Microscopic Spacetime Research Articles

Experimental test of noncommutative quantum gravity by VIP-2 Lead

Pauli exclusion principle (PEP) violations induced by space-time noncommutativity, a class of universality for several models of quantum gravity, are investigated by the VIP-2 Lead experiment at the Gran Sasso underground National Laboratory of INFN. The VIP-2 Lead experimental bound on the noncommutative space-time scale $\mathrm{\ensuremath{\Lambda}}$ excludes $\ensuremath{\theta}$-Poincar\'e far above the Planck scale for non anishing ``electriclike'' components of ${\ensuremath{\theta}}_{\ensuremath{\mu}\ensuremath{\nu}}$, and up to $6.9\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}2}$ Planck scales if they are null. Therefore, this new bound represents the tightest one so far provided by atomic transitions tests. This result strongly motivates high sensitivity underground x-ray measurements as critical tests of quantum gravity and of the very microscopic space-time structure.

Strongest Atomic Physics Bounds on Noncommutative Quantum Gravity Models.

Investigations of possible violations of the Pauli exclusion principle represent critical tests of the microscopic space-time structure and properties. Space-time noncommutativity provides a class of universality for several quantum gravity models. In this context the VIP-2 lead experiment sets the strongest bounds, searching for the Pauli exclusion principle violating atomic transitions in lead, excluding the θ-Poincaré noncommutative quantum gravity models far above the Planck scale for nonvanishing θ_{μν} electriclike components, and up to 6.9×10^{-2} Planck scales if θ_{0i}=0.

Editorial: Coarse Graining in Quantum Gravity: Bridging the Gap Between Microscopic Models and Spacetime-Physics

The Renormalization Group encodes three concepts that could be key to accelerate progress in quantum gravity. First, it provides a micro-macro connection that could connect microscopic spacetime physics to phenomenology at observationally accessible scales. Second, it enables a search for universality classes that could link diverse quantum-gravity approaches and allow us to discover that distinct approaches could encode the same physics in mathematically distinct structures. Third, it enables the emergence of symmetries at fixed points of the Renormalization Group flow, providing a way for spacetime symmetries to emerge from settings in which these are broken at intermediate steps of the construction. These three concepts make the Renormalization Group an attractive method and conceptual underpinning of quantum gravity. Yet, in its traditional setup as a local coarse-graining, it could appear at odds with concepts like background independence that are expected of quantum gravity. Within the last years, several approaches to quantum gravity have found ways how these seeming contradictions could be reconciled and the power of the Renormalization Group approach unleashed in quantum gravity. This special issue brings together research papers and reviews from a broad range of quantum gravity approaches, providing a partial snapshot of this evolving field.

Critical Behavior of Non-intersecting Brownian Motions

We study $n$ non-intersecting Brownian motions corresponding to initial configurations which have a vanishing density in the large $n$ limit at an interior point of the support. It is understood that the point of vanishing can propagate up to a critical time, and we investigate the nature of the microscopic space-time correlations near the critical point and critical time. We show that they are described either by the Pearcey process or by the Airy line ensemble, depending on whether a simple integral related to the initial configuration vanishes or not. Since the Airy line ensemble typically arises near edge points of the macroscopic density, its appearance in the interior of the spectrum is surprising. We explain this phenomenon by showing that, even though there is no gap of macroscopic size near the critical point, there is with high probability a gap of mesoscopic size. Moreover, we identify a path which follows the Airy$_2$ process.

Causal Fermion Systems: Discrete Space-Times, Causation and Finite Propagation Speed

The theory of causal fermion systems is a recent approach to fundamental physics. Giving quantum mechanics, general relativity and quantum field theory as limiting cases, it is a candidate for a unified physical theory. The dynamics is described by a novel variational principle, the so-called causal action principle. The causal action principle does not rely on a presupposed space-time structure. Instead, it is a variational principle for space-time itself as well as for all structures in space-time (like particles, fields, etc.).After a general motivation and introduction, we report on mathematical results for two-particle causal fermion systems which state that every minimizer describes a discrete space-time. We explain and make precise that on scales which are much larger than the scale of the microscopic space-time structures, the dynamics of a causal fermion system respects causality with a finite speed of propagation.

Observables and Dynamics Quantum to Classical from a Relativity Symmetry and Noncommutative-Geometric Perspective

With approaching quantum/noncommutative models for the deep microscopic spacetime in mind, and inspired by our recent picture of the (projective) Hilbert space as the model of physical space behind basic quantum mechanics, we reformulate here the WWGM formalism starting from the canonical coherent states and taking wavefunctions as expansion coefficients in terms of this basis. This provides us with a transparent and coherent story of simple quantum dynamics where both the wavefunctions for the pure states and operators acting on them arise from the single space/algebra, which exactly includes the WWGM observable algebra. Altogether, putting the emphasis on building our theory out of the underlying relativity symmetry -- the centrally extended Galilean symmetry in the case at hand -- allows one to naturally derive both a kinematical and a dynamical description of a quantum particle, which moreover recovers the corresponding classical picture (understood in terms of the Koopman-von Neumann formalism) in the appropriate (relativity symmetry contraction) limit. Our formulation here is the most natural framework directly connecting all of the relevant mathematical notions and we hope it may help a general physicist better visualize and appreciate the noncommutative-geometric perspective behind quantum physics. It also helps to inspire and illustrate our perspective on looking at quantum mechanics and quantum physics in general in direct connection to the notion of quantum (deformed) relativity symmetries and the corresponding quantum/noncommutative models of spacetime as various levels of approximations all the way down to the Newtonian.

On the microscopic spacetime convexity principle for fully nonlinear parabolic equations II: Spacetime quasiconcave solutions

In [13], Chen-Ma-Salani established the strict convexity of spacetime level sets of solutions to heat equation in convex rings, using the constant rank theorem and a deformation method. In this paper, we generalize the constant rank theorem in [13] to fully nonlinear parabolic equations, that is,establish the corresponding microscopic spacetime convexity principles for spacetime level sets. In fact, the results hold for fully nonlinear parabolic equations under a general structural condition, including the $p$-Laplacian parabolic equations ($p >1$) and some mean curvature type parabolic equations.

High-energy recollision processes of laser-generated electron-positron pairs.

Two oppositely charged particles created within a microscopic space-time region can be separated, accelerated over a much larger distance, and brought to a recollision by a laser field. Consequently, new reactions become feasible, where the energy absorbed by the particles is efficiently released. By investigating the laser-dressed polarization operator, we identify a new contribution describing high-energy recollisions experienced by an electron-positron pair generated by pure light when a gamma photon impinges on an intense, linearly polarized laser pulse. The energy absorbed in the recollision process over the macroscopic laser wavelength corresponds to a large number of laser photons and can be exploited to prime high-energy reactions. Thus, the recollision contribution to the polarization operator differs qualitatively and quantitatively from the well-known one, describing the annihilation of an electron-positron pair within the microscopic formation region.

Quantization of emergent gravity

Emergent gravity is based on a novel form of the equivalence principle known as the Darboux theorem or the Moser lemma in symplectic geometry stating that the electromagnetic force can always be eliminated by a local coordinate transformation as far as space–time admits a symplectic structure, in other words, a microscopic space–time becomes noncommutative (NC). If gravity emerges from U(1) gauge theory on NC space–time, this picture of emergent gravity suggests a completely new quantization scheme where quantum gravity is defined by quantizing space–time itself, leading to a dynamical NC space–time. Therefore the quantization of emergent gravity is radically different from the conventional approach trying to quantize a phase space of metric fields. This approach for quantum gravity allows a background-independent formulation where space–time and matter fields are equally emergent from a universal vacuum of quantum gravity.

On the microscopic spacetime convexity principle of fully nonlinear parabolic equations I: Spacetime convex solutions

In \cite{CMS}, Chen-Ma-Salani established the strict convexity of spacetime level sets of solutions to heat equation in convex rings, using the constant rank theorem and a deformation method. In this paper, we generalize the constant rank theorem in \cite{CMS} to fully nonlinear parabolic equations, that is, establish the corresponding microscopic spacetime convexity principles of spacetime level sets. In fact, the results hold for fully nonlinear parabolic equations under a general structural condition, including the $p$-Laplacian parabolic equations ($p >1$) and some mean curvature type parabolic equations.

A microscopic convexity principle for spacetime convex solutions of fully nonlinear parabolic equations

We study microscopic spacetime convexity properties of fully nonlinear parabolic partial differential equations. Under certain general structure condition, we establish a constant rank theorem for the spacetime convex solutions of fully nonlinear parabolic equations. At last, we consider the parabolic convexity of solutions to parabolic equations and the convexity of the spacetime second fundamental form of geometric flows.

EQUIPARTITION OF MICROSCOPIC DEGREES OF FREEDOM, SPACE–TIME ENTROPY AND HOLOGRAPHY

One can identify the number density of the microscopic space–time degrees of freedom in any diffeomorphism-invariant theory of gravity by using the principle of equipartition, applied to the area elements of a surface [Formula: see text] which are at the local Unruh temperature. The entropy associated with these degrees of freedom, which matches with the Wald entropy for the theory, can be used to obtain the field equations of the theory through an extremization priciple. When the microscopic degrees of freedom are in local thermal equilibrium, the entropy of a bulk region of space–time resides on its boundary. These facts support an emergent perspective of gravity.

Surface density of spacetime degrees of freedom from equipartition law in theories of gravity

I show that the principle of equipartition, applied to area elements of a surface which are in equilibrium at the local Davies-Unruh temperature, allows one to determine the surface number density of the microscopic spacetime degrees of freedom in any diffeomorphism invariant theory of gravity. The entropy associated with these degrees of freedom matches with the Wald entropy for the theory. This result also allows one to attribute an entropy density to the spacetime in a natural manner. The field equations of the theory can then be obtained by extremising this entropy. Moreover, when the microscopic degrees of freedom are in local thermal equilibrium, the spacetime entropy of a bulk region resides on its boundary.

Fields and States of Hadrons Extended in the Microscopic Finslerian Space-Time

From a consideration of extended hadron structure in the microlocal anisotropic space-time, the mesonic and baryonic states with their internal quantum numbers such as strangeness, hypercharge, baryon number are constructed. The SU 3 baryonic multiplets of baryons with spin (j + $${\raise0.7ex\hbox{$1$} \!\mathord{\left/ {\vphantom {1 2}}\right.\kern-\nulldelimiterspace}\!\lower0.7ex\hbox{$2$}}$$ )ħ are generated from the SU 3 mesonic multiplets of mesons with spin jħ. The meson–baryon mass differences are also derived here. The composite particle field of hadrons for the macroscopic space-time are obtained. In particular, the meson field and one particle meson state are considered here. These one particle hadron states of the macroscopic space-time also possess the quantum numbers (strangeness, hypercharge, etc.) which are regarded as the manifestations of the anisotropic nature of the microlocal space-time. The composite fields constructed here are usable in the reduction formulae of the S-matrix approach for strong interaction.

A general scheme for microscopic theories

We discuss from an operational point of view some fundamental concepts of the micro-scopic physical theories, with the aim of providing a background for a successive investigation of the microscopic space-time structure. We consistently develop the remark that a frame of reference is determined by physical objects which may interact with the objects under investigation. As it is not clear that a state can be prepared by means of physical operations, we do not use the concept of physical state for the foundation of the theory. In our approach, the primitive concepts are the measurement procedures, following which one gets a numerical result, and the transformation procedures, which have the aim of building a frame of reference. We discuss several rules which allow us to define new procedures in terms of known procedures. The statistical laws of physics are formulated in terms of an order relation between measurement procedures, which defines also an equivalence relation. The equivalence classes of measurement procedures are called measurements. We define also equivalence classes of transformation procedures, called transformations. The mathematical structure of the set of measurements and of the set of transformations is discussed in detail. We consider measurements with an arbitrary finite number of possible results, as this enables us to give a rigorous definition of compatibility. Finally, we point out that all the physical theories necessarily contain ideal measurements and transformations which do not correspond to any known physical procedure. The introduction of these ideal objects permits a considerable simplification of the mathematical structure of the theory, but reduces its physical content.

The Photon Self-energy Problem and Microscopic Space-time Structure

The Photon Self-energy Problem and Microscopic Space-time Structure