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Negative, Infinite, and Hotter than Infinite Temperatures

Philip Ehrlich
Synthese
Vol. 50, No. 2, Philosophical Problems of Modern Physics, Part II (Feb., 1982), pp. 233-277
Published by: Springer
Stable URL: http://www.jstor.org/stable/20115715
Page Count: 45
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Negative, Infinite, and Hotter than Infinite Temperatures
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Abstract

We examine the notions of negative, infinite and hotter than infinite temperatures and show how these unusual concepts gain legitimacy in quantum statistical mechanics. We ask if the existence of an infinite temperature implies the existence of an actual infinity and argue that it does not. Since one can sensibly talk about hotter than infinite temperatures, we ask if one could legitimately speak of other physical quantities, such as length and duration, in analogous terms. That is, could there be longer than infinite lengths or temporal durations? We argue that the answer is surprisingly yes, and we outline the properties of a number system that could be employed to characterize such magnitudes.

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