The Weirdness of Quantum Mechanics

Document technical information

Format ppt
Size 1.7 MB
First found May 22, 2018

Document content analysis

Category Also themed
Language
English
Type
not defined
Concepts
no text concepts found

Persons

Isaac Newton
Isaac Newton

wikipedia, lookup

Mick Doohan
Mick Doohan

wikipedia, lookup

Peter Atkins
Peter Atkins

wikipedia, lookup

Organizations

Places

Transcript

The Weirdness of
Quantum Mechanics
Dr. Neil Shenvi
Department of Chemistry
Yale University
Talk Outline
1. The history of quantum mechanics
2. What is quantum mechanics?
a. The postulates of quantum mechanics
b. The weirdness of the postulates
3. Quantum weirdness in action
a. The two slit experiment
b. The EPR experiment
4. Interpretations of Quantum Mechanics
a. The Copenhagen Interpretation
b. The Neorealist Interpretation
c. The Many Worlds Interpretation
5. Philosophical Implications
Classical mechanics is the mechanics of everyday
objects like tables and chairs
1. An object in motion tends to stay in motion.
2. Force equals mass times acceleration
3. For every action there is an equal and
opposite reaction.
Sir Isaac Newton
Classical mechanics reigned as the dominant theory of
mechanics for centuries
1687 – Newton’s Philosophiae
Mathematica
1788 – Lagrange’s Mecanique
Analytique
1834 – Hamiltonian mechanics
1864 – Maxwell’s equations
1900 – Boltzmann’s
entropy equation
However, several experiments at the beginning of
the 20th-century defied explanation
The Ultraviolet
Catastrophe
The Stern-Gerlach
Experiment
Newtonian explanations for
these phenomena were wildly
insufficient
The Hydrogen
Spectrum
?
Quantum mechanics was developed to explain these
results and developed into the most successful
physical theory in history
Increasing weirdness
1900 – Planck’s constant
1913 – Bohr’s model
of the atom
1925 – Pauli exclusion principle
1926 – Schrodinger equation
1948 – Feynmann’s path
integral formulation
1954 – Everett’s many-world
theory
Although quantum mechanics applies to all objects,
the effects of quantum mechanics are most
noticeable only for very small objects
How small is very small?
1 meter
Looks classical
1 millimeter
Looks classical
1 micrometer
Looks classical
1 nanometer
Looks quantum!
Nonetheless, quantum mechanics is still very important.
How important is very important?
Without quantum mechanics:
Many biological reactions
would not occur.
Life does
not exist
Chemical bonding would be
impossible.
All molecules
disintegrate
All atoms would be unstable.
Universe
explodes
Neil Shenvi’s dissertation title:
Vanity of Vanities, All is Vanity
Minimal
consequences
Talk Outline
1. The history of quantum mechanics
2. What is quantum mechanics?
a. The postulates of quantum mechanics
b. The weirdness of the postulates
3. Quantum Weirdness in action
a. The two slit experiment
b. The EPR experiment
4. Interpretations of Quantum Mechanics
a. The Copenhagen Interpretation
b. The Neorealist Interpretation
c. The Many Worlds Interpretation
5. Philosophical Implications
The laws of quantum mechanics are founded upon
several fundamental postulates
The Fundamental Postulates of Quantum Mechanics:
Postulate 1: All information about a system is provided
by the system’s wavefunction.
Postulate 2: The motion of a nonrelativistic particle is
governed by the Schrodinger equation
Postulate 3: Measurement of a system is associated with
a linear, Hermitian operator
Postulate 1: All information about a system is
provided by the system’s wavefunction.
 ( x)
Pr( x )
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 can change with time.
4. The existence of a wavefunction implies particle-wave duality.
The Weirdness of Postulate 1: Quantum particles
are usually delocalized, meaning they do not have a
well-specified position
Classical particle
Quantum particle
Position = x
Wavefunction = (x)
The particle
is here.
With some high probability,
the particle is probably
somewhere around here
The Weirdness of Postulate 1: At a given instant in
time, the position and momentum of a particle
cannot both be known with absolute certainty
Classical particle
Quantum particle
Wavefunction = (x)
Hello, my name is:
Classical particle
my position is
11.2392…Ang
my momentum is -23.1322… m/s
“I can tell you my exact position, but then I
can’t tell you my momentum. I can tell
you my exact momentum, but then I can’t
tell you my position. I can give you a
pretty good estimate of my position, but
then I have to give you a bad estimate of
my momentum. I can…”
?
??
?
This consequence is known as Heisenberg’s uncertainty principle
The Weirdness of Postulate 1: a particle can be put
into a superposition of multiple states at once
Classical elephant:
Valid states:
Quantum elephant:
Valid states:
Gray
Gray
Multicolored
Multicolored
+
Gray AND Multicolored
Postulate 2: The motion of a nonrelativistic particle is
governed by the Schrödinger equation

i
 (t )  Hˆ  (t )
t
Time-dependent S.E.:
Time-dependent S.E.:


2
 2m dx
2
Molecular S.E.:
d
2
Ĥ   E 

ˆ
 V ( x )   ( x )  E  ( x)

Interesting facts about the Schrödinger Equation:
1. It is a wave equation whose solutions display interference effects.
2. It implies that time evolution is unitary and therefore reversible.
3. It is very, very difficult to solve for large systems (i.e. more
than three particles).
The Weirdness of Postulate 2: 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 insufficient energy.
This effect is the basis for the scanning tunneling electron
microscope (STEM)
The Weirdness of Postulate 2: Quantum particles
take all paths.
Classical mouse
Quantum mouse
Classical particles take a
single path specified by
Newton’s equations.
The Schrodinger equation
indicates that there is a
nonzero probability for a
particle to take any path
This consequence is stated rigorously in Feymnann’s path integral
formulation of quantum mechanics
Postulate 3: Measurement of a quantum mechanical
system is associated with some linear, Hermitian
operator Ô.
Oˆ   Oˆ 
Oˆ   dx * ( x) Oˆ ( x)( x)
Interesting facts about the measurement postulate:
1. It implies that certain properties can only achieve a discrete set
of measured values
2. It implies that measurement is inherently probabilistic.
3. It implies that measurement necessarily alters the observed
system.
The Weirdness of Postulate 3: Even if the exact
wavefunction is known, the outcome of measurement
is inherently probabilistic
Classical Elephant:
Quantum Elephant:
Before
measurement
or
After
measurement
For a known state, outcome
is deterministic.
For a known state, outcome
is probabilistic.
The Weirdness of Postulate 3: Measurement
necessarily alters the observed system
Classical Elephant:
Quantum Elephant:
Before
measurement
After
measurement
State of the system is
unchanged by measurement.
Measurement changes
the state of the system.
The Weirdness of Postulate 3: Properties are actions
to be performed, not labels to be read
Classical Elephant:
Quantum Elephant:
Position = here
Color = grey
Size
= large
Position:
The ‘position’ of an object exists
independently of measurement and is
simply ‘read’ by the observer
‘Position’ is an action performed on an
object which produces some particular
result
In other words, properties like position or momentum do not exist
independent of measurement! (*unless you’re a neorealist…)
Talk Outline
1. The history of quantum mechanics
2. What is quantum mechanics?
a. The postulates of quantum mechanics
b. The weirdness of the postulates
3. Quantum Weirdness in action
a. The two slit experiment
b. The EPR experiment
4. Interpretations of Quantum Mechanics
a. The Copenhagen Interpretation
b. The Neorealist Interpretation
c. The Many Worlds Interpretation
5. Philosophical Implications
The two-slit experiment is one of the classic
validations of the predictions of quantum theory
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
In the one-slit experiment, particles that pass through
the single slit produce an image on the detector
The One Slit Experiment
Gaussian distribution
of detected particles
Detector
Particle
emitter
Particles
What happens if we use two slits instead of only one?
If we use two slits, we might expect to obtain the
sum of two single-slit distributions…
The Two Slit Experiment
Expected result: sum
of two Gaussians
Detector
Particle
emitter
Particles
Warning: the “expected result” presented by this slide is patently false
…but in reality, we obtain an interference pattern.
The Two Slit Experiment
Actual result:
interference pattern.
Detector
Particle
emitter
Particles
Question: Is this a quantum phenomenon?
A clever physicist might attempt to explain this
result as the consequence of “crowd waves”…
The Classical “Explanation” - Interference phenomena are caused
by disturbances propagating through huge numbers of water particles
Detector
Large
rock
Large pond
Warning: the “classical ‘explanation’” presented on this slide is patently false
…but an even cleverer physicist can test this
hypothesis by configuring the emitter to emit the
particles one at a time
The Two Slit Experiment
Detector
Particle
emitter
Result: Interference pattern remains!
The quantum mechanical explanation is that each
particle passes through both slits and interferes with
itself
The Quantum Explanation
Superposition
state
+
+
Detector

The wavefunction of each particle is a probability wave which
produces a probability interference pattern when it passes
through the two slits.
If a measurement device is placed on one of the slits,
then the interference pattern disappears
Curioser and Curioser
Measurement
device
+

Detector
The measurement device has collapsed the
wavefunction, leading to a loss of interference
Curioser and Curioser
Wavefunction
collapse!
Measuring
device
+

or
Detector
Quantum mechanics makes several revolutionary
claims about the fundamental behavior of particles
The claims of quantum mechanics:
1. Particles act like waves.
Particles can interfere with themselves.
2. Particles do whatever they want.
There is a non-zero probability of finding a particle
essentially anywhere in the universe.
3. Measurement is inherently probabilistic.
No supplemental knowledge will make measurement
deterministic.
Anyone who is not shocked by quantum mechanics has not
understood it. -Niels Bohr
Einstein was so shocked by these claims that he was
convinced that quantum mechanics must be wrong
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
To call attention to the problems with quantum
mechanics, Einstein devised a brilliant thought
experiment
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
The EPR paper asked the question “what does it
mean for a theory to be complete”?
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.”
In the hypothetical experiment, two particles are first
placed in an entangled state
The Thought Experiment
1. Create a valid two particle quantum state like:
| = |HT +
|TH
Particle 1
Particle 2
The particles are then separated by an extremely
large distance
The Thought Experiment
2. Separate the particles by a spacelike distance.
| = |H
|T
T +
H
Particle 1
Particle 2
Since the particles are very far apart (light years, say), relativity
tells us that manipulating one particle cannot instantaneously
affect the other particle.
The state of particle 1 is measured, immediately
yielding the state of the particle 2
The Thought Experiment
3. Measure Particle 1.
| = |H
|T
T +
H
Particle 1
Particle 2
QM tells us that there is a 50-50 chance of Particle 1 being in
state |H or |T. But as soon as we measure Particle 1, we
immediately know the state of Particle 2!
According to Einstein’s definition, the state of
particle 2 was therefore an element of reality
The Thought Experiment
4. Think about the definition of an element of reality.
| = |H
|T
T +
H
Particle 1
Particle 2
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.
The EPR paper concluded that QM does not predict
all elements of reality and must be incomplete
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.”
HT
TH
TH HT
In 1964, John Bell showed that Einstein’s claim of
realism and the predictions of QM yield testable results.
The Bell Inequality:
Sx1Sv1  Sz1Sv1  Sz1Sv 2  S x1Sv 2  2
All local hidden
variable theories
S x1Sv1  S z1Sv1  S z1Sv 2  S x1Sv 2  2 2
Quantum mechanics
| = |HT |TH
Particle 1
Particle 2
By performing the Bell experiment,
we can let nature tell us which is
correct: Einstein’s hidden variable
theory or quantum mechanics
In the last few decades, the Bell experiment has been
carried out numerous times using entangled photons…
The Real Experiment
| = |HT - |TH
Photon 1
Paris
Photon 2
London
In Paris and in London, we measure each photon in a
randomly chosen basis and collect a large amount of data.
…and vindicates the predictions of quantum
mechanics
The Real Results
Paris
Measurement Result
+1
-1
London
Measurement Result
+1
+1
+1
+1
…
-1
-1
...
…
+1
+1
-1
-1
...
Result: Too much correlation to be explained classically!
Quantum mechanics wins!
The Bell experiment demonstrates that local realism
is false; either locality or realism must be jettisoned.
The Bell experiment demands that we choose one (and only
one) of the following principles can be valid:
Locality - the principle that effects cannot
propagate faster than the speed of light.
c
Realism - the principle that objects have
properties independent of measurement.
Warning: 4 out of 5 physicists recommend keeping locality.
Talk Outline
1. The history of quantum mechanics
2. What is quantum mechanics?
a. The postulates of quantum mechanics
b. The weirdness of the postulates
3. Quantum Weirdness in action
a. The two slit experiment
b. The EPR experiment
4. Interpretations of Quantum Mechanics
a. The Copenhagen Interpretation
b. The Neorealist Interpretation
c. The Many Worlds Interpretation
5. Philosophical Implications
Given the weirdness of quantum mechanics, the
obvious question is: why does reality appear so
normal?
QM tells me
that this is reality:
|HT - |TH
x
But all I ever see is:
v

There are three major interpretations of quantum
mechanics: Copenhagen, neorealist, and many-worlds
The Copenhagen interpretation:
measurement induces
wavefunction collapse
Neorealist: hidden variables or
pilot waves produce nonlocal
phenomena
Many-worlds: measurement leads
to bifurcation of multiverse
|
The Copenhagen interpretation views the measurement
device as distinct from a “normal” quantum system
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
|
The major downside of the Copenhagen interpretation
is that it fails to define what a “measurement device” is
The Copenhagen (“orthodox”) Interpretation - N. Bohr
Pros:
The traditional textbook explanation (perhaps this is a 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? How
is it related to human consciousness?
What determines the outcome of a measurement if hidden
variables are not allowed?
The neorealist interpretation posits the existence of
hidden variables or pilot waves that preserve realism
The neorealist interpretation - A. Einstein
Particle properties do have values independent
of measurement, so the 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
But these hidden variables and pilot waves have
never been detected and have suspicious properties
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.
The many-worlds interpretation asserts that whenever
measurement occurs, the universe splits
The Many Worlds Interpretation - H. Everett
The wavefunction never collapses. The universe is
really a multi-verse.
|H
|H + |T
|H
+
|T
|T
Many-worlds is the most beautiful of the
interpretations, but is also the most bizarre
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.
Talk Outline
1. The history of quantum mechanics
2. What is quantum mechanics?
a. The postulates of quantum mechanics
b. The weirdness of the postulates
3. Quantum Weirdness in action
a. The two slit experiment
b. The EPR experiment
4. Interpretations of Quantum Mechanics
a. The Copenhagen Interpretation
b. The Neorealist Interpretation
c. The Many Worlds Interpretation
5. Philosophical Implications
Quantum mechanics has many important
implications for epistemology and metaphyics
•
•
•
•
•
The possibility of almost anything
The absence of causality/determinism
The role of human consciousness
The limits of human knowledge
The cognitive dissonance of reality
First, quantum mechanics implies that almost no event
is strictly impossible
Classical physics
100%
Quantum physics
99.99..%
1000000
-10
10
“the random nature of quantum physics means that there is always a minuscule, but
nonzero, chance of anything occurring, including that the new collider could spit out
man-eating dragons [emph. added]” - physicist Alvaro de Rujula of CERN regarding the
Large Hadron Collider, quoted by Dennis Overbye, NYTimes 4/15/08
Second, quantum mechanics abrogates notions of
causality and (human?) determinism
Classical physics
cause
Quantum physics
effect
effect
H + T
H
?
(MacBeth)
(MacBeth)
Physics no longer rigorously provides an answer to the
question “what caused this event?”
?
Third, within the Copenhagen interpretation, human
consciousness appears to have a distinct role
When does the wave function collapse during measurement?
|
Wavefunction….wavefunction…wavefunction…………particle!
time
“The very study of the physical world leads to the conclusion that the concept of
consciousness is an ultimate reality” “it follows that the being with a consciousness
must have a different role in quantum mechanics than the inanimate object” – physicist
Eugene Wigner, Nobel laureate and founder of quantum mechanics
Fourth, the fact that the wavefunction is the ultimate
reality implies that there is a severe limit to human
knowledge
|
KEEP OUT
“…classical mechanics took to superficial a view of the world: it dealt with appearances.
However, quantum mechanics accepts that appearances are the manifestation of a
deeper structure (the wavefunction, the amplitude of the state, not the state itself)” –
Peter Atkins
Finally, quantum mechanics challenges our
assumption that ultimate reality will accord with our
natural intuition about what is reasonable and normal
Classical physics
Quantum physics
I think it is safe to say that no one understands quantum mechanics. Do not keep
saying to yourself, if you can possibly avoid it, 'But how can it possibly be like
that?' … Nobody knows how it can be like that. – Richard Feynman
What effect does QM have on the fundamental
assumptions of science?
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 (Occam’s razor)
11. Value of scientific enterprise
12. Validity of inductive reasoning
13. Truthfulness of other scientists
It makes things complicated…
?
?
?
?
?
?
?
1. Rationality of the world
Weirdness of Quantum mechanics
2. Efficacy of human reason
3. Metaphysical realism
Copenhagen interpretation
4. Regularity of universe
5. Spatial uniformity of universe
EPR Experiment: Pick one (only)
6. Temporal uniformity of universe
7. Causality
8. Contingency of universe
Many worlds interpretation
9. Desacralization of universe
10. Methodological reductionism (Occam’s razor)
Neo-realism
11. Value of scientific enterprise
12. Validity of inductive reasoning
13. Truthfulness of other scientists
Probabilistic nature
of QM
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
The more success the quantum theory has the sillier it looks.
- A. Einstein
I do not like it, and I am sorry I ever had anything to do with
it. -E. Schrödinger
Acknowledgements
•
•
•
•
Dr. Christina Shenvi
Prof. John Tully
Prof. K. Birgitta Whaley
Prof. Bob Harris
Cartoons provided by: prescolaire.grandmonde.com and www.clker.com
×

Report this document