Imagine an event (A) in the origin of our Minkowski diagram.
We want to investigate, what consequences this event could have.
If the event (A) sends out light, it can affect all possible events that take place along
the light's world line.
If (A) sends out a slower signal, like an accoustic signal, propagating with the speed
of sound, (A) can have an effect on those events that lie on this world line, like (B)
here.
This goes for all possible - that is, allowed - velocities.
What about here?
If there were an event (C) right here, then (A) would have to send a signal to (C), traveling
faster than the speed of light.
According to Einstein, that's not possible.
We conclude that every event above the light world line could have been - in principle
- caused by the event (A).
Now look at the Minkowski distance between (A) and (B), as well as between (A) and (C).
Between (A) and (B), the time component is greater than the space component, so s^2,
which is t^2-x^2 has a positive value.
The vector (A) to (B) is called timelike, because the events (A) and (B) are „timelike
separated".
This means, that there exists a frame, where (A) and (B) take place at the same position,
but no frame, where (A) and (B) happen at the same time!
Now on to (A) and (C).
Here, the spatial component is greater than the time component.
For the Minkowski distance s^2, this implies a negative sign.
The vector (A) to (C) is called spacelike, because the events (A) and (C) are „spacelike
separated".
We can draw a frame, where (A) and (C) happen at the same time, but none where they happen
to be at the same position.
What if (A) doesn't happen at the origin?
In this case, we draw the light world lines starting at (A) anyway.
Again, the events up here can be caused by (A), whereas those here cannot.
This construction is called the light cone.
In one time and one spatial dimension, it's more of a light triangle, but if we were to
draw two spatial components, it's really a cone.
The part above (A) is called it future, the part below is its past.
And everything else is called… elsewhere.
So let's recap: After drawing the light cone, we know that (A) can have an effect on everything
inside its future.
Everything in (A)'s past could've had an effect on (A) and any event elsewhere cannot
interact with (A) in any way.
That's pretty much it for this time, thanks for watching and see you next week!



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