Theory of relativity

• 1. Introduction

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  The theory of relativity arrived in two parts, separated by a decade. Albert Einstein published special relativity in 1905, then general relativity in 1915. Together they pushed aside a theory of mechanics that had stood for roughly two hundred years, built largely by Isaac Newton. One half deals with all physical phenomena in the absence of gravity. The other half explains gravitation itself and how it relates to the forces of nature, reaching out to the cosmological and astrophysical realm. What does it mean to fold space and time into a single thing? Why did one half of Einstein's work win acceptance quickly while the other languished for decades? And how does a set of abstract equations end up inside the satellite navigation in your pocket? The answers run from a famous null result in the 1880s to black hole candidates spotted in 1981.

• 2. A Slow Acceptance

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  Max Planck reached for the word "relative" first. In 1906 he used the expression "relative theory," the Relativtheorie, to stress how Einstein's work leans on the principle of relativity. In the discussion section of that same paper, Alfred Bucherer used the phrase "theory of relativity," the Relativitätstheorie, for the first time. The name we now take for granted was coined by someone other than Einstein.

  By the 1920s the physics community had absorbed special relativity. It quickly became a necessary tool for theorists and experimentalists working in the new fields of atomic physics, nuclear physics, and quantum mechanics. Einstein had not worked alone. He built on results from Albert A. Michelson, Hendrik Lorentz, Henri Poincaré, and others, with later contributions from Planck, Hermann Minkowski, and more.

  General relativity, by contrast, looked far less useful at first. It seemed to offer little more than minor corrections to Newtonian gravitation, and most of its claims sat on an astronomical scale that resisted experimental test. Its mathematics struck many as difficult, fully grasped by only a small number of people. Around 1960 that changed. New mathematical techniques streamlined the calculations and made the concepts easier to visualize, and a string of discoveries gave the theory something to explain: quasars in 1963, the 3-kelvin microwave background radiation in 1965, pulsars in 1967, and the first black hole candidates in 1981.

• 3. The Two Postulates

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  Special relativity rests on two postulates that contradict each other in classical mechanics. The first says the laws of physics are the same for all observers in any inertial frame of reference moving relative to one another. The second says the speed of light in vacuum is the same for all observers, no matter their relative motion or the motion of the light source. Einstein laid this out in his 1905 paper titled "On the Electrodynamics of Moving Bodies."

  The consequences run against intuition. Two events that happen at the same moment for one observer may not be simultaneous for another observer in relative motion. Moving clocks are measured to tick more slowly than a stationary clock. Objects are measured to shorten in the direction they are moving. No physical object, message, or field line can travel faster than light in vacuum, and even the effect of gravity travels through space only at that speed, never instantly.

  Energy and mass turn out to be equivalent and transmutable, the famous mass-energy equivalence. The structure that holds all of this together is a change of mathematics. Special relativity replaces the Galilean transformations of classical mechanics with the Lorentz transformations.

• 4. Curving Spacetime

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  The equivalence principle is where general relativity begins. Under it, accelerated motion and resting in a gravitational field, such as standing on the surface of the Earth, are physically identical. The upshot is startling: free fall is inertial motion. An object in free fall drops not because gravity pushes it, but because that is simply how objects move when no force acts on them.

  This clashes with both classical mechanics and special relativity, where inertially moving objects cannot accelerate relative to each other, yet objects in free fall plainly do. To resolve it, Einstein proposed that spacetime is curved. He talked the idea through with the mathematician Marcel Grossmann, and the two concluded that the theory could be framed using Riemannian geometry, developed back in the 1800s.

  In 1915 Einstein devised the Einstein field equations, which tie the curvature of spacetime to the mass, energy, and momentum within it. The solutions to these equations are metric tensors, and they define the topology of spacetime and how objects move inertially. The theory predicts effects Newton never anticipated. Clocks run slower in deeper gravitational wells. Orbits precess unexpectedly, as seen in Mercury and in binary pulsars. Light bends near a gravitational field, rotating masses drag the surrounding spacetime along, and the universe itself expands, with certain components able to accelerate that expansion.

• 5. Principle Versus Construction

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  Einstein placed relativity in a category he called "principle-theories." These start not from speculative constructs or imagined mechanisms but from well-established empirical facts and observed regularities in nature. Constructive theories work the other way, building models of phenomena from assumed underlying processes.

  A principle-theory takes an analytic approach. It begins with experimentally verified principles and reasons deductively to the logical consequences and constraints that any physical process must obey. You observe natural processes, grasp their general characteristics, devise mathematical models to describe them, and deduce the necessary conditions any measurement must satisfy. The test is simple in spirit: separate events, when measured, must meet those conditions and match the theory's conclusions.

• 6. Hunting The Aether

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  Three experiments between 1881 and 1938 were critical to validating special relativity: the Michelson-Morley experiment, the Kennedy-Thorndike experiment, and the Ives-Stilwell experiment. Maxwell's equations described light as a wave moving at a characteristic velocity, and Maxwell and his contemporaries believed it traveled through a medium, much as sound moves through air. They called this medium the luminiferous aether, imagined at rest relative to the fixed stars while the Earth moved through it.

  Michelson built an instrument, the Michelson interferometer, to detect the aether wind, the motion of the aether relative to the Earth. It was accurate enough to catch the expected effect, yet it returned a null result in 1881 and again in 1887. To save the aether, FitzGerald and Lorentz independently proposed that material bodies change length according to their motion through it. This was the origin of FitzGerald-Lorentz contraction, a hypothesis with no theoretical basis. The null result showed the round-trip travel time for light is the same in every direction, but on its own it could neither discount the aether nor confirm relativity.

  The Kennedy-Thorndike experiment was first performed in 1932 by Roy Kennedy and Edward Thorndike to check whether the magnitude of light's velocity changed between inertial frames. They too found a null result, concluding there was no effect unless the velocity of the solar system was no more than about half that of the Earth in its orbit. That coincidence seemed too unlikely to accept, so the round-trip time for light was taken to be the same in all inertial frames. Herbert Ives and G.R. Stilwell carried out their experiment first in 1938, then more accurately in 1941, testing the transverse Doppler effect that Einstein had predicted in 1905. They observed the Lorentz factor correction, confirming that a moving atomic clock's frequency shifts as special relativity requires.

• 7. Relativity In Orbit

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  Relativistic effects are not confined to theory; they are practical engineering concerns. The classic confirmations of general relativity include the perihelion precession of Mercury's orbit, the deflection of light by the Sun, and the gravitational redshift of light, with further tests of the equivalence principle and frame dragging.

  Satellite-based measurement must account for these effects. Each satellite moves relative to an Earth-bound user and therefore sits in a different frame of reference under the theory. Global positioning systems such as GPS, GLONASS, and Galileo have to correct for all of the relativistic effects, including the consequences of the Earth's gravitational field, in order to work with precision. The same holds for high-precision timekeeping. Instruments from electron microscopes to particle accelerators simply would not work if relativistic considerations were left out.