# The set of allowed trajectories in spacetime

## Main Question or Discussion Point

I was reading Spacetime and Geometry by Caroll and I came across this notion:

In special relativity there is no absolute notion of "all of space at one
moment in time." Instead, there is a rule that particles always travel at less than or equal to the
speed of light. We can therefore define light cones at every event, which locally describe
the set of allowed trajectories. For two events that are outside each others' light cones,
there is no universal notion of which event occurred earlier in time.
I have never understood this and I was wondering if someone could enlighten me.

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I was reading Spacetime and Geometry by Caroll and I came across this notion:

In special relativity there is no absolute notion of "all of space at one
moment in time." Instead, there is a rule that particles always travel at less than or equal to the
speed of light. We can therefore define light cones at every event, which locally describe
the set of allowed trajectories. For two events that are outside each others' light cones,
there is no universal notion of which event occurred earlier in time.
I have never understood this and I was wondering if someone could enlighten me.
Simultaneity of events?

clem
I am afraid that statement is as clear to me as anything I could write.
What don't you understand?

JesseM
Simultaneity of events?
Are you familiar with the notion of the relativity of simultaneity? See here and here for some more info, and you might also want to take a look at some of the basic SR tutorials on this thread which all cover the relativity of simultaneity. They also cover the notion of "light cones", but for a particularly good discussion of that notion see this page.

I understand the simultaneity of events just fine. I apologize I should have clarified. The notion of light cones is a little fuzzy to me. Simultaneity is clear.

clem