The main result of this paper were announced in Kosheleva — Kreinovich [7, 8]; for other algorithmic aspects of Hilbert's Third Problem see Kosheleva [6]. The authors are greatly thankful to Alexandr D. Alexandrov , Vladimir G. Boltianskii and Patrick Suppes for valuable discussions, and to the anonymous referee for important suggestions. This work was partially supported by an NSF grant No. CDA-9015006.

Joule’s Energy Conservation Law was the first “meta-law”: a general principle that all physical equations must satisfy. It has led to many important and useful physical discoveries. However, a recent analysis seems to indicate that this meta-law is inconsistent with other principles—such as the existence of free will. We show that this conclusion about inconsistency is based on a seemingly reasonable—but simplified—analysis of the situation. We also show that a more detailed mathematical and physical analysis of the situation reveals that (...) not only Joule’s principle remains true—it is actually strengthened: it is no longer a principle that all physical theories should satisfy—it is a principle that all physical theories do satisfy. (shrink)