Abstract—We have observed a reciprocal relation between Planck's hypothesis and Einstein's postulate. Particle velocity and de Broglie wave velocity are also reciprocally related. We have postulated reciprocal symmetry and shown that it relates Special Relativity to quantum mechanics. Reciprocal symmetry implies that there is a boundary value velocity c, which is the limiting value and which is also constant under addition. This corresponds to Einstein's postulate. We have, then, developed reciprocal symmetric law of addition of velocities. In case of collinear velocities it agrees with Lorentz-Einstein law of addition. We have found the expression for the distance traveled. It agrees with the hyperbolic transform of the distance in Galilean space. If velocities are replaced by reciprocal velocities the distance traveled still gives the correct value, but only for integral multiples of unit time. For non integral values, the distance is complex.

Index Terms—Reciprocal symmetry, reciprocal symmetric addition, reciprocal symmetric multiplication, Lorentz transformation

M. Ahmad is with the Department of Physics, Rajshahi University, Rajshahi-6205, Bangladesh (e-mail: mushfiqahmad@gmail.com).

Cite: Mushfiq Ahmad, "Reciprocal Relation between Special Relativity and Quantum Mechanics and Correspondence between Continuous and Discrete Motion," International Journal of Applied Physics and Mathematics  vol. 2, no. 5, pp. 336-337, 2012.