The Physics of Spin

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The Physics of Spin
Otto Stern
1922 Wrong theory ? right experiment
Walther Gerlach
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Deflected Up
Undeflected
Beam of Atoms
Oven
Stern-Gerlach
Detection Screen

Tiny Spinning Bar Magnet
Silver Atom
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Nonuniform Magnetic Field
weaker
STONGER
Deflected Up
4

Nonuniform Magnetic Field
N
weaker
STONGER
Undeflected
S
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Experiment 1
50
50
Random Spin Directions
EXPECT TO SEE
ACTUALLY SEE (!!)
This result has no classical or commonsense
explanation
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Experiment 2
100
0
50
1
Working Hypothesis
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Random
50
0
100
It is consistent to hypothesize
Beam 1 atoms are all spin up
Beam 2 atoms are all spin down
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Experiment 3
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Random
50
50
HORIZONTAL
VERTICAL
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HORIZONTAL atom has 50/50 CHANCE of emerging
spin up or spin down
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Summary of Experiments
100
0
0
100
50
50
1 Quantization of spin direction
2 Probability plays fundamental role
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The Mathematics of Spin
Spin seems to be a VECTOR
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What do we know about VECTORS?
Unit basis vectors
Any vector
(Length)2
q
Unit vector
a cos q, b sin q
Thus
And
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Examples of
q 45

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Application to Spin
Analogue of unit basis vectors ?
1 Quantization of spin suggests



a

b
??
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a

b
2 Probability suggests a natural
interpretation for
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a

b
2 Probability suggests a natural
interpretation for
a2
b2
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a2 1 b2 0
a2 0 b2 1
100
0
0
100
50
50


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Summary
z
q
cos q sin q
(?) (?)


Question
y
x
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Result
E.g.
75
25
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We have constructed a successful mathematical
model of spin!
Does the mathematics predict anything interesting
we have not thought of yet?
The power of mathematics in the process of science
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(No Transcript)
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The Mysterious Minus Sign
1 Can be observed experimentally
2 Most important - sign in the universe
3 Has no commonsense interpretation
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So why might students care?
(assuming the previous reasons are not enough)
Spin is an excellent introduction to the Quantum
Information Age