1. What’s the Matter?: Quantum Physics for Ordinary People
Absorber
Talk given at The Grange, Whallonsburg, NY, April 20, 2011

2. 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.

3. 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 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.
Werner Heisenberg
(1901 – 1976)

4. 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 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.
Erwin Schrödinger
(1887 – 1961)

5. A Wave Mechanics Primer
Start with a wave equation, e.g., the electromagnetic wave equation (used here) 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.
Quantum Sandwich

6. 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?

7. 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 non-locality. Useful in quantum computing.
Transactional
Uses “advanced-retarded handshake” to explain wave function collapse and non-locality. Provides a way of “visualizing” quantum events.

8. The Copenhagen Interpretation
Niels Bohr
( )
Quantum Mechanics
Werner Heisenberg
(1901 – 1976)
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!

9. Many-Worlds Interpretation
Hugh Everett III
( )
Many-Worlds Interpretation
John A. Wheeler
( )
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.

10. The Transactional Interpretation
John G. Cramer
( )
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.

11. The TI “Listens” to the Quantum Formalism
Consider a quantum matrix element:
<S> = òv 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)
A retarded wave carries positive energy into the future.
An advanced wave carries negative energy into the past.

12. The Quantum Transaction Model
Step 1: The emitter sends out an “offer wave” Y.

13. The Quantum Transaction Model
Step 1: The emitter sends out an “offer wave” Y.
Step 2: The absorber responds with a “confirmation wave” Y*.

14. 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).

15. Quantum Paradoxes & The Transactional Interpretation

16. Paradox 1 (non-locality): Einstein’s Bubble
Situation: A photon is emitted
from a source having no directional preference.

17. 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.

18. 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?

19. 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.

20. 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.

21. 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?
When does the wave function collapse? Only after the box is opened?

22. 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?
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?

23. 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?

24. 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.

25. Paradox 3 (non-locality): EPR Experiments
Entangled
Photon
Source
photon 1
photon 2
Nonlocal
Connection
Measurement 1
Measurement 2
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.”

26. 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]

27. 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.

28. 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.

29. 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.

30. Paradox 3 (non-locality): EPR Experiments
Transactional Explanation:
An EPR experiment requires a consistent double advanced- retarded 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

31. 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.
or (b) measure at which slit image it appears in plane s2, indicating that it has passed only through slit 2. * * *
The observer waits until after the photon has passed the slits to decide which measurement to do.

32. 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!

33. 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.

34. 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.

35. 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.

36. Testing Interpretations

37. 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.

38. 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.

39. 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).

40. 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?)

41. 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.

42. 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.

43. 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%).

44. 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’!

45. Afshar Test Results Predicts no interference.
Copenhagen
Many
Worlds
Predicts no interference.
Predicts no interference.
Transactional
Predicts interference, as does the QM formalism.

46. 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, Consistent- Histories, 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.

47. References
Transactional
The Transactional Interpretation of Quantum Mechanics:
Schrodinger’s Kittens by John Gribbin (1995).
A .ppt file for the PowerPoint version of this talk will soon be available at:

48. The End