Cramer John[1]

8/11/2019 Cramer John[1]

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The Blind Men and the Quantum The Blind Men and the Quantum The Blind Men and the Quantum

Quantum Mechanics

John G. Cramer Dept. of Physics, Univ. of Washington

Seattle, Washington 98195, USA

John G. CramerJohn G. Cramer Dept. of Physics, Univ. of Washington

Seattle, Washington 98195, USA

NIAC Keynote Talk Atlanta, GA, March 7, 2006


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The Brookhaven National LaboratoryRelativistic Heavy Ion Collider (RHIC)The Brookhaven National Laboratory

Relativistic Heavy I on Collider ( RHIC)

RHIC BRAHMSPHOBOS

PHENIX STAR

AGS

TANDEMS

Diameter = 1 km

v = 0.99995 c = 186,000 miles/sec

Collision Energy = 200 GeV/A


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One STAR Au+Au CollisionOne STAR Au+Au CollisionRun: 1186017, Event: 32, central

colors ~ momentum: low - - - high


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A QuantumA QuantumMetaphor Metaphor

(With apologies to Indostanis with Disabilities)(With apologies to Indostanis with Disabilities)


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The Blind Men

and the Elephant by John Godfrey Saxe (1816-1887)

The Blind Men The Blind Men

and the Elephant and the Elephant

by John Godfrey Saxe (1816 by John Godfrey Saxe (1816 -- 1887) 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: Een 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 interpretational discussions

a quantum process


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Quantum TheoryQuantum Theoryand and

Interpretations Interpretations


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The Role of an InterpretationThe Role of an InterpretationAn interpretation of a formalism should:

Provide links between the mathematical

symbols of the formalism and elementsof the physical world;Neutralize the paradoxes; all of them;addressing only a few of the formalismsinterpretational problems is undesirable;Provide tools for visualization, forspeculation, and for extension.An interpretation 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 beinconsistent with the formalism and/or with experiment)!


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Example: Newtons 2 nd LawExample: Newtons 2 nd Law

Formalism :

Interpretation: The vector force Fon a body is proportional to the product

of its scalar mass m , which is positive,and the 2 nd time derivative a of its vector position.

F = m ar

What this interpretation does: It relates the formalism to physical observables.It avoids the paradoxes that would arise if m


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The Transactional The Transactional Interpretation Interpretation

of Quantum of Quantum Mechanics Mechanics


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Listening to the QuantumMechanical Formalism

Listening to the QuantumMechanical Formalism

Consider a quantum matrix element:

= v S dr 3

= a* - sandwich. What does this suggest?

Hint: The complex conjugation in is the Wigneroperator 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 to the future.An advanced wave carries negative energy to the past.


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Maxwells ElectromagneticWave Equation (Classical)

Maxwells ElectromagneticWave Equation (Classical) 2 F i = 1/ c 2 2F i /t2

This is a 2 nd order differentialequation, which has two time

solutions, retarded and advanced .

Wheeler-Feynman Approach: Use retarded and advanced(time symmetry).

Conventional Approach: Choose only the retarded solution(a causality boundary condition).


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A Wheeler-FeynmanElectromagnetic Transaction

A Wheeler-Feynman

Electromagnetic Transaction The emitter sends retarded andadvanced waves. It offers totransfer energy.


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A Wheeler-Feynman

Electromagnetic Transaction The emitter sends retarded andadvanced waves. It offers totransfer energy.The absorber responds with anadvanced wave thatconfirms the transaction.

Absorber


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A Wheeler-Feynman

Electromagnetic Transaction The emitter sends retarded andadvanced waves. It offers totransfer energy.The absorber responds with anadvanced wave thatconfirms the transaction.The loose ends cancel anddisappear, and energy istransferred.


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Offer Wave: The initial wave function is interpreted as aretarded-wave offer to form a quantum event.

Confirmation wave: The conjugate wave function * is interpreted as an advanced-waveconfirmation to proceed with the quantum event.

Transaction the Quantum Handshake:

The many * combinations present in the QM formalism are interpretedas indicating the formation of a forward/back-in-time standing wave thattransfers energy, momentum, and other conserved quantities.

No Observers:

Transactions involving observers are no different from othertransactions; Observers and their knowledge play no special roles.No Paradoxes:

Transactions are intrinsically nonlocal, and paradoxes are resolved.

Few Postulates (Economical): Heisenbergs uncertainty principle and Borns statistical interpretation can be derived from the Transactional Interpretation.

Overview of the

Transactional Interpretation

Overview of the

Transactional Interpretation


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The QuantumTransactional Model


We apply the same logic to QM:

Step 1: The emitter sendsout an offer wave .


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Step 2: The absorberresponds with a confirmationwave*.


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Step 2: The absorberresponds with a confirmationwave*.Step 3: The process repeatsuntil energy and momentum istransferred and thetransaction is completed

(wave function collapse).


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The TI and theUncertainty Principle

The TI and theUncertainty Principle

The completed transactionprojects out only that part ofthe offer wave that had beenreinforced by the confirmationwave (=> measurement).Consequently, the transactioncan project out only one of twocomplementary variables.This accounts for HeisenbergsUncertainty Principle.


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The TI and theBorn Probability Law

The TI and theBorn Probability Law

Starting from E&M and theWheeler-Feynman approach, theE-field echo that the emitterreceives from the absorber isthe product of the retarded-waveE-field at the absorber and theadvanced-wave E-field at the emitter.

Translating this to quantummechanical terms, the echo thatthe emitter receives from eachpotential absorber is i i*, leadingto the Born Probability Law.

Wave amplitudehere is *


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Role of the Observerin the TI

Role of the Observerin the TI

In the Copenhagen Interpretation,observers are given the special roleas Collapsers of Wave Functions.This leads to problems, e.g., in quantum cosmologywhere no observers are present.In the Transactional Interpretation, transactions

involving an observer are the same as any othertransactions.Thus, the observer-centric aspects of the

Copenhagen Interpretation are avoided.


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Can the TI be Tested?Can the TI be Tested?The simple answer is No!. It is the formalism of quantummechanics that makes all of the testable predictions.

As long as an interpretation like the TI is consistent withthe formalism, it will make the same predictions as any othervalid interpretation, and no experimental tests are possible.

However, an interpretations may be inconsistent with thequantum mechanical formalism and its predictions.

If this is true, then the interpretation can be falsified .The Transactional Interpretation follows the quantumformalism very closely and does not appear to have problemsin this area.


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The TI andQuantum

Paradoxes

The TI andThe TI andQuantumQuantum

Paradoxes Paradoxes

P d 1 ( l li )P d 1 ( l lit )


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Paradox 1 (non-locality):

Einsteins Bubble


Einsteins BubbleSituation: A photon is emitted

from a source having nodirectional preference.

P d 1 ( l lit )P d 1 ( l lit )


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Einsteins Bubble



from a source having nodirectional preference.Its spherical wave function

expands like an inflating bubble.

P d 1 ( l lit )P d 1 ( l lit )


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Einsteins Bubble



from a source having nodirectional preference.Its spherical wave function

expands like an inflating bubble.It reaches Detector A, and the bubble pops and disappears.

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

photons wave function at the locations ofDetectors B & C know that it should vanish?


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P d 2 ( ll )Paradox 2 ( collapse):


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Paradox 2 ( collapse):Schrdingers Cat

Paradox 2 ( collapse):

Schrdingers CatExperiment: A cat is placed in a sealed box

containing a device that has a 50% chanceof killing the cat.

Question 1: What is thewave function of the cat just before the box isopened?

When does the wave function collapse? Only after the boxis opened?

1 12 2( dead + alive ?)=

1 1

2 2( dead + alive ?)=

P r do 2 ( coll pse)Paradox 2 ( collapse):


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Schrdingers CatExperiment: A cat is placed in a sealed box

containing a device that has a 50% chanceof killing the cat.Question 1: What is the

wave function of the cat just before the box isopened?

When does the wave function collapse? Only after the boxis opened?

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

1 12 2( dead + alive ?)=

1 1

2 2( dead + alive ?)=

Paradox 2 ( collapse):Paradox 2 ( collapse):


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Schrdingers CatThe issues are: when and 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 ( collapse):Paradox 2 ( collapse):


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Schrdingers CatTI Explanation:

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

at some particular time.Therefore, asking when the wave functioncollapsed was asking the wrong question.

Paradox 3 (non-locality):Paradox 3 (non-locality):


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Paradox 3 (non locality):

EPR ExperimentsMalus and Furry

Paradox 3 (non locality):EPR ExperimentsMalus and Furry

An EPR Experiment measures thecorrelated polarizations of a pairof entangled photons, obeyingMalus Law:[P( rel ) = Cos 2 rel ]



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An EPR Experiment measures thecorrelated polarizations of a pairof entangled photons, obeyingMalus Law:[P( rel ) = Cos 2 rel ]

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


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Apparently, the measurement on the right

side of the apparatus causes (in somesense of the word cause ) the photonon the left side to be in the same quantum mechanical state, and thisdoes not happen until well after theyhave left the source.

This EPR influence across space time

works even if the measurements arekilometers (or light years) apart.Could that be used for faster than light

signaling?Sorry, NIAC, Eberhards Theorem tells us

that the answer is No!



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a ado 3 ( o oca ty):


a ado 3 ( o oca ty):EPR ExperimentsMalus and Furry

TI Explanation: An EPR experiment requires a

consistent double advanced -retarded handshake

between the emitter andthe two detectors.The lines of communication

are not spacelike butnegative and positivetimelike. While spacelikecommunication has

relativity problems, timelikecommunication does not.

Paradox 4 (wave/particle):Paradox 4 (wave/particle):


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Paradox 4 (wave/particle):

Wheelers Delayed Choice



The observer waitsuntil after the photonhas passed the slitsto decide whichmeasurement to do.

***

A source emits one photon.Its wave function passes

through slits 1 and 2, makinginterference beyond the slits.The observer can choose to either:

(a) measure the interference patternat plane 1, requiring that the photontravels through both slits .

or (b) measure at which slit image itappears in plane 2, indicating that

it has passed only through slit 2 .



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Wheelers Delayed ChoiceThus, in Wheelers accountof the process, the photon does

not 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 passthrough both slits .

Wheeler asserts that the measurement choice determineswhether the photon is a particle or a wave retroactively !


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Wheelers Delayed ChoiceTI Explanation: If the screen at s1 is up, atransaction forms between1 and the source andinvolves waves passingthrough both slits 1 and 2.If the screen at 1 is down, atransaction forms betweendetectors 1 or 2 and thesource S, and involves wavespassing through only one slit .


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Paradox 5 (interference):Paradox 5 (interference):


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The Afshar ExperimentThe Afshar Experiment

In a Delayed Choice setup, place wires with 6% opacity atthe positions of the interference minima at 1;

Place detector at 2 on plane

2 and observe the particlespassing through slit 2.Question: What fraction of the light is blocked by the gridand not transmitted to 2? (i.e., is the interference pattern still there when one is measuring particle behavior ?)

Paradox 5 (interference):h f h

Paradox 5 (interference):Th Af h E i


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No Grid & 2 Slits

No Loss

Grid & 1 Slit6% Loss

Grid & 2 Slits


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Astra Image Line Plot - Rotate - Row [531]

4/6/2004 6:05:39 AM

Pixel Number 1,3001,2001,1001,0009008007006005004003002001000

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Astra Image Line Plot - Rotate - Row [531]4/6/2004 6:09:36 AM

Pixel Number 1,3001,2001,1001,0009008007006005004003002001000

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Astra Image Line Plot - Rotate - Row [531]4/6/2004 6:17:35 AM

Pixel Number 1,3001,2001,1001,0009008007006005004003002001000

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One openWire present

Both open No Wire

Both openWire present


Paradox 5 (interference):h f h



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Conclusions:

Interference is still present, even when an unambiguousWelcher-Weg (which-way) experiment is performed.

Measuring particle-like behavior does not suppress wave-likebehavior, if careful non-interactive measurements are made.

It appears that light waves must pass both slits to create theinterference, but the photon passes through only one slit.




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TI Explanation: The initial offer waves pass throughboth slits on their way to possible absorbers. At the

wires, the offer waves cancel in first order, so thatno transactions can form and no photons can beintercepted by the wires.

Therefore, the absorption by the wires should be verysmall (


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TI Diagrams TI Diagrams The TI makes it possible to diagram for analysis complicated

situations in quantum optics and other areas. The diagrams below arefrom a TI analysis (FoP, 2005) of a Quantum-Zeno version of theElitzur and Vaidmann interaction-free Photon Bomb experiment.


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Time,Pseudo-Time,

and Causal Loops

Time,Time,Pseudo Pseudo -- Time,Time,and Causal Loops and Causal Loops

Competing TransactionsCompeting Transactions


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Competing Transactionsand Maudlins Paradox

Competing Transactionsand Maudlins ParadoxIn the pseudo-time scenario, the

competition of possible future

transactions can be viewed asgenerating the Born Probability LawP = *, because each i i* is thestrength of an echo from a possiblefuture absorber. All such echos arepresent together at the emitter,which chooses probabilisically onthe basis of echo strength which

transaction (if any) to complete.

Maudlin has used this scenario toconstruct a paradox, in which thefailure of an early transaction to formcreates conditions that set up a later competing transaction that wouldotherwise not be there. He argues that both offer waves cannot be presentat the emitter to compete.


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Hierarchical Pseudo-TimeHierarchical Pseudo-TimeMaudlins argument is not actually aparadox, but a demonstration that the

pseudo-time scenario is too nave andrequires modification.

There must be a hierarchy oftransaction formation , in which

transactions across small space-timeintervals must form or fail beforetransactions from larger intervals canenter the competition. This give thenice result of building the emergenceof the future into the pseudo-timetransaction competition scenarios.

Is the TI Deterministic?Is the TI Deterministic?


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Of course, Maudlins argument isirrelevant if the TI is deterministic.But is it?

In my view, it is not. The constraintsof a transaction do not determine thefuture, but rather place the constraintsof physical conservation laws on it.

It is rather like the transaction thatoccurs at the grocery store when youpresent your debit card to the cashier.

There is an electronic handshake transaction between the cash registerand the bank, which insures that you have enough in your account to pay for

your purchases and deducts the money, but does not determine what youdecide to purchase. (It enforces the Law of Conservation of Money.)

The emergence of the future from the present is rather like frostforming on a cold window pane. Long fingers of causal handshakes probe thefuture, but the present is not determined by them, only constrained.

Is the TI Deterministic?Is the TI Deterministic?

The TI and the Arrows of TimeThe TI and the Arrows of Time


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The TI and the Arrows of TimeThe TI and the Arrows of TimeThere are several distinct Arrows of Time in our

universe, and their hierarchy and relationship is avery interesting question.

The orthodox view (see Hawking) is that some CP-violation in the early universe lead to the matter-antimatter asymmetry and the cosmological arrow oftime, which produced the thermodynamic arrow oftime, leading separately to the dominance of EMretarded waves and to our perception that weremember the past but not the future.

The Transactional Interpretation leads to a

somewhat different scenario. The Big Bang in ourpast terminated the back-propagation of advancedwaves, leading to the electromagnetic arrow of time,the time-delay of which leads to the thermodynamicarrow of time, which produces the subjective arrowof time.


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Last Words Last Last

Words Words

ConclusionsConclusions


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ConclusionsConclusionsThe Transactional Interpretation provides a way ofunderstanding the counter-intuitive aspects ofquantum mechanics.Its advance-retarded handshake provides a way ofunderstanding the intrinsic nonlocality of quantummechanics, while preserving the constraints of specialrelativity.Among quantum interpretations, the TI is unusual inproviding a graphic way of visualizing quantumprocesses (including quantum computing).It also provides insights into the nature of time andthe emergence of the future from the present.

ReferencesReferences


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e e e cesTransactional

The Transactional Interpretation of Quantum Mechanics,Reviews of Modern Physics 58, 647 (1986). Available athttp://www.npl.washington.edu/TI or the RMP web site.

The Plane of the Present and the Transactional Paradigm ofTime, Chapter 9 of Time and the Instant , Robin Drurie, ed.,Clinamen Press, UK (2001); ArXiv reprint: quant-ph/0507089

The PowerPoint version of this talk will soon be available at:http://faculty.washington.edu/jcramer
http://www.npl.washington.edu/TIhttp://faculty.washington.edu/jcramerhttp://faculty.washington.edu/jcramerhttp://www.npl.washington.edu/TI


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