Since light speed is finite, there are regions in space-time (outside the light cone) with no causal relationship to you at the origin. (If a tree falls in the forest and nobody is around...)
For simplicity, the diagram assumes a 2-D space with 1 time dimension. We are familiar with 3-D space + time, but a corresponding 4-D diagram is not simple to draw. You may interpret the hypersurface as the volume that is 3-D space at an instant in time.
-
-
shorter answer: pretend the hypersurface plane is a volume

-
I get the 2-d simplification. But what distinguishes that plane from one tilted 15° , or a hyperbola with 40° asymptotes, or any other surface that stays outside the past and future lightcones?
-
Those examples sound like spaces where the speed of light differs by orientation/region. Or maybe it's nonsense, because the y-axis is time and a non-planar space occupies multiple times. Not sure what to make of it.
-
The point is that “simultaneous” is observer-dependent in special relativity (if you had a different velocity the plane would be tilted), and I dom’t think it’s even globally defined in general relativity.
-
Thanks for the insight, indeed a tilted plane is a reference frame with a velocity whereras flat is stationary. What do you mean about general relativity?
-
I mean that, to the best of my (very limited) knowledge, there is no coherent way to define “simultaneous” for distant events under GR, and the best you can do is “spacelike separated” (not in each others’ lightcones).
End of conversation
New conversation -
Loading seems to be taking a while.
Twitter may be over capacity or experiencing a momentary hiccup. Try again or visit Twitter Status for more information.