Jk Transformation Laws of Coordinates and Composition of Velocities

Abstract

Relative motion is redefined under the real-time analysis of universe by introducing use of imaginary velocity. Among inherent discrepancies in relative motion unraveled by the author, the one underlines, how the transfer of a real magnitude of an object to the opposite velocity of the other object is justified in two dimensional motion. Quite noticeable is that imaginary velocity gives correct values of relative velocities as the transfer of magnitude is imaginary and not real (refer 1.2). Hence, the new transformation laws [1] are obtained named as “jk”, denoting two constants, signifying the difference with the inverse law of Lorentz. In an isotropic universe, it is discovered that each frame holds references for its position at rest or when moving in a localised domain, where a frame at rest does not change its position over time in relation to its surroundings. However, the mechanism only allows the moving frame to see a mirror of its own motion in the resting frame, giving the impression that it is moving in the opposite direction. Hence, the relative motion is a synthesis of the real and imaginary motions with direction reversibility allowing jk laws to include complex velocity.  Under these laws vector quantities be in cross product or in dot product remain invariant such as Maxwell equations, space-time intervals and rotating frame as vectors show reciprocity. However, inherent scalar quantities such as mass, time, length etc. show inverse variation. So, unlike Lorentz transformation jk transformation is not a vector dominated law. The physical processes without reciprocity effects justify quantization of red-shift and particle decay. These ideas are helpful in comprehending the subtleties of the micro universe, including the asymmetry of Doppler's shifting images and short-lived particles, antimatter, subatomic particles, gamma rays, GRBs, cosmic rays, and subatomic particles.