PHYS195 NotesChapter10 - Chapter 10 The Sp ecial Theory of...

Chapter 10
The Special Theory of
Relativity
10.1 Pre-History of concepts about light
10.2 Pursuit of a special frame
10.3 Galilean Invariance
Almost anyone who has sat quietly waiting to depart from a bus depot
or a dock and has had the bus or boat gently start to leave has had the
experience of feeling that it is the depot or dock that has moved away. This
simple physiological phenomena has its basis in a very general physical law
that was first articulated by Galileo and thus is called Galilean Invariance.
It is one of the most striking and far reaching of all of the laws of physics.
It is impossible to over emphasize its importance; it is the basis of our
understanding of space-time and motion. The simplest statement of the law
is that there is no experiment that can be performed that can measure a
uniform velocity. Since we can only know what can be measured, we can
never know how fast we are moving. There is no speedometer on the starship
Enterprise.
Stated this boldly, the idea is very counter to our experience. This is
because what we generally observe as a velocity is not a velocity in space but
is our velocity relative to the earth. Relative velocities are detectable. We
note the amount of street that passes below our car or feel the flow of the
air that moves over our face and infer a speed but we do not know how fast
the earth is moving and thus do not know what our absolute velocity is. We
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do know that the earth moves around the sun and thus can determine our
velocity relative to the sun. We know that the sun is moving in our galaxy
and even that our galaxy is moving relative to other nearby galaxies and
thus can know our velocity relative to the local cluster of galaxies. With the
recent advances in astronomical detection, we are able to note our velocity
relative to the place that we occupied in the early universe, our motion
relative a background microwave radiation that is a detectable relic of the
early universe, but again we cannot know whether that place had a velocity.
The inability to detect velocity is one of the most mysterious and counter
intuitive concepts that has ever been articulated. Consider a remote and
empty part of the universe, no stars or galaxies nearby. Here there are no
discernible forces and a released body moves in a straight line with a con-
stant velocity. This is one of Newton’s Laws and was his way of articulating
Galilean Invariance. Although when we start to work on General Relativity,
we will have to revisit these issues, let us assume that this empty region is
space. We envision this as that stable structure that Descartes and New-
ton needed as a background against which motion took place. In this day
and age, it is generally easy to convince someone that this space obeys the
Copernican Principle; it is not centered on some special place like the earth.