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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.
206:
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
127:
in the early twentieth century preserved the
Newtonian concept of time in the Schrödinger equation. The ability of non-relativistic quantum mechanics and special relativity to successfully describe observations motivated efforts to extend quantum concepts to the relativistic domain. Physicists had to
96:
Some researchers view the evolution parameter as a mathematical artifact while others view the parameter as a physically measurable quantity. To understand the role of an evolution parameter and the fundamental difference between the standard theory and evolution parameter theories, it is necessary
100:
Time t played the role of a monotonically increasing evolution parameter in classical
Newtonian mechanics, as in the force law F = dP/dt for a non-relativistic, classical object with momentum P. To Newton, time was an “arrow” that parameterized the direction of evolution of a system.
162:
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
115:. Einstein's view of time requires a physical equivalence between coordinate time and coordinate space. In this view, time should be a reversible coordinate in the same manner as space. Particles moving backward in time are often used to display
119:
in
Feynman-diagrams, but they are not thought of as really moving backward in time usually it is done to simplify notation. However a lot of people think they are really moving backward in time and take it as evidence for time reversibility.
175:
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
36:
concepts to describe the relationships between the motion and properties of a relativistic system and the forces acting on the system. What distinguishes relativistic dynamics from other physical theories is the use of an
128:
decide what role time should play in relativistic quantum theory. The role of time was a key difference between
Einsteinian and Newtonian views of classical theory. Two hypotheses that were consistent with
45:
events. In a scale-invariant theory, the strength of particle interactions does not depend on the energy of the particles involved. Twentieth century experiments showed that the physical description of
180:, 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
58:
raised questions about such fundamental concepts as space, time, mass, and energy. The theoretical description of the physical phenomena required the integration of concepts from relativity and
84:
wrote a nice historical exposition of
Feynman's investigation of such a theory. A resurgence of interest in evolution parameter theories began in the 1970s with the work of Horwitz and
199:(QFT) was adopted as the standard paradigm. The QFT perspective, particularly its formulation by Schwinger, is a subset of the more general Relativistic Dynamics.
171:, 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
68:
was the first to propose an evolution parameter theory for describing relativistic quantum phenomena, but the evolution parameter theory introduced by
626:
Horwitz, L.P.; Shashoua, S.; Schieve, W.C. (1989). "A manifestly covariant relativistic
Boltzmann equation for the evolution of a system of events".
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The problems associated with the standard formulation of relativistic quantum mechanics provide a clue to the validity of
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Pavšič, Matej (1991). "On the interpretation of the relativistic quantum mechanics with invariant evolution parameter".
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195:, non-covariant expectation values, and so forth. Most of these problems were never solved; they were avoided when
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Pavšič, M. (1991). "Relativistic quantum mechanics and quantum field theory with invariant evolution parameter".
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PrugoveÄŤki, Eduard (1994). "On foundational and geometric critical aspects of quantum electrodynamics".
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Pavšič, Matej (2001). "Clifford-Algebra Based
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Fanchi, John R.; Collins, R. Eugene (1978). "Quantum mechanics of relativistic spinless particles".
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Fanchi, J. R. (1993). "Review of invariant time formulations of relativistic quantum theories".
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Schweber, Silvan S. (1986-04-01). "Feynman and the visualization of space-time processes".
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is more closely aligned with recent work. Evolution parameter theories were used by
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and others to formulate quantum field theory in the late 1940s and early 1950s.
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Schwinger, Julian (1951-06-01). "On Gauge Invariance and Vacuum Polarization".
381:"Mathematical Formulation of the Quantum Theory of Electromagnetic Interaction"
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Fanchi, John R. (1986-09-01). "Parametrizing relativistic quantum mechanics".
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concept and identified t as the fourth coordinate of a space-time four-
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Schwinger, Julian (1951-06-15). "The Theory of Quantized Fields. I".
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191:. These problems included negative probabilities, hole theory, the
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Stueckelberg, E.C.G. (1941): Helv. Phys. Acta 14, 322, 588.
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evolution parameter to monitor the historical evolution of
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861:(9). Springer Science and Business Media LLC: 1337–1354.
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703:(3). Springer Science and Business Media LLC: 335–362.
319:(3). Springer Science and Business Media LLC: 487–548.
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An invariant evolution parameter in the sense of Newton
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Stueckelberg, E.C.G. (1942): Helv. Phys. Acta 14, 23.
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978:(3). American Physical Society (APS): 1677–1681.
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283:Fock, V.A. (1937): Phys. Z. Sowjetunion 12, 404.
531:(2). American Physical Society (APS): 449–508.
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437:(5). American Physical Society (APS): 664–679.
394:(3). American Physical Society (APS): 440–457.
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92:Invariant Evolution Parameter Concept
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369:, Hauppauge, New York), pp 117-159.
148:Introduce two temporal variables:
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28:refers to a combination of
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545:10.1103/revmodphys.58.449
525:Reviews of Modern Physics
363:Horizons in World Physics
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768:10.1103/physrevd.20.3108
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