Foundations of Physics

, Volume 47, Issue 12, pp 1559–1581 | Cite as

A Time–Space Symmetry Based Cylindrical Model for Quantum Mechanical Interpretations

  • Thuan Vo VanEmail author


Following a bi-cylindrical model of geometrical dynamics, our study shows that a 6D-gravitational equation leads to geodesic description in an extended symmetrical time–space, which fits Hubble-like expansion on a microscopic scale. As a duality, the geodesic solution is mathematically equivalent to the basic Klein–Gordon–Fock equations of free massive elementary particles, in particular, the squared Dirac equations of leptons. The quantum indeterminism is proved to have originated from space–time curvatures. Interpretation of some important issues of quantum mechanical reality is carried out in comparison with the 5D space–time–matter theory. A solution of lepton mass hierarchy is proposed by extending to higher dimensional curvatures of time-like hyper-spherical surfaces than one of the cylindrical dynamical geometry. In a result, the reasonable charged lepton mass ratios have been calculated, which would be tested experimentally.


Time–space symmetry Higher-dimensional general relativity Wave-like solution Klein–Gordon–Fock equation Heisenberg inequality Lepton mass hierarchy 



The author is grateful to Dr. Tran Chi Thanh (Vietnam Atomic Energy Institute) for VINATOM’s support. We thank Nguyen Anh Ky and Nguyen Ai Viet (Hanoi Institute of Physics), Do Quoc Tuan (Physics Faculty, Hanoi University of Natural Sciences) for useful discussions. A heart-felt thanks is also extended to N. B. Nguyen (Thang Long University) for valuable technical assistance, T. Thu and M. L. Le-Vo for their continuous support and encouragement.


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© Springer Science+Business Media, LLC 2017

Authors and Affiliations

  1. 1.Duy Tan UniversityDanangVietnam
  2. 2.Vietnam Atomic Energy Institute (VINATOM)HanoiVietnam

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