Chapter R
Relativity
Conceptual Problems
1
•
You are standing on a corner and a friend is driving past in an
automobile. Each of you is wearing a wristwatch. Both of you note the times
when the car passes two different intersections and determine from your watch
readings the time that elapses between the two events. Have either of you
determined the proper time interval? Explain your answer.
Determine the Concept
In the reference frame of the car both events occur at the
same location (the location of the car). Thus, your friend’s watch measures the
proper time between the two events.
2
•
In Problem 1, suppose your friend in the car measures the width of the
car door to be 90 cm. You also measure the width as he goes by you.
(
a
) Does either of you measures the proper width of the door? Explain your
answer. (
b
) How will your value for the door width compare to his? (1) Yours will
be smaller, (2) yours will be larger, (3) yours will be the same, (4) you can’t
compare the widths, as the answer depends on the car’s speed.
Determine the Concept
The proper length of an object is the length of the object
in the rest frame of the object.
The proper length of a meter stick is one meter.
(
a
) Because the door is at rest in the reference frame of the car, its width in that
frame is its proper width.
If your friend measures this width, say by placing a
meter stick against the door, then he will measure the proper width of the door.
(
b
) In the reference frame in which you are at rest, the door is moving, so its
width is less than its proper width.
To measure this width would be challenging.
(You could measure the width by measuring the time for the door to go by. The
width of the door is the product of the speed of the car and the time.)
3
•
[SSM]
If event A occurs at a different location than event B in some
reference frame, might it be possible for there to be a second reference frame in
which they occur at the same location? If so, give an example. If not, explain why
not.
Determine the Concept
Yes. Let the initial frame of reference be frame 1.
In
frame 1 let
L
be the distance between the events, let
T
be the time between the
events, and let the +
x
direction be the direction of event B relative to event A.
Next, calculate the value of
L/T
. If
L/T
is less than
c
, then consider the two events
in a reference frame 2, a frame moving at speed
v
=
L/T
in the +
x
direction.
In
frame 2 both events occur at the same location.
1051
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4
•
[SSM]
If event A occurs prior to event B in some frame, might it be
possible for there to be a second reference frame in which event B occurs prior to
event A? If so, give an example. If not, explain why not.
Determine the Concept
Yes.
Let
L
and
T
be the distance and time between the
two events in reference frame 1.
If
L
≤
cT
, then something moving at a speed
less than or equal to
c
could travel from the location of event A to the location of
event B in a time less than
T
.
Thus, it is possible that event A could cause event
B. For events like these, causality demands that event A must precede event B in
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 Spring '12
 Goussiou
 Physics, Special Relativity, ΔT, Substitute numerical values

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