Comparison between Spin and Rotation Properties Of Lorentz Einstein and Reflection Symmetri.pdf

COMPARISON BETWEEN SPIN AND ROTATION PROPERTIES OF LORENTZ EINSTEIN AND REFLECTION SYMMETRIC TRANSFORMATIONS Mushfiq Ahmad Department of Physics, Rajshahi University, Rajshahi, Bangladesh. E-mail: mushfiqahmad@ru.ac.bd M. Shah Alam Department of Physics, Shah Jalal University of Science and Technology, Sylhet, Bangladesh. E-mail: salam@ M.O.G. Talukder Department of Applied Physics and Electronics, Rajshahi University, Rajshahi, Bangladesh. E-mail: ogtalukder@ru.ac.bd Abstract We have shown that reflection symmetric transformation is Lorentz invariant; it is also associative. We have also shown that reflection symmetric sum of vectors has a spin-like term comparable to the spin of Dirac electron. As a consequence of reflection symmetry we have found that the sum is bounded. This corresponds to Einstein’s postulate. Key words: Reflection symmetry, Lorentz invariance, Spin, Associativity. 03.30.+p., 03.65.Ca, 03.65.Pm 1. Introduction We have defined a reflection symmetry sum +? ( + with a cap ^) of vectors A and B as [1]. A.B1 AxBBABA + ++ =+ i? (1) A will be called a reciprocal of if A 1=A.A With the help of an arbitrarily chosen vector , we define reciprocals of as G A A.G iAxGGA ±=± (2) We now have the symmetry relation BABA +=+ ?+ ?? (3) We intend to study the relation of reflection symmetric sum to Lorentz invariance and also its rotational (spin) property. 2. Pauli Quaternion We construct a 4-dimensional vector [2] and follow the convention adopted by Kyrala [3] to write it as a sum of a scalar and a Cartesian vector A+= 0AA 1 (4) with the help of basis vectorsσ (they are slightly different from those of Kyrala [3])we write