world line and, in appropriate units, have equal space and time components for every observer. A consequence of Maxwell's theory of electromagnetism is that light carries energy and momentum, and that their ratio is a constant: . Rearranging, , and since for photons, the space and time components are equal, E/c must therefore be equated with the time component of the spacetime momentum vector. Photons travel at the speed of light, yet have finite momentum and energy. For this to be so, the mass term in γmc must be zero, meaning that photons are massless particles. Infinity times zero is an ill-defined quantity, but E/c is well-defined. By this analysis, if the energy of a photon equals E in the rest frame, it equals in a moving frame. This result can be derived by inspection of Fig. 3-9 or by application of the Lorentz transformations, and is consistent with the analysis of Doppler effect given previously. Mass–energy relationship Consideration of the interrelationships between the various components of the relativistic momentum vector led Einstein to several famous conclusions. In the low speed limit as approaches zero, approaches 1, so the spatial component of the relativistic momentum approaches mv, the classical term for momentum. Following this perspective, γm can be interpreted as a relativistic generalization of m. Einstein proposed that the relativistic mass of an object increases with velocity according to the formula . Likewise, comparing the time component of the relativistic momentum with that of the photon, , so that Einstein arrived at the relationship . Simplified to the case of zero velocity, this is Einstein's famous equation relating energy and mass. Another way of looking at the relationship between mass and energy is to consider a series expansion of at low velocity: The second term is just an expression for the kinetic energy of the particle. Mass indeed appears to be another form of energy. The concept of relativistic mass that Einstein introduced in 1905, mrel, although amply validated every day in particle accelerators around the globe (or indeed in any instrumentation whose use depends on high velocity particles, such as electron microscopes, old-fashioned color television sets, etc.), has nevertheless not proven to be a fruitful concept in physics in the sense that it is not a concept that has served as a basis for other theoretical development. Relativistic mass, for instance, plays no role in general relativity. For this