Mehran Shaghaghi: Quantum Mechanics Dilemmas

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

What do we comprehend? ,[object Object],[object Object],[object Object],[object Object]

What do we comprehend? ,[object Object],[object Object],[object Object]

Brain: a quantum computer? ,[object Object],[object Object],[object Object],[object Object]

Ancient insoluble problems ,[object Object],[object Object],[object Object],[object Object],[object Object],Still some people believe they are solving them

Modern insoluble questions ,[object Object],[object Object],[object Object],[object Object],[object Object],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

Examples ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object]

Examples ,[object Object],[object Object],[object Object]

Afshar Experiment Rejection ,[object Object],[object Object],[object Object],[object Object]

A simple way to reject Afshar claim ,[object Object],The experiment: We may detect an obstacle quantum mechanically without even touching it! Mach-Zehnder interferometer

A simple way to reject Afshar claim ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object]

Einstein Box ,[object Object],[object Object],[object Object],[object Object],Bohr response the next day: Using position-momentum uncertainty relation he rejected the challenge

Inaccuracies vs. Uncertainties ,[object Object],[object Object],[object Object],Illustration courtesy of Ballentine 1970

Background ,[object Object],[object Object],[object Object],“ Time in the Quantum Theory and the Uncertainty Relation for Time and Energy”

Time Operators in QM ,[object Object],Pauli (1958): make the operator which generate energy translations Inconsistent with bounded or inhomogeneous energy spectrum =>

Time Operators in QM ,[object Object],[object Object]

A time-Energy Relation ,[object Object],[object Object],[object Object],Define a metric on a generalized Bloch sphere to measure distance between two states Distance between states Maximum distance happens for orthogonal states

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 ,[object Object],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

Quantum Clocks ,[object Object],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

Quantum Clocks ,[object Object],we had Therefore for the clock energy uncertainty we get Energy uncertainty of the clock is proportional to the clock time resolution

Einstein Box revisited ,[object Object],[object Object],[object Object],[object Object]

Einstein Box revisited ,[object Object],[object Object]

Interesting QM problems ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object]

Mehran Shaghaghi: Quantum Mechanics Dilemmas

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Mehran Shaghaghi: Quantum Mechanics Dilemmas