In this paper, the special theory of relativity in different media is established, based on the fundamental invariant of the space-time four-dimensional space x2 + y2 + z2 - c2 t2 = x'2 + y'2 + z'2 - c' t'2 . First of all, the inertial coordinate system is strictly defined in mathematical language. The inertial coordinate system that uses the actual measured different speeds of light as the limit speed still retains its most basic characteristics as an inertial coordinate system. Then, the space-time coordinate transformation and velocity transformation formulas between inertial coordinate systems with different light velocity are derived. These results not only break through the limitation of "vacuum", but also all are exactly the same as the conclusions of the traditional special theory of relativity when c = c' ; and when c ≠ c' give the new physical content. This all lifted the threat of the theory of relativity by the speed of light experiment, making c = c' ; and c ≠ c' both inclusively under the basic point of view of the theory of relativity; which will inevitably broaden the way of using relativity to deal with physics problems and clarify many problems left over in the study of relativity. The article discusses the problem of relativistic kinematics involving the measurement of time and space, correctly interprets the effects of “ruler contraction” and “clock retardation”, and uncovers and correctly answers the “clock paradox” that accompanied the birth of relativity. For two motion systems S and S', that are separated from each other by constant velocity, at any time and where, the product of the proper time elapsed evenly and uniformly and the speed of light in the respective system are equal, cτ = c' τ'; and the product of the coordinates time read out in observing and recognizing the other party's proper time and the speed of light in the respective system are also equal, ct = c' t' . It is confirmed that the product of any moving individual's uniform disappearance proper time and its measured speed of light remain unchanged; and the proper time cannot be determined purely by the individual's subjective way. Deduced the uncertain relationship between the proper time and the coordinate time for an inertial coordinate system which was not noticed by the traditional special theory of relativity. Remind the practical astronomy workers who do the time measurement and the time service work to understand that it is impossible to equate practical scientific coordinate time and the proper time of ideal uniform disappearance (the so-called “Ephemeris Time”). Thereby pay attention to the impact of this uncertain relationship on the time measurement and the time service work, and propose ways to verify. Subsequent work will use this expanded special theory of relativity to conduct a comprehensive review of related physics, which will inevitably extend to issues that have not been or cannot be examined by traditional special theory of relativity.