Relativistic Dynamics - Invariant Evolution Parameter Concept - Hypothesis II

Hypothesis II

Introduce two temporal variables:

• A coordinate time in the sense of Einstein
• An invariant evolution parameter in the sense of Newton

Hypothesis I led to a relativistic probability conservation equation that is essentially a re-statement of the non-relativistic continuity equation. Time in the relativistic probability conservation equation is Einstein’s time and is a consequence of implicitly adopting Hypothesis I. By adopting Hypothesis I, the standard paradigm has at its foundation a temporal paradox: motion relative to a single temporal variable must be reversible even though the second law of thermodynamics establishes an “arrow of time” for evolving systems, including relativistic systems. Thus, even though Einstein’s time is reversible in the standard theory, the evolution of a system is not time reversal invariant. From the perspective of Hypothesis I, time must be both an irreversible arrow tied to entropy and a reversible coordinate in the Einsteinian sense. The development of relativistic dynamics is motivated in part by the concern that Hypothesis I was too restrictive.

The problems associated with the standard formulation of relativistic quantum mechanics provide a clue to the validity of Hypothesis I. These problems included negative probabilities, hole theory, the Klein paradox, non-covariant expectation values, and so forth. Most of these problems were never solved; they were avoided when quantum field theory (QFT) was adopted as the standard paradigm. The QFT perspective, particularly its formulation by Schwinger, is a subset of the more general Relativistic Dynamics.

Relativistic Dynamics is based on Hypothesis II and employs two temporal variables: a coordinate time, and an evolution parameter. The evolution parameter, or parameterized time, may be viewed as a physically measurable quantity, and a procedure has been presented for designing evolution parameter clocks. By recognizing the existence of a distinct parameterized time and a distinct coordinate time, the conflict between a universal direction of time and a time that may proceed as readily from future to past as from past to future is resolved. The distinction between parameterized time and coordinate time removes ambiguities in the properties associated with the two temporal concepts in Relativistic Dynamics.