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Special relativity is a theory proposed by
Albert Einstein
 that describes the propagation of
matter and light at high speeds. It was invented to explain the observed behavior of electric and magnetic fields,
which it beautifully reconciles into a single so-called electromagnetic field, and also to resolve a number of paradoxes
that arise when considering travel at large speeds. Special relativity also explains the behavior of fast-traveling
particle, including the fact that fast-traveling unstable particles appear decay more slowly than identical particles
traveling more slowly. Special relativity is an indispensable tool of modern physics, and its predictions have been
experimentally tested time and time again without any discrepancies turning up. Special relativity reduces to Newtonian
mechanics in the limit of small speeds.
According to special relativity, no wave or particle may travel at a speed greater than the
speed of light
c
. Therefore, the usual rules from Newtonian mechanics do not apply when adding velocities that are large enough. For
example, if a particle travels at a speed
v
with respect to a stationary observer, and another particle travels at a
speed
 with respect to the first particle, the speed
u
of particle two seen by the observer is not
 as would
be the case in Newtonian mechanics, but rather
 |
(1)
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This fact is intimately connected with the relationships between so-called inertial reference frames, including the
phenomena known as
Lorentz contraction
,
time dilation
, and
mass increase
. These phenomena manifest
themselves as an observer moving at speed
v
with respect to a fixed observing seeing lengths, times, and masses
shifted from the rest values
 ,
 ,
and
 according to
where
 is a function of
v
known as
relativistic gamma
and described below.
In special relativity, time and space are not independent, so the time and space coordinates of a particle in one
inertial reference frame
(the "rest frame") is most conveniently represented by a so-called
four-vector
 .
Here, the superscripts do not represent exponents, but are rather
indices of the vector (in this case, so-called contravariant indices). The transformation rule that takes this
four-vector and expresses its coordinates in a new inertial reference frame traveling with speed
v
relative to the
rest frame is then given by the so-called
Lorentz transformation
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(5)
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where
 is a tensor known as the
Lorentz tensor
and given by
 |
(6)
|
As is common in special relativity, the frequently-occurring quantities
and
 are dimensionless functions
of the speed
v
defined by
and are sometimes called
relativistic gamma
and
relativistic beta
, respectively.
Perhaps the most famous statement of special relativity is
 |
(9)
|
an equation which relates the energy of a stationary particle to its
rest mass
through the speed of light. The more general
statement for a particle in motion is
 |
(10)
|
and a more general statement still relates energy, mass, and momentum via
 |
(11)
|
These and a number of other important identities follow from the properties of so-called
Lorentz invariants
,
which are physical quantities that remain the same under Lorentz transformations. Such quantities are of particular importance in
special relativity, and can naturally be encoded in the language of
four-vectors
.
Important four-vectors include
the
position four-vector
and
momentum four-vector
.
It is often incorrectly stated that special relativity does not correctly deal with
accelerations
and
general relativity
must be used when accelerations are involved. While
general relativity
does indeed describe the relationship between mass and gravitational acceleration, special relativity
is perfectly adequate for dealing with relativistic kinematics.
 Four-Vector
,
General Relativity
,
Improper Time
,
Inertial Reference Frame
,
Lorentz Contraction
,
Lorentz Invariant
,
Lorentz Transformation
,
Principle of
Special Relativity
,
Proper Time
,
Relativistic Beta
,
Relativistic Gamma
,
Speed of Light
,
Superluminal
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© 1996-2007 Eric W. Weisstein
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