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Course Business: PHYS342 Lecture 5
Due Friday Jan 28th in class Problem set 2
From Modern Physics chapter 2:
Problems: 12 through 17 and 19 through 21 and problem 23
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View Full Document Let’s be precise in our definitions!
Events and Spacetime Coordinates:
An
event
is any physical occurrence that happens at a definite place in
space and at a definite instant in time.
The event’s
spacetime
coordinates are the 4 numbers that specify
where and when an event took place:
3 spatial coordinates (x, y, z)
and 1 for time.
A
reference frame’s
fundamental task is to provide a means of
measuring the spacetime coordinates of events.
2
2
v
1 v /
x
t
x
c

′
=

2
2
2
v /
1 v /
t
x c
t
c

′
=

y
y
′
=
z
z
′
=
The complete Lorentz Transformation
If
v <<
c
, i.e.,
β
≈ 0
and
γ
≈ 1, yielding the familiar Galilean transformation.
Space and time are now linked, and the frame velocity cannot exceed
c
.
2
2
v
1 v /
x
t
x
c
′
′
+
=

2
2
2
v /
1 v /
t
x
c
t
c
′
′
+
=

y
y
′
=
z
z
′
=
Length
contractio
n
Simultaneit
y problems
Time
dilation
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Timing events occurring in different places can
be tricky.
Depending on how they’re measured,
different events will be perceived in different
orders by
different observers.
Due to the finite speed of light, the order in which these two events will be
seen will depend on the observer’s
position
.
The time intervals will be:
Fred:

2
L/c
;
Frank:
0
;
Fil:
+2
L/c
But this obvious positionrelated simultaneity problem disappears if Fred and
Fil have
synchronized watches
.
Frank
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This note was uploaded on 04/23/2011 for the course PHYS 342 taught by Professor Staff during the Spring '08 term at Purdue UniversityWest Lafayette.
 Spring '08
 Staff
 Physics, Theory Of Relativity

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