The Physics of a Believer:
5. Our System Denies to Physical Theory any Metaphysical or Apologetical Import
by Pierre Duhem
That our physics is the physics of a believer is said to follow from the fact that it so radically denies any validity to the objections obtained from physical theory to spiritualistic metaphysics and the Catholic faith! But it might just as well be called the physics of a nonbeliever, for it does not render better or stricter justice to the arguments in favor of metaphysics or dogma that some have tried to deduce from physical theory. It is just as absurd to claim that a principle of theoretical physics contradicts a proposition formulated by spiritualistic philosophy or by Catholic doctrine as it is to claim that it confirms such a proposition. There cannot be disagreement or agreement between a proposition touching on an objective reality and another proposition which has no objective import. Every time people cite a principle of theoretical physics in support of a metaphysical doctrine or a religious dogma, they commit a mistake, for they attribute to this principle a meaning not its own, an import not belonging to it.
Let us again explain what we are saying by an illustration.
In the middle of the last century, Clausius, after profoundly transforming Carnot's principle, drew from it the following famous corollary: The entropy of the universe tends toward a maximum. From this theorem many a philosopher maintained the conclusion of the impossibility of a world in which physical and chemical changes would go on being produced forever; it pleased them to think that these changes had had a beginning and would have an end; creation in time, if not of matter, at least of its aptitude for change, and the establishment in a more or less remote future of a state of absolute rest and universal death were for these thinkers inevitable consequences of the principles of thermodynamics.
The deduction here in wishing to pass from the premises to these conclusions is marred in more than one place by fallacies. First of all, it implicitly assumes the assimilation of the universe to a finite collection of bodies isolated in a space absolutely void of matter, and this assimilation exposes one to many doubts. Once this assimilation is admitted, it is true that the entropy of the universe has to increase endlessly, but it does not impose any lower or upper limit on this entropy; nothing then would stop this magnitude from varying from minus infinity or to plus infinity so while the time itself varied from minus infinity to plus infinity; then the allegedly demonstrated impossibilities regarding an eternal life for the universe would vanish. But let us confess these criticisms wrong; they prove that the demonstration taken as an example is not conclusive, but do not prove the radical impossibility of constructing a conclusive example which would tend toward an analogous end. The objection we shall make against it is quite different in nature and import: basing our argument on the very essence of physical theory, we shall show that it is absurd to question this theory for information concerning events which might have happened in an extremely remote past, and absurd to demand of it predictions of events a very long way off.
What is a physical theory? A group of mathematical propositions whose consequences are to represent the data of experiment; the validity of a theory is measured by the number of experimental laws it represents and by the degree of precision with which it represents them; if two different theories represent the same facts with the same degree of approximation, physical method considers them as having absolutely the same validity; it does not have the right to dictate our choice between these two equivalent theories and is bound to leave us free. No doubt the physicist will choose between these logically equivalent theories, but the motives which will dictate his choice will be considerations of elegance, simplicity, and convenience, and grounds of suitability which are essentially subjective, contingent, and variable with time, with schools, and with persons; as serious as these motives may be in certain cases, they will never be of a nature that necessitates adhering to one of the two theories and rejecting the other, for only the discovery of a fact that would be represented by one of the theories, and not by the other, would result in a forced option.
Thus the law of attraction in the inverse ratio of the square of the distance, proposed by Newton, represents with admirable precision all the heavenly motion we can observe. However, for the inverse square of the distance we could substitute some other function of the distance in an infinity of ways so that some new celestial mechanics represented all our astronomical observations with the same precision as the old one. The principles of experimental method would compel us to attribute exactly the same logical validity to both these different celestial mechanics. This does not mean that astronomers would not keep the Newtonian law of attraction in preference to the new law, but they would keep it on account of the exceptional mathematical properties offered by the inverse square of the distance in favor of the simplicity and elegance that these properties introduced into their calculations. Of course, these motives would be good to follow; yet they would constitute nothing decisive or definitive, and would be of no weight the day when a phenomenon would be discovered which the Newtonian law of attraction would be inept to represent and of which another celestial mechanics would give a satisfactory representation; on that day astronomers would be bound to prefer the new theory to the old one.
That being understood, let us suppose we have two systems of celestial mechanics, different from the mathematical point of view, but representing with an equal degree of approximation all the astronomical observations made until now. Let us go further: let us use these two celestial mechanics to calculate the motions of heavenly bodies in the future; let us assume that the results of one of the calculations are so close to those of the other that the deviation between the two positions they assign to the same heavenly body is less than the experimental errors even at the end of a thousand or even ten thousand years. Then we have here two systems of celestial mechanics which we are bound to regard as logically equivalent; no reason exists compelling us to prefer one to the other, and what is more, at the end of a thousand or ten thousand years, men will still have to weigh them equally and hold their choice in suspense.
It is clear that the predictions from both these theories will merit equal degrees of confidence; it is clear that logic does not give us any right to assert that the predictions of the first theory, but not those of the second theory, will be in conformity with reality.
In truth these predictions agree perfectly for a lapse of a thousand or ten thousand years, but the mathematicians warn us that we should be rash to conclude from this that this agreement will last forever, and by concrete examples they show us to what errors this illegitimate extrapolation could lead us. The predictions of our two systems of celestial mechanics would be peculiarly discordant if we asked these two theories to describe for us the state of the heavens at the end of ten million years; one of them might tell us that the planets at that time would still describe orbits scarcely different from those they describe at present; the other, however, might very well claim that all the bodies of the solar system will then be united into a single mass, or else that they will be dispersed in space at enormous distances from one another. Of these two forecasts, one proclaiming the stability of the solar system and the other its instability, which shall we believe? The one, no doubt, which will best fit our extra-scientific preoccupations and predilections; but certainly the logic of the physical sciences will not provide us with any fully convincing argument to defend our choice against an attacking party and impose it on him.
So it goes with any long-term prediction. We possess a thermodynamics which represents very well a multitude of experimental laws, and it tells us that the entropy of an isolated system increases eternally. We could without difficulty construct a new thermodynamics which would represent as well as the old thermodynamics the experimental laws known until now, and whose predictions would go along in agreement with those of the old thermodynamics for ten thousand years; and yet, this new thermodynamics might tell us that the entropy of the universe after increasing for a period of 100 million years will decrease over a new period of 100 million years in order to increase again in an eternal cycle.
By its very essence experimental science is incapable of predicting the end of the world as well as of asserting its perpetual activity. Only a gross misconception of its scope could have claimed for it the proof of a dogma affirmed by our faith.
[from Jaki, Scientist and Catholic: Pierre Duhem, quoting P. Duhem, The Aim and Structure of Physical Theory, tr. Philip P. Wiener (Princeton, NJ.: Princeton University Press, 1954), pp. 273-79, 287-90, 305-11.]