Entropy and the Arrow of Time

The universally observed flow of time is another example of a broken symmetry. A theoretical formulation of this proposition is not known, but in principle it should parallel the theory of superconductivity. A high-symmetry state could be associated with Euclidean Minkowski space that spontaneously transforms into a curved manifold of lower symmetry. In this case the hidden symmetry emerges from a Lagrangian which is invariant under the temporal evolution group 

Since world lines in the tangent spaces at neighbouring points on the manifold are no longer parallel, as shown in figure 13, a static distribution of mass points must be inherently unstable. In time, interactions occur and produce a chaotic situation such as the motion in an ideal gas. This 

In essence, real world-space is not Euclidean and space is generally curved into the time dimension, consistent with the theory of general relativity. The curvature may not be sufficient to become obvious in a local context. However, it is sufficient to break the time-reversal symmetry that seems to characterize the laws of physics. Not only does it cause perpetual time flow with respect to all mass, but actually identifies a fixed direction for this flow. It creates an arrow of time and thereby eliminates an inconsistency in the logic of physics how reversible microscopic laws can underpin an irreversible macroscopic world. General curvature of space breaks the time-reversal symmetry and produces chiral space, manifest in the right-hand 

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