Special relativity
In physics,[Annus Mirabilis papers|] the special theory of relativity, or special relativity for short, is a scientific theory of the relationship between space and time. In Albert Einstein's 1905 paper,
"On the Electrodynamics of Moving Bodies", the theory is presented as being based on just two postulates:
- The laws of physics are invariant in all inertial frames of reference. This is known as the principle of relativity.
- The speed of light in vacuum is the same for all observers, regardless of the motion of light source or observer. This is known as the principle of light constancy, or the principle of light speed invariance.
Overview
Relativity is a theory that accurately describes objects moving at speeds far beyond normal experience. Relativity replaces the idea that time flows equally everywhere in the universe with a new concept that time flows differently for every independent object. The flow of time can be expressed by counting ticks on a clock. Moving clocks run slower. At speeds encountered in normal experience, the slow down cannot be observed. Two events measured at the same time on a stationary clock occur at different times if measured on moving clocks. Near the speed of light many physical effects can only be understood by including the effects of special relativity.Basis
Unusual among modern topics in physics, the theory of special relativity needs only mathematics at high school level and yet it fundamentally alters our understanding, especially our understanding of the concept of time. Built on just two postulates or assumptions, many interesting consequences follow.The two postulates both concern observers moving at a constant speed relative to each other. The first postulate, the, says the laws of physics do not depend on objects being at absolute rest: for example, an observer on a train sees natural phenomena on that train that look the same whether the train is moving or not. The second postulate, constant speed of light, says observers in a train station see light travel at the same speed whether they measure light from within the station or light from a moving train. A light signal from the station to the train has the same speed, no matter how fast a train goes.
In the theory of special relativity, the two postulates combine to change the definition of "relative speed". Rather than the simple concept of distance traveled divided by time spent, the new theory incorporates the speed of light as the maximum possible speed. In special relativity, covering ten times more distance on the ground in the same amount of time according to a moving watch does not result in a speed up as seen from the ground by a factor of ten.
Consequences
Special relativity has a wide range of consequences that have been experimentally verified. The conceptual effects include:- The relativity of simultaneity events that appear simultaneous to one observer may not be simultaneous to an observer in motion
- time measured between two events by observers in motion differ
- distances between two events by observers in motion differ
- The velocities no longer simply add
Special relativity replaced the conventional notion of an absolute, universal time with the notion of a time that is local to each observer. Information about distant objects can arrive no faster than the speed of light so visual observations always report events that have happened in the past. This effect makes visual descriptions of the effects of special relativity especially prone to mistakes.
Special relativity also has profound technical consequences.
A defining feature of special relativity is the replacement of Euclidean geometry with Lorentzian geometry. Distances in Euclidean geometry are calculated with the Pythagorean theorem and only involved spatial coordinates. In Lorentzian geometry, 'distances' become 'intervals' and include a time coordinate with a minus sign. Unlike spatial distances, the interval between two events has the same value for all observers independent of their relative velocity. When comparing two sets of coordinates in relative motion the Lorentz transformation replaces the Galilean transformation of Newtonian mechanics.
Other effects include the relativistic corrections to the Doppler effect and the Thomas precession.
It also explains how electricity and magnetism are related.
History
The principle of relativity, forming one of the two postulates of special relativity, was described by Galileo Galilei in 1632 using a thought experiment involving observing natural phenomena on a moving ship. His conclusions were summarized as Galilean relativity and used as the basis of Newtonian mechanics. This principle can be expressed as a coordinate transformation, between two coordinate systems. Isaac Newton noted that many transformations, such as those involving rotation or acceleration, will not preserve the observation of physical phenomena. Newton considered only those transformations involving motion with respect to an immovable absolute space, now called transformations between inertial frames.In 1864 James Clerk Maxwell presented a theory of electromagnetism which did not obey Galilean relativity. The theory specifically predicted a constant speed of light in vacuum, no matter the motion of the light emitter or receiver or its frequency, wavelength, direction, polarization, or phase. This, as yet untested theory, was thought at the time to be only valid in inertial frames fixed in an aether. Numerous experiments followed, attempting to measure the speed of light as Earth moved through the proposed fixed aether, culminating in the 1887 Michelson–Morley experiment which only confirmed the constant speed of light.
Several fixes to the aether theory were proposed, with those of George Francis FitzGerald, Hendrik Antoon Lorentz, and Jules Henri Poincare all pointing in the direction of a result similar to the theory of special relativity. The final important step was taken by Albert Einstein in a paper published on 26 September 1905 titled "On the Electrodynamics of Moving Bodies". Einstein applied the Lorentz transformations known to be compatible with Maxwell's equations for electrodynamics to the classical laws of mechanics. This changed Newton's mechanics situations involving all motions, especially velocities close to that of light.
Another way to describe the advance made by the special theory is to say Einstein extended the Galilean principle so that it accounted for the constant speed of light, a phenomenon that had been observed in the Michelson–Morley experiment. He also postulated that it holds for all the laws of physics, including both the laws of mechanics and of electrodynamics.
The theory became essentially complete in 1907, with Hermann Minkowski's papers on spacetime.
Special relativity has proven to be the most accurate model of motion at any speed when gravitational and quantum effects are negligible. Even so, the Newtonian model remains accurate at low velocities relative to the speed of light, for example, everyday motion on Earth.
When updating his 1911 book on relativity, to include general relativity in 1920, Robert Daniel Carmichael called the earlier work the "restricted theory" as a "special case" of the new general theory; he also used the phrase "special theory of relativity". In comparing to the general theory in 1923 Einstein specifically called his earlier work "the special theory of relativity", saying he meant a restriction to frames in uniform motion.
Just as Galilean relativity is accepted as an approximation of special relativity that is valid for low speeds, special relativity is considered an approximation of general relativity that is valid for weak gravitational fields, that is, at a sufficiently small scale and in conditions of free fall. But general relativity incorporates non-Euclidean geometry to represent gravitational effects as the geometric curvature of spacetime. Special relativity is restricted to the flat spacetime known as Minkowski space. As long as the universe can be modeled as a pseudo-Riemannian manifold, a Lorentz-invariant frame that abides by special relativity can be defined for a sufficiently small neighborhood of each point in this curved spacetime.
Terminology
Special relativity builds upon important physics ideas. Among the most basic of these are the following:- speed or velocity, how fast an object moves relative to a reference point.
- speed of light, the maximum speed of information, independent of the speed of the source and receiver,
- clock, a device to measure differences in time; in relativity every object is imagined to have its own proper clock and moving clocks run slower.
- event: something that happens at a definite place and time. For example, an explosion or a flash of light from an atom; a generalization of a point in geometrical space,
The more technical background ideas include:
- spacetime: geometrical space and time considered together.
- spacetime interval between two events: a measure of separation between events that incorporates both the spatial distance between them and the duration of time separating them:
- coordinate system or reference frame: a way to locate events in spacetime. Events have coordinates x, y, z for space and t for time. The coordinates of the event are different in a different reference frame.
- inertial reference frame: a region of a reference frame where objects at rest with respect to the frame stay as rest, or if in uniform motion, stay in motion; also called a free-float frame.
- prime system, frame, or coordinate. To emphasize the relationship between two systems of coordinates, both use the same x,y,z axes but one will be marked with a prime symbol.
- coordinate transformation: changing how an event is described from one reference frame to another.
- invariance: when physical laws or quantities do not change in different inertial frames. The speed of light is invariant in special relativity: it is always the same.