In the 1950s, few years before his death, Wolfgang Pauli ( 1900-1958 ) delivered a series of German lectures at the Swiss Federal Institute of Technology in Zurich. These were later carefully edited and painstakingly translated into six superb English volumes. Volume three titled: Thermodynamics and the Kinetic Theory of Gases. Section 23 gave a short account on the unattainability of absolute zero of thermodynamic temperature. Pauli asserted that the only physical reason why absolute zero temperature cannot be reached is because the value of absolute entropy can never be zero. On the one hand, zero entropy connotes absolute time zero. Since the arrow of time is equivalent to the direction of increasing entropy, the change in entropy is always temporally positive definite. This potentially circular argument implies that the change in physical time is also always positive definite. This is the same as saying that absolute time zero never existed and the physical universe has no beginning and no end.

Unfortunately, this new or revived old empirical assertion does not explain why the physical universe keeps on its accelerated expansion with exponential increase of its scalar volume. On the contrary, the use of oriented (directed) volume allows universal expansion to exist as a consequence of directional changes of absolute acceleration with its corresponding directional changes of the space-time metrics equivalent to changes within a Hopf-Möbius topology such that the inner scalar dot product of changes in absolute acceleration and changes of space-time metric is equal to the square of lightspeed: [∆a,∆r]=c. This formulation is mass independence if unit quantum of mass is defined. However, if mass ratio m/M can be defined where m << M and ∑m = Mthen ∑m[∆a,∆r]=M c = Eas Einstein’s mass and energy equivalence derived from his theory of special relativity. Nonetheless, the changes of the square of E can be shown to vary inversely with the square of changes in time which is the same as the square of the uncertainty principle: ∆t∆E≥h where h is Planck’s constant of action. This implies that if time is zero then energy reaches infinity, vice versa and within the space-time domain of Hopf-Möbius topology zero and infinity is connected end to end, or end to beginning, or beginning to end whichever is more logically pleasing.