Nonstatic Model of Universe with Reversible Annihilation of Matter

In a recent article, it has been shown that the system of relativistic thermodynamics previously developed and applied by the author furnishes an important extension in our ideas as to the kind of processes which can take place at a finite rate and at the same time reversibly without increase in entropy. This makes it necessary to re-examine from the new point of view of relativistic thermodynamics those processes,—in particular the annihilation of matter by transformation into radiation and the flow of radiation out into space,—which have hitherto been regarded as furnishing unmistakable evidence that the entropy of the universe is increasing at an enormous rate. In the article mentioned, the importance of such a re-examination was made evident by treating the highly over-simplified model of a nonstatic universe filled solely with black-body radiation. In the present article a treatment is given by the methods of relativistic thermodynamics to a less simplified model of the universe containing a perfect monatomic gas in equilibrium with black-body radiation. Under the assumption that equilibrium conditions are always maintained between the gas and radiation, it is shown that the conversion of matter into radiation would then take place in such a universe at a finite rate and yet entirely reversibly without increase in entropy, and that this reversible annihilation would necessarily be accompanied also at a finite rate by an expansion of the universe,—that is by the kind of behaviour which appears in the actual universe to be associated with a red-shift in the light from the extra-galactic nebulae. It is also shown that an ordinary observer, who marks out with rigid meter sticks a small region in such a universe for his study, would find the matter in this region continually being converted into radiation; would find the energy content, energy density, and temperature of the region continually dropping; and would find a continuous net flow of radiation outward through the boundary of the region into surrounding space, which he would assume to be at a lower temperature than the contents of his region not only because of the direction of the net flow, but also because he would find the frequency of radiation entering his region from the outside on the average less than that of the radiation which was escaping. From the classical point of view these findings would evidently be interpreted by the observer as evidences for a continual increase in the entropy of his universe, in spite of the fact that all the processes in the model would actually be found to be taking place entirely reversibly when analyzed from the more legitimate point of view of the relativistic thermodynamics which must be used under the circumstances. The simplified model used for these considerations is of course by no means a satisfactory representation of the actual universe, and the assumption that the gas in the model immediately adjusts itself as to temperature and concentration so as to remain in equilibrium with the radiation appears arbitrary. Nevertheless, the analogy between the reversible phenomena occurring in such a model, and phenomena in the actual universe which have hitherto been regarded as necessarily irreversible, is so close as to emphasize the necessity of using relativistic rather than classical thermodynamics in order to obtain a real insight into the problem of the entropy of the universe as a whole.