is both particle and wave, so the traditional Particle Model (mass point model)
is actually not applicable for it. Here to describe its motion, we expand the
definition of time and space and pick up the spatial degrees of freedom hidden
by particle model. We say that micro-object is like a rolling field-matter-ball,
which has four degrees of freedom including one surface curvature degree and
three mapping degrees in the three-dimensional phenomenal space. All the
degrees are described by four curvature coordinate components, namely “k1, k2, k3, k4”, which form the imaginary
part of a complex phase space, respectively. While as to the real part, we use “x1, x2, x3, x4” to describe the micro
object’s position in our real space. Consequently, we build a Dual
4-dimensional complex phase space whose imaginary part is 4-dimension k space and real part is 4-dimension x space to describe the micro-object’s
motion. Furthermore, we say that wave function can describe the information of
a field-matter-ball’s rotation & motion and also matter-wave can spread the
information of micro-object’s spatial structure & density distribution.
Matter-wave and probability-wave can transform to each other though matter-wave
is a physical wave. The non-point property is the foundational source of the
probability in Quantum Mechanics.
Cite this paper
Zhao, G. (2014) Describe Quantum Mechanics in Dual 4 d Complex Space-Time and the Ontological Basis of Wave Function. Journal of Modern Physics, 5, 1684-1697. doi: 10.4236/jmp.2014.516168.
 Fan, D.N. and Hu, X.H. (2007) Schrodinger: Schrodinger’s Lectures. Peking University Press, Beijing, 8, 9, 12.
 (2004) L. de Broglie on the Theory of Quanta. Annales de Physique 10e serie t.3 (Janvier-Fevrier) 1925. Translated by A. F. Kraklauer.
 Huang, H.Q. (1979) Myth of Quantum Mechanics. Science Press, Beijing.
 Qin, K.C. (1989) The Philosophy of Quantum Mechanics. The Commercial Press, Beijing, 67-99.
 An, D. (2001) Sakata Shyoichi Proceedings of a Philosophy of Science. Shanghai Translation Publishing House, Shanghai.
 Zhou, Z.L. (1989) Mutation Theory, Thoughts and Application. Shanghai Translation Publishing House, Shanghai.
 Zhao, G.Q. (2013) Curvature Interpretation of Quantum Mechanics on the Outline.
 Smolin, L. (2008) The Trouble with Physics. Translated by Yong Li. Hunan Science and Technology Press, Changsha.
 Zhao, G.Q. (2008) From the Interaction to the Newly Issued Curvature Interpretation of Quantum Mechanics.
 Bjorken, A.D., et al. (1984) Relativistic Quantum Mechanics. Beijing Science Press, Beijing.
 Cao, T.Y. (2012) Quantum Mechanics Foundation International Research and Curvature Explanation Workshop Report.
 Li, K., Wang, J.H., Dulat, S. and Ma, K. (2010) International Journal of Theoretical Physics, 49, 134-143.
 Quantum (2012) Cai Gen Tan. Tsinghua University Press, Beijing.
 Cao, T.Y. (2010) From Current Algebra to Quantum Chromodynamics: A Case for Structural Realism. Cambridge University Press, Cambridge, 202-241.
 Ye, Y. and He, X.S. (1981) Feynman Physics. Science Press, Beijing.
 Zhang, Z.J. (1997) Relativistic Physics. Central China Normal University Press, Wuhan.
 Yang, F.J. (1979) The Physics in 20th Century. Beijing Science Press, Beijing.