How Does Distance to Proxima Centauri Affect Simultaneous Events?

[Ben S]

TL;DR Summary

Explain this statement: "Proxima Centauri is approximately four light-years away. For any particular event on Earth, there is an eight-year span of events on Proxima Centauri that could count as simultaneous with it, depending on your reference frame."

Referring to this statement:
"Proxima Centauri is approximately four light-years away. For any particular event on Earth, there is an eight-year span of events on Proxima Centauri that could count as simultaneous with it, depending on your reference frame."

How does the distance between Earth and Proxima Centauri (~4 light-years) affect the span of time of simultaneous events on Proxima Centauri?


This statement is from Sean Carroll's book- The Biggest Ideas in the Universe (Space, Time, and Motion).

 

[Orodruin]

In order for there to exist a frame where two events are simultaneous, they must not be within each other's light cones. For a given event on Earth, consider what the light cone of that event looks like, particularly around a distance 4 ly away from Earth.

 

[Ibix]

How does the distance between Earth and Proxima Centauri (~4 light-years) affect the span of time of simultaneous events on Proxima Centauri?

Anything you have seen happening is definitely in your past. Any event where people see something you do now is definitely in your future. For the Centauri system, there's an eight year gap between a little green man waving at you and him being able to see you react. If "now" is when you react, "now on Proxima" must lie somewhere in those eight years.

In Newtonian physics we simply assert that now is now and everybody agrees what that means. Part of the development of relativity was discovering that this isn't correct - you can pick literally any time in that eight year gap and call it "now on Proxima". There are no physical consequences because the fact that nothing can travel faster than light means that you can't react to something that's happening "now" anyway.

So as long as you keep your definition of "now" out of your definite past (formally called your causal past) and definite future (causal future) then you're pretty much free to define it. Which is the point Carroll is making.

Note that he doesn't say "the span of time of simultaneous events". He just says that's the span of time from which you get to pick a moment to call now.