Physics 123A Waves and Modern Physics

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Physics 123A Waves and Modern Physics
Lecture 17 (TM 34.6-10)Particles, Quantum
Interpretations November 18, 2008 (23 Slides)

• John G. Cramer
• Professor of Physics
• B451 PAB
• cramer_at_phys.washington.edu

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Lecture 17 Announcements

• Regrade requests for Exam 2 must be turned in
  to Susan Hong by noon on Monday, November 23.
• Homework 6 is due at 1159 PM on Friday,
  November 20.
• So far 185/196 students have registered their
  clickers. All clickers must be registered by
  December 11 to receive Clicker Credit.

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Exam 2 Statistics
Average 57.2 Std Dev 14.2
High 94 Median 56.5 Low 22
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Lecture Schedule (Part 3)
We are here!
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Interference andDiffraction of Matter
Subsequently, G. P. Thompson showed electron
diffraction when the electrons pass through a
crystal. He observed Laue-type spots in the
diffraction pattern. The figures below show
diffraction patterns when different beams are
passed through an aluminum foil (made of randomly
oriented micro-crystals)
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Interference andDiffraction of Matter (2)
Actually, it is not necessary to use
crystals to demonstrate the interference of
particle waves, if the wavelengths are made long
enough (by using very slow moving particles).
The figures below show two-slit interference
patterns.
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Electron Interference
These figures show the build up of the
electron two-slit interference pattern as the
electrons arrive at the detector.
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Inventing Quantum Mechanics
In the early 20th century as the body of
experimental evidence grew that particles behaved
like waves and waves behaved like particles,
physics was in trouble. It was time for a
paradigm shift. The solution to the problem,
the new physics, was provided independently by
two theorists, Schrödinger and Heisenberg, in
rather unusual ways. Heisenberg produced a
mathematics (matrix quantum mechanics) that
accurately predicted experimental observations
without having any vision of what underlying
processes the mathematics was describing.
Schrödingers wave mechanics was based on a
picture of the processes, based on
electromagnetic wave theory, but his picture was
subsequently shown to be wrong. The result
was that the QM formalism became well established
without any vision of the underlying processes.
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A Wave Mechanics Primer

• Start with a wave equation, e.g., the
  electromagnetic wave equation or the Schrödinger
  equation, that describes the system dynamics.
• Solve the wave equation for wave functions, using
  complex algebra.
• Define operators that operate on the wave
  function y to extract observable quantities like
  energy, momentum, etc.
• Combine the operators, wave functions, and their
  complex conjugates in integrals that predict
  experimental observations.

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Interpretational Problemsof Quantum Mechanics

• What is the quantum wave function? Is it
  a real wave present in space? Is it a
  mathematical representation of the
  knowledge (or possible knowledge) of an observer?
• How and why does the wave function collapse?
  Due to measurement? Due to the change in
  knowledge of an observer? Due to a
  handshake between waves? Or does it
  never collapse, but instead, the universe
  splits?
• Why can we not know simultaneously the precise
  values of conjugate quantities like position
  and momentum or energy and time?

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Paradox 1 (non-locality)Einsteins Bubble
Situation A photon is emitted from a source
having no directional preference.
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Paradox 1 (non-locality)Einsteins Bubble
Situation A photon is emitted from a source
having no directional preference. Its
spherical wave function Y expands like an
inflating bubble.
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Paradox 1 (non-locality)Einsteins Bubble
Situation A photon is emitted from a source
having no directional preference. Its
spherical wave function Y expands like an
inflating bubble. It reaches Detector A, and the
Y bubble pops and disappears.

• Question (originally asked by Albert Einstein)
• If a photon is detected at Detector A, how does
  thephotons wave function Y at the locations of
  Detectors B C know that it should vanish?

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Paradox 1 (non-locality)Einsteins Bubble
It is as if one throws a beer bottle into Boston
Harbor. It disappears, and its quantum ripples
spread all over the Atlantic. Then in Copenhagen,
the beer bottle suddenly jumps onto the dock, and
the ripples disappear everywhere else. Thats
what quantum mechanics says happens to electrons
and photons when they move from place to place.
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Paradox 2 (collapse)Schrödingers Cat

• Experiment A cat is placed in a sealed
  boxcontaining a device that has a 50 chanceof
  killing the cat.
• Question 1 What is thewave function of the
  catjust before the box isopened?
• When does the wave function collapse? Only after
  the box is opened?

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Paradox 3 (nonlocality)EPR Experiments

• An EPR Experiment measures the correlated
  polarizations of a pairof entangled photons,
  obeyingMalus Law P(qrel) Cos2qrel
• The measurement gives the same resultas if both
  filters were in the same arm.
• Furry proposed to place both photons inthe same
  random polarization state.This gives a different
  and weaker correlation.

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Paradox 4 (duality)Wheelers Delayed Choice

• A source emits one photon.Its wave function
  passesthrough slits 1 and 2, makinginterference
  beyond the slits.
• The observer can choose to either(a) measure
  the interference pattern at plane s1, requiring
  that the photon travels through both slits.
• or(b) measure at which slit image it appears in
  plane s2, indicating thatit has passed only
  through slit 2.

The observer waits until after the photon has
passed the slits to decide which measurement to
do.
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Interpretational Problems of Quantum Mechanics

• What is the quantum wave function? Is it
  a real wave present in space? Is it a
  mathematical representation of the
  knowledge (or possible knowledge) of an observer?
• How and why does the wave function collapse?
  Due to measurement? Due to the change in
  knowledge of an observer? Due to a
  handshake between waves? Or does it
  never collapse, but instead, the universe
  splits?
• Why can we not know simultaneously the precise
  values of conjugate quantities like position
  and momentum or energy and time?

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Summary of QM Interpretations
Copenhagen
Many Worlds
Uses observer knowledge to explainwave
function collapse and non-locality.Advises
dont-ask/dont tell about reality.
Uses world-splitting to explain wave function
collapse. Has problems with non-locality.
Useful in quantum computing.
Transactional
Uses advanced-retarded handshake to
explainwave function collapse and non-locality.
Providesa way of visualizing quantum events.
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The Copenhagen Interpretation
QuantumMechanics
Werner Heisenberg (1901 1976)
Heisenbergs uncertainty principleWave-particle
duality, conjugate variables, e.g., x and p, E
and tThe impossibility of simultaneous
conjugate measurements Borns statistical
interpretation The meaning of the wave
function y as probability P y y Quantum
mechanics predicts only the average behavior of a
system. Bohrs complementarity The wholeness
of the system and the measurement apparatus
Complementary nature of wave-particle duality a
particle OR a wave The uncertainty principle is
property of nature, not of measurement. Heisenberg
s "knowledge" interpretation Identification
of y with knowledge of an observer y collapse
and non-locality reflect changing knowledge of
observer. Heisenbergs positivism
Dont-ask/Dont tell about the meaning or
reality behind formalism Focus exclusively on
observables and measurements. Shut up and
calculate!
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Many-Worlds Interpretation
QuantumMechanics
Retain Heisenbergs uncertainty principle
andBorns statistical interpretation from the
Copenhagen Interpretation. No Collapse. The
wave function y never collapses it splits into
new wave functions that reflect the different
possible outcomes of measurements. The split off
wave functions reside in physically
distinguishable worlds. No Observer Our
perception of wave function collapse is because
our consciousness has followed a particular
pattern of wave function splits. Interference
between Worlds Observation of quantum
interference occurs because wave functions in
several worlds have not been separated because
they lead to the same physical outcomes.
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The Transactional Interpretation
Heisenbergs uncertainty principle and Borns
statistical interpretation are not postulates,
because they can be derived from the
Transactional Interpretation. Offer Wave The
initial wave function y is interpreted as a
retarded-wave offer to form a quantum
event. Confirmation wave The response wave
function y (present in the QM formalism) is
interpreted as an advanced-wave confirmation to
proceed with the quantum event. Transaction the
Quantum Handshake A forward/back-in-time y y
standing wave forms, transferring energy,
momentum, and other conserved quantities, and the
event becomes real. No Observers Transactions
involving observers are no different from other
transactionsObservers and their knowledge play
no special roles. No ParaoxesTransactions are
intrinsically nonlocal, and all paradoxes are
resolved.
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End of Lecture 17

• Before the next lecture, read TM, Chapter
  35.1-3.
• Regrade requests for Exam 2 must be turned in
  to Susan Hong by noon on Monday, November 23.
• Homework 6 is due at 1159 PM on Friday,
  November 20.
• So far 185/196 students have registered their
  clickers. All clickers must be registered by
  December 11 to receive Clicker Credit.