Re Birth of Einstein’s Relativity via Unified Transformation Law

N. Hussain¹, H.A. Hussain², A. Tariq³, M. F. Yaseen⁴, J. Amjad⁴ and A. Qayyum^4,

¹Punjab College Multan Pakistan

²Department of Physics, MNS University of Engineering and Technology Multan Pakistan

³National College of Business Administration & Economics, Multan Campus Pakistan

⁴Department of Mathematics, Institute of Southern Punjab Multan Pakistan

Cite this paper:
N. Hussain, H.A. Hussain, A. Tariq, M. F. Yaseen, J. Amjad and A. Qayyum. Re Birth of Einstein’s Relativity via Unified Transformation Law. International Journal of Physics. 2023; 11(1):6-16. doi: 10.12691/ijp-11-1-2

Abstract

Einstein principle of relativity (EPR) demands that all the spacetime laws of physics must remain same in every frame of reference. Einstein provided us powerful techniques to express the laws of physics in terms of 4-vectors, tensors and their unification. Maxwell’s equations in tensor form as divergence of electromagnetic field tensor is equal to 4-current density that is a physical relation between tensor and 4-vector. The first problem arises when we transform divergence of electromagnetic field tensor and 4-current density under Lorentz transformation matrix (LTM) by different transformation laws then the results of both sides do not agree. This situation led to discover a single transformation law (STL) for 4-vectors and tensors and universal Lorentz transformation matrix (ULTM) such that their results after transformation remain same. The second problem lies with the present form of LTM as 4-vectors and tensors do not remain same under LTM except inner product of 4-vectors and tensors. Special relativity (SR) is based on inertial frame while general relativity (GR) requires noninertial frame. ULTM is valid for SR and GR equally to fulfill the requirement of EPR. In this paper, we will mainly focus on transformation of electromagnetic theory consisting of 4-current density, electromagnetic field, Maxwell’s equations and conservation law in tensor notation. Matrix method is employed for all calculations. As a consequence of STL, new symmetry terms appear in electromagnetic field, Maxwell’s equations and conservation law. These terms not only obey EPR but also Noether’s symmetry principle. The significance of discovery of STL and ULTM is that all the spacetime laws of physics namely 4-vectors, tensors and their inner product remain same independent of inertial or noninertial frame. Constancy of speed of light is a special case of 4-velocity. This is the reason that it is named as rebirth of Einstein’s theory of relativity.

Keywords:
unification of SR and GR via ULTM single transformation law for 4-Vectors and tensors emergence of new symmetry terms form invariance of all the laws of physics constancy of speed of light and 4-velocity

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