physics Physics is the scientific study of matter, its Elementary particle, fundamental constituents, its motion and behavior through space and time, and the related entities of energy and force. "Physical science is that department of knowledge whi ...

, relativistic aberration is the relativistic version of

aberration of light In astronomy, aberration (also referred to as astronomical aberration, stellar aberration, or velocity aberration) is a phenomenon where celestial objects exhibit an apparent motion about their true positions based on the velocity of the obser ...

, including relativistic corrections that become significant for observers who move with velocities close to the

speed of light The speed of light in vacuum, commonly denoted , is a universal physical constant exactly equal to ). It is exact because, by international agreement, a metre is defined as the length of the path travelled by light in vacuum during a time i ...

, as described by

special relativity In physics, the special theory of relativity, or special relativity for short, is a scientific theory of the relationship between Spacetime, space and time. In Albert Einstein's 1905 paper, Annus Mirabilis papers#Special relativity, "On the Ele ...

. Suppose, in the

reference frame In physics and astronomy, a frame of reference (or reference frame) is an abstract coordinate system, whose origin, orientation, and scale have been specified in physical space. It is based on a set of reference points, defined as geometric ...

of the observer, the source is moving with speed at an angle relative to the

vector Vector most often refers to: * Euclidean vector, a quantity with a magnitude and a direction * Disease vector, an agent that carries and transmits an infectious pathogen into another living organism Vector may also refer to: Mathematics a ...

from the observer to the source at the time when the

light Light, visible light, or visible radiation is electromagnetic radiation that can be visual perception, perceived by the human eye. Visible light spans the visible spectrum and is usually defined as having wavelengths in the range of 400– ...

is emitted. Then the following formula, which was derived by

Albert Einstein Albert Einstein (14 March 187918 April 1955) was a German-born theoretical physicist who is best known for developing the theory of relativity. Einstein also made important contributions to quantum mechanics. His mass–energy equivalence f ...

in 1905 using

Lorentz transformations In physics, the Lorentz transformations are a six-parameter family of linear transformations from a coordinate frame in spacetime to another frame that moves at a constant velocity relative to the former. The respective inverse transformation ...

, describes the aberration of the light source, , measured by the observer:

(1905)
''Zur Elektrodynamik bewegter Körper''
, ''Annalen der Physik'' 17: 891
English translation
by George Barker Jeffery and Wilfrid Perrett (1923), in "The Principle Of Relativity", Dover, page 56.

\cos \theta_o = \frac

This expression can also be written in the form

\tan\frac =\sqrt\tan\frac

In this circumstance, the rays of light from the source which reach the observer are tilted towards the direction of the source's motion (relative to the observer). It is as if light emitted by a moving object is concentrated conically, towards its direction of motion; an effect called relativistic beaming. Also, light received by a moving object (e.g. the view from a very fast spacecraft) also appears concentrated towards its direction of motion.

Searchlight effect

A consequence is that a forward observer should normally be expected to intercept a greater proportion of the object's light than a rearward one; this concentration of light in the object's forward direction is referred to as the "searchlight" or "headlight" effect. Light from a relativistic source becomes more forward directed and Doppler shifted with increasing velocity (

\beta=v/\mathrm

References

External links

Detailed explanation of relativistic aberration
at MathPages.com Aberration Light {{relativity-stub

Searchlight effect

See also

References

External links