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Physics 228 Spring 2008
Special Relativity (Ch. 37)
Due at 11:59pm on Monday, March 10, 2008
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Understanding Lorentz Transformations
Learning Goal:
To be able to perform Lorentz transformations between inertial reference frames.
Suppose that an inertial reference frame
S'
moves in the positive
x
direction at speed
with respect to another inertial
reference frame
S
. In classical physics, the
Galilean transformations
relate the coordinates measured for an event in
frame
S
to the coordinates measured for the same event in frame
S'
. Assuming that both frames have the same origin
(i.e., at
,
), the Galilean transformations take the following simple form:
,
.
The Galilean transformations are not valid at very large speeds. To transform between inertial frames when
is close
to the speed of light
, we need to use the
Lorentz transformations
of special relativity. Again, assuming that both
frames have the same origin, the Lorentz transformations take the following form:
.
These equations become more manageable with the introduction of the quantity
,
so that the Lorentz transformations become
,
.
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View Full Document Often, the spacetime coordinates for an event will be given in the form
, or just
when the
y
and
z
coordinates are not important.
Suppose that you are stationary with respect to an inertial reference frame
Z
. A spaceship flies by you in the
positive
x
direction with speed
. Let
Z'
be the frame of reference associated with the spaceship; that is, the ship is
stationary with respect to
Z'
. The frames
Z
and
Z'
have the same origin at
. The
proper length
of the ship
(the length of the ship as measured in the ship's frame,
Z'
) is
. In other words, a passenger on the ship measures
the back of the ship to be at
and the front to be at
.
Part A
Consider an event with spacetime coordinates
in an inertial frame of reference
S
. Let
S'
be a second inertial frame of reference moving, in the positive
x
direction, with speed
relative to frame
S
. Find the value of
that will be needed to transform coordinates between frames
S
and
S'
. Use
for the speed of light in vacuum.
Express your answer to three significant figures.
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This note was uploaded on 11/25/2010 for the course PHYSICS 228 taught by Professor Staff during the Spring '08 term at Rutgers.
 Spring '08
 Staff
 Special Relativity

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