The Weirdness of Quantum Mechanics

1
The Weirdness of Quantum Mechanics
Neil Shenvi Whaley Group Department of Chemistry
2
Talk Outline
1. Introduction to Quantum Mechanics a. The
postulates of quantum mechanics b. The
weirdness of the postulates 2. Quantum Weirdness
in action a. The two slit experiment b.
Quantum cryptography c. Quantum computation d.
The EPR experiment 3. Interpretations of
Quantum Mechanics a. The Copenhagen
Interpretation b. The Neorealist
Interpretation c. The Many Worlds Interpretation
3
Classical Mechanics fact or fiction
1. An object in motion tends to stay in
motion. 2. Force mass times acceleration 3.
For every action there is an equal and opposite
reaction.
Sir Isaac Newton
Classical mechanics is everyday mechanics.
4
Quantum Mechanics Why?
Classical mechanics explains most of what we
usually observe in nature, which is why it lasted
for centuries. But it could not explain the
results of certain experiments.
The Hydrogen Spectrum
The Stern-Gerlach Experiment
The Ultraviolet Catastrophe
Quantum mechanics was developed to explain these
results.
5
Quantum Mechanics When?
Large objects obey the laws of classical
mechanics.
But small objects obey the laws of quantum
mechanics.
6
Quantum Mechanics When?
How small is Small?
1 meter Classical mechanics

1 millimeter Classical mechanics
1 micrometer Classical mechanics
1 nanometer Quantum mechanics
But quantum mechanics is very important!
7
Quantum Mechanics When?
How important is Important?
Without quantum mechanics
Universe implodes
All atoms would be unstable.
All molecules dissociate
Chemical bonding would be impossible.
Life does not exist
Many biological reactions would not occur.
Minimal consequences
Neil Shenvis dissertation title Vanity of
Vanities, All is Vanity
8
Quantum Mechanics What?
The Fundamental Postulates of Quantum Mechanics
1. The wavefunction postulate
2. The Schrödinger Equation
3. The measurement postulate
9
Postulate 1 The Wavefunction
Postulate 1 All information about a system is
given by the systems wavefunction.
x
x
Interesting facts about the wavefunction 1. The
wavefunction can be positive, negative, or
complex-valued. 2. The squared amplitude of the
wavefunction at position x is equal to the
probability of observing the particle at position
x. 3. The wave function evolves with time. 4.
The existence of a wavefunction implies
particle-wave duality.
10
The Weirdness of Postulate 1
Variables versus Wavefunctions

Classical particle
Quantum particle
x
x
v
11
The Weirdness of Postulate 1
Variables versus Wavefunctions

Classical Hydrogen
Quantum Hydrogen
(Warning not real)
Bohr model the electron orbits the nucleus at a
set radius
Quantum model an electron cloud surrounds the
nucleus.
Question for hecklers How can it be a cloud if
there is only one electron?
12
The Weirdness of Postulate 1
Variables versus Wavefunctions

Classical coin
Quantum coin
Two values
Two values
H
V
Possible states of quantum coin
Possible states of quantum coin
These states are called superpositions

13
The Weirdness of Postulate 1
The Heisenberg Uncertainty Principle It is
impossible to know all properties of a particle
simultaneously.
Classical elephant
Quantum elephant
The elephant is definitely big.
or
The elephant is definitely big and gray.
The elephant is definitely gray.
14
The Weirdness of Postulate 1
The Heisenberg Uncertainty Principle It is
impossible to know all properties of a particle
simultaneously.
Classical particle
Quantum particle
x
x
v
15
The Weirdness of Postulate 1
The Heisenberg Uncertainty Principle It is
impossible to know all properties of a particle
simultaneously.
Classical particle
Quantum particle
x
x
v
16
The Weirdness of Postulate 1
The Heisenberg Uncertainty Principle It is
impossible to know all properties of a particle
simultaneously.
Classical particle
Quantum particle
x
x
v
17
Postulate 2 The Schrödinger Equation
Postulate 2 The wavefunction of a system obeys
the Schrödinger Equation
Interesting facts about the Schrödinger
Equation 1. It is linear. 2. It implies that
time evolution is unitary. 3. It is difficult to
solve for large systems.
18
The Weirdness of Postulate 2
Tunneling A quantum mechanical particle can
tunnel through barriers rather than going over
them.
Classical ball
Classical ball does not have enough energy to
climb hill.
Quantum ball
Quantum ball tunnels through hill despite lack
of energy.
19
The Weirdness of Postulate 2
Quantum trajectories quantum particles take all
paths. (See Feynman path integral formulation of
QM.)
Quantum mouse
Classical mouse
Takes all paths, even forbidden ones!
Takes one path.
20
Postulate 3 Measurement
Postulate 3 Measurement of a quantum mechanical
system is associated with some linear, Hermitian
operator Ô.
Interesting facts about the measurement
postulate 1. It implies that measurement is
inherently probabilistic. 2. It implies that
measurement necessarily alters the
observed system.
21
The Weirdness of Postulate 3
Measurement Deterministic versus probabilistic
Classical Elephant
Quantum Elephant
Before measurement
or
After measurement
For a known state, outcome is probabilistic.
For a known state, outcome is deterministic.
22
The Weirdness of Postulate 3
Measurement Objective versus destructive
Classical Elephant
Quantum Elephant
Before measurement
After measurement
Measurement alters state.
State is unchanged by measurement.
23
Quantum Weirdness in Action
The Two Slit Experiment - the one slit
experiment - the two slit experiment - the
results - the classical explanation - the
test - the quantum explanation - curioser and
curioser
Experiments on interference made with particle
rays have given brilliant proof that the wave
character of the phenomena of motion as assumed
by the theory does, really, correspond to the
facts. -A. Einstein
24
The Two Slit Experiment
The One Slit Experiment
What happens if we use two slits instead of only
one?
25
The Two Slit Experiment
The Two Slit Experiment
26
The Two Slit Experiment
The Results
Actual result interference pattern.
Is this a quantum phenomenon?
27
The Two Slit Experiment
The Classical Explanation
Explanation This is just a crowd wave
phenomenon like waves in water.
28
The Two Slit Experiment
The Test
Emit particles one at a time.
29
The Two Slit Experiment
The Quantum Explanation
Particle is really described by a wavefunction
which acts like a probability wave. This wave
interferes with itself.
30
The Two Slit Experiment
Curioser and Curioser
Result Interference pattern disappears! Why?
31
The Two Slit Experiment
Curioser and Curioser
Result Interference pattern disappears! Why?
32
Quantum Consequences
Quantum Cryptography
Eavesdropping on classical information goes
undetected
0 1 1 0 1
0 1 1 0 1
Eve the eavesdropper
Bob
Alice
Because measurement alters quantum
states, eavesdropping on quantum information
can be detected.
?????
?????
33
Quantum Cryptography
The no cloning theorem
Classical information can be copied, but quantum
information cannot.
34
Quantum Cryptography
Quantum key distribution
Problem Alice and Bob want to share a secret
key, (i.e. a string of bits), but Eve the
eavesdropped is listening.
0 1 1 0 1
0 1 1 0 1
0 1 1 0 1
Bob
Alice
Eve
Solution use quantum information to encode the
bits.
35
Quantum Cryptography
Quantum key encoding
36
Quantum Cryptography
Eves dilemma
Which basis should Eve use to measure the qubits?
H R L H V L H L
Eve must choose either Basis A H?, V? or Basis
B R?, L?
37
Quantum Cryptography
Detecting eavesdropping
Alice and Bob compare bases over open channel
B B A A A B A A
A B B A A B A B
When their bases dont match, they discard that
bit. At no point does Alice reveal her key, or
Bob his result.
38
Quantum Cryptography
Detecting eavesdropping
Now they pick a few of the remaining bits and
compare their results.


39
Quantum Cryptography
Detecting eavesdropping
?????
?????
It can be shown that no strategy Eve employs can
prevent Alice and Bob from detecting her
eavesdropping. So quantum key distribution
protocols can provide a guarantee for secure key
distribution.
C.H. Bennett and G. Brassard "Quantum
Cryptography Public Key Distribution and Coin
Tossing", Proceedings of IEEE International
Conference on Computers Systems and Signal
Processing, Bangalore India, December 1984, pp
175-179.
40
Quantum Consequences
Quantum Computation
Because quantum particles can be in many states
at once, we can build quantum computers which are
much faster than normal computers.
Example Find the number 555-1422 in the phone
book
Quantum computers can search all the entries at
the same time.
Classical computers must search sequentially
Smith, A 555-1032 Smith, A B 555-4023 Smith, A
S 555-9192 Smith, Amos 555-1126 Smith, B
A 555-7287 Smith, Bob 555-1102 Smith, Bob
L 555-1443 Smith, Cynthia 555-3739 Smith, David
555-4487 Smith, Ernest 555-1271
Smith, A 555-1032 Smith, A B 555-4023 Smith, A
S 555-9192 Smith, Amos 555-1126 Smith, B
A 555-7287 Smith, Bob 555-1102 Smith, Bob
L 555-1443 Smith, Cynthia 555-3739 Smith, David
555-4487 Smith, Ernest 555-1271
41
Quantum Computation
Quantum Search
Imagine we are looking for the solution to a
problem with N possible solutions. We have a
black box that can check whether a given answer
is correct.
Question What number between 1 and 100 am I
thinking of?
Black box
78
No
Black box
3
Yes
42
Quantum Computation
Quantum Search
Classical computer
Quantum computer
Black box
123...
nonoyesno...
Superposition over all N possible inputs.
Using Grovers algorithm, a quantum computer can
find the answer in ?N queries.
...
The best a classical computer can do on average
is N/2 queries.
43
Quantum Computation
Quantum Factoring
Find the factors of 57
Find the factors of 1623847601650176238761076269
17226121712398721039746218761871207362384612987398
2634897121861102379691863198276319276121
3 x 19
whimper
All known algorithms for factoring an n-bit
number on a classical computer take time
proportional to O(n!).
But Shors algorithm for factoring on a quantum
computer takes time proportional to O(n2 log n).
44
Significance of Quantum Factorization
with a classical computer
bits 1024 2048 4096 factoring in 2006 105
years 5x1015 years 3x1029 years factoring in
2024 38 years 1012 years 7x1025 years factoring
in 2042 3 days 3x108 years 2x1022 years
with potential quantum computer (e.g., clock
speed 100 MHz)
bits 1024 2048 4096 qubits
5124 10244 20484 gates 3x109 2X1011 X10
12 factoring time 4.5 min 36 min 4.8 hours
R. J. Hughes, LA-UR-97-4986
45
The Scandalous Claims of QM
Are the claims of quantum mechanics really so
revolutionary?
46
Objections to Quantum Mechanics
Einstein was shocked.
Quantum mechanics is 1. Incomplete 2.
Incorrect 3. Or both
Quantum mechanics is certainly imposing. But an
inner voice tells me that it is not yet the real
thing. Quantum theory says a lot, but does not
really bring us any closer to the secret of the
Old One. I, at any rate, am convinced that He
does not throw dice. - A. Einstein
Quantum Mechanics Real Black Magic Calculus. -
A. Einstein
47
Quantum Weirdness in Action
The EPR Experiment - elements of reality - the
thought experiment - the thought results - the
Bell Inequality - the real experiment - the
real results - the quantum conclusion
Earth
Mars
I still do not believe that the statistical
method of the Quantum Theory is the last word,
but for the time being I am alone in my opinion.
- A. Einstein
48
The EPR Experiment
Elements of Reality
A. Einstein, B. Podolsky, N. Rosen. Can
Quantum-Mechanical Description of Physical
Reality Be Considered Complete? Phys. Rev. 47,
1935, 777-780.
1. A theory is complete if every element of the
physical reality must have a counterpart in the
physical theory.
2. If, without in any way disturbing the
system, we can predict with certainty the value
of a physical quantity, then there exists an
element of reality (emphasis added) corresponding
to this physical quantity.
49
The EPR Experiment
The Thought Experiment
1. Create a valid two particle quantum state
like
?? HV? - VH?
Particle 2
Particle 1
50
The EPR Experiment
The Thought Experiment
2. Separate the particles by a spacelike
distance.
?? H V? - V H?
Particle 2
Particle 1
Since the particles are very far apart (light
years, say), relativity tells us that
manipulating one particle cannot
instantaneously affect the other particle.
51
The EPR Experiment
The Thought Experiment
3. Measure Particle 1.
?? H V? - V H?
Particle 2
Particle 1
QM tells us that there is a 50-50 chance of
Particle 1 being in state H? or V?. But as
soon as we measure Particle 1, we immediately
know the state of Particle 2!
52
The EPR Experiment
The Thought Experiment
4. Think about the definition of an element of
reality.
?? H V? - V H?
Particle 2
Particle 1
In other words, we can determine the state of
Particle 2, without disturbing Particle 2 in any
way (by measuring Particle 1). Thus, the state
of Particle 2 must correspond to an element of
reality.
53
The EPR Experiment
The Thought Results
?? H V? - V H?
Particle 2
Particle 1
But quantum mechanics cannot predict a priori the
state of Particle 2 with certainty. It only
gives us probabilities!
54
The EPR Experiment
The Thought Results
Conclusion of the EPR paper Since it has been
shown that quantum mechanics cannot predict all
elements of reality with certainty, we are
forced to conclude that the quantum-mechanical
description of reality given by wave functions is
not complete.
55
The EPR Experiment
The Bell Inequality
In 1964, John Bell showed that Einsteins claim
of realism and the predictions of QM yield
testable results.
56
The EPR Experiment
The Real Experiment
?? HV? - VH?
Photon 1
Photon 2
Earth
Mars
On Earth and on Mars, we measure each photon in a
randomly chosen basis and collect a large amount
of data.
57
The EPR Experiment
The Real Results
1
1
-1
1
1
1
1
1
-1
-1
-1
-1


...
...
58
The EPR Experiment
The Quantum Conclusion
Local realism is false.
Choose one (and only one)
Warning 4 out of 5 physicists recommend keeping
locality.
59
The Interpretations of QM
Or What happens to the wavefunction?
1. The Copenhagen Interpretation 2.
Neorealism 3. Many Worlds
The fundamental question
60
The Interpretations of QM
The Copenhagen (orthodox) Interpretation - N.
Bohr
Particles properties cannot be assigned values
independent of measurement.
Measurement collapses the wavefunction.
Observations not only disturb what is to be
measured, they produce it. - P. Jordan
61
The Interpretations of QM
The Copenhagen (orthodox) Interpretation - N.
Bohr
Pros Favored by the vast majority of physicists
(con?).
Cons If universe is quantum mechanical, then so
is the measurement device. Why does it behave
differently? What is a measurement device?
How do you define it? What determines the
outcome of a measurement if hidden variables are
not allowed?
62
The Interpretations of QM
The neorealist interpretation - A. Einstein
Particle properties do have values independent of
measurement, so wavefunction never collapses.
I recall that during one walk Einstein suddenly
stopped, turned to me and asked whether I really
believed that the moon exists only when I look at
it. The rest of this walk was devoted to a
discussion of what a physicist should mean by the
term "to exist." - A. Pais
63
The Interpretations of QM
The neorealist interpretation - A. Einstein
Pros Retains metaphysical realism. Particles
really do exist.
Cons Retains metaphysical realism at the cost
of postulating undetectable, superluminescent
pilot waves responsible for all of our quantum
effects. Fiddles with causality effects
propagate backwards in time.
64
The Interpretations of QM
The Many Worlds Interpretation - H. Everett
The wavefunction never collapses. The universe
is really a multi-verse.
65
The Interpretations of QM
The Many Worlds Interpretation - H. Everett
Pros Uniform. No wavefunction collapse. No
measurement problems.
Cons Postulates a infinite number of
undetectable alternate universes with which we
are currently in coherence. Removes possibility
of actually knowing anything about the real
universe. What determines which universe we
are in? Quantum Russian Roulette.
66
Some Classical Scientific Axioms
1. Rationality of the world 2. Efficacy of
human reason 3. Metaphysical realism 4.
Regularity of universe 5. Spatial uniformity of
universe 6. Temporal uniformity of universe 7.
Causality 8. Contingency of universe 9.
Desacralization of universe 10. Methodological
reductionism (Occams razor) 11. Value of
scientific enterprise 12. Validity of inductive
reasoning 13. Truthfulness of other scientists
67
Some Classical Scientific Axioms
1. Rationality of the world 2. Efficacy of
human reason 3. Metaphysical realism 4.
Regularity of universe 5. Spatial uniformity of
universe 6. Temporal uniformity of universe 7.
Causality 8. Contingency of universe 9.
Desacralization of universe 10. Methodological
reductionism (Occams razor) 11. Value of
scientific enterprise 12. Validity of inductive
reasoning 13. Truthfulness of other scientists
68
Concluding Quotes
QM has accounted in a quantitative way for
atomic phenomena with numerical precision never
before achieved in any field of science. N.
Mermin
I think it is safe to say that no one understands
quantum mechanics. - R. Feynman
I do not like it, and I am sorry I ever had
anything to do with it. -E. Schrödinger
69
Acknowledgements

• Christina Shenvi
• Prof. K. Birgitta Whaley
• Prof. Bob Harris
• Veritas Fellowship and the Wednesday Night Mens
  Bible Study

Cartoons provided by prescolaire.grandmonde.com