**Authors:** Yingtao Yang

Abstract: The theory of electrodynamic space-time relativity (TESTR) is the study of the transformation of time and space between two electrodynamic inertial frames of reference, which have both inertial velocity difference and electric potential difference. It is a fundamental space-time theory of theoretical physics based on the Einstein’s special theory of relativity (STR), the electric potential limit postulate and the high-precision experimental facts of the inversion proportional square law of Coulomb’s force. It also proposed new basic physical concepts, such as electric potential limit, quaternion velocity, quaternion electric potential and etc. The two basic physical quantities, electric potential and velocity, are unified through the form of quaternions. It revealed the inherent relationships between the quaternion velocity or the quaternion electric potential and space-time. In mathematical form, it starts with the special theory of relativity in the real form and develop into the complex form and then further into the quaternion form. In the physical sense, it expands the special relativity from having an only inertial frame of reference to having both the inertial frame of reference and electric equipotential frame of reference. This paper discusses in detail the process of establishing the theory of complex electrodynamic space-time relativity and theory of quaternion electrodynamic space-time relativity as well as their various conversions and transformations. With the use of the new concept of system time, it leads to the expression of the fundamental equations of TESTR to be as concise as the form of Galilean transformation. In addition, its content is also more symmetrical and universal. It can correctly derive a set of more complex equations of the special three-dimensional theory of relativity. At the same time, proved that the special theory of relativity is a special case of TESTR, and found another important new special case: the theory of electric potential relativity (TEPR). The basic effects of TESTR were also discussed. It predicts some important new space-time change effects, for example, the electric potential time expansion effect. Such proposed effects would provide some theoretical basis for the experimental validation of TESTR. The appendix of the paper proves mathematically that the basic equations of the theory are consistent with the hypothesis. Keyword: special theory of relativity, postulates of electric potential limit, the theory of electric potential relativity，theory of complex electrodynamic space-time relativity, the theory of quaternion electrodynamic space-time relativity,

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[v1] 2018-06-11 21:36:15

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