A Classical Approach to the Modeling of Quantum Mass

ABSTRACT

In modern physics, a particle is regarded as the quantum excitation
of a field. Then, where does the mass of a particle come from? According to the
Standard Model, a particle acquires mass through its interaction with the Higgs
field. The rest mass of a free particle is essentially identified from the
Klein-Gordon equation (through its associated Lagrangian density). Recently it
was reported that a key feature of this theory (*i.e*., prediction of Higgs boson) is supported by experiments
conducted at LHC. Nevertheless, there are still many questions about the Higgs
model. In this paper, we would like to explore a different approach based on
more classical concepts. We think mass should be treated on the same footing as
momentum and energy, and the definition of mass should be strictly based on its
association with the momentum. By postulating that all particles in nature (including
fermions and bosons) are excitation waves of the vacuum medium, we propose a
simple wave equation for a free particle. We find that the rest mass of the
particle is associated with a “transverse wave number”, and the Klein-Gordon
equation can be derived from the general wave equation if one considers only
the longitudinal component of the excitation wave. Implications of this model
and its comparison with the Higgs model are discussed in this work.

Cite this paper

D. Chang, "A Classical Approach to the Modeling of Quantum Mass,"*Journal of Modern Physics*, Vol. 4 No. 11, 2013, pp. 21-30. doi: 10.4236/jmp.2013.411A1004.

D. Chang, "A Classical Approach to the Modeling of Quantum Mass,"

References

[1] G. Z. Liu, G. Cheng, Physical Review B, Vol. 65, 2002, p. 13.

[2] ATLAS Collaboration, Physical Review B, Vol. 716, 2012, p. 1.

[3] CMS Collaboration, Physical Review B, Vol. 716, 2012, p. 30.

[4] ATLAS Collaboration, Physics Letters B, 2013.

arXiv:1307.1427 [hep-ex]

[5] R. Oerter, “The Theory of Almost Everything: The Standard Model, the Unsung Triumph of Modern Physics,” Penguin Group, 2006.

[6] F. Englert and R. Brout, Physical Review Letters, Vol. 13, 1964, pp. 321-323.

http://dx.doi.org/10.1103/PhysRevLett.13.321

[7] P. W. Higgs, Physical Review Letters, Vol. 13, 1964, pp. 508-509. http://dx.doi.org/10.1103/PhysRevLett.13.508

[8] G. S. Guralnik, C. R. Hagen and T. W. B. Kibble, Physical Review Letters, Vol. 13, 1964, pp. 585-587.

http://dx.doi.org/10.1103/PhysRevLett.13.585

[9] C. N. Yang and R. Mills, Physical Review, Vol. 96, 1954, pp. 191-195. http://dx.doi.org/10.1103/PhysRev.96.191

[10] S. Weinberg, Physical Review Letters, Vol. 19, 1967, pp. 1264-1266.

http://dx.doi.org/10.1103/PhysRevLett.19.1264

[11] A. Salam, “Elementary Particle Physics: Relativistic Groups and Analyticity,” In: N. Svartholm, Ed., Eighth Nobel Symposium, Almquvist and Wiksell, Stockholm, 1968.

[12] W. N. Cottingham and D. A. Greenwood, “An Introduction to the Standard Model of Particle Physics,” Cambridge University Press, Cambridge, 1998, pp. 103-105.

[13] W. N. Cottingham and D. A. Greenwood, “An Introduction to the Standard Model of Particle Physics,” Cambridge University Press, Cambridge, 1998, pp. 105-106.

[14] J. Goldstone, “Field Theories with ‘Superconductor’ Solutions,” Il Nuovo Cimento, Vol. 19, 1961, pp. 154-164.

http://dx.doi.org/10.1007/BF02812722

[15] G. S. Guralnik, International Journal of Modern Physics A, Vol. 24, 2009, pp. 2601-2627.

http://dx.doi.org/10.1142/S0217751X09045431

[16] W. N. Cottingham and D. A. Greenwood, “An Introduction to the Standard Model of Particle Physics,” Cambridge University Press, Cambridge, 1998, pp. 107-109.

[17] W. N. Cottingham and D. A. Greenwood, “An Introduction to the Standard Model of Particle Physics,” Cambridge University Press, Cambridge, 1998, pp. 131-139.

[18] J. Ellis, “What Is the Higgs Boson?”

http://lybio.net/tag/john-ellis-what-is-the-higgs-boson-quotes/

[19] A. Messiah, “Quantum Mechanics,” John Wiley & Sons, New York, 1965, pp. 59-72.

[20] E. Whittaker, “A History of the Theories of Aether and Electricity,” Thomas Nelson and Sons Ltd., London, 1951.

[21] A. A. Michelson and E. W. Morley, “On the Relative Motion of the Earth and the Luminiferous Ether,” American Journal of Science, Vol. 34, 1887, pp. 333-345.

http://dx.doi.org/10.2475/ajs.s3-34.203.333

[22] A. P. French, “Special Relativity,” Nelsen, London, 1968.

[23] D. C. Chang, “What Is Rest Mass in the Wave-Particle Duality? A Proposed Model,” 2004.

ArXiv: physics/0404044

[24] D. C. Chang, “On the Wave Nature of Matter,” 2005.

ArXiv: physics/0505010

[25] P. A. M. Dirac, “The Principles of Quantum Mechanics,” 4th Edition, Oxford University Press, Oxford, 1981.

[26] A. Messiah, “Quantum Mechanics,” John Wiley & Sons, New York, 1965, pp. 56-59.

[27] S. Nettel, “Wave Physics,” 3rd Edition, Springer, Berlin, 2003, pp. 221-223.

http://dx.doi.org/10.1007/978-3-662-05317-1

[28] A. Einstein, “Relativity. The Special and the General Theory,” Three River Press, New York, 1961, pp. 1-64.

[29] J. J. Sakurai, “Advanced Quantum Mechanics,” Addison-Wesley, Reading, 1973, pp. 78-89.

[30] W. N. Cottingham and D. A. Greenwood, “An Introduction to the Standard Model of Particle Physics,” Cambridge University Press, Cambridge, 1998, p. 72.

[31] D. C. Chang, Bulletin of the American Physical Society, Vol. 29, 1984, p. 6.

[1] G. Z. Liu, G. Cheng, Physical Review B, Vol. 65, 2002, p. 13.

[2] ATLAS Collaboration, Physical Review B, Vol. 716, 2012, p. 1.

[3] CMS Collaboration, Physical Review B, Vol. 716, 2012, p. 30.

[4] ATLAS Collaboration, Physics Letters B, 2013.

arXiv:1307.1427 [hep-ex]

[5] R. Oerter, “The Theory of Almost Everything: The Standard Model, the Unsung Triumph of Modern Physics,” Penguin Group, 2006.

[6] F. Englert and R. Brout, Physical Review Letters, Vol. 13, 1964, pp. 321-323.

http://dx.doi.org/10.1103/PhysRevLett.13.321

[7] P. W. Higgs, Physical Review Letters, Vol. 13, 1964, pp. 508-509. http://dx.doi.org/10.1103/PhysRevLett.13.508

[8] G. S. Guralnik, C. R. Hagen and T. W. B. Kibble, Physical Review Letters, Vol. 13, 1964, pp. 585-587.

http://dx.doi.org/10.1103/PhysRevLett.13.585

[9] C. N. Yang and R. Mills, Physical Review, Vol. 96, 1954, pp. 191-195. http://dx.doi.org/10.1103/PhysRev.96.191

[10] S. Weinberg, Physical Review Letters, Vol. 19, 1967, pp. 1264-1266.

http://dx.doi.org/10.1103/PhysRevLett.19.1264

[11] A. Salam, “Elementary Particle Physics: Relativistic Groups and Analyticity,” In: N. Svartholm, Ed., Eighth Nobel Symposium, Almquvist and Wiksell, Stockholm, 1968.

[12] W. N. Cottingham and D. A. Greenwood, “An Introduction to the Standard Model of Particle Physics,” Cambridge University Press, Cambridge, 1998, pp. 103-105.

[13] W. N. Cottingham and D. A. Greenwood, “An Introduction to the Standard Model of Particle Physics,” Cambridge University Press, Cambridge, 1998, pp. 105-106.

[14] J. Goldstone, “Field Theories with ‘Superconductor’ Solutions,” Il Nuovo Cimento, Vol. 19, 1961, pp. 154-164.

http://dx.doi.org/10.1007/BF02812722

[15] G. S. Guralnik, International Journal of Modern Physics A, Vol. 24, 2009, pp. 2601-2627.

http://dx.doi.org/10.1142/S0217751X09045431

[16] W. N. Cottingham and D. A. Greenwood, “An Introduction to the Standard Model of Particle Physics,” Cambridge University Press, Cambridge, 1998, pp. 107-109.

[17] W. N. Cottingham and D. A. Greenwood, “An Introduction to the Standard Model of Particle Physics,” Cambridge University Press, Cambridge, 1998, pp. 131-139.

[18] J. Ellis, “What Is the Higgs Boson?”

http://lybio.net/tag/john-ellis-what-is-the-higgs-boson-quotes/

[19] A. Messiah, “Quantum Mechanics,” John Wiley & Sons, New York, 1965, pp. 59-72.

[20] E. Whittaker, “A History of the Theories of Aether and Electricity,” Thomas Nelson and Sons Ltd., London, 1951.

[21] A. A. Michelson and E. W. Morley, “On the Relative Motion of the Earth and the Luminiferous Ether,” American Journal of Science, Vol. 34, 1887, pp. 333-345.

http://dx.doi.org/10.2475/ajs.s3-34.203.333

[22] A. P. French, “Special Relativity,” Nelsen, London, 1968.

[23] D. C. Chang, “What Is Rest Mass in the Wave-Particle Duality? A Proposed Model,” 2004.

ArXiv: physics/0404044

[24] D. C. Chang, “On the Wave Nature of Matter,” 2005.

ArXiv: physics/0505010

[25] P. A. M. Dirac, “The Principles of Quantum Mechanics,” 4th Edition, Oxford University Press, Oxford, 1981.

[26] A. Messiah, “Quantum Mechanics,” John Wiley & Sons, New York, 1965, pp. 56-59.

[27] S. Nettel, “Wave Physics,” 3rd Edition, Springer, Berlin, 2003, pp. 221-223.

http://dx.doi.org/10.1007/978-3-662-05317-1

[28] A. Einstein, “Relativity. The Special and the General Theory,” Three River Press, New York, 1961, pp. 1-64.

[29] J. J. Sakurai, “Advanced Quantum Mechanics,” Addison-Wesley, Reading, 1973, pp. 78-89.

[30] W. N. Cottingham and D. A. Greenwood, “An Introduction to the Standard Model of Particle Physics,” Cambridge University Press, Cambridge, 1998, p. 72.

[31] D. C. Chang, Bulletin of the American Physical Society, Vol. 29, 1984, p. 6.