In this essay the topological properties of thermodynamics are used to derive a topological equation of state in 4 topological dimensions. The equation of state corresponds to an Open thermodynamic environment (the Cosmological Aether) that permits local exchange of both particles (mass) and waves (radiation). For dilute systems near the critical point, the cubic factor in the equation of state is homeomorphic to a van der Waals gas.
Traditional physical theories have been constrained historically by assumptions of "geo-metrical" di?eomorphisms, invariant symmetries, and topological invariance. These ideas are useful to the understanding of equilibrium thermodynamic states, and processes that lead to time reversibility of equilibrium topological systems, and the conservation of energy. However, the geometrical constraints o?er no insight into non-equilibrium thermodynamic systems and irreversible processes, such as observed in the biological environment. Geometrical tensor methods are inadequate and must be replaced by topological thinking. Emphasis must be placed upon methods that describe continuous topological evolution, and not topological invariance. For example, to form a categorical marriage between gravity and quantum mechanics requires the recognition that the topological structure of "particles" is di?erent from the topological structure of "waves".
The responsibility of a dissident scientist is to create a new version of a testable hypothesis to replace a dogmatic proclamation, not just to proclaim new dogma.based on personal opinion.