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The Rise and Fall of the Electromagnetic 4-Potential

DOI: 10.4236/oalib.1104979, PP. 1-18

Subject Areas: Quantum Mechanics, Theoretical Physics

Keywords: Special Relativity, Maxwellian Electrodynamics, The Variational Principle, Quantum Theories, 4-Potential

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Abstract

The Lienard-Wiechert 4-potential depends on local coordinates and on retarded coordinates of a charge at the source. Therefore, the 4-potential of incoming radiation fields (namely, a photon) cannot be written as a 4-vector which satisfies the locality requirement of fields of a Lagrangian density. This unsolvable problem is the underlying reason for the extremely unusual phenomenon where respectable textbooks make contradictory statements concerning whether the electromagnetic 4-potential is a 4-vector. Moreover, an analysis of well-established experimental data proves that radiation fields and bound fields are inherently different physical objects. These results indicate that the present form of quantum electrodynamics should be revised. It is further proved that in both cases the 4-potential is not a fundamental element of electrodynamics but an auxiliary quantity. For this reason, there are problems with some specific theoretical ideas that pertain to the 4-potential, like gauge transformations, the Dirac monopole theory and the Aharonov-Bohm effects.

Cite this paper

Comay, E. (2018). The Rise and Fall of the Electromagnetic 4-Potential. Open Access Library Journal, 5, e4979. doi: http://dx.doi.org/10.4236/oalib.1104979.

References

[1]  Wigner, E. (1960) The Unreasonable Effectiveness of Mathematics in the Natural Sciences. Richard Courant Lecture in Mathematical Sciences Delivered at New York University, May 11, 1959. Communications on Pure and Applied Mathe-matics, 13, 1-14.
https://doi.org/10.1002/cpa.3160130102
[2]  Landau, L.D. and Lifshitz, E.M. (2005) The Classical Theory of Fields. Elsevier, Amsterdam.
[3]  Weinberg, S. (1995) The Quantum Theory of Fields, Vol. I. Cambridge University Press, Cambridge.
https://doi.org/10.1017/CBO9781139644167
[4]  Bjorken, J.D. and Drell, S.D. (1965) Relativistic Quantum Fields. McGraw-Hill, New York.
[5]  Peskin, M.E. and Schroeder, D.V. (1995) An Introduction to Quantum Field Theory. Addison-Wesley, Reading, Mass.
[6]  Griffiths, D. (2008) Introduction to Elementary Particles. 2nd Edition, Wiley-VCH, Weinheim.
[7]  Jackson, J.D. (1975) Classical Electrodynamics. 2nd Edition, John Wiley, New York.
[8]  Immanuel Kant (2018).
https://en.wikipedia.org/wiki/Immanuel_Kant
[9]  Wu, A.C.T. and Yang, C.N. (2006) Evolution of the Concept of the Vector Potential in the Description of Fundamental Interactions. International Journal of Modern Physics A, 21, 3235-3277.
https://doi.org/10.1142/S0217751X06033143
[10]  Feynman, R.P., Leighton, R.B. and Sands, M. (1965) The Feynman Lectures on Physics, V. II. Addison-Wesley, Reading, Mass.
[11]  Schiff, L.I. (1955) Quantum Mechanics. McGraw-Hill, New York.
[12]  Patrignani, C., et al. (Particle Data Group) (2016) Review of Particle Physics. Chinese Physics C, 40, Article ID: l100001.
[13]  Comay, E. (2018) Inherent Differences between Bound and Radiation Fields. OALib, 5, e4517.
https://www.scirp.org/journal/PaperInformation.aspx?PaperID=83992
[14]  Wigner, E. (1939) On Unitary Representations of the Inhomogeneous Lorentz Group. Annals of Mathematics, 40, 149-204.
https://doi.org/10.2307/1968551
[15]  Schweber, S.S. (1964) An Introduction to Relativistic Quantum Field Theory. Harper & Row, New York, 44-53.
[16]  Comay, E. (2018) Lorentz Transformation of Radiation 4-Potential. Acta Physica Polonica A, 133, 1294-1298.
https://doi.org/10.12693/APhysPolA.133.1294
[17]  Bethe, H.A. and Salpeter, E.E. (1957) Quantum Mechanics of One- and Two-Electron Atoms. Springer, Berlin.
[18]  Bjorken, J.D. and Drell, S.D. (1964) Relativistic Quantum Mechanics. McGraw-Hill, New York.
[19]  Condon, E.U. and Shortley, G.H. (1964) The Theory of Atomic Spectra. University Press, Cambridge.
[20]  Munoz, G. (1996) Lagrangian Field Theories and Energy-Momentum Tensors. American Journal of Physics, 64, 1153.
https://doi.org/10.1119/1.18336
[21]  Comay, E. (2018) A Consistent Construction of the Electromagnetic Energy-Momentum Tensor. Open Access Library Journal, 5, 1-8.
http://www.scirp.org/journal/PaperInformation.aspx?paperID=82391
[22]  Feynman, R.P. (1990) QED, the Strange Theory of Light and Matter. Penguin, London.
[23]  Dirac, P.A.M. (1963) The Evolution of the Physicist’s Picture of Nature. Scientific American, 208, 45-53.
https://doi.org/10.1038/scientificamerican0563-45
[24]  Ryder, L.H. (1997) Quantum Field Theory. Cambridge University Press, Cambridge.
[25]  Pohl, R., et al. (2010) The Size of the Proton. Nature, 466, 213-216.
https://doi.org/10.1038/nature09250
[26]  Comay, E. (2008) Mathematical Constraints on Gauge in Maxwellian Electrodynamics. Apeiron, 15, 123.
https://www.tau.ac.il/~elicomay/GAUGE.pdf
[27]  Comay, E. (2016) A New Quantum Paradox. Physical Science International Journal, 12, 1.
http://www.sciencedomain.org/abstract/16442
https://doi.org/10.9734/PSIJ/2016/28572
[28]  Comay, E. (2017) Gauge Contradictions in the QED Lagrangian Density. Open Access Library Journal, 4, 1-7.
http://www.scirp.org/journal/PaperInformation.aspx?PaperID=76182
[29]  Pauli, W. (1941) Relativistic Field Theories of Elementary Particles. Reviews of Modern Physics, 13, 203-232.
https://doi.org/10.1103/RevModPhys.13.203
[30]  Yang, C.N. and Mills, R. (1954) Conservation of Isotopic Spin and Isotopic Gauge Invariance. Physical Review, 96, 191-196.
https://doi.org/10.1103/PhysRev.96.191
[31]  Messiah, A. (1967) Quantum Mechanics. Vol. 1, North Holland, Amsterdam.
[32]  Jackson, J.D. and Okun, L.B. (2001) Historical Roots of Gauge Invariance. Reviews of Modern Physics, 73, 663-680.
[33]  Goddard, P. and Olive, D.I. (1978) Magnetic Monopoles in Gauge Field Theories. Reports on Progress in Physics, 41, 1357-1437.
https://doi.org/10.1088/0034-4885/41/9/001
[34]  Dirac, P.A.M. (1931) Quantised Singularities in the Electromagnetic Field. Proceedings of the Royal Society A, 133, 60-72.
https://doi.org/10.1098/rspa.1931.0130
[35]  Dirac, P.A.M. (1948) The Theory of Magnetic Poles. Physical Review, 74, 817-830.
https://doi.org/10.1103/PhysRev.74.817
[36]  http://pdg.lbl.gov/2018/reviews/rpp2018-rev-mag-monopole-searches.pdf
[37]  Zwanziger, D. (1965) Dirac Magnetic Poles Forbidden in S-Matrix Theory. Physical Review, 137, 647-648.
https://doi.org/10.1103/PhysRev.137.B647
[38]  Comay, E. (1985) Will Magnetic Monopoles Be Detected in Our Instruments. Lettere al Nuovo Cimento, 43, 150-152.
https://doi.org/10.1007/BF02749596
[39]  Aharonov, Y. and Bohm, D. (1959) Significance of Electromagnetic Potentials in the Quantum Theory. Physical Review, 115, 485-491.
https://doi.org/10.1103/PhysRev.115.485
[40]  Aharonov, Y. and Bohm, D. (1961) Further Considerations on Electromagnetic Potentials in the Quantum Theory. Physical Review, 123, 1511-1524.
https://doi.org/10.1103/PhysRev.123.1511
[41]  Comay, E. (2000) Interrelations between the Neutron’s Magnetic Interactions and the Magnetic Aharonov-Bohm Effect. Physical Review A, 62, Article ID: 042102.
https://doi.org/10.1103/PhysRevA.62.042102
[42]  https://arxiv.org/pdf/0910.3289.pdf
[43]  Vaidman, L. (2012) Role of Potentials in the Aharonov-Bohm Effect. Physical Review A, 86, Article ID: 040101.
https://doi.org/10.1103/PhysRevA.86.040101
[44]  Pearle, P. and Rizzi, A. (2017) Quantum-Mechanical Inclusion of the Source in the Aharonov-Bohm Effects. Physical Review A, 95, Article ID: 052123.
https://doi.org/10.1103/PhysRevA.95.052123
[45]  Pearle, P. and Rizzi, A. (2017) Quantized Vector Potential and Alternative Views of the Magnetic Aharonov-Bohm Phase Shift. Physical Review A, 95, Article ID: 052124.
https://doi.org/10.1103/PhysRevA.95.052124
[46]  Comay, E. (1987) Conservation Laws and the Electric Aharo-nov-Bohm Effect. Physics Letters A, 120, 196-198.
https://doi.org/10.1016/0375-9601(87)90335-5
[47]  Comay, E. (1987) Further Comments on the Original Derivation of the Electric Aharonov-Bohm Effect. Physics Letters A, 125, 403-404.
https://doi.org/10.1016/0375-9601(87)90170-8
[48]  Tonomura, A, et al. (1986) Evidence for Aharonov-Bohm Effect with Magnetic Field Completely Shielded from Electron Wave. Physical Review Letters, 56, 792-795.
https://doi.org/10.1103/PhysRevLett.56.792

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