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Physics 344
Foundations of 21
st
Century Physics:
Relativity, Quantum Mechanics and
heir Applications
Their Applications
Instructor:
Dr. Mark Haugan
Office:
PHYS 282
[email protected]
TA:
Dan Hartzler
Office:
PHYS 7
[email protected]
Grader:
Shuo Liu
Office:
PHYS 283
[email protected]
Office Hours: If you have questions, just email us to make an
ppointment.
e enjoy talking about physics!
appointment.
We enjoy talking about physics!
Reading: Chapter 9 of the text.
Notices: Exam I will be at 8:00pm Thursday, October 7 in MTHW 210
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View Full Document Recitation Recap
The first problem gave you an opportunity to use some of the new concepts
and methods of calculation we’ve been discussing. These are important
because of the powerful new perspective on special relativity they make
possible. We will develop that perspective further today.
The problem focused on the 4velocity
of an object moving at constant speed
t
V
= 3/5 in the
x
direction relative to a
Home inertial coordinate system.
The idea was to focus on a couple of
2
21
ˆ
tt
Δ
21
s
⇒
Δ
21
t
Δ
events on the object’s worldline so
that we could use the definition
21
s
u
⇒
⇒
Δ
=
21
ˆ
x x
Δ
1
21
τ
Δ
21
t
Δ
⎡
⎤
⎥
where Homeframe measurements
give,
x
21
x
Δ
21
21
21
21
ˆ
ˆ
0
0
x
st
t
x
x
⇒
⎢⎥
Δ
⎢
⎥
Δ=
Δ
+
Δ
⎢
⎥
⎢
⎥
⎣
⎦
±
ince
= 3/5 we know the ratio of
1
1
= 3/5, so lets use
1
=3s
Since
V
3/5 we know the ratio of
Δ
x
21
/
Δ
t
21
3/5, so lets use
Δ
x
21
3 s
and
Δ
t
21
= 5 s so the corresponding proper time interval is
22
2
2
21
21
21
21
21
25
9
4
ss
t
x
s
s
s
τ
⇒⇒
Δ=
Δ
⋅
Δ
−
−
=
2
2
21
21
21
21
21
21
21
21
1
/
5/4
tt
tx
x
t
t
γ
ΔΔ
Δ
−
Δ=−
Δ
Δ
Δ
=
=
/4
⇒
⎡
⎤⎡
⎤
⎥
⎢
⎥
also
So,
t
2
21
21
3/4
53
ˆ
ˆ
00
44
V
s
ut
x
⇒
⎢⎥
Δ
⎢
⎥⎢
⎥
==
+
=
⎢
⎥
Δ
⎢
⎥
⎣
⎦⎣
⎦
±
21
ˆ
Δ
21
s
⇒
Δ
21
t
Δ
The “squared magnitude” of this
timelike 4vector is
2
u u
⇒
⎛⎞
≡
=
=
21
ˆ
x x
Δ
1
1
uu u
⋅≡
−
⎜⎟
⎝⎠
which we could have guessed because
⇒
x
21
x
Δ
21
21
21
21
21
21
s
s
u
s
⇒
⇒
⇒
Δ
Δ
⋅
Δ
⇒
=
Δ
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View Full Document Since the object is moving at a constant speed in the
x
direction relative to the
Home frame, there is an Other coordinate system in standard orientation in
which it is at rest. Obviously, in that Other frame
Δ
x’
21
= 0 s, so,
′
⎤
⎤
21
21
21
0
ˆ
0
t
st
t
⇒
Δ
⎡⎤
⎢⎥
′′
Δ=
Δ
⎥
±
21
0
ˆ
1
0
t
ut
⇒
Δ
⎢
⎥
⎢
⎥
′
⇒=
⎢
⎥
⎥
±
t
2
t
0
⎣⎦
since the coordinate time interval
measured between events 1 and 2 in
is frame
also the proper time
0
21
s
⇒
Δ
x
’
this frame
Δ
t
21
is also the proper time
interval between them.
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This note was uploaded on 11/26/2010 for the course PHYS 344 taught by Professor Garfinkel during the Spring '08 term at Purdue University.
 Spring '08
 Garfinkel
 mechanics

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