2.3 Basic Information About the Diagrams we will Construct (Space-Time Diagrams)
Description
This article is from the Relativity and FTL Travel FAQ, by Jason W. Hinson jason@physicsguy.com with numerous contributions by others.
2.3 Basic Information About the Diagrams we will Construct (Space-Time Diagrams)
In Diagram 2-1 we saw how one can use three dimensions to represent two
dimensions of space and one of time, but for simplicity the diagrams we use
will be two dimensional--one of space and one of time. We will consider the
one dimension of space to be the x direction. So, the space-time diagram
consists of a coordinate system with one axis to represent space (the x
direction) and another to represent time. Where these two principal axes
meet is the origin. This is simply a point in space that we have defined as
x = 0 and a moment in time that we have defined as t = 0. In Diagram 2-2
(below) I have drawn these two axes and marked the origin with an o.
For certain reasons we want to define the units that we will use for
distances and times in a very specific way. Let's define the unit for time
to be the second. This means that moving one unit up the time axis will
represent waiting one second of time. We then want to define the unit for
distance to be a light second (the distance light travels in one second). So
if you move one unit to the right on the x axis, you will be considering a
point in space that is one light second away from your previous location. In
Diagram 2-2, I have marked the locations of the different space and time
units (Note: In my ASCII diagrams, I am using four spaces to represent one
unit along the x axis and two character heights to represent one unit on the
time axis).
With these units, it is interesting to note how a beam of light is
represented in our diagram. Consider a beam of light leaving the origin and
traveling to the right. One second later, it will have traveled one light
second away. Two seconds after it leaves it will have traveled two light
seconds away, and so on. So a beam of light will always make a line at an
angle of 45 degrees to the x and t axes. I have drawn such a light beam in
Diagram 2-3.
Diagram 2-2 Diagram 2-3
t t
^ ^
| | light
+ + /
| | /
+ + /
| | /
-+---+---o---+---+---> x -+---+---o---+---+-> x
| |
+ +
| |
+ +
| |
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