Notes on Relativity and Cosmology - Physics Department, UCSB

28 CHAPTER 1. SPACE, TIME, AND NEWTONIAN PHYSICS
⋆ Think of them this way!!! It will make your life easier later.
1.2 Reference Frames
A particular case of interest is when we choose the line x = 0 to be the position
of some object: e.g. let x = 0 be the position of a piece of chalk.
In this case, the coord system is called a ‘Reference Frame’; i.e., the reference
frame of the chalk is the (collection of) coordinate systems where the chalk lies
at x = 0 (All measurements are ‘relative to’ the chalk.)
⋆ ⋆ ⋆ Note that I have said nothing about the motion of the chalk. We can talk
about the chalk’s reference frame whether it is “at rest,” moving at constant
velocity, or wiggling back and forth in a chaotic way. In both cases we draw the
x = 0 line as a straight line in the object’s own frame of reference.
Also: The reference frame of a clock has t = 0 whenever the clock reads zero.
(If we talk about the reference frame of an object like a piece of chalk, which is
not a clock, we will be sloppy about when t = 0.)
⋆ Note: A physicist’s clock is really a sort of stopwatch. It reads t = 0 at some
time and afterwards the reading increases all the time so that it moves toward
+∞. Before t = 0 it reads some negative time, and the distant past is −∞. A
physicist’s clock does not cycle from 1 to 12.
Unfortunately, we’re going to need a bit more terminology. Here are a couple
of key definitions:
• Your Worldline: The line representing you on the spacetime diagram.
In your reference frame, this is the line x = 0.
• Event: A point of spacetime; i.e., something with a definite position and
time. Something drawn as a dot on a spacetime diagram. Examples: a
firecracker going off, a door slamming, you leaving a house; see below.