Chapter 1 Special Relativity
1 m1v12 + 1 m2v22 = 1 m1V12 + 1 m2V22
2
2
2
2
(1.22)
By replacing the velocities in equation 1.22 by their Galilean counterparts,
equation 1.20, and after much algebra we
Chapter 2: Spacetime and General Relativity
Figure 2.10 represents a rod 4.00 units long at rest in a rocket ship S,
moving at a speed of c/2. The world line of the top of the stick in S is drawn para
Contents
5 nuclear Physics
6 elementary Particle Physics and
5.1 Introduction
5.2 Nuclear Structure
5.3 Radioactive Decay Law
5.4 Forms of Radioactivity
5.5 Radioactive Series
5.6 Energy in Nuclear Re
Chapter 1 Special Relativity
the collision, V1 is the velocity of ball 1 after the collision, and V2 is the velocity of
ball 2 after the collision. But the relation between the velocity in the S and S
Chapter 1 Special Relativity
1.3 The Invariance of the Mechanical Laws of Physics
under a Galilean Transformation
Although the velocity of a moving object is different when observed from a
stationary
Chapter 1 Special Relativity
We find the time to cross the river by dividing the distance traveled by the boat by
the boats speed, that is,
tacross = L
V
The time to return is the same, that is,
tretu
Chapter 1 Special Relativity
A sound wave in water propagates through the water while a sound wave in a solid
propagates through the solid. The one thing that all of these waves have in common
is that
Chapter 1 Special Relativity
or
r2 c2t2 = 0
(1.24)
The radius r of the spherical wave is
r2 = x2 + y2 + z2
Substituting this into equation 1.24, gives
x2 + y2 + z2 c2t2 = 0
(1.25)
for the light wave a
Chapter 2: Spacetime and General Relativity
drawn parallel to the -axis. The occurrence of two events, A and B, are noted and
the time interval elapsed between these two events on earth is d = 4.0 2.0
Chapter 1 Special Relativity
Using the above analogy can help us to understand the experiment
performed by Michelson and Morley to detect the ether current. The equipment
used to measure the ether cur
Chapter 1 Special Relativity
t ' lim
v c
t xv / c2
1 v2 / c 2
That is, for v = c, the coordinates x and t are infinite, or at least undefinable. If v >
c then v2/c2 > 1 and 1 v2/c2 < 1. This means tha
Preface
Preface
This text gives a good, traditional coverage for students of Modern Physics.
The organization of the text follows the traditional sequence of Special Relativity,
General Relativity, Qu
Preface
x' =
5.00 m (0.800)(3.00 108 m/s)(3.00 s)
1 (0.800c )2 / c 2
= 1.20 109 m
This distance is quite large because the astronaut is moving at such high speed. The
event occurs on the astronauts cl
Chapter 1 Special Relativity
To simplify this equation, we use the binomial theorem. That is,
(1 x)n = 1 nx + n(n 1)x2 n(n 1)(n 2)x3 + .
2!
3!
(1.33)
This is a valid series expansion for (1 x)n as lon
Chapter 1 Special Relativity
experiment to detect this ether. The experiment was performed by A. A. Michelson
and E. E. Morley and is described in section 1.5.
1.5 The Michelson-Morley Experiment
If t
Chapter 1 Special Relativity
These new transformation equations are called the Lorentz transformations.2
The Lorentz transformation equations are summarized as
x'
t'
x vt
(1.49)
1 v2 / c 2
y = y
z =
Chapter 1 Special Relativity
t
Length contraction
Time dilation
y = y
z = z
t ' vx '/ c2
(1.52)
(1.53)
(1.54)
1 v2 / c 2
L L0 1 v2/c2
(1.60)
t0
(1.64)
t
Lorentz transformation of velocities
1 v2 / c
Chapter 1 Special Relativity
dx dx vdt
1 v 2 /c 2
(1.72)
The time interval dt is found from the Lorentz transformation equation 1.50, as
t'
t xv / c2
1 v2 / c 2
Taking the time differential dt we get
Preface
illustrative problem. The illustrative problem shows you what to do at that step.
Then continue to solve the problem on your own. Every time you get stuck, look
again at the appropriate soluti
Chapter 1 Special Relativity
x2'
x1'
x2 vt
1 v2 / c 2
x1 vt
1 v2 / c 2
Thus, the length of the rod becomes
x 2 vt
x 1 vt
1 v 2 /c 2
1 v 2 /c 2
x 2 vt x 1 vt
1 v 2 /c 2
x2 x1
1 v 2 /c 2
L0 x 2 x 1
B
Chapter 1 Special Relativity
land when (a) viewed from the ground (S frame) and (b) when viewed from the
truck (S frame)?
3. A truck moving east at a constant speed of 50.0 km/hr passes a traffic ligh
Chapter 1 Special Relativity
It should be noted that the time dilation effect, like the Lorentz contraction,
is also reciprocal. That is, a clock on the surface of the earth reads the proper time
inte
Chapter 1 Special Relativity
1.8 The Lorentz-Fitzgerald Contraction
12. The USS Enterprise approaches the planet Seti Alpha 5 at a speed of
0.800c. Captain Kirk observes an airplane runway on the plan
Chapter 1 Special Relativity
Relativistic linear momentum
The product of the relativistic mass of a body and its velocity (p. ).
Relativistic energy
The product of the relativistic mass of a body and
Chapter 1 Special Relativity
And now in our time, there has been unloosed a cataclysm which
has swept away space, time, and matter hitherto regarded as the
firmest pillars of natural science, but only
Chapter 1 Special Relativity
electrons. The atomic mass of helium, as determined by the rest masses of its
constituents, is
mHe = 2mp + 2mn + 2me
= 2(938.256 MeV) + 2(939.550 MeV) + 2(0.511006 MeV)
=
Chapter 1 Special Relativity
Questions for Chapter 1
1. If you are in an enclosed truck and cannot see outside, how can you tell if
you are at rest, in motion at a constant velocity, speeding up, slow
Chapter 1 Special Relativity
x = ct
(1.46)
Figure 1.12 The same light wave observed from two inertial frames.
Substituting for x from equation 1.41, and for t from equation 1.44, into equation
1.46, y
Chapter 1 Special Relativity
If there is more than one body in motion with respect to the stationary frame,
the relative velocity between the two bodies is found by placing the S frame on one of
the b