1) An event is a physical happening that occurs at a specific place and time, as recorded by observers using reference frames consisting of coordinate systems and clocks at rest relative to the frames. 2) Special relativity has two postulates: 1) the laws of physics are the same in all inertial reference frames, and 2) the speed of light has the same value in all inertial frames regardless of the motion of the light source or observer. 3) Time dilation occurs such that clocks in motion run slower than clocks at rest, as observed from another frame, with the time interval between ticks increasing with the relative velocity between frames. Proper time is the time interval measured in the frame at rest with the clock

1. Chapter 28
Special Relativity

2. 28.1 Events and Inertial Reference Frames
An event is a physical “happening” that occurs at a certain place and
time.
To record the event, each observer uses a reference frame that consists of a
coordinate system and a clock.
Each observer is at rest relative to her own reference frame.
An inertial reference frame is one in which Newton’s law of inertia is
valid.

3. 28.1 Events and Inertial Reference Frames
In this example, the event is the space shuttle lift off.

4. 28.2 The Postulates of Special Relativity
THE POSTULATES OF SPECIAL RELATIVITY
1. The Relativity Postulate.
The laws of physics are the same
in every inertial reference frame.
2. The Speed of Light Postulate.
The speed of light in a vacuum, measured in any inertial
reference frame, always has the same value
of c, no matter how fast the source of light and the observer are
moving relative to one another.

5. 28.3 The Relativity of Time: Time Dilation
TIME DILATION
A light clock

6. 28.3 The Relativity of Time: Time Dilation
An observer on the earth sees the light pulse travel a greater distance
between ticks.

7. 28.3 The Relativity of Time: Time Dilation
Suppose two identical clocks are built. One is kept on
earth, and the other is placed aboard a spacecraft that
travels at a constant velocity relative to the earth.
The astronaut is at rest with respect to the clock on
the spacecraft and, therefore, sees the light pulse
move along the up/down path shown in Figure 28.5a
Since the spacecraft is moving, the earth-based observer sees the light pulse follow the diagonal path
shown in red in part b of the drawing.
This path is longer than the up/down path seen by the astronaut.

8. 28.3 The Relativity of Time: Time Dilation

9. 28.3 The Relativity of Time: Time Dilation
Example 1 Time Dilation
The spacecraft is moving past the earth at a constant speed of
0.92 times the speed of light. the astronaut measures the time
interval between ticks of the spacecraft clock to be 1.0 s. What is
the time interval that an earth observer measures?

10. 28.3 The Relativity of Time: Time Dilation
( )
s6.2
92.01
s0.1
1 222
=
−
=
−
∆
=∆
cccv
t
t o

11. 28.3 The Relativity of Time: Time Dilation
PROPER TIME INTERVAL
The time interval measured at rest with respect to the clock is
called the proper time interval.
In general, the proper time interval between events is the time
interval measured by an observer who is at rest relative to the
events.
Proper time interval
ot∆

12. 28.4 The Relativity of Length: Length Contraction
The shortening of the distance between two points is one
example of a phenomenon known as length contraction.
Length contraction
2
2
1
c
v
LL o −=
Note that the length contraction occurs only along the direction of
motion and the dimensions that are perpendicular to the motion are
Shortened. See example 4

13. 28.4 The Relativity of Length: Length Contraction
Example 4 The Contraction of a Spacecraft
An astronaut, using a meter stick that is at rest relative to a cylindrical
spacecraft, measures the length and diameter to be 82 m and 21 m
respectively. The spacecraft moves with a constant speed of 0.95c
relative to the earth. What are the dimensions of the spacecraft,
as measured by an observer on earth.

14. 28.4 The Relativity of Length: Length Contraction
( ) ( ) m2695.01m821
2
2
2
=−=−= cc
c
v
LL o
Diameter stays the same.

15. 28.5 Relativistic Momentum
Relativistic
momentum
22
1 cv
mv
p
−
=

16. 28.6 The Equivalence of Mass and Energy
THE TOTAL ENERGY OF AN OBJECT
Total energy
of an object
Rest energy
of an object
22
2
1 cv
mc
E
−
=
2
mcEo =








−
−
=
−=
−=
−
1
1
1
KE
2
2
2
2
2
2
2
1
c
v
mc
o
mc
mc
EE
c
v
Check examples
7 and 8

17. The relation between total
energy and momentum
Show that the relation between total energy and momentum is given by
22
2
1 cv
mc
E
−
=
22
2
1 cv
mc
E
−
=
Tutorials: no 3, 20, 32 and 33

18. 28.6 The Equivalence of Mass and Energy
Example 8 The Sun is Losing Mass
The sun radiates electromagnetic energy at a rate of 3.92x1026
W.
What is the change in the sun’s mass during each second that it
is radiating energy? What fraction of the sun’s mass is lost during
a human lifetime of 75 years.

19. 28.6 The Equivalence of Mass and Energy
( )( )
( )
kg1036.4
sm103.00
s0.1sJ1092.3 9
28
26
2
×=
×
×
=
∆
=∆
c
E
m o
( )( ) 12
30
79
sun
100.5
kg1099.1
s1016.3skg1036.4 −
×=
×
××
=
∆
m
m

20. The relation between total
energy and momentum
Show that the relation between total energy and momentum is given by
22
2
1 cv
mc
E
−
=
22
2
1 cv
mc
E
−
=
Tutorials: no 3, 20, 32 and 33