Lecture 10 Notes, 95.658, Spring 2012, Electromagnetic Theory II
Dr. Christopher S. Baird, UMass Lowell
1. PreEinstein Relativity
 In the science world, Einstein did not invent the concept of “relativity,” but instead created a more
accurate physical theory to describe the concept of relativity.
 “Relativity” is the concept of how the physics in one frame of reference relates to the physics in
another frame of reference.
 The most common and useful relationship that can exist between two frames of reference is that
one frame of reference is moving with a constant velocity compared to the other. There are other
relationships, such as an accelerating frame, a rotating frame, or a stretching frame in comparison to
the other frame. But these types are more complex and should be handled later.
 For the purpose of definitions, let us always say one frame of reference is at rest and call it the
“lab frame”
K
and the other frame of reference that we call the “moving frame”
K
' always moves at
a velocity
v
relative to the lab frame. Frame
K
has coordinates (
x
,
y
,
z
,
t
) and
K
' has coordinates
(
x
',
y
',
z
',
t
'):
 Mathematically, the concept of relativity involves answering the question: If we know the physics
equations in
K
, what must we do to them to make them still hold in
K
'?
 This question was first answered in GalileanNewtonian mechanics. It was observed that Newton's
second law (
F
=
m
a
) held exactly the same form in every inertial (nondeforming, nonaccelerating)
reference frame.
F
x
=
m
d
2
x
dt
2
and
F
x
'
=
m
'
d
2
x
'
dt
'
2
so that:
m
d
2
x
dt
2
=
m
'
d
2
x
'
dt
'
2
 GalileanNewtonian mechanics also assumed universal time, in other words all clocks run at the
same speed in all frames and at all points in space. This leads to
t
=
t
' and
dt
/
d
x
= 0. It also assumed
universal mass so that
m
=
m
' and
dm
/
d
x
= 0, leading to:
d
2
x
dt
2
=
d
2
x
'
dt
2
 This observation leads directly to Galilean relativity, or the Galilean concept of how to transform
v
K
K'
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View Full Documentequations from one frame to the next.
 Simplify to one dimension and integrate both sides of the equations, being careful to keep
integration constants:
d x
dt
=
d x
'
dt
A
x
=
x
'
A t
B
 The constant
B
simply tells us where the spatial origins are set at
t
= 0. We can easily get
B
= 0 be
aligning both origins at the same point at
t
= 0.
x
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 Spring '11
 Staff
 Mass, Special Relativity, galilean relativity

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