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Light cones start at a point in 2-dimensional space. I am a observer and not a point so how is my light cone defined?

Also I see persons next to me and can remember their position in the past. Do the origin of our light cones overlap?

Light cones start at a point in 2-dimensional space.

I am a observer and not a point so how is my light cone defined?

Do the origins of our light cones overlap?