Note on the Validity of the Principles of Inertia
and Conservation of Energy
from Garrigou-Lagrange, Reginald, O.P.,
_God: His Existence and His Nature_, vol. 2,
Appendix I
We have spoken on several occasions 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 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. Poincare[1] "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?
1. _La science et l'hypothese_, pp. 112-119.
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 tanta-
mount to saying that it is impossible for motion ever to cease; if it
disappears under one form it reappears under another; thus the mo-
tion 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. Likewise, 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 ex-
pressed in modern terms with regard to energy by saying that a form
of energy does not disappear without another appearing. Does it fol-
low 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 de-
clare 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 another
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 meta-
physical 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 ac-
tualization. To maintain with Descartes that for this, it is sufficient
that God _conserve_ the motion, we must understand by this expres-
sion that God continues to move.
Thus only can the mechanical principles of intertia and conserva-
tion of energy can be reconciled with the metaphysical principle of
causality. Every other reconciliation, which rejects the necessity of the
intervention of the first cause, is illusive[2].
2. The reconciliation of the principle of inertia with the law of
universal attraction would have to be studied from the same point
of view.
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 Theorie physique_.[3]
3. _La Theorie physique, son object et sa structure_.
"I begin by stating precisely that I shall take the words mathe-
matics, 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 geom-
etry 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 formu-
late these problems.
"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 _laws_, that is, general propositions
reached directly by induction from the teachings of experience.
"It may be that certain rational probabilities or certain facts of ex-
perience _suggest_ them to us; but this suggestion is in no way a _dem-
onstration_; 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 _postu-
lates freely posited by the mind_.
"From the ensemble of these postulates, deductive reasoning de-
duces 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 any one of the prin-
ciples 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 con-
sequences of the deduction of which this principle constitutes one of
the premises_.
"What I have just said appies particularly to the principle of
inertia. _The physicist has not the right to say that 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 circum-
stances in which the _free will_ of man intervenes) that compels us to
construe a physical theory from which this principle would be ex-
cluded.
"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 affirma-
tion 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 meta-
physicians.
"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 prin-
ciple in the physical theory, would lead to consequences in contradic-
tion 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 _Identite et realite_ (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 Pesci, 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 mo-
tionless, that there is nothing new in it (p. 201).
