GetWiki
Light cone
ARTICLE SUBJECTS
being →
database →
ethics →
fiction →
history →
internet →
language →
linux →
logic →
method →
news →
policy →
purpose →
religion →
science →
software →
truth →
unix →
wiki →
ARTICLE TYPES
essay →
feed →
help →
system →
wiki →
ARTICLE ORIGINS
critical →
forked →
imported →
original →
Light cone
please note:
- the content below is remote from Wikipedia
- it has been imported raw for GetWiki
{{Short description|Set of spacetime events, light-connected to a given event}}{{Not to be confused with|Cone cell|Cone of light}}300px|right|thumb|Light cone in 2D space plus a time dimension.{{Special relativity sidebar}}In special and general relativity, a light cone (or "null cone") is the path that a flash of light, emanating from a single event (localized to a single point in space and a single moment in time) and traveling in all directions, would take through spacetime.- the content below is remote from Wikipedia
- it has been imported raw for GetWiki
Details
If one imagines the light confined to a two-dimensional plane, the light from the flash spreads out in a circle after the event E occurs, and if we graph the growing circle with the vertical axis of the graph representing time, the result is a cone, known as the future light cone. The past light cone behaves like the future light cone in reverse, a circle which contracts in radius at the speed of light until it converges to a point at the exact position and time of the event E. In reality, there are three space dimensions, so the light would actually form an expanding or contracting sphere in three-dimensional (3D) space rather than a circle in 2D, and the light cone would actually be a four-dimensional version of a cone whose cross-sections form 3D spheres (analogous to a normal three-dimensional cone whose cross-sections form 2D circles), but the concept is easier to visualize with the number of spatial dimensions reduced from three to two.This view of special relativity was first proposed by Albert Einstein's former professor Hermann Minkowski and is known as Minkowski space. The purpose was to create an invariant spacetime for all observers. To uphold causality, Minkowski restricted spacetime to non-Euclidean hyperbolic geometry.BOOK, Cox, Brian, 1968-,weblink Why does E=mc2 : (and why should we care?), 2009, Da Capo Press, Forshaw, J. R. (Jeffrey Robert), 1968-, 978-0-306-81758-8, Cambridge, MA, 246894061, {{Page needed|date=February 2017}}Because signals and other causal influences cannot travel faster than light (see special relativity), the light cone plays an essential role in defining the concept of causality: for a given event E, the set of events that lie on or inside the past light cone of E would also be the set of all events that could send a signal that would have time to reach E and influence it in some way. For example, at a time ten years before E, if we consider the set of all events in the past light cone of E which occur at that time, the result would be a sphere (2D: disk) with a radius of ten light-years centered on the position where E will occur. So, any point on or inside the sphere could send a signal moving at the speed of light or slower that would have time to influence the event E, while points outside the sphere at that moment would not be able to have any causal influence on E. Likewise, the set of events that lie on or inside the future light cone of E would also be the set of events that could receive a signal sent out from the position and time of E, so the future light cone contains all the events that could potentially be causally influenced by E. Events which lie neither in the past or future light cone of E cannot influence or be influenced by E in relativity.WEB, Curiel, Erik, Singularities and Black Holes > Light Cones and Causal Structure (Stanford Encyclopedia of Philosophy),weblink plato.stanford.edu, Stanford Encyclopedia of Philosophy, 3 March 2020, 2019,Mathematical construction
In special relativity, a light cone (or null cone) is the surface describing the temporal evolution of a flash of light 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.{hide}Citation
| last=Penrose
| first=Roger
| title=The Road to Reality
| publisher=Vintage Books
| place=London
| year=2005
| isbn = 978-0-09-944068-0
{edih}
The light cone is constructed as follows. Taking as event p a flash of light (light pulse) at time t0, all events that can be reached by this pulse from p form the future light cone of p, while those events that can send a light pulse to p form the past light cone of p.Given an event E, the light cone classifies all events in spacetime into 5 distinct categories: | first=Roger
| title=The Road to Reality
| publisher=Vintage Books
| place=London
| year=2005
| isbn = 978-0-09-944068-0
{edih}
- Events on the future light cone of E.
- Events on the past light cone of E.
- Events inside the future light cone of E are those affected by a material particle emitted at E.
- Events inside the past light cone of E are those that can emit a material particle and affect what is happening at E.
- All other events are in the (absolute) elsewhere of E and are those that cannot affect or be affected by E.
In general relativity
(File:light_cones_near_black_hole.svg|thumb|200px|Light cones near a black hole resulting from a collapsing star. The purple (dashed) line shows the path of a photon emitted from the surface of a collapsing star. The green (dot-dash) line shows the path of another photon shining at the singularity.)In flat spacetime, the future light cone of an event is the boundary of its causal future and its past light cone is the boundary of its causal past.In a curved spacetime, assuming spacetime is globally hyperbolic, it is still true that the future light cone of an event includes the boundary of its causal future (and similarly for the past). However gravitational lensing can cause part of the light cone to fold in on itself, in such a way that part of the cone is strictly inside the causal future (or past), and not on the boundary.Light cones also 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 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.See also
- Absolute future
- Absolute past
- Hyperbolic partial differential equation
- Hypercone
- Light-cone coordinates
- Lorentz transformation
- Method of characteristics
- Minkowski diagram
- Monge cone
- Wave equation
References
{{Reflist}}External links
- The Einstein-Minkowski Spacetime: weblink" title="web.archive.org/web/20061205015249weblink">Introducing the Light Cone
- The Paradox of Special Relativity
- RSS feed of stars in one's personal light cone
- content above as imported from Wikipedia
- "Light cone" does not exist on GetWiki (yet)
- time: 12:23am EDT - Fri, Apr 26 2024
- "Light cone" does not exist on GetWiki (yet)
- time: 12:23am EDT - Fri, Apr 26 2024
[ this remote article is provided by Wikipedia ]
LATEST EDITS [ see all ]
GETWIKI 23 MAY 2022
The Illusion of Choice
Culture
Culture
GETWIKI 09 JUL 2019
Eastern Philosophy
History of Philosophy
History of Philosophy
GETWIKI 09 MAY 2016
GetMeta:About
GetWiki
GetWiki
GETWIKI 18 OCT 2015
M.R.M. Parrott
Biographies
Biographies
GETWIKI 20 AUG 2014
GetMeta:News
GetWiki
GetWiki
© 2024 M.R.M. PARROTT | ALL RIGHTS RESERVED