I mean, I started a podcast about it. I might even finish it someday. This book explores the meaning of quantum mechanics through paradoxical thought experiments. The first eight chapters motivate mainly how quantum mechanics works using paradoxes. I am very enamored of the format.

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Instability of Flatspace and the Early Quantum Fluctuations by Considering an Unbounded Hamiltonian Introducing a new field which makes the Hamiltonian unbounded, we show that vacuum fluctuations of a scalar field destabilized the flatspace. Perturbation in this new scalar field, may also explain some astrophysical phenomena in the galactic scale.

This formula also leads to a strong uncertainty relation for unitary operators which displays a new preparation uncertainty relation for quantum systems. Furthermore, the two system observables that are weakly and strongly measured in a weak measurement context are shown to obey a complementarity relation under the interchange of these observables, in the form of an upper bound on the product of the corresponding weak values.

Moreover, we derive general tradeoff relations, between weak purity, quantum purity and quantum incompatibility using the weak value formalism. Our results may open up new ways of thinking about uncertainty and complementarity relations using products of weak values. Quantized Vector Potential and the Magnetic Aharonov-Bohm Effect The state vector describing the physical situation of the magnetic A-B effect should depend upon all three quantizeable entities in the problem, the electron orbiting the solenoid, the moving charged particles in the solenoid and the vector potential.

One may imagine three approximate solutions to the exact dynamics, where two of the three entities do not interact at all, and the third, quantized, entity interacts with a classical approximation. I shall first show why these two results have to be the same. Then, I shall show that, if the interaction is between the quantized vector potential and the classical approximation to the electron and solenoid currents, the state vector acquires the A-B phase shift.

Lastly, I shall show how to reconcile these three mathematically and conceptually different calculations. However, our understanding of quantum tunneling dynamics is far from complete, and there are still a number of theoretical and experimental challenges. The dynamics of the quantum tunneling process can be investigated if we can create a large tunneling region.

We have achieved this using a linear Paul trap and a quantum tunneling rotor, which has resulted in the successful observation of the Aharonov—Bohm effect in tunneling particles. Also, this result shows that the spatially separated phonon can be interfered. Aephraim Steinberg, University of Toronto How to count one photon and get a n average result of I will present our recent experimental work using electromagnetically induced transparency in laser-cooled atoms to measure the nonlinear phase shift created by a single post-selected photon, and its enhancement through "weak-value amplification.

I will say a few words about possible practical applications of this "weak value amplification" scheme, and their limitations. Time permitting, I will also describe other future and past work using "weak measurement," such as our studies quantifying the disturbance due to a measurement and what happens when it destroys interference; and our project to measure "where a particle has been" as it tunnels through a classically forbidden region — our prediction being that it will make it from one side of the barrier to the other without spending any significant time in the middle.

The atoms interact with an optical cavity and their state is postselected in a noninvasive way by measuring the optical field after the interaction. We show that the resulting quantum operation can be exploited to implement an entanglement purification protocol, where a fidelity larger than one half with respect to any Bell state is not a necessary condition.

Spekkens presented a generalization of noncontextuality that applies to imperfect measurements POVMs by allowing the underlying ontological model to be indeterministic. Unlike traditional Bell-Kochen-Specker noncontextuality, ontological models of a single qubit were shown to be contextual under this definition.

Recently, M. Pusey showed that, under certain conditions, exhibiting an anomalous weak value implies contextuality. We will present a single qubit prepare and measure QKD protocol that uses observation of anomalous weak values of particular observables to estimate the quantum channel error rate and certify the security of the channel.

Nevertheless, we argue that the physical meaning of the weak value is much more close to the physical meaning of an eigenvalue than to the physical meaning of an expectation value. Theoretical analysis and experimental results performed in the MPQ laboratory of Harald Weinfurter are presented. Quantum systems described by numerically equal eigenvalue, weak value and expectation value cause identical average shift of an external system interacting with them during an infinitesimal time.

However, there are differences between the final states of the external system. In the case of an eigenvalue, the shift is the only change in the wavefunction of the external system. In case of the expectation value, there is an additional change in the quantum state of the same order, while in the case of the weak value the additional distortion is negligible.

The understanding of weak value as a property of a single system refutes recent claims that there exist classical statistical analogue to the weak value.

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## Quantum Paradoxes

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## Quantum Paradoxes: Quantum Theory for the Perplexed

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