and Quantum Spacetime in Physics
Harald Grosse2006
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Abstract
Organized by Yukawa Institute for Theoretical Physics Organizers M. Fukuma (Kyoto) S. Iso (KEK) K. Ito (TIT) H. Kunitomo (YITP) N. Sasakura (YITP, Cochair) S. Watamura (Tohoku, Cochair) Organizers M. Fukuma (Kyoto) S. Iso (KEK) K. Ito (TIT) H. Kunitomo (YITP) N. Sasakura (YITP, Cochair) S. Watamura (Tohoku, Cochair)
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Preview Of Quantum Concepts in Space and Time Oxford Science Publications
Quantum concepts in space and time.
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.
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.
O ct 2 01 5 Towards relativistic quantum geometry
2018
The study of geometrodynamics was introduced by Wheeler in the 50’s decade in order to describe particle as geometrical topological defects in a relativistic framework[1], and, in the last years has becoming a very intensive subject of research[2]. In the last decades Loop Quantum Gravity (LQG) have provided a picture of the quantum geometry of space, thanks in part to the theory of spin networks[3]. The concept of spin foam is intended to serve as a similar picture for the quantum geometry of spacetime. LQG is a theory that attempts to describe the quantum properties of the universe and gravity. In LQG the space can be viewed as an extremely fine favric of finite loops. These networks of loops are called spin networks. The evolution of a spin network over time is called a spin foam. The more traditional approach to LQG is the canonical LQG, and there is a newer approach called covariant LQG, more commonly called spin foam theory. However, at the present time, it is not possible to ...
A perspective on the theory and phenomenology of quantum spacetime
2010
Thesis not yet defended Flavio Mercati. A perspective on the theory and phenomenology of quantum spacetime. Ph.D. thesis. Sapienza -University of Rome
New Quantum of the Space of the Universe and New Opportunities for the Development of Quantum Physics
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.
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.
An Exact Mathematical Picture of Quantum Spacetime
Using von Neumann’s continuous geometry in conjunction with A. Connes’ noncommutative geometry an exact mathematical-topological picture of quantum spacetime is developed ab initio. The final result coincides with the general conclusion of E-infinity theory and previous results obtained in the realm of high energy physics. In particular it is concluded that the quantum particle and the quantum wave spans quantum spacetime and conversely quantum particles and waves mutates from quantum spacetime.
The emergence of spacetime in quantum theories of gravity
Studies in History and Philosophy of Science Part B Studies in History and Philosophy of Modern Physics, 2013
Nonstandard optics from quantum space-time
Physical Review D, 1999
We study light propagation in the picture of semi-classical space-time that emerges in canonical quantum gravity in the loop representation. In such picture, where space-time exhibits a polymerlike structure at microscales, it is natural to expect departures from the perfect non-dispersiveness of ordinary vacuum. We evaluate these departures, computing the modifications to Maxwell's equations due to quantum gravity, and showing that under certain circumstances, non-vanishing corrections appear that depend on the helicity of propagating waves. These effects could lead to observable cosmological predictions of the discrete nature of quantum spacetime. In particular, recent observations of non-dispersiveness in the spectra of gamma-ray bursts at various energies could be used to constrain the type of semi-classical state that describes the universe. CGPG-98/9-1 gr-qc/9809038 The recent discovery of the cosmological nature of gamma-ray bursts opens new possibilities to use them as a laboratory to test fundamental physics. This has been emphasized by Amelino-Camelia et al. [1]. What these authors point out is that the light coming from gamma-ray bursts travels very large distances before being detected on Earth, and is therefore quite sensitive to departures from orthodox theories. In particular, the bursts present detailed time structures, with features smaller than 1ms, that are received simultaneously through a broad band of frequencies, ranging from 20keV to 300keV , as reported by the BATSE detector of the Compton Gamma Ray observatory [2]. This implies stringent limits on any dispersive effects that light might suffer in travel towards the Earth. Various models of string quantum gravity imply dispersive frequency wavelength relations for light propagation, and in reference [1] it was shown that the simultaneity of time structures in the patterns of light received gamma ray bursts are possible candidates to set limits on these models. In this note we would like to probe similar issues for loop quantum gravity. An attractive feature of this approach is that it might imply a unique signature of the discrete nature of space time tantamount to an "intrinsic birefringence" of quantum space-time. This effect would imply a distinctive "doubling" of patterns observed in the time series analysis of the bursts, making it attractive from the observational point of view. We will see however, that the nature of the effects predicted by loop quantum gravity depend on the type of semi-classical state that one considers. In a sense, one can turn the argument around and suggest that rather than viewing these effects as a prediction of the theory, they can be used to constrain the type of semi-classical states one considers to represent realistic cosmologies. Loop quantum gravity [3] is usually formulated in the canonical framework. The states of the theory are given by functions of spin networks, which are a convenient label for a basis of independent states in the loop representation. This kinematic framework is widely accepted throughout various formulations of the theory, and has led to several physical predictions associated with the "polymer-like" structure of quantum space-time [4]. For instance, a quite clear picture of the origin of the black hole entropy emerges [5]. The dynamics of the theory is embodied in the Hamiltonian constraint, and consistent proposals are currently being debated [6]. To show the existence of the birefringent effect we will not need too many details of the dynamics of the theory. We prefer to leave the discussion a bit loose, reflecting the state of the art in the subject, since there is no agreement on a precise dynamics. Also, the spirit of our calculation is to attempt to make contact with observational predictions, something that is importantly lacking in the canonical approach, in part as a consequence of the absence of a detailed prescription for constructing the semi-classical limit of the theory. One should therefore view the current work as a further elaboration towards probing the nature of the semi-classical limit. Initial explorations on this subject can be found in reference [8]. The term in the Hamiltonian constraint coupling Maxwell fields to gravity is the usual "E 2 + B 2 " term, but in a curved background, * Associate member of ICTP.
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Class. Quantum Grav. 17 (2000) L53–L59. Printed in the UK PII: S0264-9381(00)09782-3 LETTER TO THE EDITOR
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Abstract. We characterize a general solution to the vacuum Einstein equations which admits isolated horizons. We show that it is a nonlinear superposition (in a precise sense) of the Schwarzschild metric with a certain free data set propagating tangentially to the horizon. This proves Ashtekar’s conjecture about the structure of spacetime near the isolated horizon. The same superposition method applied to the Kerr metric gives another class of vacuum solutions admitting isolated horizons. More generally, a vacuum spacetime admitting any null, non-expanding, shear-free surface is characterized. The results are applied to show that, generically, the non-rotating isolated horizon does not admit a Killing vector field and a spacetime is not spherically symmetric near a symmetric horizon. PACS numbers: 0470B, 0420 The quantum geometry considerations applied to black hole entropy [1] led Ashtekar et al to a new approach to black hole mechanics. The idea is to consider a null surface which...
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Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences, 2005
A generalized equivalence principle is put forward according to which space-time symmetries and internal quantum symmetries are indistinguishable before symmetry breaking . Based on this principle, a higher-dimensional extension of Minkowski space is proposed and its properties examined. In this scheme the structure of space-time is intrinsically quantum mechanical. It is shown that the causal geometry of such a quantum space-time (QST) possesses a rich hierarchical structure. The natural extension of the Poincaré group to QST is investigated. In particular, we prove that the symmetry group of this space is generated in general by a system of irreducible Killing tensors. After the symmetries are broken, the points of the QST can be interpreted as space-time valued operators . The generic point of a QST in the broken symmetry phase then becomes a Minkowski space-time valued operator. Classical space-time emerges as a map from QST to Minkowski space. It is shown that the general such ...
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The main research programs in quantum gravity tend to suggest in one way or another that most (if not all) spacetime structures are not fundamental. At the same time, work in quantum foundations highlights fundamental features that are in tension with any straightforward spacetime understanding. This paper aims to explore the little investigated but potentially fruitful links between these two fields.
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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.
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Space-Time from quantum Physics
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A construction of the real 4D Minkowski space-time starting from quantum harmonic oscillators is proposed. First, a 2D spinor space and its dual are derived from the standard commutation relations obeyed by the ladder operators of two independent 1D harmonic oscillators. The complex 4D Minkowski vector space V is then constructed from these spinor space. The flat, real 4D Minkowski manifold is finally built as an approximate description of a manifold of unitary operators constructed from V . Lorentz invariance is recovered and several possible extensions are discussed, which connections to quantum optics and condensed matter physics.
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.
Spinorial space-time and the origin of Quantum Mechanics. The dynamical role of the physical vacuum
EPJ Web of Conferences, 2016
Is Quantum Mechanics really and ultimate principle of Physics described by a set of intrinsic exact laws? Are standard particles the ultimate constituents of matter? The two questions appear to be closely related, as a preonic structure of the physical vacuum would have an influence on the properties of quantum particles. Although the first preon models were just « quark-like » and assumed preons to be direct constituents of the conventional « elementary » particles, we suggested in 1995 that preons could instead be constituents of the physical vacuum (the superbradyon hypothesis). Standard particles would then be excitations of the preonic vacuum and have substantially different properties from those of preons themselves (critical speed...). The standard laws of Particle Physics would be approximate expressions generated from basic preon dynamics. In parallel, the mathematical properties of space-time structures such as the spinoral space-time (SST) we introduced in 1996-97 can have strong implications for Quantum Mechanics and even be its real origin. We complete here our recent discussion of the subject by pointing out that: i) Quantum Mechanics corresponds to a natural set of properties of vacuum excitations in the presence of a SST geometry ; ii) the recently observed entanglement at long distances would be a logical property if preons are superluminal (superbradyons), so that superluminal signals and correlations can propagate in vacuum ; iii) in a specific description, the function of space-time associated to the extended internal structure of a spin-1/2 particle at very small distances may be incompatible with a continuous motion at space and time scales where the internal structure of vacuum can be felt. In the dynamics associated to iii), and using the SST approach to space-time, a contradiction can appear between macroscopic and microscopic space-times due to an overlap in the time variable directly related to the fact that a spinorial function takes nonzero values simultaneously in a whole time interval. Then, continuous motion can be precluded at very small spacetime scales. If discrete motion is required at such scales, the situation will possibly be close to that generating the Feynman path integral. More generally, Quantum Mechanics can naturally emerge from the spinorial space-time and from other unconventional spacetime structures in a fundamental preon dynamics governing the properties of vacuum. In such scenarios, the application of Gödel -Cohen mathematics to quantum-mechanical calculations can possibly yield substantially different results from those recently obtained using the standard quantum approach without any preonic underlying structure. This is also a crucial open question for Quantum Mechanics and Particle Physics. T his paper is dedicated to the memory o f Bernard d Espagnat
Nexus: A Quantum Theory of Space-Time, Gravity and the Quantum Vacuum
International Journal of Astronomy and Astrophysics, 2013
One of the main problems of contemporary physics is to find a quantum description of gravity. This present approach attempts to remedy the problem through the quantization of a finite but large flat Minkowski space-time by means of Fourier expansion of the displacement four vector x . By applying second quantization techniques, space-time emerges as a superposition of space-time eigen states or lattices of quantized space-time vibrations also known as gravitons. Each lattice element four vector is a graviton and traces out an elementary four volume (lattice cell). The stress-momentum tensor of each graviton defines its curvature and also the curvature of the associated lattice as described by General Relativity. The eigen states of space-time are found to be separated by a quantum of energy equal to the product of the Hubble constant and the Planck constant. The highest energy state is at Planck energies. This paper also shows that gravitons can be absorbed and emitted by the space-time lattice changing the volume of its primitive cells and that particles of observable matter are associated with a graviton whose frequency is equal to the particle's Compton frequency which the lattice can absorb producing a perturbation in the lattice. The space-time lattice is found to be unstable and decays by radiating low energy gravitons of energy equal to the product of the Hubble constant and the Planck constant. This decay causes the space-time superstructure to expand. The graviton is seen a composite spin 2 particle made from a combination of spin half components of the displacement four vector elements. The spin symmetry of its constituent elements can breakdown to give rise to other vector or scalar bosons. Dark Matter is seen as a consequence of Bose-Einstein statistics of gravitons which results in some regions of the lattice having more energy than others.
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.
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