fbpx
Wikipedia

Relativistic dynamics

January 01, 1970

For classical dynamics at relativistic speeds, see relativistic mechanics.

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. In a scale-invariant theory, the strength of particle interactions does not depend on the energy of the particles involved.[1] 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[2] was the first to propose an evolution parameter theory for describing relativistic quantum phenomena, but the evolution parameter theory introduced by Ernst Stueckelberg[3][4] is more closely aligned with recent work.[5][6] Evolution parameter theories were used by Feynman,[7] Schwinger[8][9] and others to formulate quantum field theory in the late 1940s and early 1950s. Silvan S. Schweber[10] 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,[11] and Fanchi and Collins.[12]

Invariant Evolution Parameter Concept edit

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.

Albert 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. Particles moving backward in time are often used to display antiparticles 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.

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 edit

Assume t = Einsteinian time and reject Newtonian time.

Hypothesis II edit

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.[13] 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.[14][15][16] 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.[17][18][19][20][21][22]

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.[23][24] 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.

See also edit

References edit

  1. ^ Flego, Silvana; Plastino, Angelo; Plastino, Angel Ricardo (2011-12-20). "Information Theory Consequences of the Scale-Invariance of Schröedinger's Equation". Entropy. 13 (12). MDPI AG: 2049–2058. Bibcode:2011Entrp..13.2049F. doi:10.3390/e13122049. ISSN 1099-4300.
  2. ^ Fock, V.A. (1937): Phys. Z. Sowjetunion 12, 404.
  3. ^ Stueckelberg, E.C.G. (1941): Helv. Phys. Acta 14, 322, 588.
  4. ^ Stueckelberg, E.C.G. (1942): Helv. Phys. Acta 14, 23.
  5. ^ Fanchi, J. R. (1993). "Review of invariant time formulations of relativistic quantum theories". Foundations of Physics. 23 (3). Springer Science and Business Media LLC: 487–548. Bibcode:1993FoPh...23..487F. doi:10.1007/bf01883726. ISSN 0015-9018. S2CID 120073749.
  6. ^ Fanchi, J.R. (2003): “The Relativistic Quantum Potential and Non-Locality,” published in Horizons in World Physics, 240, Edited by Albert Reimer, (Nova Science Publishers, Hauppauge, New York), pp 117-159.
  7. ^ Feynman, R. P. (1950-11-01). "Mathematical Formulation of the Quantum Theory of Electromagnetic Interaction" (PDF). Physical Review. 80 (3). American Physical Society (APS): 440–457. Bibcode:1950PhRv...80..440F. doi:10.1103/physrev.80.440. ISSN 0031-899X.
  8. ^ Schwinger, Julian (1951-06-01). "On Gauge Invariance and Vacuum Polarization". Physical Review. 82 (5). American Physical Society (APS): 664–679. Bibcode:1951PhRv...82..664S. doi:10.1103/physrev.82.664. ISSN 0031-899X.
  9. ^ Schwinger, Julian (1951-06-15). "The Theory of Quantized Fields. I". Physical Review. 82 (6). American Physical Society (APS): 914–927. Bibcode:1951PhRv...82..914S. doi:10.1103/physrev.82.914. ISSN 0031-899X. S2CID 121971249.
  10. ^ Schweber, Silvan S. (1986-04-01). "Feynman and the visualization of space-time processes". Reviews of Modern Physics. 58 (2). American Physical Society (APS): 449–508. Bibcode:1986RvMP...58..449S. doi:10.1103/revmodphys.58.449. ISSN 0034-6861.
  11. ^ Horwitz, L.P. and C. Piron (1973): Helv. Phys. Acta 46, 316.
  12. ^ Fanchi, John R.; Collins, R. Eugene (1978). "Quantum mechanics of relativistic spinless particles". Foundations of Physics. 8 (11–12). Springer Nature: 851–877. Bibcode:1978FoPh....8..851F. doi:10.1007/bf00715059. ISSN 0015-9018. S2CID 120601267.
  13. ^ Horwitz, L.P.; Shashoua, S.; Schieve, W.C. (1989). "A manifestly covariant relativistic Boltzmann equation for the evolution of a system of events". Physica A: Statistical Mechanics and Its Applications. 161 (2). Elsevier BV: 300–338. Bibcode:1989PhyA..161..300H. doi:10.1016/0378-4371(89)90471-8. ISSN 0378-4371.
  14. ^ Fanchi, J.R. (1993): Parametrized Relativistic Quantum Theory (Kluwer, Dordrecht)
  15. ^ Weinberg, S. (1995): Quantum Theory of Fields, Volume I (Cambridge University Press, New York).
  16. ^ Prugovečki, Eduard (1994). "On foundational and geometric critical aspects of quantum electrodynamics". Foundations of Physics. 24 (3). Springer Science and Business Media LLC: 335–362. Bibcode:1994FoPh...24..335P. doi:10.1007/bf02058096. ISSN 0015-9018. S2CID 121653916.
  17. ^ Fanchi, John R. (1979-12-15). "A generalized quantum field theory". Physical Review D. 20 (12). American Physical Society (APS): 3108–3119. Bibcode:1979PhRvD..20.3108F. doi:10.1103/physrevd.20.3108. ISSN 0556-2821.
  18. ^ Fanchi, J.R. (1993): Parametrized Relativistic Quantum Theory (Kluwer, Dordrecht)
  19. ^ Pavšič, Matej (1991). "On the interpretation of the relativistic quantum mechanics with invariant evolution parameter". Foundations of Physics. 21 (9). Springer Nature: 1005–1019. Bibcode:1991FoPh...21.1005P. doi:10.1007/bf00733384. ISSN 0015-9018. S2CID 119436518.
  20. ^ Pavšič, M. (1991). "Relativistic quantum mechanics and quantum field theory with invariant evolution parameter". Il Nuovo Cimento A. 104 (9). Springer Science and Business Media LLC: 1337–1354. Bibcode:1991NCimA.104.1337P. doi:10.1007/bf02789576. ISSN 0369-3546. S2CID 122902647.
  21. ^ Pavšič, Matej (2001). "Clifford-Algebra Based Polydimensional Relativity and Relativistic Dynamics". Foundations of Physics. 31 (8): 1185–1209. arXiv:hep-th/0011216. doi:10.1023/a:1017599804103. ISSN 0015-9018. S2CID 117429211.
  22. ^ Pavsič, M. (2001): The Landscape of Theoretical Physics: A Global View (Kluwer, Dordrecht).
  23. ^ Fanchi, John R. (1986-09-01). "Parametrizing relativistic quantum mechanics". Physical Review A. 34 (3). American Physical Society (APS): 1677–1681. Bibcode:1986PhRvA..34.1677F. doi:10.1103/physreva.34.1677. ISSN 0556-2791. PMID 9897446.
  24. ^ Fanchi, J.R. (1993): Parametrized Relativistic Quantum Theory (Kluwer, Dordrecht)

External links edit

  • Relativistic dynamics of stars near a supermassive black hole (2014)
  • International Association for Relativistic Dynamics (IARD)

January 01, 1970
relativistic, dynamics, classical, dynamics, relativistic, speeds, relativistic, mechanics, refers, combination, relativistic, quantum, concepts, describe, relationships, between, motion, properties, relativistic, system, forces, acting, system, what, distingu. For classical dynamics at relativistic speeds see relativistic mechanics 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 In a scale invariant theory the strength of particle interactions does not depend on the energy of the particles involved 1 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 2 was the first to propose an evolution parameter theory for describing relativistic quantum phenomena but the evolution parameter theory introduced by Ernst Stueckelberg 3 4 is more closely aligned with recent work 5 6 Evolution parameter theories were used by Feynman 7 Schwinger 8 9 and others to formulate quantum field theory in the late 1940s and early 1950s Silvan S Schweber 10 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 11 and Fanchi and Collins 12 Contents 1 Invariant Evolution Parameter Concept 1 1 Hypothesis I 1 2 Hypothesis II 2 See also 3 References 4 External linksInvariant Evolution Parameter Concept editSome 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 Albert 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 Particles moving backward in time are often used to display antiparticles 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 The development of non relativistic quantum mechanics in the early twentieth century preserved the Newtonian concept of time in the Schrodinger 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 edit Assume t Einsteinian time and reject Newtonian time Hypothesis II edit 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 13 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 14 15 16 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 17 18 19 20 21 22 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 23 24 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 See also editErnst StueckelbergReferences edit Flego Silvana Plastino Angelo Plastino Angel Ricardo 2011 12 20 Information Theory Consequences of the Scale Invariance of Schroedinger s Equation Entropy 13 12 MDPI AG 2049 2058 Bibcode 2011Entrp 13 2049F doi 10 3390 e13122049 ISSN 1099 4300 Fock V A 1937 Phys Z Sowjetunion 12 404 Stueckelberg E C G 1941 Helv Phys Acta 14 322 588 Stueckelberg E C G 1942 Helv Phys Acta 14 23 Fanchi J R 1993 Review of invariant time formulations of relativistic quantum theories Foundations of Physics 23 3 Springer Science and Business Media LLC 487 548 Bibcode 1993FoPh 23 487F doi 10 1007 bf01883726 ISSN 0015 9018 S2CID 120073749 Fanchi J R 2003 The Relativistic Quantum Potential and Non Locality published in Horizons in World Physics 240 Edited by Albert Reimer Nova Science Publishers Hauppauge New York pp 117 159 Feynman R P 1950 11 01 Mathematical Formulation of the Quantum Theory of Electromagnetic Interaction PDF Physical Review 80 3 American Physical Society APS 440 457 Bibcode 1950PhRv 80 440F doi 10 1103 physrev 80 440 ISSN 0031 899X Schwinger Julian 1951 06 01 On Gauge Invariance and Vacuum Polarization Physical Review 82 5 American Physical Society APS 664 679 Bibcode 1951PhRv 82 664S doi 10 1103 physrev 82 664 ISSN 0031 899X Schwinger Julian 1951 06 15 The Theory of Quantized Fields I Physical Review 82 6 American Physical Society APS 914 927 Bibcode 1951PhRv 82 914S doi 10 1103 physrev 82 914 ISSN 0031 899X S2CID 121971249 Schweber Silvan S 1986 04 01 Feynman and the visualization of space time processes Reviews of Modern Physics 58 2 American Physical Society APS 449 508 Bibcode 1986RvMP 58 449S doi 10 1103 revmodphys 58 449 ISSN 0034 6861 Horwitz L P and C Piron 1973 Helv Phys Acta 46 316 Fanchi John R Collins R Eugene 1978 Quantum mechanics of relativistic spinless particles Foundations of Physics 8 11 12 Springer Nature 851 877 Bibcode 1978FoPh 8 851F doi 10 1007 bf00715059 ISSN 0015 9018 S2CID 120601267 Horwitz L P Shashoua S Schieve W C 1989 A manifestly covariant relativistic Boltzmann equation for the evolution of a system of events Physica A Statistical Mechanics and Its Applications 161 2 Elsevier BV 300 338 Bibcode 1989PhyA 161 300H doi 10 1016 0378 4371 89 90471 8 ISSN 0378 4371 Fanchi J R 1993 Parametrized Relativistic Quantum Theory Kluwer Dordrecht Weinberg S 1995 Quantum Theory of Fields Volume I Cambridge University Press New York Prugovecki Eduard 1994 On foundational and geometric critical aspects of quantum electrodynamics Foundations of Physics 24 3 Springer Science and Business Media LLC 335 362 Bibcode 1994FoPh 24 335P doi 10 1007 bf02058096 ISSN 0015 9018 S2CID 121653916 Fanchi John R 1979 12 15 A generalized quantum field theory Physical Review D 20 12 American Physical Society APS 3108 3119 Bibcode 1979PhRvD 20 3108F doi 10 1103 physrevd 20 3108 ISSN 0556 2821 Fanchi J R 1993 Parametrized Relativistic Quantum Theory Kluwer Dordrecht Pavsic Matej 1991 On the interpretation of the relativistic quantum mechanics with invariant evolution parameter Foundations of Physics 21 9 Springer Nature 1005 1019 Bibcode 1991FoPh 21 1005P doi 10 1007 bf00733384 ISSN 0015 9018 S2CID 119436518 Pavsic M 1991 Relativistic quantum mechanics and quantum field theory with invariant evolution parameter Il Nuovo Cimento A 104 9 Springer Science and Business Media LLC 1337 1354 Bibcode 1991NCimA 104 1337P doi 10 1007 bf02789576 ISSN 0369 3546 S2CID 122902647 Pavsic Matej 2001 Clifford Algebra Based Polydimensional Relativity and Relativistic Dynamics Foundations of Physics 31 8 1185 1209 arXiv hep th 0011216 doi 10 1023 a 1017599804103 ISSN 0015 9018 S2CID 117429211 Pavsic M 2001 The Landscape of Theoretical Physics A Global View Kluwer Dordrecht Fanchi John R 1986 09 01 Parametrizing relativistic quantum mechanics Physical Review A 34 3 American Physical Society APS 1677 1681 Bibcode 1986PhRvA 34 1677F doi 10 1103 physreva 34 1677 ISSN 0556 2791 PMID 9897446 Fanchi J R 1993 Parametrized Relativistic Quantum Theory Kluwer Dordrecht External links editRelativistic dynamics of stars near a supermassive black hole 2014 International Association for Relativistic Dynamics IARD Retrieved from https en wikipedia org w index php title Relativistic dynamics amp oldid 1187392465, wikipedia, wiki, book, books, library,

article

, read, download, free, free download, mp3, video, mp4, 3gp, jpg, jpeg, gif, png, picture, music, song, movie, book, game, games.