In
electromagnetism
In physics, electromagnetism is an interaction that occurs between particles with electric charge. It is the second-strongest of the four fundamental interactions, after the strong force, and it is the dominant force in the interactions of a ...
,
electromagnetic waves
In physics, electromagnetic radiation (EMR) consists of waves of the electromagnetic (EM) field, which propagate through space and carry momentum and electromagnetic radiant energy. It includes radio waves, microwaves, infrared, (visible) lig ...
in
vacuum
A vacuum is a space devoid of matter. The word is derived from the Latin adjective ''vacuus'' for "vacant" or "void". An approximation to such vacuum is a region with a gaseous pressure much less than atmospheric pressure. Physicists often dis ...
travel at the
speed of light
The speed of light in vacuum, commonly denoted , is a universal physical constant that is important in many areas of physics. The speed of light is exactly equal to ). According to the special theory of relativity, is the upper limit ...
''c'', according to
Maxwell's Equations
Maxwell's equations, or Maxwell–Heaviside equations, are a set of coupled partial differential equations that, together with the Lorentz force law, form the foundation of classical electromagnetism, classical optics, and electric circuits.
...
. The retarded time is the time when the field began to propagate from the point where it was emitted to an observer. The term "retarded" is used in this context (and the literature) in the sense of
propagation delay
Propagation delay is the time duration taken for a signal to reach its destination. It can relate to networking, electronics or physics. ''Hold time'' is the minimum interval required for the logic level to remain on the input after triggering e ...
s.
Retarded and advanced times
![Universal charge distribution](https://upload.wikimedia.org/wikipedia/commons/f/f4/Universal_charge_distribution.svg)
The calculation of the retarded time ''t
r'' or ''t''
′ is nothing more than a simple "
speed-distance-time" calculation for EM fields.
If the EM field is radiated at
position vector
In geometry, a position or position vector, also known as location vector or radius vector, is a Euclidean vector that represents the position of a point ''P'' in space in relation to an arbitrary reference origin ''O''. Usually denoted x, r, or s ...
r
′ (within the source charge distribution), and an observer at position r measures the EM field at time ''t'', the time delay for the field to travel from the charge distribution to the observer is , r − r
′, /''c'', so subtracting this delay from the observer's time ''t'' gives the time when the field ''actually began to propagate'' - the retarded time, ''t''
′.
The retarded time is:
which can be rearranged to
:
showing how the positions and times correspond to source and observer.
Another related concept is the advanced time ''t
a'', which takes the same mathematical form as above, but with a “+” instead of a “−”:
:
and is so-called since this is the time the field will advance from the present time ''t''. Corresponding to retarded and advanced times are
retarded and advanced potentials.
Retarded position
The retarded position can be obtained from the current position of a particle by subtracting the distance it has travelled in the lapse from the retarded time to the current time.
For an inertial particle, this position can be obtained by solving this equation:
:
,
where r
c'' is the current position of the source charge distribution and v its velocity.
Application
Perhaps surprisingly - electromagnetic fields and forces acting on charges depend on their history, not their mutual separation.
[Classical Mechanics, T.W.B. Kibble, European Physics Series, McGraw-Hill (UK), 1973, ] The calculation of the electromagnetic fields at a present time includes integrals of
charge density
In electromagnetism, charge density is the amount of electric charge per unit length, surface area, or volume. Volume charge density (symbolized by the Greek letter ρ) is the quantity of charge per unit volume, measured in the SI system in co ...
ρ(r', ''t
r'') and
current density
In electromagnetism, current density is the amount of charge per unit time that flows through a unit area of a chosen cross section. The current density vector is defined as a vector whose magnitude is the electric current per cross-sectional ar ...
J(r', ''t
r'') using the retarded times and source positions. The quantity is prominent in
electrodynamics
In physics, electromagnetism is an interaction that occurs between particles with electric charge. It is the second-strongest of the four fundamental interactions, after the strong force, and it is the dominant force in the interactions of a ...
,
electromagnetic radiation
In physics, electromagnetic radiation (EMR) consists of waves of the electromagnetic field, electromagnetic (EM) field, which propagate through space and carry momentum and electromagnetic radiant energy. It includes radio waves, microwaves, inf ...
theory, and in
Wheeler–Feynman absorber theory
The Wheeler–Feynman absorber theory (also called the Wheeler–Feynman time-symmetric theory), named after its originators, the physicists Richard Feynman and John Archibald Wheeler, is an interpretation of electrodynamics derived from the assump ...
, since the history of the charge distribution affects the fields at later times.
See also
*
Antenna measurement
Antenna measurement techniques refers to the testing of antennas to ensure that the antenna meets specifications or simply to characterize it. Typical parameters of antennas are gain, bandwidth, radiation pattern, beamwidth, polarization, and imp ...
*
Electromagnetic four-potential
An electromagnetic four-potential is a relativistic vector function from which the electromagnetic field can be derived. It combines both an electric scalar potential and a magnetic vector potential into a single four-vector.Gravitation, J.A. Whe ...
*
Jefimenko's equations
In electromagnetism, Jefimenko's equations (named after Oleg D. Jefimenko) give the electric field and magnetic field due to a distribution of electric charges and electric current in space, that takes into account the propagation delay ( reta ...
*
Liénard–Wiechert potential
The Liénard–Wiechert potentials describe the classical electromagnetic effect of a moving electric point charge in terms of a vector potential and a scalar potential in the Lorenz gauge. Stemming directly from Maxwell's equations, these descr ...
*
Light-time correction
Light-time correction is a displacement in the ''apparent'' position of a celestial object from its ''true'' position (or geometric position) caused by the object's motion during the time it takes its light to reach an observer.
Light-time corr ...
References
{{DEFAULTSORT:Retarded Time
Time
Electromagnetic radiation