an unlimited provision of liquid air. Contrary to those plunged in a medium at 6000 degrees, they would find in the blocks of ice around them a considerable source of energy. By plunging these latter, in fact, into the liquid air at 180 degrees, they would obtain a considerable alteration of temperature. At the contact of the ice, which is to liquid air a very hot body, this latter would immediately boil, and its vapor could be employed to put motors in operation. The inhabitants of that world would therefore replace the coal of our steam engine by blocks of ice, which they would consider, certainly with more reason than we do coal, reservoirs of energy.
With this ice and this liquid air, it would be very easy for them to produce the highest temperatures. The tension of the vapor obtained could be employed, in fact, to drive dynamos, by means of which can be obtained electric currents capable of producing temperatures sufficient to fuse and volatilize all metals.
That which has just been said concerning interruptions of equilibrium as the condition of the production of energy, applies to all its forms, including that possessed by bodies in motion. It can only be born from the encounter of bodies not having the same tension -- that is to say, the same velocity -- and which cannot therefore be put in equilibrium. If the hunter’s bullet kills the animal flying before him, it is because the velocities of the two are different. If these were equal, the bullet would evidently have no effect. Equalities of velocity render manifestations of kinetic energy impossible.
The locomotive, notwithstanding its mass, can do nothing to the fly which hovers in front of it at the same rate of speed. The effects of masses, endowed with kinetic energy, on the bodies they meet, result solely from the inertia of matter, which prevents its instantaneously adopting the velocity of the elements which act upon it. If bodies were not possessed of inertia -- that is to say, of resistance to movement -- they would simply take the velocity of the masses striking them, and would not be destroyed by them.
Kinetic energy, therefore, on final analysis, represents movement which passes or tends to pass from one body to another. It is the same, moreover, with thermal energy. It manifests itself by molecular movements from a heated body to the elements of a cold body, the movements of which have less velocity. It is always movement which is transmitted in order to make itself equal with another movement, and to be in equilibrium with it.
Into the disturbances of equilibrium which I have invoked in order to explain the origin of energy, the notion of quantity has not entered. The quantity of heat, electricity, movement, or gravity possessed by the bodies put in motion matters little. They will only act on each other if the movement, the electricity, or the heat, with which they are charged, have different tensions. Whether one or one hundred kilograms are placed in the two pans of a balance, it will remain motionless as long as there is no difference between the two weights. All the manifestations of energy are subject to the same law. Bodies in the presence of each other can, I repeat, only yield something to one another if they are at different tensions.
Differences of tension -- that is to say, of equilibrium-- are the first condition of all productions of energy, but the magnitude of this energy results evidently from the masses brought into play by the differences of tension. It is evident that a weight of 100 kilograms falling from a height of 100 meters will produce more energy than 1 kilogram falling from the same height. The magnitude of the energy is therefore necessarily represented by the product of two factors -- quantity and tension. Tension represents a difference of level. Whether applied to very great or very small masses, it is the fundamental condition of the production of energy.
We see, finally, that all the forms of energy are transitory effects resulting from the interruption of equilibrium between several magnitudes -- weight, heat, electricity, or velocity. It is therefore quite erroneous to speak of energy as a kind of entity having a real existence analogous to that of matter. The considerations just set forth allow is to imagine a world the physicists of which would accept the second principle of thermodynamics, but would reject the first -- that is to say, that of the conservation of energy. Let us suppose a universe with an invariable temperature where the sole source of energy known is that of the waterfalls coming from immense lakes situated on mountain tops, such as one sometimes meets with in different regions of the earth. The learned men of such a work would no doubt have discovered pretty quickly the possibility of converting into heat, light, and electricity the energy of these waterfalls, but they would also have established by experiment that they could not without enormous leakage restore the water to its original level with the forces produced by its own flow. They would thus be led to believe that energy is a thing which is used up and lost, and that the energy of their world would be exhausted when all the water of the lakes should have descended to the plains.
2. Of What Elements the Entity Called Energy are Composed
It may be objected to the preceeding remarks, that it is not because a thing does not produce any effect that it does not exist. A weight held up by a thread is still a weight. Heat not in action is still heat; a force annulled by the action of another force does not on that account lose its existence. But when we reflect on the phenomena called heat, gravity, electricity, etc., we recognize that they are only known and measured as disturbances of equilibrium, and have, outside of these disturbances, no existence verifiable by our senses or instruments. Heat produces kinetic energy by its fall; but heat which does not change its level is no more energy than the tile fixed on a roof. No doubt the sun warms us, and there we see an energy which seems to be quite independent and to have an existence of its own. And yet all the energy produced results solely from a difference of temperature -- that is to say, of equilibrium -- between the caloric effects of the rays emitted by the star which warms us and the bodies which receive them. Let any body at the same heat as itself be brought as near as you please to the sun, and there will be no possible exchange of what we call caloric energy.
Physicists argue, moreover, exactly as if they admitted all this. They are fully aware that there must be alterations of level to effect work, and that no work can be manifested when the alteration of level has ceased. But as it would be possible to produce a flow of energy with a fresh alteration of level, they assert that this energy which is not manifested exists in a potential state.
All these concepts of potential energy, unusable energy, degraded energy, etc., are the consequences of a confusion of ideas, according to which energy is a sort of substance of which the existence is as real as that of matter. This invisible entity, the secret mover of things, is supposed to circulate unceasingly through the universe by constantly transforming itself. This hypothesis was, moreover, necessary when matter was believed to be an aggregate of inert elements only able to restore the energy it received, and incapable of creating any. Something was indeed necessary to animate it, and it was that something which constituted energy.
If this mysterious entity was necessary for the epoch when a superior cause had to be imagined for the animation of inert matter, its existence has no object at the present day. Instead of imagining an unexplained power perpetually circulating through the world without ever being exhausted, I say: --
At the origin of things there was condensed in matter, under the form of movement of its elements, an enormous but yet limited quantity of energy. This phase of concentration was followed by a period of expenditure of the accumulated energies, on which the sun and analogous stars have now entered. The disintegration of their atoms is the origin of all the natural forces now utilized. These atoms form an immense reservoir, but one which must inevitably exhaust itself. Then that which we call energy will, like matter, have disappeared forever.
By thus reasoning we only appeal to conceivable phenomena. Our explanation brings us to the brief enunciation of a limited provision of forces stored up in matter at the time of its formation, which produce, when this last disintegrates, different energies having only momentary existence. This is very simple, whereas the entity, supposed to be immortal, termed energy is completely incomprehensible. Science has not driven forth the gods from their ancient empire to replace them by metaphysical processes still more unintelligible than they.
The Evolution of the Cosmos -- Origin of Matter and of the Forces of the Universe ~
1. The Origin of Matter
The origin of things and their end are the two great mysteries of the universe which have cost religions, philosophies, and science the most meditation and thought. As these mysteries appear unfathomable, many thinkers turn away from them. But the human mind has never resigned itself to ignorance. It invents chimeras when it is refused explanations, and these chimeras soon become its masters.
Science has not yet lighted torches capable of illuminating the darkness which envelops our past and veils the future. It is able, however, to project some beams into this deep night.
If everything proceeds from the ether and afterwards returns to it, we are forced to inquire first of all how a substance so immaterial can transform itself into heavy and rigid bodies, such as a rock or a block of metal.
The ideas I have set forth on the structure of matter allow us in some degree to understand this and to deduce from them the following theory: --
Bodies are constituted by a collection of atoms, each composed of an aggregate of rotating particles, probably formed by vortices of ether. By reason of their velocity these particles possess an enormous kinetic energy. According to the way in which their equilibria are disturbed they generate different forces -- heat, light, electricity, etc.
It is probable that matter owes its rigidity only to the rapidity of the rotary motion of its elements, and that if this movement stopped it would instantaneously vanish into ether without leaving a trace behind. Gaseous vortices, animated by a rapidity of rotation on the order of that of the cathode rays, would in all probability become as hard as steel. This experiment is not realizable, but we can imagine its results by noting the considerable rigidity which is acquired by a fluid animated by great velocity.
Experiments made in hydroelectric factories have shown that a liquid column only 2 centimeters in diameter, falling through a tube of the height of 500 meters, cannot be broken into by a violent blow from a saber. The arm is stopped as if by a wall when it arrives at the surface of the liquid. Prof. Bernard Brunbes, who witnessed this experiment, is persuaded that if the velocity of the liquid column were sufficient a cannon ball would not go through it. A layer of water a few centimeters thick, animated by a sufficient velocity, would be as impenetrable to shells as the steel plates of an ironclad.
Lat us give to the above column of water the form of a vortex ring, and we shall get an image of the particles of mater and the explanation of its rigidity.
This enables us to understand how the immaterial ether, when transformed into small vortex-rings animated by sufficient velocity, may become very material. It will also be understood that, if these whirling movements were stopped, matter would instantaneously vanish by return to the ether.
Matter, which seems to give us the image of stability and repose, only exists, then, by reason of the rapidity of the rotary movement of its particles. Matter is velocity, and, as a substance animated by velocity is also energy, matter may be considered a particular form of energy.
Velocity being the fundamental condition of the existence of matter, we may say that this last is born so soon as the vortex rings of the ether have acquired, by reason of their increasing condensation, a rapidity sufficient to give them rigidity. Matter grows old when the speed of its elements slackens. It will cease to exist so soon as its particles lose their movement.
We are therefore brought to this first essential notion: Particles of a substance, however minute we may imagine them to be, may, by the sole fact of their velocity, acquire a very great rigidity and become transformed into matter. Let us now examine how, with these two elements, particles of ether and velocity, it is possible to understand the genesis of a universe.
2. The Formation of a Solar System
The fist scientific theory on the origin of the world was, as we know, formulated by Kant and developed by Laplace. According to this last, our solar system with its retinue of planets must be derived from a primal nebula similar to those observed in space. Agglomerated under the influence of gravitation, which would thus be the primitive force, it formed a central globe animated with a movement of rotation, whose particles by constant attraction have drawn closer and closer together.
By reason of the increasing rapidity of its rotation, following on its condensation, this first nucleus of the sun became flattened, and at a certain moment there were detached from it by centrifugal force rings similar to those existing round Saturn.
Continuing their movement of rotation, these rings finally, still under the influence of centrifugal force, broke into fragments. From these fragments, projected into space, were born the planets which revolve round the sun. Incandescent at first like this last, but cooling relatively quickly by reason of their small volume, they at length became inhabitable by living beings.
Laplace stopped his investigation at the cooled planet, and did not busy himself wither with the elements which formed it nor with those which might enter into the constitution of other solar systems.
It is now possible to go further, and to apply to atoms the laws which seem to have presided at the birth and formation of our universe.
It is now admitted that atoms are formed of numerous particles revolving round one or several masses with a velocity of the order of light. The atom may therefore be compared to a sun surrounded by its retinue of planets. Its small size does not prevent such a comparison. In an immensity without limits extreme littleness does not sensibly differ from extreme greatness. Beings sufficiently small would consider the planetary system formed by the elements of an atom as important as are to us the gigantic stars of which astronomy observes the march.
In the study of the evolution of worlds it is today easy to go, as has been said above, far beyond Laplace. No one could suspect in his time that spectrum analysis would make known the composition of the sun, and would reveal therein elements identical with those of our globe -- an evident proof that the terrestrial elements are derived from those of the sun.
Spectrum analysis has, moreover, enabled us to follow the genesis of the elements which compose the various worlds. The variation of the spectra of the stars in the red and the ultraviolet regions indicates their temperature, and consequently their relative age; while the other spectral rays make known their composition. We have thus determined the bodies appearing in the stars with the variations of temperature corresponding to different phases of evolution. In the youngest stars -- that is to say, the hottest -- there hardly exists anything but a few gases, principally hydrogen; then, as these stars become cooler, there successively appear the simple bodies we know, beginning with those of the lowest atomic weight.
Since astronomy has learnt to fix by photography the image of the stars, it has established that their number is much larger than it once thought. It now estimates at more than 400 millions the number of luminous stars, planets, and nebulae existing in the firmament, without speaking, naturally, of those that are invisible and consequently unknown. Spectrum analysis shows that they are at very different stages of evolution. Their past must be of fearful length, since geologists estimate the existence of our planet at several hundred million years.
During these accumulations of ages unknown to history, the millions of stars with which space is peopled must have begun or ended cycles of evolution analogous to that now pursued by our globe. Worlds peopled like ours, covered with flourishing cities filled with the marvels of science and the arts, must have emerged from eternal night and returned thereto without leaving a trace behind them. The pale nebulae with shadowy forms represent perhaps the last vestiges of worlds about to vanish into nothingness or to become the nuclei of a new universe.
How can the worlds undergo the phase of descending evolution succeeding that of ascending evolution briefly pointed out in this chapter? This we shall soon study.
We will especially bear in mind from what has been said that the transformations revealed by observation of the stars point out the general march of the evolution of worlds. It is always enclosed in that fatal cycle of things -- birth, growth, decline and death.
Whether it is the transformation of worlds or that of the beings living on their surface that is the question, slowness is always the law of evolution. In order to succeed in forming beings gifted with the small amount of intelligence possessed by man, nature has caused to evolve through thousands of centuries the animal forms which preceded him. Her transformations are only realized at the cost of very slow efforts. She cannot create a world in seven days like the god of early legends. If mighty divinities reign in some distant region, they are not sovereign divinities, for Time dominates them, and they can do nothing without him.
3. Molecular and Intra-Atomic Energies
In order to avoid all confusion in what is to follow, we must first clearly separate molecular from intra-atomic energies. These are probably close relations between them.
Molecular energies are the only ones hitherto known to science. They generate cohesion, affinity, and chemical combinations and decompositions. The manifestations of intra-atomic energy sometimes accompany them, as in the phenomena of incandescence, but they formerly escaped all investigation.
It is solely to molecular energies that the laws of thermodynamics and of thermochemistry have been applied. They always come back to this: A material body can emit no energy but that which it has first received.
The forces manifested in all chemical and industrial operations represent simply restitutions or displacements of energy; and it is conceived that, under such conditions, the quantity of this last remains invariable. These operations are identical with those effected by the introduction into reservoirs of various shapes of a certain quantity of water contained in another reservoir. This substitution naturally does not change the weight of the liquid.
Science, then, has only examined those intra-molecular energies with which bodies can be charged. This study has led to matter being considered as entirely distinct from energy, and simply serving as its support. Matter, when heated or electrified, could indeed absorb energy; but it restored this borrowed energy afterwards, as a sponge does the water it has absorbed, without ever increasing its quantity.
Matter being only the support of energy, we seemed perfectly justified in establishing a difference profound and, as it was thought, irreducible between matter and energy.
4. Intra-Atomic Energy as the Source of the Forces of the Universe
The readers of my last work know how I sought to cause this great dichotomy to disappear by showing that matter, far from only being able to restore the energy borrowed by it from without, is, on the contrary, a colossal reservoir of forces. It is itself only a particular form of energy characterized by its relative fixity and its concentration in immense quantity but in small volume. The energy accumulated in 1 gram of any matter represents as much as about 3 billion kilograms of coal. I showed finally that this intra-atomic energy was the source of solar heat, of electricity, and of most of the forces of the universe.
Intra-atomic energy is, moreover, very stable or the world would long ago have vanished. It is even so sable that chemists considered the aggregation of energy called matter to be absolutely indestructible. We have now learnt to dissociate matter, but only in extremely feeble quantities. It may, however, be hoped that the science of the future will find means to disaggregate it more thoroughly. It will then have at its disposal an immense source of forces. I have shown in my former work that by artificial means very stable bodies can be rendered -- surface for surface -- 40 times more radioactive than substances spontaneously dissociable, such as uranium.
The study of intra-atomic energy, which is now only beginning, has enabled us to penetrate into an entirely new world where the ancient laws of chemistry and of physics are no longer applicable. One of the most important of these differences is the following: --
In handling intra-atomic energy we can only draw from an isolated material system a quantity of energy at the most equal and never superior to the amount primarily supplied to it. In the manifestations of intra-atomic energy, we observe just the contrary. Matter is able to liberate spontaneously large quantities of energy either without any aid from without, as is seen in highly radioactive bodies such as uranium and radium, or under such feeble influences as a ray of light. With a very minute quantity of energy we can therefore produce a very large quantity, which fact is contrary to principles formerly considered indestructible.
When seeking, in my previous work, for the causes of solar heat and of the incandescence of the nocturnal stars, I showed that intra-atomic energy greater than that which exists on the cooled globes ought to suffice for the maintenance of these stars’ temperature. Studying subsequently the properties of the emissions from the isolated poles of an electrical machine, I showed their identity with the products of dissociation of radioactive bodies. Electricity might, then, be considered as one of the manifestations of intra-atomic energy. And it is thus that its part in natural phenomena, so unsuspected a few years ago, appeared to me entirely preponderant. Our sun, in the phase of the world into which it has entered, only expends the energies accumulated by its atoms during an earlier phase of concentration.
This dissociation of the provision of intra-atomic energy accumulated in matter at the commencement of things explains the origin of the forces of the universe. At those far-off epochs of the chaos of our solar system of which the nebulae show a confused image, the ether slowly condensed. The localized vortices of ether, forming probably the primitive elements of matter, accumulated by the increasing velocity of their rotation the intra-atomic energy of which we note the existence. To the phase of concentration succeeded, later on, a phase of dissociation. Our universe has entered upon a new cycle and the energy slowly accumulated in the atom has commenced to liberate itself by reason of its dissociation. The solar heat, whence is derived the greater part of the energies of which we make use, represents the most important manifestation of this dissociation.
Although this provision of intra-atomic energy is immense, it is not infinite, and its emission, consequently, cannot last forever. The planets surrounding the stars have cooled because this energy is reduced. The sun itself must be subject to the same law. When its intra-atomic energy has been dissipated, it will cease to light the planets around it, and the earth will become uninhabitable, unless science discovers the means of easily liberating the immense quantity of intra-atomic energy still contained in matter. But even should its succeed in this, it will but retard the repose, since the provision of intra-atomic energy is limited.
Thus, then, the sun, the generator of most of the terrestrial energies, only expends the forces slowly accumulated in matter at the epoch when within the primordial clouds of the ether the atoms stored up the energies they were one day to restore.
How can this intra-atomic energy, the source of solar heat, electricity, and most of the forces of the universe, be dissociated and lost? We will new examine this point.
The Vanishing of Energy and the End of Our Universe
1. The Old Age of Energy and the Vanishing of Forces
We have just seen that intra-atomic energy is a limited magnitude, which is reduced day by day. How can it be lost? Having already treated this question in my last work, I will only summarize what I have already there explained.
To say how matter finally vanishes is to explain how forces vanish, since matter is a special form of energy, only differing from others by its relative fixity and its very great concentration in a very feeble volume.
I have shown that one of the most constant products of the dissociation of matter was the so-called particle of electricity, deprived, according to the last researches, of all material support, and considered as constituted solely by a vortex-ring of ether.
The experiments previously described have shown that these particles emit lines of force, and are always accompanied in their various manifestations by those vibrations of the ether called Hertzian waves, radiant heat, visible light, invisible ultraviolet light, etc.. These vibrations represent for us the vanishing phase of the elements of the atom and the energies of which they are the seat.
How can the vortex-rings of ether and the energies generated by them lose their individuality and vanish into the ether? The question reduces itself to this: How can a vortex formed in a fluid disappear into this fluid by causing vibrations in it?
Stated in this form the solution of the problem is fairly simple. It can be easily seen, in fact, how a vortex generated at the expense of a liquid can, when its equilibrium is disturbed, vanish in spite of its theoretical rigidity by radiating away the energy it contains under the form of vibrations of the medium in which it is plunged. It is in this way, for instance, that a waterspout formed by a whirl of liquid loses its existence and disappears in the ocean.
In the same manner, doubtless, the whirls of ether constituting the elements of atoms can transform themselves into vibration of the ether. These last represent the final stage of the dematerialization of matter and of its transformation into energy before its final disappearance.
Thus, then, when the atoms have radiated all their energy in the form of luminous caloric, or other vibrations, they return, by the very fact of these radiations following on their dissociation, to the primitive ether whence they came. Matter and energy have returned to the nothingness of things, like the wave into the ocean.
The defenders of the postulate of the conservation of energy will evidently answer to the above, that energy being, by the hypothesis, supposed to be indestructible, by vanishing into the ether is not lost, and remains in the potential state, drowned in its immensity. Thus regarded, the theory of the conservation of energy evidently represents nothing but an unverifiable conception, especially created by our desire to believe that there exists in the universe something immortal. Not wishing to consent to being only a flash in the infinite, we dream of a movement that shall last forever.
But even if, in accordance with the preceding hypothesis, energy should continue to circulate in some form or other in space, yet, cast forth from the sphere of our universe, it would no longer forma part of it, and in one way or another the energy of the universe would have vanished. It is to this point, which is moreover fundamental, that we limit our demonstration.
It does not seem at first sight very comprehensible that worlds which appear more and more stable as they cool could become so unstable as to afterwards dissociate entirely. To explain this phenomenon we will inquire whether astronomical observations do not allow us to witness this dissociation.
We know that the stability of a body in motion, such as a top or a bicycle, ceases to be possible when its velocity of rotation descends below a certain limit. Once this limit is reached it loses its stability and falls to the ground. Prof J.J. Thomson even interprets radioactivity in this manner, and points out that when the speed of rotation of the elements composing the atoms descends below a certain limit they become unstable and tend to lose their equilibrium. There would result from this a commencement of dissociation with diminution of their potential energy, and a corresponding increase of their kinetic energy sufficient to launch into space the products of intra-atomic disintegration.
It must not be forgotten that the atom being an enormous reservoir of energy is by this very fact comparable with explosive bodies. These last remain inert so long as their internal equilibria are not disturbed. So soon as some cause or other modifies these, they explode and smash everything around them after being themselves broken to pieces.
Atoms therefore which grow old in consequence of the diminution of a part of their intra-atomic energy gradually lose their stability. A moment then arrives when this stability is so weak that the matter disappears by a sort of explosion more or less rapid. The bodies of the radium group offer an image of this phenomenon -- a rather faint image, however, because the atoms of this body have only reached a period of instability when the dissociation is rather slow. It probably precedes another and more rapid period of dissociation capable of producing their final explosion. Bodies such as radium, thorium, etc., represent no doubt a state of old age at which all bodies must arrive some day, and which they already begin to manifest in our universe, since all matter is slightly radioactive. It would suffice for the dissociation to be fairly general and fairly rapid for an explosion to occur in a world where it was manifested.
These theoretical considerations find a solid support in the sudden appearances and disappearances of stars. The explosions of a world which produces them reveal to us, perhaps, how the universes perish when they become old.
As astronomical observations show the relative *** these rapid destructions, we may ask ourselves whether the end of a universe by a sudden explosion after a long period of old age does not represent its most general ending. These abrupt annihilations manifest themselves as the sudden apparition in the heavens of an incandescent star, which pales and vanishes sometimes in a few days, leaving generally no trace behind it, or at most a faint nebula.
When the new star first appears, its spectrum, at first analogous to that of the sun, proves that it contains metals similar to those of our solar system. Then, in a short time, the spectrum is transformed, and becomes finally that of the planetary nebulae -- that is, it only contains rays of a few simple elements, some of which are unknown. It is therefore evident that the atoms of the temporary star have been rapidly and profoundly transformed. This downward evolution is the converse of that indicated in the upward evolution of stars. These contain, when very hot, simple elements which become more and more complicated and numerous as they continue to cool.
These transitory stars, resulting no doubt from the sudden explosion of a world accompanied by the disintegration of its atoms, are not rare. Hardly a year passes without some being observed either directly or by the study of photographic plates. One of the most remarkable was the one recently observed in the constellation of Perseus. In a few days it attained a brilliancy which made it the most brilliant star in the sky; but 24 hours later it began to pale, its spectrum was slowly transformed, and became, as said before, that of the planetary nebula -- an evident proof, I repeat, of atomic dissociation. At the very moment when this transformation was taking place, photographs of long exposure showed nebulous masses round the star, produced no doubt by atomic dissociation, which rapidly left it behind at a speed of the order of light -- that is to say, analogous to that of the Beta particles emitted by radioactive bodies when disintegrating. The astronomers were, then, enabled to be present at the rapid destruction of a world.
2. Summary of the Doctrine of the vanishing of Forces and Discussion of Objections
The account of the general evolution of worlds to which this and the preceding chapter have been devoted, includes facts of experiment or of observation which I have endeavored to connect by hypotheses. I will sum up this account by a recapitulation showing the different phases of evolution of a system analogous to ours and to those which continue to be born and transformed in the firmament.
3. The Periods of Evolution of a World
(1) Phase of Chaos or of the Birth of Energy -- Formation, by the action of gravitation or of unknown causes, of clouds and ether. Under their influence inequalities are established whence result differences of potential. The ether condenses into scattered particles which assume the form of vortex-rings. Animated at first by rather slow movements, they contain but very little energy.
(2) Phase of Nebulae or of Concentration of Energy -- The whirls of ether accelerate their movements. Thence attractions result which agglomerate them into nuclei, the future germs of matter. A general concentration of the mass is established. A nebula is formed, vague at first in shape, which ends by becoming spherical, and will eventually be the origin of a solar system. In proportion as the particles of this mass condense, the ether-whirls precipitate their movements, agglomerate and form the nuclei of atoms which, by reason of the increasing rapidity of their rotation, become more and more saturated with energy.
(3) Phase of Stellar Incandescence or of Expenditure of Energy -- This phase is that of the formation of a sun and analogous stars. By continuous condensation, the atoms have finally acquired a quantity of intra-atomic energy which they can no longer contain and therefore radiate in the form of heat, light, or various forms of electricity, of which heat is perhaps only a secondary manifestation. The temperature of the orb is excessive. The future atoms are not yet individualized.
(4) Phase of the Commencement of Stellar Refrigeration and of the Individualization of Matter -- By reason of the continuity of its radiation, the temperature of the orb becomes lower, although it still remains incandescent. The elements of the atoms form new equilibria, and give birth to the various simple bodies which differentiate and multiply in proportion as the cooling of the star increases.
(5) Phase of Planets, or of Refrigeration and of the Equilibrium of Intra-Atomic Energy -- The planets, detached by the centrifugal force of the central sun round which they continue to revolve, become cooler by reason of the relative smallness of their volume, and finally reach a temperature low enough for life to be possible on their surface. The energies accumulated in the form of matter have attained a phase of stable equilibrium. Fixity succeeds to mobility. The worlds are about to become inhabitable for long series of ages.
(6) Phase of Final Dissociation of Intra-Atomic Energy and Return of the World to the Ether -- While maintaining themselves in equilibrium for long centuries, the atoms have not ceased to radiate slightly, and in consequence of this radiation and of the reduction of the speed of rotation of their elements which ensues, they lose some of their stability. Then commences a period of disaggregation, which increases very quickly in proportion as the stability of the intra-atomic elements decreases. Progressive at first, it afterwards becomes instantaneous; at a certain period of old age, the elements return to the ether whence they came.
To this period of final destruction succeeds, perhaps, in the course of ages, a new cycle of birth and of evolution, without its being possible to assign a term to these destructions and recommencements, probably eternal (1).
[(1) The above rather reminds one of the "retour eternal" of Nietzsche; it is an hypothesis, moreover, void of importance, which I formulated long before that author, as Prof. Lichtenberger recalls in a book devoted to the doctrines of the philosopher.]
The above account, deduced from researches related in my preceding volume, may be summarized in a few lines. I borrow these from one of the scholars who have had the kindness to analyze my doctrine:--
"We imagine the world to be formed at first of diffuse atoms of ether which, under the action of unknown forces, have stored up energy. This energy, one of the forms of which is matter, dissociates and appears in various forms -- electricity, heat, etc., so as to bring matter back to ether. ‘Nothing is created’ signifies that we cannot create matter. ‘Everything is lost’ means that matter disappears entirely, as does matter by its return to the ether. The cycle is therefore complete. There are two phases in the history of the world: 1, Condensation of energy under the form of matter; 2, Expenditure of this energy".
This conception of the concentration of energy at the origin of a world and of its expenditure in a subsequent phase of its existence has been disputed by a distinguished physicist, M. Bernard Brunhes, in a recent memoir. The following is the objection he makes to it: --
"The concentration of cosmic matter and the dissociation of matter are two phenomena which appeared opposed to each other, but which possess a common characteristic. Both liberate heat and correspond to a degradation of energy. Be therefore assured that if any radioactive body whatever has been produced which has stored up an enormous provision of reserve energy, it is by favor of a still greater degradation of energy... Matter which dissociates at the end of transformations which seem to bring it back to the starting point will have undergone a definite loss of utilizable energy".
The above exception is supported by the principle of Carnot; but a principle applicable to the downward phase of evolution is not necessarily applicable to its earlier upward phase.
The illustrious mathematician Maxwell had already shown by a much bolder hypothesis than mine -- since it implies the existence of very subtle demons -- how the principle of Carnot might be violated and the course of things retraced. We must wait till we are better acquainted with the laws of nature before supposing that she has not found out the means of bringing out of the gloomy void of the ether the forces condensed in the atom. If hypotheses analogous to mine are rejected, we must return to that of a creator drawing forth worlds from his will -- that is to say, from a nothing much more mysterious still than the substratum from which I have endeavored to raise them. The gods having been eliminated from nature, where our ignorance alone had placed them, we must try to explain things without them. Evidently since the dawn of geological times, phenomena seem to have always evolved in accordance with the second law of thermodynamics; but this law is, I repeat, one of the period of the wearing out of a universe and not of the ages during which the energies now expended were condensed -- since we must admit that our solar system has had a beginning like all the analogous systems of which astronomy has noted the evolution. It is likewise necessary to admit that a concentration of energy was first formed. N. Brunhes, moreover, himself recognizes this in a passage of his memoir, which constitutes the best answer I can make to him: --
"There is no inconsequence in imagining that the present period of degradation has been preceded and may be followed by periods in which the energy utilizable may increase instead of diminishing".
It is, moreover, as the same author points out, at a similar conclusion that Boltzmann arrived in his great work on the theory of gases. The march of the world in the direction opposed to the present evolution no longer appears to him as an absolute impossibility, but simply as a very faint probability which may nevertheless have been realized during the succession of ages.
It is to these brief and uncertain notions that all we can say regarding the evolution of the worlds in the infinite duration of time is reduced. We will now leave these mysterious regions to return to those in which experiments can serve as a guide. The study of the actions of light on a fragment of metal, which was the origin of my researches, led me into very different fields of physics. I will now conduct the reader into these, and examine a few new problems.
As the general conclusion of this first part of my work, I shall formulate the following proposition: --
Energy is not indestructible. It is unceasingly consumed, and tends to vanish like the matter which represents one of its forms.