Spin, the Classical Theory

Author(s)
Richard T. Hammond

ABSTRACT

With the development of local gauge theories of gravitation, it became evident that intrinsic spin was an integral part of the theory. This gave spin a classical formulation that predicted the existence of a new kind of field, the torsion field. To date only one class of experiments has been developed to detect this field, a search for a long range dipole force. In this article, the torsion equations are de-coupled from the curved space of general relativity derived from basic principles using vector calculus and the theory of electromagnetism as a guide. The results are written in vector form so that they are readily available to experimentalists, paving the way for new kinds of experiments.

With the development of local gauge theories of gravitation, it became evident that intrinsic spin was an integral part of the theory. This gave spin a classical formulation that predicted the existence of a new kind of field, the torsion field. To date only one class of experiments has been developed to detect this field, a search for a long range dipole force. In this article, the torsion equations are de-coupled from the curved space of general relativity derived from basic principles using vector calculus and the theory of electromagnetism as a guide. The results are written in vector form so that they are readily available to experimentalists, paving the way for new kinds of experiments.

Cite this paper

R. Hammond, "Spin, the Classical Theory,"*Journal of Modern Physics*, Vol. 3 No. 1, 2012, pp. 1-8. doi: 10.4236/jmp.2012.31001.

R. Hammond, "Spin, the Classical Theory,"

References

[1] R. T. Hammond, “New Fields in General Relativity,” Contemporary Physics, Vol. 36, No. 2, 1995, pp. 103-114. doi:10.1080/00107519508222143

[2] F. W. Hehl, P. von der Heyde, G. D. Kerlick and J. M. Nester, “General Relativity with Spin and Torsion: Foundations and Prospects,” Reviews of Modern Physics, Vol. 48, No. 3, 1976, pp. 393-416. doi:10.1103/RevModPhys.48.393

[3] C. N. Yang and R. L. Mills, “Conservation of Isotopic Spin and Isotopic Gauge Invariance,” Physical Review, Vol. 96, No. 1, 1954, pp. 191-195. doi:10.1103/PhysRev.96.191

[4] F. W. Hehl, J. D. McCrea, E. W. Mielke and Y. Ne’eman, “Metric-Affine Gauge Theory of Gravity: Field Equations, Noether Identities, World Spinors, and Breaking of Dilation Invariance,” Physics Reports, Vol. 258, No. 1-2, 1995, pp. 1-171. doi:10.1016/0370-1573(94)00111-F

[5] M. Kalb and P. Ramond, “Classical Firect Interstring Action,” Physical Review, Vol. 9, 1974, pp. 2273-2284.

[6] J. Scherk and J. H. Schwarz, “Dual Models and the Geometry of Space-Time,” Physics Letters, Vol. B52, 1974, pp. 347-350.

[7] R. T. Hammond, “The Necessity of Torsion,” General Relativity and Gravitation, Vol. 42, No. 10, 2010, pp. 2345-2348. doi:10.1007/s10714-010-1045-x

[8] R. T. Hammond, “Dynamic Torsion from a Linear Lagrangian,” General Relativity and Gravitation, Vol. 22, 1990, p. 451.

[9] R. T. Hammond, “Spin, Torsion, Forces,” General Relativity and Gravitation, Vol. 26, No. 3, 1994, pp. 247-263. doi:10.1007/BF02108005

[10] J. D. Jackson, “Classical Electrodynamics,” 2nd Edition, John Wiley & Sons, New York, 1975.

[11] B. Zweibach, “A First Course in String Theory,” Cambridhe University Press, Cambridge, 2004.

[12] R. T. Hammond, “Strings Have Spin,” General Relativity and Gravitation, Vol. 32, No. 2, 2000, pp. 347-351. doi:10.1023/A:1001948028584

[13] T. C. P. Chui and W.-T. Ni, “Experimental Search for an Anomalous Spin-Spin Interaction between Electrons,” Physical Review Letters, Vol. 71, No. 20, 1993, pp. 3247- 3250. doi:10.1103/PhysRevLett.71.3247

[14] W.-T. Ni, et al., “Search for an Axionlike Spin Coupling Using a Paramegnetic Salt with a dc SQUID,” Physical Review Letters, Vol. 82, No. 12, 1999, pp. 2439-2442. doi:10.1103/PhysRevLett.82.2439

[15] R. T. Hammond, “Upper Bound of Torsion Coupling Constants,” Physical Review D, Vol. 52, No. 12, 1995, pp. 6918-6921. doi:10.1103/PhysRevD.52.6918

[16] B. E. Lautrup and A. Peterman, “Recent Developments in the Comparison between Theory and Experiments in Quantum Electrodynamics,” Physics Reports, Vol. 3, No. 4, 1972, pp. 193-259. doi:10.1016/0370-1573(72)90011-7

[17] S.-X. Qui and C.-G. Shao, “Spin-Rotation Coupling in Graviation with Torsion,” Communications in Theoretical Physics, Vol. 48, No. 3, 2007, pp. 473-476. doi:10.1088/0253-6102/48/3/019

[18] R. T. Hammond, “Helicity Flip Cross Section from Gravitation with Torsion,” Classical and Quantum Gravity, Vol. 13, No. 7, 1996, p. 1691. doi:10.1088/0264-9381/13/7/002

[19] R. T. Hammond, “Nonlinear Quantum Equation from Curved Space,” Physics Letters A, Vol. 184, No. 6, 1994, pp. 409-412. doi:10.1016/0375-9601(94)90514-2

[20] R. T. Hammond, “Torsion Gravity,” Reports on Progress in Physics, Vol. 65, No. 5, 2002, pp. 599-649. doi:10.1088/0034-4885/65/5/201

[21] E. Cartan and A. Einstein, “Letters of Absolute Parallelism,” Princeton University Press, Princeton, 1975.

[1] R. T. Hammond, “New Fields in General Relativity,” Contemporary Physics, Vol. 36, No. 2, 1995, pp. 103-114. doi:10.1080/00107519508222143

[2] F. W. Hehl, P. von der Heyde, G. D. Kerlick and J. M. Nester, “General Relativity with Spin and Torsion: Foundations and Prospects,” Reviews of Modern Physics, Vol. 48, No. 3, 1976, pp. 393-416. doi:10.1103/RevModPhys.48.393

[3] C. N. Yang and R. L. Mills, “Conservation of Isotopic Spin and Isotopic Gauge Invariance,” Physical Review, Vol. 96, No. 1, 1954, pp. 191-195. doi:10.1103/PhysRev.96.191

[4] F. W. Hehl, J. D. McCrea, E. W. Mielke and Y. Ne’eman, “Metric-Affine Gauge Theory of Gravity: Field Equations, Noether Identities, World Spinors, and Breaking of Dilation Invariance,” Physics Reports, Vol. 258, No. 1-2, 1995, pp. 1-171. doi:10.1016/0370-1573(94)00111-F

[5] M. Kalb and P. Ramond, “Classical Firect Interstring Action,” Physical Review, Vol. 9, 1974, pp. 2273-2284.

[6] J. Scherk and J. H. Schwarz, “Dual Models and the Geometry of Space-Time,” Physics Letters, Vol. B52, 1974, pp. 347-350.

[7] R. T. Hammond, “The Necessity of Torsion,” General Relativity and Gravitation, Vol. 42, No. 10, 2010, pp. 2345-2348. doi:10.1007/s10714-010-1045-x

[8] R. T. Hammond, “Dynamic Torsion from a Linear Lagrangian,” General Relativity and Gravitation, Vol. 22, 1990, p. 451.

[9] R. T. Hammond, “Spin, Torsion, Forces,” General Relativity and Gravitation, Vol. 26, No. 3, 1994, pp. 247-263. doi:10.1007/BF02108005

[10] J. D. Jackson, “Classical Electrodynamics,” 2nd Edition, John Wiley & Sons, New York, 1975.

[11] B. Zweibach, “A First Course in String Theory,” Cambridhe University Press, Cambridge, 2004.

[12] R. T. Hammond, “Strings Have Spin,” General Relativity and Gravitation, Vol. 32, No. 2, 2000, pp. 347-351. doi:10.1023/A:1001948028584

[13] T. C. P. Chui and W.-T. Ni, “Experimental Search for an Anomalous Spin-Spin Interaction between Electrons,” Physical Review Letters, Vol. 71, No. 20, 1993, pp. 3247- 3250. doi:10.1103/PhysRevLett.71.3247

[14] W.-T. Ni, et al., “Search for an Axionlike Spin Coupling Using a Paramegnetic Salt with a dc SQUID,” Physical Review Letters, Vol. 82, No. 12, 1999, pp. 2439-2442. doi:10.1103/PhysRevLett.82.2439

[15] R. T. Hammond, “Upper Bound of Torsion Coupling Constants,” Physical Review D, Vol. 52, No. 12, 1995, pp. 6918-6921. doi:10.1103/PhysRevD.52.6918

[16] B. E. Lautrup and A. Peterman, “Recent Developments in the Comparison between Theory and Experiments in Quantum Electrodynamics,” Physics Reports, Vol. 3, No. 4, 1972, pp. 193-259. doi:10.1016/0370-1573(72)90011-7

[17] S.-X. Qui and C.-G. Shao, “Spin-Rotation Coupling in Graviation with Torsion,” Communications in Theoretical Physics, Vol. 48, No. 3, 2007, pp. 473-476. doi:10.1088/0253-6102/48/3/019

[18] R. T. Hammond, “Helicity Flip Cross Section from Gravitation with Torsion,” Classical and Quantum Gravity, Vol. 13, No. 7, 1996, p. 1691. doi:10.1088/0264-9381/13/7/002

[19] R. T. Hammond, “Nonlinear Quantum Equation from Curved Space,” Physics Letters A, Vol. 184, No. 6, 1994, pp. 409-412. doi:10.1016/0375-9601(94)90514-2

[20] R. T. Hammond, “Torsion Gravity,” Reports on Progress in Physics, Vol. 65, No. 5, 2002, pp. 599-649. doi:10.1088/0034-4885/65/5/201

[21] E. Cartan and A. Einstein, “Letters of Absolute Parallelism,” Princeton University Press, Princeton, 1975.