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Line 36: − − == Relation between energy and mass == − − The famous equation attributed to Einstein, ''E=mc<sup>2</sup>'', describes the relationship between energy and the minimum energy of a body in its own inertial frame, also called the rest mass. In nuclear physics, during fission or fusion reactions, the sum of the rest mass of the constituents changes, releasing energy in form of radiation or kinetic energy. − − == Classical mechanics as a limiting case == − − At low speeds (relative to light-speed), the Einstein-Lorentz relativity equations are equivalent to Newton's equations. Particles at low mass and low speed can be approximated by [[classical mechanics]] ([[Isaac Newton]]'s laws of motion). If an objects energy is mainly constituted by it rest mass, the classic limit is valid. Relativity is essential for fast-moving bodies. Electromagnetism, including for light and gamma radiation, where the quanta (photons) have no rest mass, is always relativistic − − == Relation between energy and mass == − − The famous equation attributed to Einstein, ''E=mc<sup>2</sup>'', describes the relationship between energy and the minimum energy of a body in its own inertial frame, also called the rest mass. In nuclear physics, during fission or fusion reactions, the sum of the rest mass of the constituents changes, releasing energy. − − − == Gravitational lensing == − (effect of general relativity) − − Light passing through a region containing many massive bodies such as galaxies will be distorted. Telescopic observations confirm that galactic clusters distort the paths of the light passing through them, and the effect can be used to focus on Objects far behind the "gravitational lense" . [[classical mechanics]], in which light travels in straight lines, can not explain this. Line 53:
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Special theory of relativity (view source)
Revision as of 22:27, November 17, 2009
, 22:27, November 17, 2009Added math, reworded unclear wording, deleted short unrelated sections
The three most prominent SRT effects are [[time dilation]], length contraction and the equivalence of mass and energy.
The three most prominent SRT effects are [[time dilation]], length contraction and the equivalence of mass and energy.
== Four Vectors and relativistic metric ==
== Mathematics ==
The central equation of special relativity is<ref>http://www2.slac.stanford.edu/vvc/theory/relativity.html</ref>:
:γ=<math>\frac{1}{\sqrt{1-\frac{v^2}{c^2}}}</math>, where:
* γ is the factor relating relativistic time, mass, and momentum to non-relativistic time, mass, and momentum.
* v is the speed of the object in question
* c is the [[speed of light]]
=== Classical mechanics ===
When <tt>v</tt>, the speed of the object in question, is low relative to <tt>c</tt>, γ approaches <math>\frac{1}{\sqrt{1-0}} = 1</math>, causing the Einstein-Lorentz relativity equations to be equivalent to Newton's equations. This is why [[classical mechanics, governed by [[Isaac Newton]]'s laws of motion, works for particles at low mass and low speed. However, at higher velocities, γ diverges, causing relativity to be essential.
Electromagnetism, including for light and gamma radiation, where the quanta (photons) travel at light speed have no rest mass, is always relativistic.
===Universal speed limit ===
At the other extreme, when <tt>v</tt> approaches <tt>c</tt>, γ approaches <math>\frac{1}{\sqrt{1-1}} = \frac{1}{0} = \infty</math>. Since infinite γ means infinite mass, no object can ever reach the speed of light. (Some theorists have postulated hypothetical [[tachyon]]s, which would always travel faster than the speed of light<ref>http://www.math.ucr.edu/home/baez/physics/ParticleAndNuclear/tachyons.html</ref>. No evidence has been found for them. If they existed, special relativity would mean that they cannot ever travel slower than the speed of light.)
== History ==
== History ==
In the beginning of the last century the two assumption mentioned before where found experimentally in the form of the Maxwell equations, which describe electromagnetic waves. The general idea at that point was that any wave is carried by some substance. This thought of substance was called [[aether (science)|luminiferous aether]]. However, as the earth is moving trough space, there should be a difference in the interferometrically determined light wavelength, when measured at noon, at evening and at night at the same geographic location. However the [[Michelson-Morley experiment]] did reject the aether hypothesis. With this rejection it became an inevitable fact that equations descibing physics, which where fitting to a three dimensional space with a single timeframe for all observers exist. The mathematical framework was developed by [[Henri Poincaré]] and [[Hendrik Lorentz]], which [[Albert Einstein]] connected to the experimental observations.
In the beginning of the last century the two assumption mentioned before where found experimentally in the form of the Maxwell equations, which describe electromagnetic waves. The general idea at that point was that any wave is carried by some substance. This thought of substance was called [[aether (science)|luminiferous aether]]. However, as the earth is moving trough space, there should be a difference in the interferometrically determined light wavelength, when measured at noon, at evening and at night at the same geographic location. However the [[Michelson-Morley experiment]] did reject the aether hypothesis. With this rejection it became an inevitable fact that equations descibing physics, which where fitting to a three dimensional space with a single timeframe for all observers exist. The mathematical framework was developed by [[Henri Poincaré]] and [[Hendrik Lorentz]], which [[Albert Einstein]] connected to the experimental observations.
== Spin as a relativistic effect ==
== Spin as a relativistic effect ==
The relativistic extension of Quantum Mechanics, described by the Dirac Equation allows, due to the symmetry of the equation in 4-space, an additional quantum number to exist, called spin. [[electron spin]] was known from chemistry before relativity arose.
The relativistic extension of Quantum Mechanics, described by the Dirac Equation allows, due to the symmetry of the equation in 4-space, an additional quantum number to exist, called spin. [[electron spin]] was known from chemistry before relativity arose.
== Interpretation and paradoxes==
== Interpretation and paradoxes==
For example, a discussion of hypothetical [[tachyons]] talks "about using tachyons to transmit information faster than the speed of light, '''in violation of Special Relativity'''."[http://www.math.ucr.edu/home/baez/physics/ParticleAndNuclear/tachyons.html] However, there is some question whether the Theory of Special Relativity really restricts faster-than-light communication of information.</ref>
For example, a discussion of hypothetical [[tachyons]] talks "about using tachyons to transmit information faster than the speed of light, '''in violation of Special Relativity'''."[http://www.math.ucr.edu/home/baez/physics/ParticleAndNuclear/tachyons.html] However, there is some question whether the Theory of Special Relativity really restricts faster-than-light communication of information.</ref>
# The laws of physics are identical, without any variation, in every location throughout the universe.
# The laws of physics are identical, without any variation, in every location throughout the universe.
# The laws of physics are identical, without any variation, no matter how fast something is traveling (in the absence of acceleration).
# The laws of physics are identical, without any variation, no matter how fast something is traveling (in an [[inertial reference frame]]).
Special relativity alters [[Isaac Newton]]'s laws of motion by assuming that the speed of light will be the same for all observers, despite their relative velocities and the source of the light. (Therefore, if A sends a beam of light to B, and both measure the speed, it will be the same for both, no matter what the relative velocity of A and B. In Newtonian/Galilean mechanics, If A sends a physical object at a particular velocity towards B, and nothing slows it, the velocity of the object relative to B depends on the velocities of the object and of B relative to A.)
Special relativity alters [[Isaac Newton]]'s laws of motion by assuming that the speed of light will be the same for all observers, despite their relative velocities and the source of the light. (Therefore, if A sends a beam of light to B, and both measure the speed, it will be the same for both, no matter what the relative velocity of A and B. In Newtonian/Galilean mechanics, If A sends a physical object at a particular velocity towards B, and nothing slows it, the velocity of the object relative to B depends on the velocities of the object and of B relative to A.)
In the framework of SRT several thought experiments can be constructed, which lead to paradoxes. The most striking one is the twin paradoxon. If you take twins, one on earth, and one in traveling to the next star with high speed and back, their biological age will not be the same, even though you could redefine the system of the traveling twin to be resting. This paradoxon is resolved when you consider that the trjectory of the second twin does not fulfill the condition on beeing in an inertial frame, because he is accelerated. This points out, that while neglected in SRT, acceleration has a non-trivial role, which is considered in the General theory of relativity.
In the framework of special relativity, several thought experiments can be constructed, which lead to apparent paradoxes. The most striking one is the twin paradox. If you take twins, one on earth, and one in traveling to the next star with high speed and back, their biological age will not be the same, even though you could redefine the system of the traveling twin to be resting. This paradox is resolved because the second twin is not in an inertial frame - he has accelerated, most significantly at his turn-around point. This points out, that while neglected in special relativity, acceleration has a non-trivial role. This is considered in the [[General theory of relativity]].
==References==
{{reflist}}
[[Category:Physics]]
[[Category:Physics]]