Weekly Papers on Quantum Foundations (16)

Authors: Diederik AertsMassimiliano Sassoli de Bianchi

We show that the extended Bloch representation of quantum mechanics also applies to infinite-dimensional entities, to the extent that the number of (possibly infinitely degenerate) outcomes of a measurement remains finite, which is always the case in practical situations.

Authors: Zong-Quan ZhouXiao LiuYaron KedemJin-Min CuiZong-Feng LiYi-Lin HuaChuan-Feng Li,Guang-Can Guo

A century after its conception, quantum mechanics still hold surprises that contradict many “common sense” notions. The contradiction is especially sharp in case one consider trajectories of truly quantum objects such as single photons. From a classical point of view, trajectories are well defined for particles, but not for waves. The wave-particle duality forces a breakdown of this dichotomy and quantum mechanics resolves this in a remarkable way: Trajectories can be well defined, but they are utterly different from classical trajectories. Here, we give an operational definition to the trajectory of a single photon by introducing a novel technique to mark its path using its spectral composition. The method demonstrates that the frequency degree of freedom can be used as a bona fide quantum measurement device (meter). The analysis of a number of setups, using our operational definition, leads to anomalous trajectories which are non-continuous and in some cases do not even connect the source of the photon to where it is detected. We carried out an experimental demonstration of these anomalous trajectories using a nested interferometer. We show that the Two-state vector formalism provides a simple explanation for the results.

Authors: Jean Michel SellierK.G. Kapanova

Recently a new formulation of quantum mechanics has been suggested which is based on the concept of signed particles, that is, classical objects provided with a position, a momentum and a sign simultaneously. In this paper, we comment on the plausibility of simulating atomic systems beyond the Born-Oppenheimer approximation by means of the signed particle formulation of quantum mechanics. First, in order to show the new perspective offered by this new formalism, we provide an example studying quantum tunnelling through a simple Gaussian barrier in terms of the signed particle formulation. Then, we perform a direct simulation of the hydrogen atom as a full quantum two-body system, showing that the formalism can be a very promising tool for first-principle-only quantum chemistry.

Arageorgis, Aristidis and Earman, John (2017) Bohmian Mechanics: A Panacea for What Ails Quantum Mechanics, or a Different and Problematic Theory? [Preprint]
Earman, John (2017) Quantum Bayesianism Assessed. [Preprint]
Christian, Joy (2017) Local Causality in a Friedmann-Robertson-Walker Spacetime. [Preprint]

Authors: Juan MaldacenaDouglas StanfordZhenbin Yang

We study various aspects of wormholes that are made traversable by an interaction beween the two asymptotic boundaries. We concentrate on the case of nearly-$AdS_2$ gravity and discuss a very simple mechanical picture for the gravitational dynamics. We derive a formula for the two sided correlators that includes the effect of gravitational backreaction, which limits the amount of information we can send through the wormhole. We emphasize that the process can be viewed as a teleportation protocol where the teleportee feels nothing special as he/she goes through the wormhole. We discuss some applications to the cloning paradox for old black holes. We point out that the same formula we derived for $AdS_2$ gravity is also valid for the simple SYK quantum mechanical theory, around the thermofield double state. We present a heuristic picture for this phenomenon in terms of an operator growth model. Finally, we show that a similar effect is present in a completely classical chaotic system with a large number of degrees of freedom.

Authors: Daniel J. BurgerRaúl Carballo-RubioNathan MoynihanJeff MuruganAmanda Weltman

The use of quantum field theory to understand astrophysical phenomena is not new. However, for the most part, the methods used are those that have been developed decades ago. The intervening years have seen some remarkable developments in computational quantum field theoretic tools. In particle physics, this technology has facilitated calculations that, even ten years ago would have seemed laughably difficult. It is remarkable, then, that most of these new techniques have remained firmly within the domain of high energy physics. We would like to change this. As alluded to in the title, this is the first in a series of papers aimed at showcasing the use of modern on-shell methods in the context of astrophysics and cosmology. In this first article, we use the old problem of the bending of light by a compact object as an anchor to pedagogically develop these new computational tools. Once developed, we then illustrate their power and utility with an application to the scattering of gravitational waves.

Authors: Louis Marchildon

Everett’s interpretation of quantum mechanics was proposed to avoid problems inherent in the prevailing interpretational frame. It assumes that quantum mechanics can be applied to any system and that the state vector always evolves unitarily. It then claims that whenever an observable is measured, all possible results of the measurement exist. This assertion of multiplicity has been understood in many ways by proponents of Everett’s theory. Here we shall illustrate how different views on multiplicity carry onto different views on spacetime.

Perception: Our useful inability to see reality

Nature 544, 7650 (2017). doi:10.1038/544296a

Author: Douwe Draaisma

There’s some deviant thinking behind perception, discovers Douwe Draaisma.

Author(s): Miloslav Znojil, Iveta Semorádová, František Růžička, Hafida Moulla, and Ilhem Leghrib

During recent developments in quantum theory it has been clarified that observable quantities (such as energy and position) may be represented by operators Λ (with real spectra) that are manifestly non-Hermitian in a preselected friendly Hilbert space H(F). The consistency of these models is known t…
[Phys. Rev. A 95, 042122] Published Tue Apr 18, 2017

Authors: Andrei Khrennikov

We discuss the problems of quantum theory (QT) complicating its merging with general relativity (GR). QT is treated as a general theory of micro-phenomena – a bunch of models. Quantum mechanics (QM) and quantum field theory (QFT) are the most widely known (but, e.g., Bohmian mechanics is also a part of QT). The basic problems of QM and QFT are considered in interrelation. For QM, we stress its nonrelativistic character and the presence of spooky action at a distance. For QFT, we highlight the old problem of infinities. And this is the main point of the paper: it is meaningless to try to unify QFT so heavily suffering of infinities with GR. We also highlight difficulties of the QFT-treatment of entanglement. We compare the QFT and QM based measurement theories by presenting both theoretical and experimental viewpoints. Then we discuss two basic mathematical constraints of both QM and QFT, namely, the use of real (and, hence, complex) numbers and the Hilbert state space. We briefly present non-Archimedean and non-Hilbertian approaches to QT and their consequences. Finally, we claim that, in spite of the Bell theorem, it is still possible to treat quantum phenomena on the basis of a classical-like causal theory. We present a random field model generating the QM and QFT formalisms. This emergence viewpoint can serve as the basis for unification of novel QT (may be totally different from presently powerful QM and QFT) and general relativity GR. (It may happen that the latter would also be revolutionary modified.)

Authors: Gerd Christian Krizek

In May of 1935 Einstein published with two co-authors the famous EPR-paper about entangled particles, which questioned the completeness of Quantum Mechanics by means of a gedankenexperiment. Only one month later he published a work that seems unconnected to the EPR-paper at first, the so called Einstein-Rosen-paper that presented a solution of the field equations for particles in the framework of general relativity. Both papers ask for the conception of completeness in a theory and from a modern perspective it is easy to believe that there is a connection between these topics. We question whether Einstein might have considered that a correlation between nonlocal features of Quantum Mechanics and the Einstein-Rosen bridge can be used to explain entanglement. We analyse this question by discussing the used conceptions of “completeness”, “atomistic structure of matter”, and “quantum phenomena”. We discuss the historical embedding of the two works and the context to modern research. Recent approaches are presented that formulate a EPR=ER principle and claim an equivalence of the basic principles of these two papers.

Author(s): Robin Harper, Robert J. Chapman, Christopher Ferrie, Christopher Granade, Richard Kueng, Daniel Naoumenko, Steven T. Flammia, and Alberto Peruzzo

We propose a framework for the systematic and quantitative generalization of Bell’s theorem using causal networks. We first consider the multiobjective optimization problem of matching observed data while minimizing the causal effect of nonlocal variables and prove an inequality for the optimal regi…
[Phys. Rev. A 95, 042120] Published Mon Apr 17, 2017

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