Can someone please explain why a point originating inside the cone can never be the cause of an event outside the cone? Is there a real life example of this? The only thing I can think of is from a point inside an event horizon to outside in regular space.
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$\begingroup$ by point do you mean event? If so, events don't originate, they just exist. Are you asking about events in the past, future, or both light cone(s)? $\endgroup$– JEBCommented Mar 19, 2023 at 18:15
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$\begingroup$ anything you do now can only influence things in the future which can be reached by speeds not greater than light speed. Or say more exact, what you mean by "originating inside the cone" what do you mean by real life experiment? $\endgroup$– trulaCommented Mar 19, 2023 at 18:39
2 Answers
That is backwards. An event outside the light cone cannot be the cause of an event inside. Some old school computer graphics:
V - This is your future
. - You are here
^ - This is your past
You can influence things in your future. Things in your past can influence you.
The vertical axis is time, perhaps in units of years. The horizontal axis is space in light-years. Light rays travel at $45^o$, parallel to the arms of the V and ^. Things that travel slower than light are steeper than $45^o$. This is why only things inside your past light cone can influence you.
An example of that cannot influence you would be any point elsewhere right now. This would be horizontal from you. It will take light or anything else some time to get to you. It will influence you when it gets to you. But you will have moved to a point farther up by then. The event will be in the past light cone of that future self.
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$\begingroup$ Your graphics are not 4K....more like 3B (comments and carriage returns notwithstanding). $\endgroup$– JEBCommented Mar 19, 2023 at 18:23
why a point originating inside the cone can never be the cause of an event outside the cone?
Because the speed of causality has an upper limit, the speed of light, which is precisely what the whole light cone idea is about.
It's like asking why a point inside a disk cannot be farther from its center than the disk radius - well, because that's the definition for a point to be inside a disk. That an event inside a (future) light cone cannot be the cause of something outside the cone is not far from being the actual definition of what 'future light cone' means: the future light cone of event $E$ is made of all events that can have $E$ in their causes (and since the future light cones of these events are all fully within the future light cone of $E$, quod erat demonstrandum).
Also, no event outside its past light cone can have any effect on $E$ - again this is simply the definition of a past ligth cone.
Note that those cones are four-dimensional mathematical objects, living in spacetime, not in space.