Volume 22: Pages 44-46, 2009
Discrete and continuous representations of the same motion
Mushfiq Ahmad 1
1Department of Physics, Rajshahi University, Rajshahi-6205, Bangladesh
We have defined slowness (v′=1/v) as the reciprocal of velocity v. Einstein’s postulate (v c) sets a lower limit to slowness (v′c′). We have shown that the lower bound condition together with the group property (that the difference between two slownesses is also slowness) implies that slowness is discrete. We have, then, shown that the same physics can be described by a continuous quantity (like velocity) and by a discrete quantity (like slowness). This shows the equivalence between continuity and discreteness. We have also represented a distance traveled by a moving body in continuous representation and in discrete representation. We have considered motion in one space dimension only.
Keywords: Galilean Velocity, Lorentz-Algebraic Velocity, Reciprocal Lorentz-Algebraic Velocity, Distance, Reciprocal Distance, Continuous, Discrete
Received: August 25, 2008; Accepted: December 28, 2008; Published Online: February 25, 2009