Preview Of Quantum Concepts in Space and Time Oxford Science Publications (original) (raw)
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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Space-time, relativity and quantum mechanics: In search of a deeper connection
It has been shown that the Lorentz transformations in special relativity can be derived in terms of the principle of relativity and certain properties of space and time such as homogeneity. In this paper, we argue that the free Schrodinger equation in quantum mechanics may also be regarded as a consequence of the homogeneity of space and time and the principle of relativity when assuming linearity of time evolution.
Quantum spacetime: what do we know
I discuss nature and origin of the problem of quantum gravity. I examine the knowledge that may guide us in addressing this problem, and the reliability of such knowledge. In particular, I discuss the subtle modification of the notions of space and time engendered by general relativity, and how these might merge into quantum theory. I also present some reflections on methodological questions, and on some general issues in philosophy of science which are are raised by, or a relevant for, the research on quantum gravity.
International Journal of Cosmology, Astronomy and Astrophysics, 2019
The paper provides the analysis of a number of well-known works on the substantiation of the shape and parameters of quanta of the space of the Universe, within which the dimensions of quanta are related to the wave parameters of the gravitational field. It is shown that this level of the material world is preceded by the levels of elementary particles, atoms and molecules, which are characterized by a dual state-substance and field (wave-corpuscle). On this basis, the quantum of the space of the Universe with the wave parameters of the gravitational field was associated with the graviton, as a minimal real particle of the Universe. A new rationale for the relationship of the wave parameters of the gravitational field with the wave parameters of the electromagnetic field is also suggested, which is obtained on the basis of strict physical relationships composed of fundamental physical constants: the speed c of light in vacuum, the gravitational constant G and Planck's constant h. On this basis, the possibility of linking the parameters of the quantum of the space of the Universe with a single photon is shown. The simplest physical and geometric scheme of the movement of a single photon in the space of the Universe is proposed. The proposed schemes reflect the initial physical structures of the material world, which do not contradict the known laws of physics, so they can be used for further studies of the graviton and photon.
AVS quantum science, 2022
We consider a global quantum system (the "Universe") satisfying a double constraint, both on total energy and total momentum. Generalizing the Page and Wootters quantum clock formalism, we provide a model of 3+1 dimensional, non-relativistic, quantum spacetime emerging from entanglement among different subsystems in a globally "timeless" and "positionless" Universe.
New Quantum Structure of Space-Time
Gravitation & Cosmology, 2019
We go beyond the classical-quantum duality of the space-time recently discussed and promote the space-time coordinates to quantum non-commuting operators. Comparison to the harmonic oscillator (X, P) variables and global phase space is enlighting. The phase space instanton (X, P = iT) describes the hyperbolic quantum space-time structure and generates the quantum light cone. The classical Minkowski space-time null generators X = ±T dissapear at the quantum level due to the relevant [X, T ] conmutator which is always non-zero. A new quantum Planck scale vacuum region emerges. We describe the quantum Rindler and quantum Schwarzshild-Kruskal space-time structures. The horizons and the r = 0 space-time singularity are quantum mechanically erased. The four Kruskal regions merge inside a single quantum Planck scale world. The quantum space-time structure consists of hyperbolic discrete levels of odd numbers (X 2 − T 2) n = (2n + 1) (in Planck units), n = 0, 1, 2.... .(X n , T n) and the mass levels being (2n + 1). A coherent picture emerges: large n levels are semiclassical tending towards a classical continuum spacetime. Low n are quantum, the lowest mode (n = 0) being the Planck scale. Two dual (±) branches are present in the local variables (√ 2n + 1 ± √ 2n) reflecting the duality of the large and small n behaviours and covering the whole mass spectrum: from the largest astrophysical objects in branch (+) to the quantum elementary particles in branch (-) passing by the Planck mass. Black holes belong to both branches (±). Starting from quantum theory (instead of general relativity) to approach quantum gravity within a minimal setting reveals successful: quantum relativity and quantum space-time structure are described. Further results are reported in another paper.