Reciprocal Symmetry and Relativity Beyond the Speed of Light

Planck's hypothesis sets a lower limit (to energy). Einstein's postulate sets an upper limit (to speed). If a particle has a velocity v, the corresponding de Broglie wave has the velocity c2/v. Therefore, de Broglie wave velocities fulfill Einstein's “reciprocal postulate” that no speed can be less than the speed of light. Planck and de Broglie suggest a reciprocal relation between quantum mechanics and special relativity. From velocity v=x/t we can obtain the reciprocal velocity by interchanging between x and t. In a two dimensional space-time plane this interchange (of coordinates) means a rotation of the velocity vector. Special relativity should be able to accommodate all relativistic velocities (even if rotated). Therefore, faster-than-light velocities belong to the quantum mechanical aspect (or rotated region) of special relativity.

Mushfiq Ahmad graduated with honours in physics from Dhaka University in 1966 and got his Ph. D. from Rajshahi University in 2010. He has taught Physics at Rajshahi University, Bangladesh from 1974 to 2010. This book is a part of the result of years of thinking, and is a modified version of the Ph. D. work submitted to Rajshahi University in 2008.