Special Relativity Take Einstein's 1905 discovery of the special theory of relativity. This is the theory for which he is best known. It says that moving rods shrink, moving clocks slow and that the speed of light is a fundamental barrier through which nothing can accelerate. The decisive moment in the discovery of the theory came after Einstein had become convinced of two apparently contradictory results. One was the principle of relativity that tells us that uniform motion has no effect on physical systems. The second--soon to be called the light postulate--asserted that the speed of light always came out to be the same number, 186,000 miles per second. How could he have both? If we chase after a beam of light, surely we must judge it slow down? The decisive insight, Einstein later recalled, came after a visit with his friend Michele Besso, when the two discussed his work. Both are possible, Einstein realized, if we give up an assumption about simultaneity. We had assumed that whether two events at different places are simultaneous is an absolute fact. It is not, Einstein now saw. Observers in relative motion will disagree on whether two events are simultaneous. What if those events are used to time how fast light goes, say how long it needs to traverse some measuring rod? Then those differing judgments of simultaneity will make the seemingly impossible, possible. The original observer and the one chasing after light will both judge the light to have the same speed. The rest was mechanical. Einstein needed only 5 to 6 weeks to write what is now often singled out as the greatest scientific paper of the 20th century, "On the Electrodynamics of Moving Bodies." So it was all in that moment? Hardly. The real work lay in the reflections that convinced Einstein of the two apparently contradictory commitments. That work took, by Einstein's own reckoning, seven and more years. From his student days, Einstein had been fascinated by the latest, hottest theory of the moment, Maxwell's electrodynamics. It is a theory of electricity, magnetism and the waves that propagate in these fields; it was the closest the time had come to a theory of everything. One of its most striking results was that light is just a wave of propagating electric and magnetic fields and that it has a single, definite speed, 186,000 miles per second. Maxwell's theory was based on an ether with a preferred state of rest. The problem Einstein found was a tension between this preferred state of rest and the failure of experiments to reveal it. Worse on his reading the theory seemed to predict that no experiment could reveal it. So Einstein pursued the only line of research that seemed promising, attempts to modify Maxwell's theory in a way that would do away with the ether state of rest. It was a long and systematic search that went nowhere. The more he tried, the worse it got. Einstein came to a crisis. All efforts to modify Maxwell's electrodynamics had failed. But how could he keep both the idea that there is no ether state of rest and also the celebrated result of Maxwell's theory that light travels at exactly 186,000 miles per second. Then an observer chasing a light beam would not find the light to slow. These long efforts prepared the ground for Einstein's celebrated visit to Michele Besso.

General Relativity We see this same mix of flash of insight and systematic construction in the case of Einstein's greatest discovery, the general theory of relativity. This is the theory that tells us that gravity is just a curvature of the geometry of spacetime. It tells us that the real geometry of space is not the one Euclid described millennia ago and opens the door for later researchers to posit black holes and other extraordinary pathologies of space and time. The flash came in Einstein's first step. In 1907, while still a patent clerk, he was pondering how one might produce a relativistic theory of gravity and he was not having much success. Then he was struck by the fact that an observer in free fall no longer feels his own weight. He then hit upon what he called "the happiest thought of my life." One can produce gravity in gravity free space merely by reversing the process. Acceleration creates a gravitational field. This is his "principle of equivalence." That thought was the first step. It took seven and more years for Einstein to complete this work in 1915. Its first phase was devoted to systematic constructions that derived directly from Einstein's "happiest thought." In it, acceleration produced a special case of a relativistic gravitational field. Einstein now turned to the task of cataloguing the properties of this special case and generalizing them to arrive at a more general theory. In the special case, clocks are slowed and light is deflected by the gravitational field, which is proportional to the a variable speed of light. Those properties, Einstein supposed, hold in all static gravitational fields and he could arrive at the description of these fields merely by slightly generalizing the ways that the speed of light could vary with position in space. These constructions occupied Einstein's efforts in gravitation theory up to mid 1912. In the year that followed, Einstein made the transition to a spacetime theory in which gravitation is related to the curvature of its geometry. Unlike the case of special relativity, we have been able to reconstruct in some detail the steps and missteps of this decisive advance. We have a series of publications documenting the various stages of the developing theory and even his private notebook calculations, which I have spent a great deal of time in reconstructing. Einstein's explorations went quickly and slowly, straight and meandering. At times they became almost recipe-like. Einstein laid out the requirements his final equations must meet and then systematically searched for equations that satisfied them. While Einstein was launched by a flash of insight, the greatest part of work on the theory was spent in this systematic exploration. That eventually brought his project to completion.