Appendix I to Part II
Nore ON THE VALIDITY OF THE PRINCIPLES OF INERTIA AND CONSERVATION OF ENERGY
We have spoken on several occasions (Vol. I, pp. 259-260; 270-278; 282) of these two principles and of the problem of their reconciliation with the principle of causality.
According to the principle of causality, there is no change without a cause; hence a cause is required as much for the change which takes place in the course of motion as for the transition from rest to motion itself. If it were otherwise, a finite and minimum impulsion could produce in the void a perpetual motion in which there would always be something new, a perpetual transition from potentiality to act; a finite power could forever be in motion, a snap of the finger ten thousand years ago would still produce its effect today, and would produce it always, eternally. This motion, which would have no need of being kept up, would have neither end nor beginning in the metaphysical sense of the terms. Would it not be contrary to the principles of causality and finality?
The principle of inertia is expressed as follows: of itself matter cannot set itself in motion or modify the motion that it has; a body in motion, if no external cause acts upon it, retains a rectilineal and uniform motion indefinitely.
If anyone objects that the facts seem to contradict the principle of inertia—v. g., that a billiard ball, shot on a very smooth plane, stops at the end of a certain time; that a train, after acquiring its normal speed, stops if the steam is not made to act on the pistons—the physicist replies that this stopping is due to the friction of the billiard ball on the plane, or to that of the wheels on the rails, and also to the resistance of the air.
Is it a demonstrated fact that this friction and this resistance are the only causes of the stopping? Is it scientifically proved that the given motion does not slow down also of itself? “Has it ever been proved from experiments with bodies removed from the influence of all external force,” asks H. Poincaré? “that these bodies are not influenced by any force?” How, without exceeding the limits of his science, can the physicist maintain that the divine motion is not necessary for a body hurled into a void to move eternally?
The principle of the conservation of energy is expressed as follows: “In a system of bodies removed from all external influence, the total energy (actual and potential) of this system remains constant.” This principle is necessarily connected with the preceding, and it is tantamount to saying that it is impossible for motion ever to cease; if it disappears under one form it reappears under another; thus the motion of a projectile ceases only in generating heat, and heat itself produces local motion. The equivalence is established by reason of the corrective administered to it by the law of the diminution of energy.
Does it follow that a given snap of the finger made a thousand years ago has still its effect today because of the transformations of energy, and that it will always be so, without any need for the energy to be renewed? Is it enough to admit that this energy is conserved by God, as Descartes says, and that the divine motion was only exerted in the past, in the beginning of the world? How, without exceeding the limits of his science, can the physicist declare that the divine motion is not necessary for the perpetual transformation of energy? It is clear that energy is not individually the same; it is not the same motion that passes from one body into another, for it is this motion, because it is the motion of this body. Likewse, human activity is relatively constant on the surface of the earth, and yet it is not individually the same; it is renewed, since human beings are born and die. Long ago Aristotle said: The corruption of one is the generation of another; matter loses one form only to receive another; and this can be expressed in modern terms with regard to energy by saying that a form of energy does not disappear without another appearing. Does it follow that the form which disappears is the first and all-sufficient cause of the one succeeding it? By no means; experimental science, which studies only the constant relations between phenomena, cannot declare itself either for or against the necessity for the intervention of a first invisible Cause for the transformation of energy. But, from the metaphysical point of view, one motion does not give rise to another1 except with the invisible concurrence of the First Being, who is the cause of all being as such, of the Prime Mover who is the supreme cause of the activity of secondary causes. Likewise, from the metaphysical point of view, a local motion cannot be perpetuated in a void, cannot be a perpetual transition from potency to act, without the invisible intervention of the pure Act, the supreme cause of all actualization. To maintain with Descartes that for this, it is sufficient that God conserve the motion, we must understand by this expression that God continues to move.
Thus only can the mechanical principles of inertia and conservation of energy be reconciled with the metaphysical principle of causality. Every other reconciliation, which rejects the necessity of the intervention of the first cause, is illusive.?
It is not for the physicist to solve this problem; he cannot pronounce finally on the validity of the solution given by the metaphysics of the Schools; he must merely recognize that this solution is in no way opposed to what physics has the right to affirm about the validity of its principles in the phenomenal order.
On this point it gives us pleasure to publish a letter from Pierre Duhem, of the Academy of Sciences, in which he gives us a summary’ of the main ideas of his fine work, La Théorie physique?
The letter reads as follows:
“Dear Father: I owe you some explanations for certain ambiguous terms in my previous letter and especially for the name ‘axiom’ or ‘socalled axiom’ which I gave to the principle of inertia.
“I begin by stating precisely that I shall take the words mathematics, physics, and metaphysics according to the meaning generally given them by our contemporaries, not according to the meaning given them by Aristotle and the Scholastics.
“In these circumstances, the law of inertia does not exist for the mathematician; the principles of the science of numbers and of geometry are the only ones that he has to admit; he is not concerned with the principles of mechanics and physics; if he happens to study the problems presented to him by the mechanist and the physicist, he does so regardless of the way by which they have been led to formulate these problems.
tion would have to be studied from the same point of view. 8 La Théorie physique, son object et sa structure.2
“I consider, therefore, the principle of inertia only as it is for the physicist.
“One may say of it, then, what may be said of all principles of the mechanical and physical theories. These fundamental principles or hypotheses (in the etymological sense of the word) are not axioms, self-evident truths. Nor are they Jaws, that is, general propositions reached directly by induction from the teachings of experience.
“It may be that certain rational probabilities or certain facts of experience suggest them to us; but this suggestion is in no way a demonstration; it does not confer on them, of itself, any certitude. From the point of view of pure logic, the fundamental principles of the theories of mechanics and physics can be looked upon only as postulates freely posited by the mind.
“From the ensemble of these postulates, deductive reasoning deduces an ensemble of more or less remote consequences which agree with the perceived phenomena; this agreement is all that the physicist expects from his postulated principles.
“This agreement confers a certain probability upon the fundamental principles of the theory. But it can never confer certitude on them, for it can never be demonstrated that, if other postulates were taken as principles, consequences would not be deduced which would agree just as well with the facts.
“Besides, it can never be affirmed that some day new facts will not be discovered which no longer agree with the consequences of the postulates that had been posited as being at the basis of the theory: new facts compelling us to deduce a new theory from new postulates. This change of postulates has been effected many a time in the course of the development of science.
“From these considerations two consequences follow: (1) We shall never have the right to affirm categorically of any one of the principles of the mechanical and physical theory, that it is true. (2) We are not allowed to affirm of any one of the principles on which the mechanical and physical theory rests, that it is false, so long as there has been no discovery of phenomena that disagree with the consequences of the deduction of which this principle constitutes one of the premises.
“What I have just said applies particularly to the principle of inertia. The physicist has not the right to say it is certainly true; but still less has he the right to say it is false, since we have so far met with no phenomenon (if we leave out of consideration the circumstances in which the free will of man intervenes) that compels us to construe a physical theory from which this principle would be excluded.
“All this is said without going beyond the domain of the physicist, for whom the principles are not affirmations of real properties of the bodies, but premises of deductions the consequences of which must be in agreement with the phenomena every time that a free will does not intervene to disarrange the determinism of the latter.
“To these principles of physics, can we and must we make certain propositions correspond which would affirm certain real properties of bodies? To the law of inertia, for instance, must we make the afirmation correspond that there is, in every body in motion, a certain reality, an impetus, endowed with such or such characteristics? Do these propositions apply or not to other beings endowed with free will? These are problems that the method of the physicist is incapable of grappling with and it leaves them to the free discussion of the metaphysicians.
“There is only one case which would induce the physicist to be opposed to this liberty of the metaphysician. It is that in which the metaphysician would formulate a proposition directly contradicting the phenomena or a proposition which, introduced in virtue of a principle in the physical theory, would lead to consequences in contradiction to the phenomena. In this case, there would be just grounds for denying the metaphysician the right to formulate such a proposition.
“Now you have, Reverend Father, the summary of what I would say if I were ever to write, concerning the principle of inertia, the article that you so kindly wish me to write.
P. Duhem.”
N.B. Conclusions more or less like those of Duhem are expressed by E. Meyerson. In his Identité et réalité (1908), he examines, from the point of view of experience and of philosophic reason, the validity of the principles of inertia and of conservation of energy. The author goes so far as to say, what seems to us quite right, that “the principle of inertia demands that we view motion as a state; if motion is a state, it must maintain itself like every state. . . . The principle of inertia demands that we view speed as a substance. Now this is an entirely paradoxical concept for the immediate understanding” (pp. 132, 134).
Professor Gustavo Pécsi, in his Crisi degli assiomi della Fisica Moderna, translated from the German (1910), goes further still and believes he can prove absolutely the falsity of the principle of inertia which would end in this contradiction: that motion is essentially motionless, that there is nothing new in it (p. 201).
Footnotes
Chapter 16 of 19