what’s the matter?: quantum physics for ordinary people john g. cramer, professor emeritus...

What’s the Matter?:What’s the Matter?:Quantum Physics for Ordinary Quantum Physics for Ordinary

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What’s the Matter?:What’s the Matter?:Quantum Physics for Ordinary Quantum Physics for Ordinary

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John G. Cramer, John G. Cramer, Professor EmeritusProfessor EmeritusDepartment of Physics

University of WashingtonSeattle, Washington, 98195

Talk given at The Grange, Whallonsburg, NY, April 20, 2011

Absorber

Light: Particle or Wave?Light: Particle or Wave? Albert Einstein explained the photoelectric effect by showing that light energy is quantized. Light, even while exhibiting wave-like interference, comesin 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 photontravels 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.

Werner Heisenberg, after his Munich PhD, workedfruitlessly in Niels Bohr’s Copenhagen group for twoyears, attempting to make sense of atomic line spectraand produce an improved version of Bohr’s atom modelthat would explain and predict them. In 1924 he movedto Gottingen to work with Max Born on the same problems.

The warm, verdant Spring of 1924 was cruel forHeisenberg, who had severe problems with allergies andhay fever. In desperation, he retreated to Helgoland, abarren, 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.

Heisenberg’s Matrix Heisenberg’s Matrix MechanicsMechanics

Werner Heisenberg(1901 – 1976)

In September, 1925, Erwin Schrödinger obtaineda copy of Louis de Broglie’s 1924 PhD thesis, whichtreated particles as waves. He gave a Zurich colloquiumdescribing de Broglie’s ideas. After this colloquium, hiscolleague Peter Debye remarked that de Broglie’s wayof discussing waves was rather naïve, and that suchmatter waves should have a wave equation.

Schrödinger took Debye’s remark seriously. InNovember, 1925, he went on a ski holiday with a younglady (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.

Schrödinger’s Wave Schrödinger’s Wave MechanicsMechanics

Erwin Schrödinger(1887 – 1961)

1. Start with a wave equation, e.g., the electromagnetic wave equation (used here) or the Schrödinger equation, that describes the system dynamics.

2. Solve the wave equation for wave functions, using complex algebra.

3. Define “operators” that operate on the wave function to extract observable quantities like energy, momentum, etc.

4. Combine the operators, wave functions, and their complex conjugates in integrals that predict experimental observations.

A Wave Mechanics A Wave Mechanics PrimerPrimer

2 2

0 02 2

d d

dx dt

( , ) cos sini kx tx t Ae A kx t i kx t

energy operator; =2 2

ih hE

t

H H

2( ) *P x 2

* 1dx dx

*E dx

H

Quantum Sandwich

Questions Raised by Questions Raised by Quantum MechanicsQuantum 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 InterpretationsThree QM InterpretationsThree QM InterpretationsThree QM Interpretations

CopenhagenMany

Worlds

Transactional

Uses “observer knowledge” to explainwave 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 non-locality. Useful in quantum computing.

Uses “advanced-retarded handshake” to explainwave function collapse and non-locality. Providesa way of “visualizing” quantum events.

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 as probability: P = *;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 with knowledge of an observer; 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!

The Copenhagen The Copenhagen InterpretationInterpretation

The Copenhagen The Copenhagen InterpretationInterpretation Quantum

MechanicsNiels Bohr(1885-1962)

Werner Heisenberg(1901 – 1976)

Retain Heisenberg’s uncertainty principle andBorn’s statistical interpretation from the Copenhagen Interpretation.

No Collapse.The wave function 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.

Many-Worlds Many-Worlds InterpretationInterpretationMany-Worlds Many-Worlds InterpretationInterpretation Quantum

MechanicsJohn A. Wheeler(1911-2008)

Hugh Everett III(1930-1982)

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 is interpreted as a retarded-wave offer to form a quantum event.

Confirmation wave:The response wave function (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 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 Transactional The Transactional InterpretationInterpretation

The Transactional The Transactional InterpretationInterpretation

John G. Cramer(1934- )

The TI “Listens” to the The TI “Listens” to the Quantum FormalismQuantum Formalism

The TI “Listens” to the The TI “Listens” to the Quantum FormalismQuantum Formalism

Consider a quantum matrix element:

<S> = vSdr3 = <f | S | i>

… a *- “sandwich”. What does this suggest?Hint: The complex conjugation in is the Wigner operator for time reversal. If is a retarded wave, then is an advanced wave.

If ei(kr t) then ei(-kr t)

(retarded) (advanced)

A retarded wave carries positive energy into the future.An advanced wave carries negative energy into the past.

The QuantumThe QuantumTransaction ModelTransaction Model


Step 1: The emitter sendsout an “offer wave” .




Step 2: The absorber responds with a “confirmation wave” *.




Step 2: The absorber responds with a “confirmation wave” *.

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).

QuantumQuantumParadoxes &Paradoxes &

The The Transactional Transactional InterpretationInterpretation

Paradox 1 (non-locality):Paradox 1 (non-locality):Einstein’s BubbleEinstein’s Bubble


Situation: A photon is emitted from a source having no directional preference.



Situation: A photon is emitted from a source having no directional preference.Its spherical wave function expands like an inflating bubble.



Question: (originally asked by Albert Einstein)If a photon is detected at Detector A, how does the

photon’s wave function at the locations of Detectors B & C “know” that it should vanish?

Situation: A photon is emitted from a source having no directional preference.Its spherical wave function expands like an inflating bubble.It reaches Detector A, and the bubble “pops” and disappears.

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.



Transactional Explanation:

A transaction developsbetween the source anddetector 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.



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?

Paradox 2 (Paradox 2 ( collapse): collapse):Schrödinger’s CatSchrödinger’s Cat


1 1

2 2( dead + alive ?)1 1

2 2( dead + alive ?)

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?



Question 2: If we observe Schrödinger, what is his wavefunction during the experiment? When does it collapse?

1 1

2 2( dead + alive ?)1 1

2 2( dead + alive ?)



The issues are: whenand how does the wavefunction collapse.

What event collapses it?(Observation by anintelligent observer?)

How does the informationthat it has collapsed spreadto remote locations, so that the laws of physics can beenforced there?

Paradox 2 (Paradox 2 ( collapse): collapse):Schrödinger’s Cat Schrödinger’s Cat

Paradox 2 (Paradox 2 ( collapse): collapse):Schrödinger’s Cat Schrödinger’s Cat


A transaction eitherdevelops between thesource and the detector,or else it does not. Ifit does, the transactionforms atemporally, notat some particular time.

Therefore, asking whenthe wave functioncollapsed was asking the wrong question.

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 theresults of measurement M1, and vice versa. This is usually a consequenceof 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

M2

EntangledPhotonSource

Entangledphoton 1

Entangled photon 2

NonlocalConnection

Measurement 1

Measurement 2

Paradox 3 (non-locality):Paradox 3 (non-locality):EPR ExperimentsEPR Experiments




An EPR Experiment measures the correlated polarizations of a pairof entangled photons, obeyingMalus’ Law: [P(rel) = Cos2rel]




The measurement gives the same result as if both filters were in the same arm.




The measurement gives the same resultas 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.



Apparently, the measurement on the right side of the apparatus causes (in some sense of the word cause) the photonon the left side to be in the same quantum mechanical state, and thisdoes 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.

X X



Transactional Explanation:An EPR experiment requires a

consistent double advanced-retarded handshakebetween the emitter andthe two detectors.

The “lines of communication”are not spacelike butnegative and positivetimelike. While spacelikecommunication hasrelativity problems, timelike communication does not.

Paradox 4 (wave/particle):Paradox 4 (wave/particle):Wheeler’s Delayed ChoiceWheeler’s Delayed ChoiceParadox 4 (wave/particle):Paradox 4 (wave/particle):Wheeler’s Delayed ChoiceWheeler’s Delayed Choice

The observer waits until after the photon has passed the slits to decide which measurement to do.

***

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 requiring that the photon travels through both slits.

or(b) measure at which slit image it appears in plane indicating thatit has passed only through slit 2.


Thus, in Wheeler’s accountof the process, the photon doesnot “decide” if it is a particleor a wave until after it passesthe slits, even though a particlemust 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!



If the screen at 1 is up, atransaction forms between1 and the source S throughboth slits.



If the screen at 1 is down,a transaction forms between one of the detectors (1’ or 2’) and the source S through only one slit.





If the screen at 1 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.

TestingTestingInterpretationInterpretation

ss

Can InterpretationsCan Interpretationsof QM be Tested?of QM be Tested?

Can InterpretationsCan Interpretationsof QM be Tested?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 Reminder: Wheeler’s DelayedDelayed

Choice ExperimentChoice Experiment

Reminder: Wheeler’s Reminder: Wheeler’s DelayedDelayed

Choice ExperimentChoice Experiment

One can choose to either:• Measure at 1 the interference pattern, giving the

wavelength and momentum of the photon, or• Measure at 2 which slit the particle passed

through, giving its position.

Wheeler’s DelayedWheeler’s DelayedChoice ExperimentChoice ExperimentWheeler’s DelayedWheeler’s DelayedChoice ExperimentChoice Experiment

Thus, one observes either:Wave-like behavior with the

interference patternor

Particle-like behavior in determiningwhich slit the photon passed through.

(but not both).

The Afshar ExperimentThe Afshar ExperimentThe Afshar ExperimentThe Afshar Experiment

Put wires with 6% opacity at the positions of the interference minima at 1, and

Place a detector at 2’ on plane 2 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?)


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.


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.


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 Afshar Experiment ResultsResults

Afshar Experiment Afshar Experiment ResultsResults

Grid + 1 Slit

6% Loss

Grid + 2 Slits

<0.1% Loss

No Grid

No Loss

By uncovering 1, the light reaching 2’ increases, even though no photons from 1 reach 2’!

Afshar Test ResultsAfshar Test ResultsAfshar Test ResultsAfshar Test Results

Copenhagen ManyWorlds

Transactional

Predicts no interference. Predicts no interference.

Predicts interference, as does the QM formalism.

Afshar Test ResultsAfshar Test ResultsAfshar Test ResultsAfshar Test ResultsTransactional

Thus, it appears that the Transactional Interpretationis the one interpretation of the three discussed that hassurvived the Afshar test. It also appears that otherinterpretations on the market (Decoherence, Consistent-Histories, etc.) should fail the Afshar Test. However, quantum interpretational theorists are fairlyslippery characters. It remains to be seen if they willfind some way to save their pet interpretations.

ReferencesReferencesReferencesReferencesTransactional

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

http://www.npl.washington.edu/TI

http://faculty.washington.edu/jcramer

TheTheEndEnd

what’s the matter?: quantum physics for ordinary people john g. cramer, professor emeritus...

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