__Mohammed Sanduk__

## A classical underpinning to analogise the relativistic quantum mechanics

Based on three wave hypotheses (Horodecki, 1981, 1983), a system of two perpendicular rolling circles was found to represent a massive particle (Sanduk, 2007, 2009). This model has been developed to a system of two rolling circles in plane, and is used to obtain a complex vector under an assumption of partial observation (Sanduk, 2012). The concept of the partial observation may be explained as a lab observer condition. The complex vector is used to derive analogous forms for: Dirac equation, Klein–Gordon equation, special relativity equations, and others. The analogous forms of relativistic quantum mechanics are obtained without base on quantum axioms. Dirac coefficients, and Dirac Hamiltonian are explained. The work shows that both of the quantum mechanics and the special relativity are of same origin and are emergent. The system exhibits a fine structure and shows an explanation for the fine structure constant.

Rferences:

1. Horodecki, R., De Broglie wave and its dual wave, Phys. Lett. 87A, 1981, pp. 95-97.

2. Horodecki, R.,“ Superluminal singular dual wave”, Lett. Novo Cimento 38,(1983) 509-511.

3. Sanduk, M. I., Does the Three Wave Hypothesis Imply a Hidden Structure?, Apeiron, 14, No.2 ,2007, pp. 113-125.

4. Sanduk, M. I., Three Wave Hypothesis, Gear Model and the Rest Mass, arXiv:0904.0790 [physics.gen-ph], 2009.

5. Sanduk, M., A kinematic model for a partially resolved dynamical system in a Euclidean plane, Journal of Mathematical Modelling and Application , 1, No.6, 2012, pp. 40-51. ISSN: 2178-2423.