During the late 1800's, many physicists recognized that James Clerk Maxwell's equations for electromagnetism were incompatible with the concepts of space and time underlying Sir Isaac Newton's three laws of motion. Attempts to explain electromagnetic waves (light and the newly discovered radio waves) as vibrations in an elastic substance called the "ether" predicted properties for light that could not be found experimentally.

Albert Einstein recognized that a key property of Maxwell's equations predicted that the speed of light must be constant for all observers under all circumstances. Einstein accepted this implied property of light as a postulate and followed this assumption to its inevitable conclusions. By applying this postulate to a simple clock based on the travel time of light pulses, he showed that time as measured by this clock (and by implication, all clocks) in motion must appear to an observer at rest to run slow. By careful consideration of how clocks are synchronized and how distances are measured, Einstein deduced that moving objects must appear to an observer at rest to shrink along the direction of motion.

All of these effects were captured in a set of transformation equations that allowed lengths and times for a moving observer to be calculated from the corresponding lengths and times as seen by a stationary observer, and vice versa. These equations had already been worked out by Hendrik Lorentz in his theory of the electron, but Einstein's independent derivation from the constancy of the speed of light was a powerful argument for the validity of special relativity.

In a later paper, Einstein examined how the emission of light (a form of energy) from a body at rest would look to a moving observer whose standards of time and length would be affected by the motion. Einstein deduced that the energy of the light would have to come from a reduction in the mass of the body. The amount of energy released would be equal to the lost mass multiplied by the square of the speed of light (the famous E=mc2 formula). This equivalence of mass and energy had been worked out for special cases as early as 1880. Einstein showed it to be a general property, true for all of physics.

It quickly became clear that gravity was a problem in special relativity. Einstein realized that on a small enough scale that gravity is indistinguishable from acceleration: An observer locked inside an elevator cannot determine whether the elevator is accelerating upward or is stationary in a constant gravitational field. Unifying this principle with special relativity occupied Einstein for the next ten years. Hermann Minkowski's insight of uniting time with three-dimensional space to make four-dimensional space-time proved crucial. At first, Einstein dismissed the space-time approach as useless theorizing, but it proved to be essential to his quest for a relativistic theory of gravity. This work culminated in the general theory of relativity.

General relativity treats space-time as a non-Euclidean geometry ("curved space"). Familiar Euclidean space is "flat," with no curvature: Unaccelerated objects move on straight lines. What appears in ordinary three-dimensional space to be a gravitational acceleration is actually motion along an unaccelerated but curved path in the non-Euclidean four-dimensional space-time.

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