The relationship between difference and ratio and a proposal: Equivalence of temperature and time, and the first spontaneous symmetry breaking

Abstract

The mathematical form of the energy-entropy relationship is that of the relationship between the difference and the ratio of any two âentities â x and y creating a geometrical 3D projection x = y · z, i.e., a surface of the shape of a hyperbolic paraboloid being a particular form of a quadric. The significance of this relationship is discussed here in a realm beyond thermodynamics. Somewhat intuitively, yet still in strict mathematical analogy to the relation between its most fundamental state variables, I propose for any isolated universe the cosmological state variables, absolute temperature and absolute time, to be equivalent much in the same way as energy and entropy are equivalent for an isolated ensemble of similar objects. According to this principle, the cosmological constant is inversely proportional to the squared product of absolute time and absolute temperature. The spontaneous symmetry breaking into a time component and a temperature component of the universe takes place when the first de facto irreversible movement occurs owing to a growing accessed total volume. © 2010 Strazewski; licensee BioMed Central Ltd.