4-Dimensional Universal Guidance Field Matrix [Form invariance of Spacetime Laws of Physics] Naveed Hussain Department of Physics, Khanewal Public School and College, Pakistan Email: naveedphy@gmail.com, Mobile Phone# +92334-6319358 (January 20, 2018) ABSTRACT: Maxwell’s equations in 4dimensional form provided the possibility of transformation of 4vectors and tensors under a single transformation law initially [1]. Later on more refined model was developed [2] then a series of surprises started [3]. An arbitrary 4 dimensional transformation matrix is constructed under which all the spacetime laws of physics including 4 vectors and tensors remain form invariant that has no counter example in the contemporary spacetime physics for the last 112 years of relativity theory. Previously three models of arbitrary matrix have been developed including spacetime exchanger matrix and arbitrary Lorentz matrix [4-6] but the present development is very general that contains a series of surprises. Under this transformation law using matrix method, contravarient 4vector or tensor remains contravariant and covariant 4 vector or tensor remains covariant. Since this matrix is based on two trigonometric quantities sin and cos where value of angle  determines the orientation of the physical object under transformation so we get the desired result. It is very interesting to note that for any value of , a 4 by 4 matrix with nonzero determinant is generated under which all the spacetime laws of physics remain form invariant. In this way a variety of matrices is obtained but all give the same result. One of them exchanges the space and time but the spacetime as a whole remains same. Singularity doesn’t exist at any value of . KEY WORDS: 4D Universal Transformation Matrix, Generator of 4 by 4 Form Invariant Matrices, Form Invariance of 4 vectors and Tensors Under Single Transformation Law, Univesality of Spacetime Laws of Physics INTRODUCTION: It is well known that Newtonian laws of physics are universal in 3dimensional world. Is it possible to get universal form of laws of physics in 4 dimensions? Form invariance of spacetime laws of physics under arbitrary frame of reference was the dream of Einstein through general theory of relativity but unfortunately spacetime physics is divided into two parts namely 4vectors and tensors. 4vectors are transformed using single matrix and tensors are transformed by different method using two matrices called similarity transformation. Furthermore, their results never agree due to different methods. The best example to demonstrate the above mentioned contradiction is observed in the case of Maxwell’s equations in tensor form and 4vector i.e. (1) F μ , = J μ Left hand side is in tensor form and right hand side is in 4vector form. Divergence of electromagnetic field behaves like a 4vector and 4current density is a well known 4vector. Since both sides are 4vectors so they must be transformed as a 4vector but unfortunately both sides are transformed under different methods so the confusion exists even today because they give different results. Is it possible to transform both sides under a single transformation law giving the same results? This possibility have been shown in my previous papers vide ref [4-6]. Development of physics in noninertial frame of reference [7] helped to discover theory of inertia and gravitation in the background of standard electromagnetic theory [8], [9]. In the present paper, the same development is shown in the most general matrix. Section-1 contains the mathematical development containing form invariance of electromagnetic field, Maxwell’s equations, conservation law, 4current density, conservation law in terms of