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In special relativity
Special relativity

Special relativity is the physical theory of measurement in inertial frames of reference proposed in 1905 by Albert Einstein in the paper "Annus Mirabilis Papers#Special relativity"....
, a light cone (or null cone) is the surface describing the temporal evolution of a flash of light
Light

Light, or visible light, is electromagnetic radiation of a wavelength that is Visible spectrum to the human eye , or up to 380?750 nm. In the broader field of physics, light is sometimes used to refer to electromagnetic radiation of all wavelengths, whether visible or not....
 in Minkowski spacetime. This can be visualized in 3-space if the two horizontal axes are chosen to be spatial dimensions, while the vertical axis is time.

The light cone is constructed as follows. Taking as event a flash of light (light pulse) at time , all events that can be reached by this pulse from form the future light cone of , while those events that can send a light pulse to form the past light cone of .

Given an event , the light cone classifies all events in spacetime into 5 distinct categories:











If space is measured in light-seconds and time is measured in seconds, the cone will have a slope of 45°, because light travels a distance of one light-second in vacuum
Vacuum

A vacuum is a volume of space that is essentially empty of matter, such that its gaseous pressure is much less than atmospheric pressure. The word comes from the Latin term for "empty," but in reality, no volume of space can ever be perfectly empty....
 during one second.






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In special relativity
Special relativity

Special relativity is the physical theory of measurement in inertial frames of reference proposed in 1905 by Albert Einstein in the paper "Annus Mirabilis Papers#Special relativity"....
, a light cone (or null cone) is the surface describing the temporal evolution of a flash of light
Light

Light, or visible light, is electromagnetic radiation of a wavelength that is Visible spectrum to the human eye , or up to 380?750 nm. In the broader field of physics, light is sometimes used to refer to electromagnetic radiation of all wavelengths, whether visible or not....
 in Minkowski spacetime. This can be visualized in 3-space if the two horizontal axes are chosen to be spatial dimensions, while the vertical axis is time.

The light cone is constructed as follows. Taking as event a flash of light (light pulse) at time , all events that can be reached by this pulse from form the future light cone of , while those events that can send a light pulse to form the past light cone of .

Given an event , the light cone classifies all events in spacetime into 5 distinct categories:

  • Events on the future light cone of .


  • Events on the past light cone of .


  • Events inside the future light cone of are those which are affected by a material particle emitted at .


  • Events inside the past light cone of are those which can emit a material particle and affect what is happening at .


  • All other events are in the (absolute) elsewhere of and are those that will never affect and can never be affected by .


If space is measured in light-seconds and time is measured in seconds, the cone will have a slope of 45°, because light travels a distance of one light-second in vacuum
Vacuum

A vacuum is a volume of space that is essentially empty of matter, such that its gaseous pressure is much less than atmospheric pressure. The word comes from the Latin term for "empty," but in reality, no volume of space can ever be perfectly empty....
 during one second. Since special relativity requires the speed of light to be equal in every inertial frame, all observers must arrive at the same angle of 45° for their light cones. This is ensured by the Lorentz transformation
Lorentz transformation

In physics, the Lorentz transformation converts between two different observers' measurements of space and time, where one observer is in constant motion with respect to the other....
. Elsewhere, an integral part of light cones, is the region of spacetime outside the light cone at a given event (a point in spacetime). Events that are elsewhere from each other are mutually unobservable, and cannot be causally connected.

Light-cones in general relativity


In general relativity
General relativity

General relativity or the general theory of relativity is the Geometry Theoretical physics of gravitation published by Albert Einstein in 1916....
, the future light cone is the boundary of the causal future of a point
Point (geometry)

In geometry, topology and related branches of mathematics a spatial point describes a specific object within a given space that consists of neither volume, area, length, nor any other higher dimensional analogue....
 and the past light cone is the boundary of its causal past.

In a curved spacetime, the light-cones cannot all be tilted so that they are 'parallel'; this reflects the fact that the spacetime is curved and is essentially different from Minkowski space. In vacuum regions (those points of spacetime
Spacetime

In physics, spacetime is any mathematical model that combines space and Time in physics into a single continuum . Spacetime is usually interpreted with space being Three-dimensional space and time playing the role of a fourth dimension that is of a different sort than the spatial dimensions....
 free of matter), this inability to tilt all the light-cones so that they are all parallel is reflected in the non-vanishing of the Weyl tensor
Weyl tensor

In differential geometry, the Weyl curvature tensor, named after Hermann Weyl, is the traceless component of the Curvature tensor. In other words, it is a tensor that has the same symmetries as the Riemann curvature tensor with the extra condition that Tensor_contraction#Metric_contraction yields zero....
.

See also

  • Minkowski diagram
    Minkowski diagram

    The Minkowski diagram was developed in 1908 by Herman Minkowski and provides an illustration of the properties of space and time in the special theory of relativity....
  • Absolute future
  • Absolute past
  • Monge cone
    Monge cone

    In the mathematics theory of partial differential equations , the Monge cone is a geometrical object associated to a first-order equation. It is named for Gaspard Monge....
  • Method of characteristics
    Method of characteristics

    In mathematics, the method of characteristics is a technique for solving partial differential equations. Typically, it applies to first order partial differential equation, although more generally the method of characteristics is valid for any hyperbolic partial differential equation....
  • Hyperbolic partial differential equation
    Hyperbolic partial differential equation

    In mathematics, a hyperbolic partial differential equation is usually a second-order partial differential equation of the formwith.This definition is analogous to the definition of a planar Hyperbola#Quadratic_equation....
  • Wave equation
    Wave equation

    The wave equation is an important second-order linear partial differential equation that describes the propagation of a variety of waves, such as sound waves, light waves and water waves....


External links

  • The Einstein-Minkowski Spacetime: