Preview Of Quantum Concepts in Space and Time Oxford Science Publications (original) (raw)
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Quantum Mechanics in Space and Time
The possibility that quantum mechanics is foundationally the same as classical theories in explaining phenomena in space and time is postulated. Such a view is motivated by interpreting the experimental violation of Bell inequalities as resulting from questions of geometry and algebraic representation of variables, and thereby the structure of space, rather than realism or locality. While time remains Euclidean in the proposed new structure, space is described by Projective geometry. A dual geometry facilitates description of a physically real quantum particle trajectory. Implications for the physical basis of Bohmian mechanics is briefly examined, and found that the hidden variables pilot-wave model is local. Conceptually, the consequence of this proposal is that quantum mechanics has common ground with relativity as ultimately geometrical. This permits the derivation of physically meaningful quantum Lorentz transformations. Departure from classical notions of measurability is discussed.
Quantum Mechanics on a Space and Time Foundation
The possibility of explaining quantum phenomena on a spatial-temporal foundation is developed further. Motivation for this alternative investigation has its origins in the EPR paradox. Analysis of Bell inequalities identified the assumption of metric variable-type for physical quantities, additional to that of local causality. Similar analysis is extended to EPR-steering, Hardy non-locality and the more recently introduced Cabello quantum contextuality inequalities. The same algebraic assumption is present in these later configurations. Because of the nexus between variable-type and underlying geometry, and by implication space structure, violation of EPR experiments can be attributed to space being non-metric. Analysis of Heisenberg gedanken experiments leads to the same conclusion. Quantum mechanics, including also QFT, is then foundationally explainable in terms of space, time and geometry consistent with relativity.
On the quantum space–time structure of light
Journal of Plasma Physics, 2010
We extend the quantum theory of Time Refraction for a generic spatial and temporal modulation of the optical properties of a medium, such as a dielectric or a gravitational field. The derivation of the local Bogoliubov transformations relating the global electromagnetic modes (valid over the entire span of space and time) with the local modes (valid for the vicinity of each spatial and temporal position) is presented and used in the evaluation of vacuum photon creation by the optical modulations of the medium. We use this approach to relate and review the results of different quantum effects such as the dynamical Casimir effect, space and Time Refraction, the Unruh effect and radiation from superluminal non-accelerated optical boundaries.
A New Look at Space-Time Towards a Unified Quantum Geometry
Abstract The fundamental relation between space and time is motion expressed as the ratio of space over time for motion in space and the ratio of time over space for motion in time. This indicates that space and time are co-existent reciprocal aspects of motion. While inseparable and interdependent both space and time have distinct geometric properties. There are two fundamental quantum holographic interference patterns which most closely exemplify these structural properties. These are separately identified and defined consistent with the space-time reciprocal relationship. Quantum time potentials and space time networks are defined. The first network consists of two interacting quantum time potentials forming a space-time network whereby space is an emergent feature; there being an inverse structure with inverse properties. The phenomenon of mass and force are emergent features from the various permutations of interconnections between nodes within this space-time network. The resulting structure implies the existence of a coordinate system where each node represents coordinates defined by the rays from each pole. The coordinates form an information field and indicate that space and time ARE information, The connections between the nodes are determined by pre-mathematical connection algorithms indicating the underlying mechanism of creation. Further properties of the space-time network are identified and reveal underlying mechanisms to account for elusive and anomalous physical phenomenon including non-locality, quantum entanglement and quantum gravity.
Quantum Space-times: Beyond the Continuum of Minkowski and Einstein
arXiv: General Relativity and Quantum Cosmology, 2008
In general relativity space-time ends at singularities. The big bang is considered as the Beginning and the big crunch, the End. However these conclusions are arrived at by using general relativity in regimes which lie well beyond its physical domain of validity. Examples where detailed analysis is possible show that these singularities are naturally resolved by quantum geometry effects. Quantum space-times can be vastly larger than what Einstein had us believe. These non-trivial space-time extensions enable us to answer of some long standing questions and resolve of some puzzles in fundamental physics. Thus, a century after Minkowski's revolutionary ideas on the nature of space and time, yet another paradigm shift appears to await us in the wings.
Arxiv preprint hep-th/9406204, 1994
Abstract: The paper consists of two parts. In the first part Schroedinger's equation for a charged quantum particle in a Galilei-Newton curved space-time is derived in a fully geometrical way. Gravitational and electromagnetic fields are coded into space metric and ...
Assembly Time, 2023
Abstract: The concept of Quantum Timespace offers a fresh perspective on the fundamental nature of time and space within the realm of quantum mechanics. In this article, we delve into the intriguing world of Quantum Timespace, where time and space are no longer viewed as separate entities but as intricately intertwined dimensions. Drawing inspiration from the principles of quantum mechanics, Quantum Timespace challenges traditional notions of time as a linear, continuous flow. Instead, it introduces the notion of time quanta, discrete units that carry their own unique properties and play a fundamental role in the behavior and evolution of quantum systems. One of the key features of Quantum Timespace is the principle of uncertainty, which imposes limitations on our ability to simultaneously measure the precise positions and timestamps of quantum particles. This uncertainty gives rise to the inherent fuzziness and probabilistic nature of quantum phenomena, where particles can exist in superposition states and exhibit entanglement and quantum teleportation. Within the framework of Quantum Timespace, we explore the intricate interplay between uncertain time quanta and the complex web of environmental factors that influence the assembly and transformation of quantum systems. We examine how the granularity of time impacts the behavior and evolution of particles, and we investigate the role of uncertain environmental factors in shaping quantum dynamics. Furthermore, this article discusses the potential implications and applications of Quantum Timespace in understanding the assembly and dynamics of quantum systems. It raises questions about the relationship between time, space, and the complex behavior of quantum particles, inviting further exploration and investigation. While Quantum Timespace presents a compelling and innovative perspective, it is crucial to acknowledge that it remains a theoretical construct. The practical challenges of measuring and quantifying time quanta and environmental factors at the quantum level pose significant obstacles to its full development and validation. In summary, this article provides an overview of Quantum Timespace as a conceptual framework that expands our understanding of time and space in the quantum realm. It explores the discrete nature of time quanta, the principle of uncertainty, and the interplay of uncertain factors in shaping the behavior and evolution of quantum systems. By shedding light on these intriguing concepts, Quantum Timespace opens up new avenues for exploring the fundamental nature of reality in the quantum domain.
This textbook deals with advanced topics in the field of quantum mechanics, material which is usually encountered in a second university course on quantum mechanics. The book, which comprises a total of 15 chapters, is divided into three parts: I. Many-Body Systems, II. Relativistic Wave Equations, and III. Relativistic Fields. The text is written in such a way as to attach importance to a rigorous presentation while, at the same time, requiring no prior knowledge, except in the field of basic quantum mechanics. The inclusion of all mathematical steps and full presentation of intermediate calculations ensures ease of understanding. A number of problems are included at the end of each chapter. Sections or parts thereof that can be omitted in a first reading are marked with a star, and subsidiary calculations and remarks not essential for comprehension are given in small print. It is not necessary to have read Part I in order to understand Parts II and III. References to other works in the literature are given whenever it is felt they serve a useful purpose. These are by no means complete and are simply intended to encourage further reading. A list of other textbooks is included at the end of each of the three parts.
2019
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