# Special relativity

In physics, special relativity (SR, also known as the special theory of relativity or STR) is the generally accepted and experimentally well-confirmed physical theory regarding the relationship between space and time. In Albert Einstein's original pedagogical treatment, it is based on two postulates:

1. The laws of physics are invariant (i.e., identical) in all inertial systems (i.e., non-accelerating frames of reference).
2. The speed of light in a vacuum is the same for all observers, regardless of the motion of the light source.

It was originally proposed by Albert Einstein in a paper published 26 September 1905 titled "On the Electrodynamics of Moving Bodies".[1] The inconsistency of Newtonian mechanics with Maxwell's equations of electromagnetism and the lack of experimental confirmation for a hypothesized luminiferous aether led to the development of special relativity, which corrects mechanics to handle situations involving motions at a significant fraction of the speed of light (known as relativistic velocities). As of today, special relativity is the most accurate model of motion at any speed when gravitational effects are negligible. Even so, the Newtonian mechanics model is still useful (due to its simplicity and high accuracy) as an approximation at small velocities relative to the speed of light.

Not until Einstein developed general relativity, to incorporate general (i.e., including accelerated) frames of reference and gravity, was the phrase "special relativity" employed. A translation that has often been used is "restricted relativity"; "special" really means "special case".[2]

Special relativity implies a wide range of consequences, which have been experimentally verified,[3] including length contraction, time dilation, relativistic mass, mass–energy equivalence, a universal speed limit and relativity of simultaneity. It has replaced the conventional notion of an absolute universal time with the notion of a time that is dependent on reference frame and spatial position. Rather than an invariant time interval between two events, there is an invariant spacetime interval. Combined with other laws of physics, the two postulates of special relativity predict the equivalence of mass and energy, as expressed in the mass–energy equivalence formula E = mc2, where c is the speed of light in a vacuum.[4][5]

A defining feature of special relativity is the replacement of the Galilean transformations of Newtonian mechanics with the Lorentz transformations. Time and space cannot be defined separately from each other. Rather space and time are interwoven into a single continuum known as spacetime. Events that occur at the same time for one observer can occur at different times for another.

The theory is "special" in that it only applies in the special case where the curvature of spacetime due to gravity is negligible.[6][7] In order to include gravity, Einstein formulated general relativity in 1915. Special relativity, contrary to some outdated descriptions, is capable of handling accelerations as well as accelerated frames of reference.[8][9]

As Galilean relativity is now considered 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, i.e. at a sufficiently small scale and in conditions of free fall. Whereas general relativity incorporates noneuclidean geometry in order to represent gravitational effects as the geometric curvature of spacetime, special relativity is restricted to the flat spacetime known as Minkowski space. A locally Lorentz-invariant frame that abides by special relativity can be defined at sufficiently small scales, even in curved spacetime.

Galileo Galilei had already postulated that there is no absolute and well-defined state of rest (no privileged reference frames), a principle now called Galileo's principle of relativity. Einstein extended this principle so that it accounted for the constant speed of light,[10] a phenomenon that had been recently 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.[11]

Albert Einstein around 1905, the year his "Annus Mirabilis papers" were published. These included Zur Elektrodynamik bewegter Körper, the paper founding special relativity.
1. ^ Albert Einstein (1905) "Zur Elektrodynamik bewegter Körper", Annalen der Physik 17: 891; English translation On the Electrodynamics of Moving Bodies by George Barker Jeffery and Wilfrid Perrett (1923); Another English translation On the Electrodynamics of Moving Bodies by Megh Nad Saha (1920).
2. ^ [Science and Common Sense, P. W. Bridgman, The Scientific Monthly, Vol. 79, No. 1 (Jul., 1954), pp. 32-39.; THE ELECTROMAGNETIC MASS AND MOMENTUM OF A SPINNING ELECTRON, G. Breit, Proceedings of the National Academy of Sciences, Vol. 12, p.451, 1926; Kinematics of an electron with an axis. Phil. Mag. 3:1-22. L. H. Thomas.] Einstein himself, in The Foundations of the General Theory of Relativity, Ann. Phys. 49 (1916), writes "The word "special" is meant to intimate that the principle is restricted to the case...". See p. 111 of The Principle of Relativity, A. Einstein, H. A. Lorentz, H. Weyl, H. Minkowski, Dover reprint of 1923 translation by Methuen and Company.]
3. ^ Tom Roberts & Siegmar Schleif (October 2007). "What is the experimental basis of Special Relativity?". Usenet Physics FAQ. Retrieved 2008-09-17.
4. ^ Albert Einstein (2001). Relativity: The Special and the General Theory (Reprint of 1920 translation by Robert W. Lawson ed.). Routledge. p. 48. ISBN 0-415-25384-5.
5. ^ Richard Phillips Feynman (1998). Six Not-so-easy Pieces: Einstein's relativity, symmetry, and space–time (Reprint of 1995 ed.). Basic Books. p. 68. ISBN 0-201-32842-9.
6. ^ Sean Carroll, Lecture Notes on General Relativity, ch. 1, "Special relativity and flat spacetime," http://ned.ipac.caltech.edu/level5/March01/Carroll3/Carroll1.html
7. ^ Wald, General Relativity, p. 60: "...the special theory of relativity asserts that spacetime is the manifold ℝ4 with a flat metric of Lorentz signature defined on it. Conversely, the entire content of special relativity ... is contained in this statement ..."
8. ^ Koks, Don (2006). Explorations in Mathematical Physics: The Concepts Behind an Elegant Language (illustrated ed.). Springer Science & Business Media. p. 234. ISBN 978-0-387-32793-8. Extract of page 234
9. ^ Steane, Andrew M. (2012). Relativity Made Relatively Easy (illustrated ed.). OUP Oxford. p. 226. ISBN 978-0-19-966286-9. Extract of page 226
10. ^ Edwin F. Taylor & John Archibald Wheeler (1992). Spacetime Physics: Introduction to Special Relativity. W. H. Freeman. ISBN 0-7167-2327-1.
11. ^ Rindler, Wolfgang (1977). Essential Relativity: Special, General, and Cosmological (illustrated ed.). Springer Science & Business Media. p. §1,11 p. 7. ISBN 978-3-540-07970-5.