Understanding Past and Future Light Cones

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SUMMARY

The discussion clarifies the concepts of past and future light cones in the context of spacetime as described in Stephen Hawking's "A Brief History of Time." The past light cone encompasses all possible worldlines of light rays arriving at a specific event from the past, while the future light cone includes all possible worldlines of light rays departing from that event into the future. These cones are visually represented in spacetime diagrams, where the past light cone appears as a downward-facing 45-degree cone and the future light cone as an upward-facing 45-degree cone, assuming light travels at speed 1.

PREREQUISITES
  • Understanding of spacetime concepts
  • Familiarity with worldlines in physics
  • Basic knowledge of light propagation
  • Ability to interpret spacetime diagrams
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  • Research the mathematical representation of light cones in Minkowski spacetime
  • Explore the implications of light cones in causality and relativity
  • Study the role of light cones in general relativity
  • Examine examples of light cones in astrophysical contexts
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Students of physics, educators explaining relativity, and anyone interested in the foundational concepts of spacetime and light propagation.

AbsoluteZer0
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Hi,

I've been reading A Brief History of Time by Stephen Hawking and I've reached a section that discusses past and future light cones of an event. I'm finding it hard to understand what a light cone is.

What is the past light cone and what is the future light cone?

Thanks,
 
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At a given event in spacetime, the past light cone is the set of worldlines of all light rays that arrive at that event from the past, and the future light cone is the set of worldlines of all light rays that depart from that event into the future.

The name comes from the fact that, if you imagine a spacetime diagram with one space dimension suppressed, and time as the vertical axis, then if we assume that the event you're interested in is at the origin, the past light cone looks like a 45-degree cone facing down from the origin, and the future light cone looks like a 45-degree cone facing up from the origin (assuming you're using units in which the speed of light is 1).
 

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