The Light Cone

# The Light Cone - and timelike if It is said to be lightlike...

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The Light Cone Let us try to visualize the surface in four-dimensional space described by the outgoing shell of light from a single flash, It is helpful to think about a simpler situation, the circular ripple spreading on the surface of calm water from a pebble falling in. Taking c here to be the speed of the water waves, it is easy to see that at time t after the splash the ripple is at Now think about this as a surface in the three-dimensional space ( x , y , t ). The plane corresponding to time t cuts this surface in a circle of radius ct . This means the surface is a cone with its point at the origin. The four-dimensional space flash-of-light surface is not so easy to visualize, but is clearly the higher-dimensional analog: the plane surface corresponding to time t cuts it in a sphere instead of a circle. This surface is called the lightcone . We have stated above that the separation of a point P ( x , y , z , t ) from the origin is spacelike if
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Unformatted text preview: and timelike if It is said to be lightlike if Points on the light cone described above are lightlike separated from the origin. To be precise, the points corresponding to an outgoing shell of light from a flash at the origin at t = 0 form the forward light cone . Since the equation depends only on t 2 , there is a solution with t negative, the “backward light cone”, just the reflection of the forward light cone in the plane t = 0. Possible causal connections are as follows: an event at the origin (0, 0, 0, 0) could cause an event in the forward light cone: so that is the “future”, as seen from the origin. Events in the backward light cone—the “past”—could cause an event at the origin. There can be no causal link between an event at the origin and an event outside the light cones, since the separation is spacelike: outside the light cones is “elsewhere” as viewed from the origin....
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