above, subsequent scholarship has established that his arguments fell short of a broadly definitive proof, the conclusions that he reached in this paper have stood the test of time. Einstein took as starting assumptions his recently discovered formula for relativistic Doppler shift, the laws of conservation of energy and conservation of momentum, and the relationship between the frequency of light and its energy as implied by Maxwell's equations. Fig. 6-1 (top). Consider a system of plane waves of light having frequency traveling in direction relative to the x-axis of reference frame S. The frequency (and hence energy) of the waves as measured in frame S that is moving along the x-axis at velocity is given by the relativistic Doppler shift formula which Einstein had developed in his 1905 paper on special relativity: Fig. 6-1 (bottom). Consider an arbitrary body that is stationary in reference frame S. Let this body emit a pair of equal-energy light-pulses in opposite directions at angle with respect to the x-axis. Each pulse has energy . Because of conservation of momentum, the body remains stationary in S after emission of the two pulses. Let be the energy of the body before emission of the two pulses and after their emission. Next, consider the same system observed from frame S that is moving along the x-axis at speed relative to frame S. In this frame, light from the forwards and reverse pulses will be relativistically Doppler-shifted. Let be the energy of the body measured in reference frame S before emission of the two pulses and after their emission. We obtain the following relationships: From the above equations, we obtain the following: The two differences of form seen in the above equation have a straightforward physical interpretation. Since and are the energies of the arbitrary body in the moving and stationary frames, and represents the kinetic energies of the bodies before and after the emission of light (except for an additive constant that fixes the zero point of energy and is conventionally set to zero). Hence, Taking a Taylor series expansion and neglecting higher order terms, he obtained Comparing the above expression with the classical expression for kinetic energy, K.E. = mv2, Einstein then noted: "If a body gives off the energy L in the form of radiation, its mass diminishes by L/c2." Rindler has observed that Einstein's heuristic argument suggested merely that energy contributes to mass. In