SPECIAL RELATIVITY
The SAT Physics Subject Test may ask a question or two on Einstein’s theory of
special relativity. Since you aren’t expected to have an in-depth mastery of this
subject, we’ll simply state some relevant facts from this theory and present some
examples.
Let’s begin with the two postulates of special relativity.
Postulate
1:All the laws of physics are the same in all inertial reference
frames.
Postulate
2:The speed of light in vacuum always has the same value (c = 3 ×
108 m/s), regardless of the motion of the source or the observer.An inertial reference frame is one in which Newton’s first law holds. Given one
inertial reference frame, any other reference frame that moves with constant
velocity relative to the first one will also be inertial. For example, a person
standing at a train station considers herself to be in an inertial reference frame. If
she places her suitcase on the ground next to her and exerts no forces on it, it stays
at rest. Now, if a train moves past the station, traveling on a smooth track in a
straight line at constant speed, then a passenger on the train considers himself to be
in an inertial reference frame, too. If he places his suitcase on the floor and exerts
no forces on it, it stays at rest (relative to him). Now, if the train is speeding by at,
say, 40 m/s, then the person standing at the train station would say that the man’s
suitcase on the train is moving at a speed of 40 m/s, but the man on the train would
say that his suitcase is at rest. So, while it’s true that these two observers will
naturally disagree about the velocity of the suitcase on the train, they won’t
disagree about physics laws, such as conservation of momentum. This is the
essence of Postulate 1. Two people playing a game of billiards on a smoothly
moving train (that is, one that travels in a straight line at constant speed) don’t have
to “adjust” their shots to account for the motion of the train.
Keeping One’s
Perspective
Here’s a simple example of
Postulate 1: If you’re traveling
60 m/s and someone
passes you at 65 m/s,
they’re traveling at 65 m/s,
but relative to you, they’re