Many of my science professors have remarked that the law of conservation of mass and energy is unprovable (or at least unproven); is this really the case, however? Isn't the problem of the conservation law precisely the problem of induction? (I.e., we observe that the mass and energy of every system we have ever examined has remained constant, but how do we know that this will hold true (1) in the future and (2) of all systems?) But presumably when my professors have said that the conservation law is unproven, they didn't mean that this is so because of the problem of induction (after all, if they took this route then all of science would be "unproven"!). I feel as though they are treating the conservation law as exceptional when in fact it is not. -ace

I agree with you that observational evidence for the hypothesis that all processes conserve energy (or mass, or mass-energy) inevitably fails to prove that hypothesis (though succeeds in confirming the hypothesis strongly), just as our observational evidence for the hypothesis that (say) "All bolts of lightning are followed by claps of thunder" inevitably fails to prove that hypothesis. Even if every lightning bolt we have observed so far has been followed by a thunder clap, no contradiction would result from the next lightning bolt occurring without a thunder clap. So the "problem of induction" applies to both examples equally.

Perhaps your science professors had something else in mind in emphasizing the "unprovability" of energy conservation. Suppose we observe a process that apparently fails to conserve energy. The system's energy before the process occurs seems to exceed the system's energy after the process occurs. Rather than rejecting the conservation of energy, couldn't we always respond by saying, "Well, I guess there's an additional form of energy of which we had previously been unaware, which makes up the difference"? The availability of this tactic might make the "law of energy conservation" (or any similar conservation law) seem especially suspicious -- unable to be tested in the same way as other hypotheses. It might seem that a conservation law does not have the status of a hypothesis that gets confirmed by evidence, because the quantity of "energy" is not specified in advance as given by a particular formula, but is just whatever it has to be (with the dimensions of force times distance) in order to be conserved.

However, it seems to me that this view of energy conservation is mistaken. Of course, new forms of energy have occasionally been discovered. And they have sometimes been ascertained by figuring out what it would take to "balance the books." Still, faced with a case that appears to violate energy conservation, it would be utterly ad hoc simply to reply, "Well, there must be some unknown form of energy out there, sufficient to make energy conserved." Rather, scientists work to figure out a general formula for the quantity of this new kind of energy, and to find other situations where the posited new kind of energy makes a difference. Scientists seek some other, independent ways to test for the existence of this new kind of energy. So the law of energy conservation is as testable as any other general scientific hypothesis, despite the fact that there may always turn out to be further types of energy that have not yet been found.

(A case in point was the discovery of the neutrino. The particle was posited precisely to restore the mass-energy and momentum balance in beta decays. The story of how evidence was accumulated for this highly elusive particle is a good example of how scientists cannot justly save a conservation principle simply by adding to the equation whatever new term is needed to balance the books.)

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