Weekly Papers on Quantum Foundations (24)

Authors: M. Giammarchi

This paper descrives the first experimental evidence of antimatter-wave interference, a process at the heart of Quantum Physics and its interpretation. For the case of ordinary matter particles, interference phenomena have been observed in a variety of cases, ranging to electrons up to complex molecules. Here I present the first demonstration of single-positrons quantum interference.

Authors: Tejinder P. Singh

In the first paper of this series, we have introduced the concept of an atom of space-time-matter [STM], which is described by the spectral action of non-commutative geometry, corresponding to a classical theory of gravity. In the present work, we use the Connes time parameter along with the spectral action, to incorporate gravity into trace dynamics. We then derive the spectral equation of motion for the STM atom, which turns out to be the Dirac equation on a non-commutative space.

Authors: Pasquale Bosso

The fundamental physical description of Nature is based on two mutually incompatible theories: Quantum Mechanics and General Relativity. Their unification in a theory of Quantum Gravity (QG) remains one of the main challenges of theoretical physics. Quantum Gravity Phenomenology (QGP) studies QG effects in low-energy systems. The basis of one such phenomenological model is the Generalized Uncertainty Principle (GUP), which is a modified Heisenberg uncertainty relation and predicts a deformed canon ical commutator. In this thesis, we compute Planck-scale corrections to angular momentum eigenvalues, the hydrogen atom spectrum, the Stern-Gerlach experiment, and the Clebsch-Gordan coefficients. We then rigorously analyze the GUP-perturbed harmonic oscillator and study new coherent and squeezed states. Furthermore, we introduce a scheme for increasing the sensitivity of optomechanical experiments for testing QG effects. Finally, we suggest future projects that may potentially test QG effects in the laboratory.

Authors: Tejinder P. Singh

In the first paper of this series, we have introduced the concept of an atom of space-time-matter [STM], which is described by the spectral action of non-commutative geometry, corresponding to a classical theory of gravity. In the present work, we use the Connes time parameter along with the spectral action, to incorporate gravity into trace dynamics. We then derive the spectral equation of motion for the STM atom, which turns out to be the Dirac equation on a non-commutative space.

Authors: Chia-Yi JuAdam MiranowiczGuang-Yin ChenFranco Nori

Recently, apparent non-physical implications of non-Hermitian quantum mechanics (NHQM) have been discussed in the literature. In particular, the apparent violation of the non-signaling theorem, discrimination of non-orthogonal states, and the increase of quantum entanglement by local operations were reported and, therefore, NHQM was not considered as a fundamental theory. Here we show that these and other no-go principles (including the no-cloning and no-deleting theorems) of conventional quantum mechanics are indeed satisfied in any NHQM if its formalism is properly applied. We have developed a modified formulation of NHQM based on the geometry of Hilbert spaces which is consistent with the conventional quantum mechanics for Hermitian systems. Using this formulation the validity of these principles can be shown in a simple and uniform approach.

Read, James and Menon, Tushar (2019) The limitations of inertial frame spacetime functionalism. [Preprint]
Swanson, Noel (2018) Deciphering the Algebraic CPT Theorem. [Preprint]
Canturk, Bilal (2019) A conceptual frame for giving physical content to the uncertainty principle and the quantum state. [Preprint]
Kastner, Ruth (2019) The “Delayed Choice Quantum Eraser” Neither Erases Nor Delays. Foundations of Physics.
Abstract

This article suggests a fresh look at gauge symmetries, with the aim of drawing a clear line between the a prioritheoretical considerations involved, and some methodological and empirical non-deductive aspects that are often overlooked. The gauge argument is primarily based on a general symmetry principle expressing the idea that a change of mathematical representation should not change the form of the dynamical law. In addition, the ampliative part of the argument is based on the introduction of new degrees of freedom into the theory according to a methodological principle that is formulated here in terms of correspondence between passive and active transformations. To demonstrate how the two kinds of considerations work together in a concrete context, I begin by considering spatial symmetries in mechanics. I suggest understanding Mach’s principle as a similar combination of theoretical, methodological and empirical considerations, and demonstrate the claim with a simple toy model. I then examine gauge symmetries as a manifestation of the two principles in a quantum context. I further show that in all of these cases the relational nature of physically significant quantities can explain the relevance of the symmetry principle and the way the methodology is applied. In the quantum context, the relevant relational variables are quantum phases.

While quantum field theory could more aptly be called the ‘quantum field framework’—as it encompasses a vast variety of varying concepts and theories—in comparison, relativity, both special and general, is more commonly portrayed as less of a ‘general framework’. Viewed from this perspective, the paradigm of analogue space-times (also often called analogue gravity) is to promote the specific theory of general relativity (Einstein gravity) to a framework which covers relativistic phenomena at large. Ultimately, this then also gives rise to new proposals for experiments in the laboratory, as it allows one to move general features of the ‘relativistic framework’ from general relativity to entirely new new areas of physics. This allows one to experimentally look into analogies of currently unobservable phenomena of general relativity proper. The only requirement for this to work is the presence of a notion of an upper limit for propagation speeds in this new setting. Systems …
Castellani, Elena and De Haro, Sebastian (2018) Duality, Fundamentality, and Emergence. [Preprint]

Author(s): H. Chau Nguyen, Huy-Viet Nguyen, and Otfried Gühne

Correlations between distant particles are central to many puzzles and paradoxes of quantum mechanics and, at the same time, underpin various applications such as quantum cryptography and metrology. Originally in 1935, Einstein, Podolsky, and Rosen (EPR) used these correlations to argue against the …

[Phys. Rev. Lett. 122, 240401] Published Mon Jun 17, 2019

Deng, Natalja (2018) What is temporal ontology? Philosophical Studies, 175 (3). pp. 793-807. ISSN 0031-8116

EPR-Bell-Schrödinger proof of nonlocality using position and momentum

Based on his extension of the classical argument of Einstein, Podolsky and Rosen, Schrödinger observed that, in certain quantum states associated with pairs of particles that can be far away from one another, the result of the measurement of an observable associated with one particle is perfectly correlated with the result of the measurement of another observable associated with the other particle. Combining this with the assumption of locality and some “no hidden variables” theorems, we showed in a previous paper [11] that this yields a contradiction. This means that the assumption of locality is false, and thus provides us with another demonstration of quantum nonlocality that does not involve Bell’s (or any other) inequalities. In [11] we introduced only “spin-like” observables acting on finite dimensional Hilbert spaces. Here we will give a similar argument using the variables originally used by Einstein, Podolsky and Rosen, namely position and momentum.

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