Relativistic dynamics
Encyclopedia
Relativistic dynamics refers to a combination of relativistic
and quantum
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 invariant scalar evolution parameter to monitor the historical evolution of space-time events.
Twentieth century experiments showed that the physical description of microscopic
and submicroscopic
objects moving at or near the speed of light
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 quantum theory
.
Vladimir Fock
was the first to propose an evolution parameter theory for describing relativistic quantum phenomena, but the evolution parameter theory introduced by Ernst Stueckelberg
is more closely aligned with recent work . Evolution parameter theories were used by Feynman
, Schwinger and others to formulate quantum field theory in the late 1940s and early 1950s. Silvan S. Schweber 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 Piron , and Fanchi and Collins .
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.
Einstein rejected the Newtonian
concept and identified t as the fourth coordinate of a space-time four-vector. 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. Evidence for such reversibility has come from particle physics, where antiparticles are interpreted as particles moving backward in time.
The development of non-relativistic quantum mechanics
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 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 special relativity
were possible:
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.
Theory of relativity
The theory of relativity, or simply relativity, encompasses two theories of Albert Einstein: special relativity and general relativity. However, the word relativity is sometimes used in reference to Galilean invariance....
and quantum
Quantum
In physics, a quantum is the minimum amount of any physical entity involved in an interaction. Behind this, one finds the fundamental notion that a physical property may be "quantized," referred to as "the hypothesis of quantization". This means that the magnitude can take on only certain discrete...
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 invariant scalar evolution parameter to monitor the historical evolution of space-time events.
Twentieth century experiments showed that the physical description of microscopic
Microscopic
The microscopic scale is the scale of size or length used to describe objects smaller than those that can easily be seen by the naked eye and which require a lens or microscope to see them clearly.-History:...
and submicroscopic
Submicroscopic
Submicroscopic is an English adjective used to describe particles of matter that cannot be seen under the most powerful optical microscope available. Atoms are examples of such submicroscopic particles....
objects moving at or near the speed of light
Speed of light
The speed of light in vacuum, usually denoted by c, is a physical constant important in many areas of physics. Its value is 299,792,458 metres per second, a figure that is exact since the length of the metre is defined from this constant and the international standard for time...
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 quantum theory
Quantum mechanics
Quantum mechanics, also known as quantum physics or quantum theory, is a branch of physics providing a mathematical description of much of the dual particle-like and wave-like behavior and interactions of energy and matter. It departs from classical mechanics primarily at the atomic and subatomic...
.
Vladimir Fock
Vladimir Fock
Vladimir Aleksandrovich Fock was a Soviet physicist, who did foundational work on quantum mechanics and quantum electrodynamics....
was the first to propose an evolution parameter theory for describing relativistic quantum phenomena, but the evolution parameter theory introduced by Ernst Stueckelberg
Ernst Stueckelberg
Ernst Carl Gerlach Stueckelberg was a Swiss mathematician and physicist.- Career :In 1927 Stueckelberg got his Ph. D. at the University of Basel under August Hagenbach...
is more closely aligned with recent work . Evolution parameter theories were used by Feynman
Feynman
Feynman may refer to:* Richard Feynman , physicist** Feynman diagram** Feynman graph** Feynman–Kac formula** The Feynman Lectures on Physics** Feynman integral, see Path integral formulation** Feynman parametrization...
, Schwinger and others to formulate quantum field theory in the late 1940s and early 1950s. Silvan S. Schweber 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 Piron , and Fanchi and Collins .
Invariant Evolution Parameter Concept
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 to review the concept of time.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.
Einstein rejected the Newtonian
Newtonian
Newtonian refers to the work of Isaac Newton, in particular:* Newtonian mechanics, also known as classical mechanics* Newtonian telescope, a type of reflecting telescope* Newtonian cosmology* Newtonian dynamics...
concept and identified t as the fourth coordinate of a space-time four-vector. 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. Evidence for such reversibility has come from particle physics, where antiparticles are interpreted as particles moving backward in time.
The development of non-relativistic quantum mechanics
Quantum mechanics
Quantum mechanics, also known as quantum physics or quantum theory, is a branch of physics providing a mathematical description of much of the dual particle-like and wave-like behavior and interactions of energy and matter. It departs from classical mechanics primarily at the atomic and subatomic...
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 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 special relativity
Special relativity
Special relativity is the physical theory of measurement in an inertial frame of reference proposed in 1905 by Albert Einstein in the paper "On the Electrodynamics of Moving Bodies".It generalizes Galileo's...
were possible:
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
Thermodynamics
Thermodynamics is a physical science that studies the effects on material bodies, and on radiation in regions of space, of transfer of heat and of work done on or by the bodies or radiation...
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
Klein paradox
In 1929, physicist Oskar Klein obtained a surprising result by applying the Dirac equation to the familiar problem of electron scattering from a potential barrier. In nonrelativistic quantum mechanics, electron tunneling into a barrier is observed, with exponential damping...
, non-covariant expectation values, and so forth . Most of these problems were never solved; they were avoided when quantum field theory
Quantum field theory
Quantum field theory provides a theoretical framework for constructing quantum mechanical models of systems classically parametrized by an infinite number of dynamical degrees of freedom, that is, fields and many-body systems. It is the natural and quantitative language of particle physics and...
(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.