here - Department of Physics, HKU

CHAPTER 1. PRE-SPECIAL RELATIVITY PHYSICS 3
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1.2.1 Inertial Frames
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Figure 1.1: An inertial frame.
Eq. (1.1) is valid only in an inertial frame. What is an inertial frame? A
reference frame or just a frame is a standard to which motion and other mechanical
quantities can be measured. Usually, it means a coordinate system
of space and time. Note that the coordinate system does not have to be
“linear.” For example, a useful coordinate system on the surface of a sphere
is non-linear. A well known example is the longitude and latitude on the
Earth.
In some textbooks, an inertial frame is defined as the frame on which
Eq. (1.1) is valid. This is, of course, not a good definition. In practice, an
inertial frame can be defined as any frame at rest or in constant velocity with
respect to the fixed stars. (In contrast, for example, a rotating frame, like
the surface of the earth, is not in constant velocity with respect to the fixed
stars.) This means, we have to choose some initial time as t = 0, a point
in space as the origin O, then three perpendicular directions as directions
of the three axes, Fig. 1.1. The origin O is allowed to move with constant
velocity with respect to the far away fixed stars, but the axes are not allowed
to rotate with respect to the stars.
After we find one inertial frame, any Cartesian coordinate system moving
with constant velocity and no rotation with respect to the inertial frame is
also an inertial frame. If we are careful enough, we can find by experiments
that the “rest” frame on the Earth is not an inertial frame.
In this course, we will only consider inertial frames. Hence, we usually will
only speak about frames, instead of the more correct term inertial frames.
1.2.2 Events
In common language, an event is something happened at some place at some
time. In special relativity, an event means exactly this: a point in space
and time. Thus, we have to specify both the space coordinates and time