Download The Blind Men and the Quantum

The Blind Men and the Quantum:
Adding Vision to the Quantum World
Quantum
Mechanics
John G. Cramer
Dept. of Physics, Univ. of Washington
Seattle, Washington, 98195
1st Hal Clement Memorial Lecture
Boskone 41, Boston, MA, February 15, 2004
A Quantum
Metaphor
(With apologies to Americans with Disabilities)
The Blind Men
and the Elephant
by John Godfrey Saxe (1816-1887)
It was six men of Indostan, To learning much inclined, Who went to see the Elephant,
(Though all of them were blind), That each by observation, Might satisfy his mind. .
The First approached the Elephant, And happening to fall, Against his broad and sturdy side, At once began to bawl:
“God bless me! but the Elephant, Is very like a wall!”
The Second, feeling of the tusk, Cried, “Ho! what have we here, So very round and smooth and sharp? To me ’tis mighty clear,
This wonder of an Elephant, Is very like a spear!”
The Third approached the animal, And happening to take, The squirming trunk within his hands, Thus boldly up and spake:
“I see,” quoth he, “the Elephant, Is very like a snake!”
The Fourth reached out an eager hand, And felt about the knee. “What most this wondrous beast is like, Is mighty plain,” quoth he;
“ ‘Tis clear enough the Elephant, Is very like a tree!”
The Fifth, who chanced to touch the ear, Said: “E’en the blindest man, Can tell what this resembles most; Deny the fact who can,
This marvel of an Elephant, Is very like a fan!”
The Sixth no sooner had begun, About the beast to grope, Than, seizing on the swinging tail, That fell within his scope,
I see,” quoth he, “the Elephant, Is very like a rope!”
And so these men of Indostan, Disputed loud and long, Each in his own opinion, Exceeding stiff and strong,
Though each was partly in the right, And all were in the wrong!
Moral: So oft in theologic wars, The disputants, I ween, Rail on in utter ignorance, Of what each other mean,
And prate about an Elephant, Not one of them has seen!
Quantum Theory
and
Interpretations
What is Quantum Mechanics?
Quantum mechanics is a theory. It is our
current “standard model” for describing
the behavior of matter and energy at the
smallest scales (photons, atoms, nuclei,
Quantum
Mechanics
quarks, gluons, leptons, …).
Like all theories, it consists of a
mathematical formalism, plus an
interpretation of that formalism.
However, quantum mechanics differs from other physical
theories because, while its formalism of has been accepted and
used for 80 years, its interpretation remains a matter of
controversy and debate. Like the opinions of the 6 blind men,
there are many rival QM interpretations on the market.
Today we’ll consider three QM interpretations (including mine),
and we’ll talk about ways for choosing between them.
The Role of an Interpretation
The interpretation of a formalism should:
• Provide links between the mathematical
symbols of the formalism and elements of
the physical world;
• Neutralize the paradoxes; all of them;
• Provide tools for visualization or for
speculation and extension.
• It should not have its own sub-formalism!
• It should not make its own testable predictions,
(but it may be falsifiable, if it is found to be
inconsistent with the formalism and experiment)!
Interpretation Example:
nd
Newton’s 2 Law
• Formalism:
F = ma
• Interpretation: “The vector force
on a body is proportional to the
product of its scalar mass, which is positive, and
the 2nd time derivative of its vector position.”
• What this interpretation does:
•It relates the formalism to physical observables.
•It avoids the paradoxes that would arise if m<0.
•It insures that F||a.
Four Quantum
Paradoxes
Paradox 1 (non-locality):
Einstein’s Bubble
Situation: A photon is emitted
from an isotropic source.
Paradox 1 (non-locality):
Einstein’s Bubble
Situation: A photon is emitted
from an isotropic source.
Its spherical wave function Y
expands like an inflating bubble.
Paradox 1 (non-locality):
Einstein’s Bubble
Situation: A photon is emitted
from an isotropic source.
Its spherical wave function Y
expands like an inflating bubble.
It reaches a detector, and the Y
bubble “pops” and disappears.
Question (Albert Einstein):
If a photon is detected at Detector A, how does the
photon’s wave function Y at the location 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 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?
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?
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 question is, when and
how does the wave function
collapse.
•What event collapses it?
•How does the collapse
spread to remote locations?
Paradox 3 (wave vs. 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
until after the photon
or
(b) measure at plane s2 which slit has passed the slits to
image it appears in, indicating that decide which
it has passed only through slit 2. measurement to do.
Paradox 3 (wave vs. particle):
Wheeler’s Delayed Choice
Thus, 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 and a wave must pass
through both slits.
Apparently the measurement choice determines
whether the photon is a particle or a wave retroactively!
Paradox 4 (non-locality):
EPR Experiments
Malus and Furry
An EPR Experiment measures the
correlated polarizations of a pair
of entangled photons, obeying
Malus’ Law [P(qrel) = Cos2qrel]
Paradox 4 (non-locality):
EPR Experiments
Malus and Furry
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 4 (non-locality):
EPR Experiments
Malus and Furry
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 proposed to place both photons in
the same random polarization state.
This gives a different and weaker
correlation.
Paradox 4 (non-locality):
EPR Experiments
Malus and Furry
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
light years apart.
Could that be used for FTL signaling?
Sorry, SF fans, the answer is No!
Three
Interpretations
of Quantum
Mechanics
The Copenhagen
Interpretation
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.
The Many-Worlds
Interpretation
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 preception 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.
The Transactional
Interpretation (JGC)
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 Observers:
Transactions involving observers are no different from other transactions;
Observers and their knowledge play no special roles.
No Paraoxes:
Transactions are intrinsically nonlocal, and all paradoxes are resolved.
Summary of 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.
The Transactional
Interpretation
of Quantum
Mechanics
“Listening” to the Formalism
of Quantum Mechanics
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-wt) then y*  A ei(-kr+wt)
(retarded)
(advanced)
Maxwell’s Electromagnetic
Wave Equation (Classical)
2 Fi  1/c2 2Fi /t2
This is a 2nd order differential
equation, which has two time
solutions, retarded and advanced.
Conventional Approach:
Choose only the retarded solution
(a “causality” boundary condition).
Wheeler-Feynman Approach:
Use ½ retarded and ½ advanced
(time symmetry).
A Classical Wheeler-Feynman
Electromagnetic “Transaction”
• The emitter sends retarded and
advanced waves. It “offers”
to transfer energy.
A Classical Wheeler-Feynman
Electromagnetic “Transaction”
• The emitter sends retarded and
advanced waves. It “offers”
to transfer energy.
• The absorber responds with an
advanced wave that
“confirms” the transaction.
A Classical Wheeler-Feynman
Electromagnetic “Transaction”
• The emitter sends retarded and
advanced waves. It “offers”
to transfer energy.
• The absorber responds with an
advanced wave that
“confirms” the transaction.
• The loose ends cancel and
disappear, and energy is
transferred.
The Quantum
Transactional Model
Step 1: The emitter sends
out an “offer wave” Y.
The Quantum
Transactional Model
Step 1: The emitter sends
out an “offer wave” Y.
Step 2: The absorber responds
with a “confirmation wave”
Y*.
The Quantum
Transactional Model
Step 1: The emitter sends
out an “offer wave” Y.
Step 2: The absorber responds
with a “confirmation wave”
Y*.
Step 3: The process repeats
until energy and momentum
is transferred and the
transaction is completed
(wave function collapse).
The Transactional
Interpretation and
Wave-Particle Duality
• The completed transaction
projects out only that part
of the offer wave that had
been reinforced by the
confirmation wave.
• Therefore, the transaction
is, in effect, a projection
operator.
• This explains wave-particle
duality.
The Transactional
Interpretation and the
Born Probability Law
• Starting from E&M and the WheelerFeynman approach, the E-field
“echo” that the emitter receives
from the absorber is the product
of the retarded-wave E-field at
the absorber and the advancedwave E-field at the emitter.
• Translating this to quantum
mechanical terms, the “echo”
that the emitter receives from
each potential absorber is YY*,
leading to the Born Probability Law.
The Role of the Observer in
the Transactional
Interpretation
• In the Copenhagen interpretation,
observers have a special role as the
collapsers of wave functions. This leads
to problems, e.g., in quantum cosmology
where no observers are present.
• In the transactional interpretation,
transactions involving an observer are the
same as any other transactions.
• Thus, the observer-centric aspects of the
Copenhagen interpretation are avoided.
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 a new experiment (Afshar), which 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.
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.
The Afshar Experiment
• Put wires with 6% opacity at the positions of the
interference minima at s1, and
• Place detector at 2’ on plane s2 and observe the particles
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 to 2. 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 that 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
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 only interpretation of the three discussed that has
survived the Afshar test. It also appears that other
interpretations on the market (Decoherence, ConsistentHistories, etc.) 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
“Schroedinger’s Kittens” by John Gribbin (1995).
The PowerPoint version of this talk will soon be
available at:
http://faculty.washington.edu/jcramer
The
End