Mehran Shaghaghi: Quantum Mechanics Dilemmas

Quantum Mechanics Dilemmas

Mehran ShaghaghiDepartment of Physics and Astronomy

University of British Columbia

December 11, 2007. Sharif University of Technology

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Abstract

What to do and what not to do in quantum mechanics theory…

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What do we comprehend?

• Numbers

• Area

• Value comparisons• Dimensions

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What do we comprehend?

Simply saying, our surrounding world

We have developed in a classical environment and so comprehend its logic

We try to learn how to understand quantum world, however can not comprehend it

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Brain: a quantum computer?

• Sir Roger Penrose

• Ha! = quantum collapse?• Free-will or determinism?

• Direction of time and our memory

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Ancient insoluble problems• Circle squaring.

• Cube duplication.

• Angle trisection. -------------------------

• Pi is irrational

Still some people believe they are solving them

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Modern insoluble questions

• Complementarities in quantum physics

• Observing wave-particle duality

• Measuring complementary observables• Measuring the (past) wave function

• Extracting all wave function’s information

Lots of papers every year on these subjects

Even people get degrees by publishing papers on solving/observing these impossible questions

Still some people believe they are solving them

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Examplesqu

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Examples

• Afshar Experiment• Afshar SS, Flores E, McDonald KF, Knoesel E. (2007). "Paradox in wave-particle duality". Foundations of Physics

37 (2): 295-305. • Afshar SS (2003). "Sharp complementary wave and particle behaviours in the same welcher weg experiment".

IRIMS:quant-ph/030503: 1-33. • Afshar SS (2005). "Violation of the principle of complementarity, and its implications". Proceedings of SPIE 5866:

229-244. • Afshar SS (2006). "Violation of Bohr's complementarity: one slit or both?". AIP Conference Proceedings 810: 294-

299. • Afshar SS (2004). "Waving Copenhagen Good-bye: Were the founders of Quantum Mechanics wrong?". Harvard

seminar announcement. • Marcus Chown (2004). "Quantum rebel". New Scientist 183 (2457): 30-35. • Afshar's Quantum Bomshell • Cramer JG (2004). "Bohr is still wrong". New Scientist 183 (2461): 26. • Afshar SS (2005). "Experimental Evidence for Violation of Bohr's Principle of Complementarity". APS Meeting,

March 21–25, Los Angeles, CA. • Cramer JG (2005). "A farewell to Copenhagen?". Analog Science Fiction and Fact. • Kastner R (2005). "Why the Afshar experiment does not refute complementarity?". Studies in History and

Philosophy of Modern Physics 36: 649–658. • Kastner R (2006). "The Afshar Experiment and Complementarity". APS Meeting, March 13–17, Baltimore, MD. • Unruh W (2004). "Shahriar Afshar - Quantum Rebel?". • Motl L (2004). "Violation of complementarity?". • Drezet A (2005). "Complementarity and Afshar's experiment". ArXiv:quant-ph/0508091. • Steuernagel O (2005). "Afshar's experiment does not show a violation of complementarity". ArXiv:quant-

ph/0512123.

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Examples

• Afshar Experiment

Stating the set-up

Claims

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Afshar Experiment Rejection

• “Quantum Rebel” (cover story in the July 24, 2004 edition of New Scientist)

• “Shahriar Afshar--Quantum Rebel?” (Unruh answer-August 7, 2004)• Afshar Blog: http://users.rowan.edu/~afshar/FAQ.htm (People have changed my experiment and

responded)

• Wikipedia entry: http://en.wikipedia.org/wiki/Afshar_experiment (he constantly edit this pages and rejects objections on the experiment)

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A simple way to reject Afshar claim

Quantum mechanical Interaction free measurement (Elitzur-Vaidman 1993)

The experiment:

We may detect an obstacle quantum mechanically without even touching it!

Mach-Zehnder interferometer

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A simple way to reject Afshar claim

Quantum mechanically inserting an object in a seemingly non-related place can affect the judgments.

The wire grid in the Afshar

experiment forbids us from

making which-way

information.

Optics principles tell us that the grid cause dispersion of the photons

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Einstein Box

• Bohr-Einstein Debate Einstein gedanken experiment

to falsify Bohr time-energy

uncertainty relation:

2

tE

Bohr response the next day: Using position-momentum uncertainty relation he rejected the challenge

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Inaccuracies vs. Uncertainties

• Inaccuracy: deficiency in providing an accurate single result in measurements, property of the measuring device

• Uncertainty: Normal width of results of measurements on a similarly prepared ensembles property of the system

=>It is meaningless to speak about uncertainties on a single performed experiment.

Illu

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Background

• Aharanov-Bohm 1961:

“it is not consistent with the general principles of the quantum theory, which require that all uncertainty relations be expressible in terms of the mathematical formalism, i.e., by means of operators, wave functions, etc .”

“the examples of measurement processes that were used to derive

the above uncertainty relation are not general enough.”

“Time in the Quantum Theory and the Uncertainty Relation for Time and Energy”

2

tE

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Time Operators in QM

• Time operators change linearly with time: iTH ,

Pauli (1958): make the operator which generate energy translations

iTe

EeEEHe iTiT

Inconsistent with bounded or inhomogeneous energy spectrum

1dt

dT=>

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Time Operators in QM

• Therefore generally we can not have time operators in QM.

=> We can not derive time-energy uncertainty relation using generalized Robertson-Schrödinger uncertainty relation:

BABA ,2

1

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A time-Energy Relation

• Time of orthogonality:

The time that takes for a quantum state to evolve into an orthogonal state

0)0(|)( t

t

• Anandan-Aharanov(1990) derivation:

Define a metric on a generalized Bloch sphere to measure distance between two states 22 1

dZdZgds

0),( s

1),( sDistance between states Maximum distance happens for

orthogonal states

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Time-Energy Relations

we can write the evolution of the state at any time as

)sin()cos()( ttt

parameterize the evolution of the system No evolution, original state

orthogonal state

0

2

22 1 ddZdZgds

dd

d2

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2

22

22

2111 dd

dds

=>

Using the Schrödinger equation )(1)(|)( 3222dtOdtEdttt

2222 )()(1 dtEdtttds => dEdt

Demand the change of the state be only due to the time coordinate change

At orthogonality and therefore2

2

Et

Et

1

2

Therefore in general we have

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Quantum Clocks

• No time operator in QM, therefore we need to read some other observables –clock pointers- to infer the time.

Clock Observable (pointer) should change linearly with time:

d

diHiH

dt

d ,1

Examples of pointer states:

Quantum Clock: a quantum system that passes through a sequence of distinguishable pointer states at equal time intervals

position of a free particle => linear clocks angle of a clock hand => periodic clocks

dd

iH

dx

diH

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Quantum Clocks

• Clock resolution

Clock pointer states change linearly by time t to the next adjacent pointer state.

At best a clock can be used to distinguish time intervals as short as the time that the clock state change.

Recall: Time of orthogonality: The time that takes for a quantum state to evolve into an orthogonal state

=>=> the clock time resolution [accuracy] is (at best) equal to the the clock time resolution [accuracy] is (at best) equal to the time of orthogonality of its pointer statestime of orthogonality of its pointer states

tt relolution

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Quantum Clocks

• Clock energy uncertainty

tE2

we had

ttrelolution

Therefore for the clock energy uncertainty we get

Et res

2

Energy uncertainty of the clock is proportional to the clock time resolution

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Einstein Box revisited

• A clock controls the shutter

• Shutter opening time t can be at best the accuracy of the clock

• Energy of the clock is uncertain by an amount

• Weighing the box can not be done better than

tE

1

2

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Einstein Box revisited

• We have the relation between the photon’s energy uncertainty and its launch time.

• Einstein challenge is refused.

2.

Et

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Interesting QM problems

• Proving Born rule

• Analysis of collapse

• EPR interpretation• Counterfactual reasoning

• Decoherence scale

• ….

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Thank you!