Since Maxwell’s classical time-dependent equations of electromagnetism is perfectly symmetric minus the symmetry of magnetic monopole, objective time, in a phenomenological sense of statistical averages still has no detectable physical direction except for the concept of entropy.
It is also interesting to note that entropy is intimately related to temperature as a property of heat energy. However, heat energy is connected to the quantum-particle nature while electromagnetic energy is connected to the continuum-field nature of physical reality. Wherever and whenever particle and field interact, the result is the quantum field energy of radiation with both temperature and direction attributes. There is a sharp distinction. Temperature is an intensive quantity, meaning its values at different space-time locations cannot be added. On the other hand, direction is a topological extensive quantity in direct proportion to the size of the system. Examples of extensive quantities are total volume, total mass, and total energy of a system. All these are additive not addictive which is subjective as is the nature of incomplete or partial reality of physical matter and energy. In the meantime, the objective nature of physical reality remains exclusively with the complete and fully operational directional invariance of the absolute vacuum of squares of quantized energy. The fundamental physical distinction is that time is truly intensive while space is truly extensive. The apparent metric (measurable) property of time is really based on the differential interval (Lagrangian formalism) which is truly subtractive not integral additive (Hamiltonian formalism), although the fundamental theorem of calculus already made the absolutely precise connection between derivative and antiderivative, between differentiation and integration.


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