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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
ant-
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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
stra
tion
cou
rtes
y of
Ba
llen
tine
197
0
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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!
