Applications of different Types of Lorenz Transformations

Abstract

The Lo rentz transformation is well known. In this paper, we have presented various types of applications of different Lorenz Transformat ions according to the nature of movement of one inertial frame relat ive to the other inertial frame such as relativistic aberration, relativ istic Doppler's effect and reflection of light ray by a moving mirro r. When one frame moves along X-axis with respect to the rest frame then we can find these applications for special Lo rentz transformation. When the motion o f the mov ing frame is not along X-axis relat ive to the rest frame but the mot ion is along any arbitrary direction then we can find these formulae for most general Lorentz transformation. We can generate these formulae fo r d ifferent types of most general Lorentz transformations using mixed number, quaternion and geometric product.

Volome Charge Density in Mixed Number Lorentz Transformation

“…Let and be two frames of references, where is at rest and is moving along x-axis with velocity with respect to frame.The space and time coordinates of and are and respectively. The relation between the coordinates of and which is called the special Lorentz Transformation [1][2][3]9], can be written as…”

“…Consider in this case and be the space part in and . Then we can write [1][2][3]9] (9) (10) Similarly we can write (11) (12) Eqs. (9), (10), (11) and (12) are the mixed number Lorentz transformation.…”

Comparative Study of the Volume Charge Density in Most General Lorentz Transformation and Quaternion Lorentz Transformation

“…Consider two inertial frames of references S and S where the frame S is at rest and S is moving along arbitrary direction then the space and time coordinates of S and S is known as MGLT [1][2][3][4][5][6][7] can be written as…”

Numerical Calculation of the Wigner Rotation

“…The space and time coordinates of S and S′ are (x, y, z, t) and (x′, y′, z′, t′) respectively. The relation between the coordinates of S and S′, which is called special Lorentz Transformation, can be written as [5][6][7][8] …”