What’s the Matter?:
Quantum Physics for Ordinary People
Absorber
John G. Cramer, Professor Emeritus
Department of Physics
University of Washington
Seattle, Washington, 98195
Talk given at The Grange, Whallonsburg, NY, April 20, 2011
Light: Particle or Wave?
Albert Einstein explained the
photoelectric effect by showing that light
energy is quantized. Light, even while
exhibiting wave-like interference, comes
in particle-like energy packets called
photons.
What are photons? Certainly not
classical particles. When traveling through
a double slit, even one photon at a time,
they build up an interference pattern.
The implication is that each photon
travels as a wave through both slits and
interferes with itself.
Photons show properties of both waves
and particles. This paradox produced a
crisis in classical physics, and led to the
development of quantum mechanics.
Heisenberg’s Matrix Mechanics
Werner Heisenberg, after his Munich PhD, worked
fruitlessly in Niels Bohr’s Copenhagen group for two
years, attempting to make sense of atomic line spectra
and produce an improved version of Bohr’s atom model
that would explain and predict them. In 1924 he moved
to Gottingen to work with Max Born on the same problems.
The warm, verdant Spring of 1924 was cruel for
Heisenberg, who had severe problems with allergies and
hay fever. In desperation, he retreated to Helgoland, a
Werner Heisenberg
(1901 – 1976)
barren, grassless island off the northern coast of Germany,
taking with him atomic physics data on spectra, energy levels, etc. He had
come to consider these measured quantities to be more significant than the
ephemeral “unseen” variables in the models behind his theoretical calculations.
In the isolation of Helgoland, the data began to “speak to him”. In a week
he devised arcane procedures by which some data could be combined to predict
other, seemingly unrelated, data. Back in Gottingen, Max Born and Pascal
Jordan recognized Heisenberg’s procedures as matrix operations. Thus was
born Heisenberg’s “matrix mechanics” version of quantum mechanics, created
without any underlying picture of what was behind the arcane mathematics.
Schrödinger’s Wave Mechanics
In September, 1925, Erwin Schrödinger obtained
a copy of Louis de Broglie’s 1924 PhD thesis, which
treated particles as waves. He gave a Zurich colloquium
describing de Broglie’s ideas. After this colloquium, his
colleague Peter Debye remarked that de Broglie’s way
of discussing waves was rather naïve, and that such
matter waves should have a wave equation.
Schrödinger took Debye’s remark seriously. In
Erwin Schrödinger
(1887 – 1961)
November, 1925, he went on a ski holiday with a young
lady (who was not his wife). He returned to Zurich with a wave equation for
matter waves. This is now known as the Schrödinger Equation.
Schrödinger originally attempted to interpret these waves as equivalent to
electromagnetic waves, physically present in space and traveling with velocities
characteristic of the particles they described. This attempt failed.
The result was that both quantum wave and matrix mechanics became well
established without any vision of the underlying processes. Quantum mechanics
had two equivalent formalisms, but no interpretation of either of them.
A Wave Mechanics Primer
1. Start with a wave equation, e.g., the electromagnetic wave equation
(used here) or the Schrödinger equation, that describes the system
dynamics.
2
2
dy
dy



0 0
dx 2
dt 2
2. Solve the wave equation for wave functions, using complex algebra.
y ( x, t )  Aei kx t   A cos  kx  t   i sin  kx  t  
3. Define “operators” that operate on the wave function y to extract
observable quantities like energy, momentum, etc.
ih 
H
 energy operator;
2 t
h
Hy = y  Ey
2
4. Combine the operators, wave functions, and their complex conjugates
in integrals that predict experimental observations.
P( x)  y *y  y
2






y *y dx   y dx  1 E   y * Hy dx
2
Quantum Sandwich
Questions Raised by
Quantum Mechanics
 What is the quantum wave function? What does it mean?
Is it a real wave present in space?
Is it a mathematical representation of the
knowledge (or possible knowledge) of some 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 cannot we know simultaneously the precise
values of certain quantities like position and
momentum or energy and time?
Three QM Interpretations
Copenhagen
Many
Worlds
Uses “observer knowledge” to explain
wave function collapse and non-locality.
Advises “don’t-ask/don’t tell” about reality.
Uses “world-splitting” to explain wave
function collapse. Has problems with nonlocality. Useful in quantum computing.
Transactional
Uses “advanced-retarded handshake” to explain
wave function collapse and non-locality. Provides
a way of “visualizing” quantum events.
Niels Bohr
(1885-1962)
The Copenhagen
Interpretation
Werner Heisenberg
(1901 – 1976)
Quantum
Mechanics
Heisenberg’s uncertainty principle:
Wave-particle duality, conjugate variables, e.g., x and p, E and t;
The impossibility of simultaneous conjugate measurements
Born’s statistical interpretation:
The meaning of the wave function y as probability: P = y y*;
Quantum mechanics predicts only the average behavior of a system.
Bohr’s 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.
Heisenberg’s positivism:
“Don’t-ask/Don’t tell” about the meaning or reality behind formalism;
Focus exclusively on observables and measurements. Shut up and calculate!
Hugh Everett III
(1930-1982)
Many-Worlds
Interpretation
John A. Wheeler
(1911-2008)
Quantum
Mechanics
Retain Heisenberg’s uncertainty principle and
Born’s 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” that have not been separated because they lead to the
same physical outcomes.
John G. Cramer
(1934- )
The Transactional
Interpretation
Heisenberg’s uncertainty principle and Born’s 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 Special Observers:
Transactions involving observers are no different from other transactions;
Observers and their knowledge play no special roles.
No Paraoxes:
Transactions are intrinsically nonlocal; all known paradoxes are resolved.
The TI “Listens” to the
Quantum Formalism
Consider a quantum matrix element:
<S> = v y* S y dr3 = <f | S | i>
… a y* - y “sandwich”. What does this suggest?
Hint: The complex conjugation in y* is the
Wigner operator for time reversal. If y is a
retarded wave, then y* is an advanced wave.
If y  A ei(kr  t) then y*  A ei(-kr  t)
(retarded)
(advanced)
A retarded wave carries positive energy into the future.
An advanced wave carries negative energy into the past.
The Quantum
Transaction Model
Step 1: The emitter sends
out an “offer wave” Y.
The Quantum
Transaction Model
Step 1: The emitter sends
out an “offer wave” Y.
Step 2: The absorber responds
with a “confirmation wave” Y*.
The Quantum
Transaction Model
Step 1: The emitter sends
out an “offer wave” Y.
Step 2: The absorber responds
with a “confirmation wave” Y*.
Step 3: The emitter selects a
confirmation “echo” and the
process repeats until energy and
momentum is transferred and
the transaction is completed
(wave function collapse).
Quantum
Paradoxes &
The Transactional
Interpretation
Paradox 1 (non-locality):
Einstein’s Bubble
Situation: A photon is emitted
from a source having no
directional preference.
Paradox 1 (non-locality):
Einstein’s Bubble
Situation: A photon is emitted
from a source having no
directional preference.
Its spherical wave function Y
expands like an inflating bubble.
Paradox 1 (non-locality):
Einstein’s 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 the
photon’s wave function Y at the locations of
Detectors B & C “know” that it should vanish?
Paradox 1 (non-locality):
Einstein’s 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.
That’s what quantum mechanics says
happens to electrons and photons when
they move from place to place.
Paradox 1 (non-locality):
Einstein’s Bubble
Transactional Explanation:
 A transaction develops
between the source and
detector A, transferring the energy there and
blocking any similar transfer to the other potential
detectors, due to the 1-photon boundary condition.
 The transactional handshakes acts nonlocally to
answer Einstein’s question.
 This is in effect an extension of the pilot-wave ideas
of deBroglie.
Paradox 2 (Y collapse):
Schrödinger’s Cat
Experiment: A cat is placed in a sealed box
containing a device that has a 50% chance
of killing the cat.
Question 1: What is the
wave function of the cat
just before the box is
opened?
(Y 12 dead + 12 alive ?)
When does the wave function collapse? Only after the box
is opened?
Paradox 2 (Y collapse):
Schrödinger’s Cat
Experiment: A cat is placed in a sealed box
containing a device that has a 50% chance
of killing the cat.
Question 1: What is the
wave function of the cat
just before the box is
opened?
(Y 12 dead + 12 alive ?)
When does the wave function collapse? Only after the box
is opened?
Question 2: If we observe Schrödinger, what is his wave
function during the experiment? When does it collapse?
Paradox 2 (Y collapse):
Schrödinger’s Cat
The issues are: when
and how does the wave
function collapse.
 What event collapses it?
(Observation by an
intelligent observer?)
 How does the information
that it has collapsed spread
to remote locations, so that the laws of physics can be
enforced there?
Paradox 2 (Y collapse):
Schrödinger’s Cat
Transactional Explanation:
 A transaction either
develops between the
source and the detector,
or else it does not. If
it does, the transaction
forms atemporally, not
at some particular time.
 Therefore, asking when
the wave function
collapsed was asking the wrong question.
Paradox 3 (non-locality):
EPR Experiments
Measurement 1
Entanglement: The separated but
“entangled” parts of the same quantum
system can only be described by
referencing the state of other part.
The possible outcomes of
measurement M2 depend of the
results of measurement M1, and vice
versa. This is usually a consequence
of conservation laws.
Nonlocality: This “connectedness”
between the separated system parts is
called quantum nonlocality. It should
act even of the system parts are
separated by light years. Einstein
called this “spooky actions at a
distance.”
M1
Entangled
Photon
Source
Entangled
photon 1
Nonlocal
Connection
Entangled
photon 2
M2
Measurement 2
Paradox 3 (non-locality):
EPR Experiments
An EPR Experiment measures the
correlated polarizations of a pair
of entangled photons, obeying
Malus’ Law: [P(qrel) = Cos2qrel]
Paradox 3 (non-locality):
EPR Experiments
An EPR Experiment measures the
correlated polarizations of a pair
of entangled photons, obeying
Malus’ Law: [P(qrel) = Cos2qrel]
The measurement gives the same result
as if both filters were in the same
arm.
Paradox 3 (non-locality):
EPR Experiments
An EPR Experiment measures the
correlated polarizations of a pair
of entangled photons, obeying
Malus’ Law: [P(qrel) = Cos2qrel]
The measurement gives the same result
as if both filters were in the same
arm.
Furry illustrated the strangeness of
nonlocality by proposing to force
both photons into the same random
polarization state. This gives a
different and weaker correlation,
and shows that the photons are not
in a definite state until measured.
Paradox 3 (non-locality):
EPR Experiments
Apparently, the measurement on the right
side of the apparatus causes (in some
sense of the word cause) the photon
on the left side to be in the same
quantum mechanical state, and this
does not happen until well after they
have left the source.
This EPR “influence across space time”
works even if the measurements are
kilometers (or light years) apart.
Could that be used for faster than light
signaling?
Perhaps. We’re looking into that question.
Paradox 3 (non-locality):
EPR Experiments
Transactional Explanation:
An EPR experiment requires a
consistent double advancedretarded handshake
between the emitter and
the two detectors.
The “lines of communication”
are not spacelike but
negative and positive
timelike. While spacelike
communication has
relativity problems, timelike
communication does not.
X
X
Paradox 4 (wave/particle):
Wheeler’s Delayed Choice
A source emits one photon.
Its wave function passes
through slits 1 and 2, making
*
interference 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.
The observer waits
or
until after the photon
(b) measure at which slit image it
has passed the slits
appears in plane s2, indicating that
to decide which
it has passed only through slit 2.
measurement to do.
Paradox 4 (wave/particle):
Wheeler’s Delayed Choice
Thus, in Wheeler’s account
of the process, the photon does
not “decide” if it is a particle
or a wave until after it passes
the slits, even though a particle
must pass through only one slit while a wave must pass
through both slits.
Wheeler asserts that the measurement choice determines
whether the photon is a particle or a wave retroactively!
Paradox 4 (wave/particle):
Wheeler’s Delayed Choice
Transactional Explanation:
 If the screen at s1 is up, a
transaction forms between
s1 and the source S through
both slits.
Paradox 4 (wave/particle):
Wheeler’s Delayed Choice
Transactional Explanation:
 If the screen at s1 is up, a
transaction forms between
s1 and the source S through
both slits.
 If the screen at s1 is down,
a transaction forms between one of the detectors
(1’ or 2’) and the source S through only one slit.
Paradox 4 (wave/particle):
Wheeler’s Delayed Choice
Transactional Explanation:
 If the screen at s1 is up, a
transaction forms between
s1 and the source S through
both slits.
 If the screen at s1 is down,
a transaction forms between one of the detectors
(1’ or 2’) and the source S through only one slit.
 In either case, when the measurement decision was
made is irrelevant.
Testing
Interpretations
Can Interpretations
of QM be Tested?
 The simple answer is “No!”. It is the formalism of quantum
mechanics that makes the testable predictions.
 As long as an interpretation is consistent with the
formalism, it will make the same predictions as any other
interpretation, and no experimental tests are possible.
 However, there is an experiment (Afshar) that suggests
that the Copenhagen and Many-Worlds Interpretations
may be inconsistent with the quantum mechanical
formalism.
 If this is true, then these interpretations can be falsified.
 The Transactional Interpretation is consistent with the
Afshar results and does not have this problem.
Reminder: Wheeler’s Delayed
Choice Experiment
One can choose to either:
• Measure at s1 the interference pattern, giving the
wavelength and momentum of the photon, or
• Measure at s2 which slit the particle passed
through, giving its position.
Wheeler’s Delayed
Choice Experiment
Thus, one observes either:
 Wave-like behavior with the
interference pattern
or
 Particle-like behavior in determining
which slit the photon passed through.
(but not both).
The Afshar Experiment
 Put wires with 6% opacity at the positions of the
interference minima at s1, and
 Place a detector at 2’ on plane s2 and observe the
intensity of the light passing through slit 2.
 Question: What fraction of the light is blocked by the
grid and not transmitted? (i.e., is the interference
pattern still there when one measures particle behavior?)
The Afshar Experiment
Copenhagen-influenced expectation:
The measurement-type forces particle-like
behavior, so there should be no interference, and
no minima. Therefore, 6% of the particles should
be intercepted.
The Afshar Experiment
Many-Worlds-influenced expectation:
The universe splits, and we are in a universe in which
the photon goes through slit 2 (and not through slit
1). Therefore, there should be no interference, and no
minima. Consequently, 6% of the particles should be
intercepted.
The Afshar Experiment
Transactional-influenced expectation:
The initial offer waves pass through both slits on their
way to possible absorbers. At the wires, the offer
waves cancel in first order, so there no transactions
can form and no photons can be intercepted by the
wires. Therefore, the absorption by the wires should
be very small (<<6%).
Afshar Experiment Results
No Grid
No Loss
Grid + 1 Slit
6% Loss
Grid + 2 Slits
<0.1% Loss
By uncovering 1, the light reaching 2’ increases, even though no photons from 1 reach 2’!
Afshar Test Results
Copenhagen
Many
Worlds
Predicts no interference.
Predicts no interference.
Transactional
Predicts interference, as does the QM formalism.
Afshar Test Results
Transactional
Thus, it appears that the Transactional Interpretation
is the one interpretation of the three discussed that has
survived the Afshar test. It also appears that other
interpretations on the market (Decoherence, ConsistentHistories, etc.) should fail the Afshar Test.
However, quantum interpretational theorists are fairly
slippery characters. It remains to be seen if they will
find some way to save their pet interpretations.
References
Transactional
The Transactional Interpretation of Quantum
Mechanics:
http://www.npl.washington.edu/TI
Schrodinger’s Kittens by John Gribbin (1995).
A .ppt file for the PowerPoint version of this talk will
soon be available at:
http://faculty.washington.edu/jcramer
The
End