**Authors:** Gordon Liu

The success of Special Relativity (SR) comes from the requirement of Lorentz co-variance to all physical equations. The explanation with regard to the Lorentz co-variance is based on two hypotheses, namely the principle of special relativity and the constancy of the speed of light. However, the statements of the principle of special relativity are various and confusing. The co-variance of physical equations and the equality of inertial frames of reference are mixed up. The equality of inertial frames of reference is obvious, but the co-variance of the physical equations is a more advanced requirement. Additionally, the way that the propagation property of light is placed in a central position of SR has caused people misunderstandings towards space-time, and also there is a logical circularity between the measurement of speed of light and the synchronization of clocks. These have obstructed to correctly extend the theory of space-time from an inertial frame of reference to a non-inertial frame of reference. These are the main reasons why many people criticize SR. In present paper, the two hypotheses have been discussed in detail and a new requirement to the equations of Physics has been proposed. The requirement is the Requirement of Special Completeness, namely, the physical equations used to describe the dynamics of matter and/or fields should include the descriptions that not only the matter and/or fields are at rest relative to an inertial frame of reference, but also they move relative to this frame. Basing on this requirement and the equality of the inertial frames of reference, we can approach to SR. Thereby let the theory of Lorentz co-variance has a clear and solid foundation. The constancy of the speed of light is just a deduction, not a premise. The Lorentz co-variance is just a characteristic of the Special Complete equations. Maxwell equations automatically satisfy the Lorentz trans-formations without any modification, while Newton law of gravity does not, because Newton law of gravity is not Special Complete and Maxwell equations are. The new approach has paved a road leading towards the generalizing of the theory of space-time from the inertial frame of reference to non-inertial frame of reference without considering gravitation.

**Comments:** 20 pages, PHYSICS ESSAYS 27, 1 (2014)

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