A Classical Approach to the Modeling of Quantum Mass

Donald C. Chang

Div of LIFS, Hong Kong University of Science and Technology, Hong Kong, China.

DOI: 10.4236/jmp.2013.411A1004                

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.

Keywords

Mass; Vacuum; Quantum Excitation; Matter Wave; Particle-Wave Duality; Higgs Mechanism

Conflicts of Interest

The authors declare no conflicts of interest.

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.