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The Coordinate System
I won't be able to explain
every little mathematical detail about spacetime diagrams; but I will explain
how to evaluate them visually. This way you can understand the spacetime
diagrams on this page. I should warn you about the axes. This is not the
standard x-y crosshair. For spacetime diagrams the y-axis (the vertical
one) represents time. The x-axis (the horizontal one) represents space.
This is a 1-1 diagram, which means there is only one time dimension (which
we are used to) and one space dimension (which we are not). We're used to
living and moving in three spatial dimensions. What does 1D space look like?
It's like living on a line: all you can do is go forward or go backward.
That's it. No left, right, up, or down. That's what these spacetime diagrams
describe, 1 time dimension and 1 space dimension. Why only 1? To represent
two spatial dimensions would require a three dimensional graph, which are
tough to draw. To represent three spatial dimensions would require a four
dimensional graph, which would probably have to be some kind of animated
thing and even more difficult to draw. I will attempt to explain this stuff
with the help of Lupin, my cockatiel. See this picture on the right? That's
him, fluffing up.
Take a look at this diagram:
 There are black
lines, red lines, and blue lines. Those thick vertical'ish lines are called
worldlines. The black one describes what I'm doing and the blue one describes
what my bird, Lupin,
is doing. In this diagram Lupin sits still for a while, flies towards me,
flies away from me and back to his previous position, and stays there. I
just stay in one place. So, you know what those thick lines are, but what
about the thin ones? Those are lines of simultaneity. Those are lines of
constant time. You know, 1 second, 2 seconds, 3 seconds. Those red lines?
They're light rays. Light rays are always drawn at 45°. Anything with
matter cannot realistically have a worldline with a slope equal to or greater
than 45° because matter cannot go the speed of light (and nothing can
go faster than light).
So far things seem
simple. Then again, maybe not. There are two sets of thin lines, mine
and Lupin's. Things that are simultaneous are simultaneous, you say. Well...not
quite. If you are standing still (which is tricky), your lines of simultaneity
are horizontal. If you are moving your lines of simultaneity tilt. The
angle between your worldline and a light ray is the same angle between
the light ray and your line of simultaneity. The faster you go, the more
those lines of simultaneity tilt from strictly horizontal. Confused? That's
okay, here's an additional section on lines
of simultaneity.
Here is the same incident
seen relative to Lupin:
 Okay, there is
an important concept in drawing spacetime diagrams: the inertial reference
frame. You'll notice that the same incident can be drawn differently,
depending on what everything is drawn relative to. Which one of these
two diagrams is the right one? Both. They are both accurate representations
of what happened. In my eyes Lupin flew towards and then away from me.
I thought I was standing still. In Lupin's eyes he was standing still
and I moved towards and then away from him. Whoever the diagram is drawn
with respect to must have a straight and vertical worldline.
GOTHOS
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