Quantum Mechanics Dilemmas Mehran Shaghaghi Department of Physics and Astronomy University of British Columbia December 11, 2007. Sharif University of Technology

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

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

What do we comprehend? Numbers Area Value comparisons Dimensions

Numbers

Area

Value comparisons

Dimensions

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

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

Brain: a quantum computer? Sir Roger Penrose Ha! = quantum collapse? Free-will or determinism? Direction of time and our memory

Sir Roger Penrose

Ha! = quantum collapse?

Free-will or determinism?

Direction of time and our memory

Ancient insoluble problems Circle squaring. Cube duplication. Angle trisection. ------------------------- Pi is irrational Still some people believe they are solving them

Circle squaring.

Cube duplication.

Angle trisection.

-------------------------

Pi is irrational

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

Complementarities in quantum physics

Observing wave-particle duality

Measuring complementary observables

Measuring the (past) wave function

Extracting all wave function’s information

Examples quant-ph/0702013v1

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 .

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 .

Examples Afshar Experiment Stating the set-up Claims

Afshar Experiment

Stating the set-up

Claims

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)

“ 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)

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

Quantum mechanical Interaction free measurement (Elitzur-Vaidman 1993)

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

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

Einstein Box Bohr-Einstein Debate Einstein gedanken experiment to falsify Bohr time-energy uncertainty relation: Bohr response the next day: Using position-momentum uncertainty relation he rejected the challenge

Bohr-Einstein Debate

Einstein gedanken experiment

to falsify Bohr time-energy

uncertainty relation:

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. Illustration courtesy of Ballentine 1970

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.

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”

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 Operators in QM Time operators change linearly with time: Pauli (1958): make the operator which generate energy translations Inconsistent with bounded or inhomogeneous energy spectrum =>

Time operators change linearly with time:

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 :

Therefore generally we can not have time operators in QM.

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

A time-Energy Relation Time of orthogonality: The time that takes for a quantum state to evolve into an orthogonal state Anandan-Aharanov(1990) derivation: Define a metric on a generalized Bloch sphere to measure distance between two states Distance between states Maximum distance happens for orthogonal states

Time of orthogonality:

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

Anandan-Aharanov(1990) derivation:

Time-Energy Relations we can write the evolution of the state at any time as parameterize the evolution of the system No evolution, original state orthogonal state => Using the Schrödinger equation => Demand the change of the state be only due to the time coordinate change At orthogonality and therefore Therefore in general we have

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: 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

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

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 time of orthogonality of its pointer states

Clock resolution

Quantum Clocks Clock energy uncertainty we had Therefore for the clock energy uncertainty we get Energy uncertainty of the clock is proportional to the clock time resolution

Clock energy uncertainty

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

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

Einstein Box revisited We have the relation between the photon’s energy uncertainty and its launch time. Einstein challenge is refused.

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

Einstein challenge is refused.

Interesting QM problems Proving Born rule Analysis of collapse EPR interpretation Counterfactual reasoning Decoherence scale … .

Proving Born rule

Analysis of collapse

EPR interpretation

Counterfactual reasoning

Decoherence scale

… .

Thank you!