Inertia
Albert Einstein's theory of special relativity, as proposed in his 1905 paper entitled "On the Electrodynamics of Moving Bodies" was built on the understanding of inertia and inertial reference frames developed by Galileo and Newton. While this revolutionary theory did significantly change the meaning of many Newtonian concepts such as mass, energy, and distance, Einstein's concept of inertia remained unchanged from Newton's original meaning (in fact, the entire theory was based on Newton's definition of inertia). However, this resulted in a limitation inherent in special relativity: the principle of relativity could only apply to reference frames that were "inertial" in nature (meaning when no acceleration was present). In an attempt to address this limitation, Einstein proceeded to develop his general theory of relativity ("The Foundation of the General Theory of Relativity," 1916), which ultimately provided a unified theory for both "inertial" and "noninertial" (accelerated) reference frames. However, in order to accomplish this, in general relativity, Einstein found it necessary to redefine several fundamental concepts (such as gravity) in terms of a new concept of "curvature" of space-time, instead of the more traditional system of forces understood by Newton.
History of special relativity
Einstein (1907a) proposed a method for detecting the transverse Doppler effect as a direct consequence of time dilation. And in fact, that effect was measured in 1938 by Herbert E. Ives and G. R. Stilwell (Ives–Stilwell experiment). And Lewis and Tolman (1909) described the reciprocity of time dilation by using two light clocks A and B, traveling with a certain relative velocity to each other. The clocks consist of two plane mirrors parallel to one another and to the line of motion. Between the mirrors a light signal is bouncing, and for the observer resting in the same reference frame as A, the period of clock A is the distance between the mirrors divided by the speed of light. But if the observer looks at clock B, he sees that within that clock the signal traces out a longer, angled path, thus clock B is slower than A. However, for the observer moving alongside with B the situation is completely in reverse: Clock B is faster and A is slower. Also Lorentz (1910–1912) discussed the reciprocity of time dilation and analyzed a clock "paradox", which apparently occurs as a consequence of the reciprocity of time dilation. Lorentz showed that there is no paradox if one considers that in one system only one clock is used, while in the other system two clocks are necessary, and the relativity of simultaneity is fully taken into account.