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Light cone

From Academic Kids

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A worldline through a light cone in 2D space plus a time dimension.

In special relativity, a light cone is the pattern 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. If a flash of light happens at an event at time t=0, only points within the light cone will be reached by this light for a given positive time t. The other, symmetric half of the light cone where t<0 then is the region from which light could have reached the event at t=0 from all the events occurring at the negative time t.

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

In general relativity, the future light cone is the boundary of the causal future of a point and the past light cone is the boundary of its causal past.

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