A recommended layman 120 plus pages book by Peter Atkins entitled ‘Four Laws that Drive the Universe’ describes in chapter 1 the origin of the zeroth law of the concept of temperature. The key word for understanding this law is ‘thermal equilibrium’.
What is thermal equilibrium? The answer might at first seem obvious but in fact it is not. One thing for sure, it is not the same as mechanical equilibrium which implies the equality of pressure. Mechanical pressure can be defined in two ways: First, as force per unit area and second as energy per unit volume. This also implies a closed physical volume separating ‘inside’ from ‘outside’ with a given topological genus of zero. The latter definition is used in defining the energy momentum tensor of general relativity implying complete closure of spacetime curvatures. It suggests the total quantization of spacetime hence the physical property of isolation analogous to isolated thermodynamic systems where and when mass and energy do not transfer at the boundary of the control closed volume.
On the other hand, thermal equilibrium suggests directional property of the spacetime continuum as well as spacetime quantization. Understanding this property requires at the least the existence of three mutually open thermodynamic systems: A, B, and C allowing the transfer of mass and energy between their boundaries. Each represents a direction of equal primary forces. Taken as a whole these comprise an orthogonal Cartesian coordinate system for a singular directional invariance. At least eight directional invariance properties are needed to represent physical reality, anything less represent virtual reality, anything more represent physical mass acquisition. However, all represent squares of energy as quanta of the spacetime continuum. These are simply directional quantization, distinct from magnitude quantization, which can represent both charge and mass quantization.


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