Spacetime Foam Research Articles

Comprehensive Theory: MEQ Quantum Foam Stabilization Framework

The Quantum Foam Stabilization Framework (QFSF) posits that higher-dimensional quantum dynamics, informed by insights from Particle 11 and the McGinty Equation (MEQ), can stabilize wormholes through the creation of stable, coherent, and low-entropy energy states. This theory integrates multiple quantum phenomena, including coherence, entanglement, nonlocality, resonance, topological effects, and thermodynamics, to provide a unified approach to maintaining wormhole stability.

New exact solutions of the conformable space-time two-mode foam drainage equation by two effective methods

In this article, the two-mode foam drainage equation in terms of time and space conformable sense has been investigated. Two effective methods, the generalized exponential rational function method (GERFM) and the improved version of the Bernoulli sub-equation function method (IBSEFM), are used to get new solutions of underlying equation. The fractional travelling wave transformation is applied to convert nonlinear partial differential equations to nonlinear ordinary differential equations. Proposed methods successfully extract trigonometric, hyperbolic and exponential solutions. Some of the obtained solutions are visualized to understand the effect of fractional orders of time and space derivatives on the wave profile and the dynamic behavior of the solutions.

Effects on neutrino propagation in space-time foam of D-branes revisited

Neutrinos from the cosmos have proven to be ideal for probing the nature of space-time. Previous studies on high-energy events of IceCube suggested that some of these events might be gamma-ray burst neutrinos, with their speeds varying linearly with their energy, implying also the coexistence of subluminal and superluminal propagation. However, a recent reanalysis of the data, incorporating revised directional information, reveals stronger signals that neutrinos are actually being slowed down compared to previous suggestion of neutrino speed variation. Thus, it is worth discussing its implications for the brane/string inspired framework of space-time foam, which has been used to explain previous observations. We revisit effects on neutrino propagation from specific foam models within the framework, indicating that the implied violation of Lorentz invariance could necessarily cause the neutrino to decelerate. We therefore argue that this sort of model is in agreement with the updated phenomenological indication just mentioned. An extended analysis of the revised IceCube data will further test these observations and stringy quantum gravity.

On properties of the distribution of virtual wormholes in a vacuum

A model of spacetime foam in the form of an arbitrary distribution of spherical Euclidean wormholes is considered. A method for constructing the exact solution of Einstein’s Euclidean equations for the metric corresponding to this model is proposed. In the framework of our model, we obtain the expression for the Euclidean action and its dependence on the parameters of wormholes in the explicit form. It is shown how the solutions obtained makes it possible to determine all possible correlation functions associated with the parameters of virtual wormholes in the vacuum state.

The nonlinear wave dynamics of fractional foam drainage and Boussinesq equations with Atangana’s beta derivative through analytical solutions

The space–time fractional foam drainage and the Boussinesq equations are valuable mathematical models to describe different complex physical phenomena, including the drainage of soap films in bubbles and foams, the behavior of surface water waves in oceans and rivers, the propagation of long waves, etc. In this research, we explore several unrivaled and some existing analytical soliton solutions to the above-stated equations using an effective expansion scheme, known as the G′/(G′+G+A)-expansion scheme within the framework of Atangana’s beta derivative. A fractional composite transformation is used to interpret the considered equations into nonlinear equations of a single independent variable. The wave dynamics of the outcomes are illustrated through three- and two-dimensional graphical representations and contour plots. The solutions include kink, flat kink-shaped, the parabolic-shaped, the bell-shaped, and the compacton solitons. The study reveals that the fractional-order derivative in the projected equations influences the wave behavior, providing deeper insights into wave composition when the fractional derivative approaches larger. The comparison table demonstrates the effectiveness of the method across various fractional orders, with results approaching accuracy as the fractional-order approaches integer values. This study emphasizes the computational robustness and adaptability of the proposed method for investigating various phenomena across a wide range of physical science and engineering disciplines.

Quantum gravity through geometric algebra

Geometric Algebra is used to construct a model of quantum gravity in which the 4D spacetime manifold is built from qubitic quantum entangled spacetime elements of geometric algebraic nature. This is achieved by first investigating the spontaneous decomposition of the spacetime continuum’s metric structure at Planck distances as one approaches what otherwise would become the Universe’s initial singularity. Considering this metric deconstruction within the model one finds that the reverse induced emergence of the spacetime continuum is generated by a coupling action triggered by the embedding action between distinct pre-spacetime manifolds. Further uncovered in this re-engineering of spacetime is a Poincaré-constrained quantum foam existing at infra-Planck scales.

From quantum foam to graviton condensation: The Zel'dovich route

Based on a previous ansatz by Zel'dovich for the gravitational energy of virtual particle-antiparticle pairs, supplemented with the holographic principle, we estimate the vacuum energy in a fairly reasonable agreement with the experimental values of the cosmological constant. We further highlight a connection between Wheeler's quantum foam and graviton condensation, as contemplated in the quantum N-portrait paradigm, and show that such connection also leads to a satisfactory prediction of the value of the cosmological constant. The above results suggest that the “unnaturally” small value of the cosmological constant may find a quite “natural” explanation once the nonlocal perspective of the large N-portrait gravitational condensation is endorsed.

Constraining quantum fluctuations of spacetime foam from BBN

A possibility to describe quantum gravitational fluctuations of the spacetime background is provided by virtual $D$-branes. These effects may induce a tiny violation of the Lorentz invariance (as well as a possible violation of the equivalence principle). In this framework, we study the formation of light elements in the early Universe (Big Bang Nucleosynthesis). By using the Big Bang Nucleosynthesis observations, We infer an upper bound on the topological fluctuations in the spacetime foam vacuum $\sigma^2$, given by $\sigma^2 \lesssim 10^{-22}$.

Spacetime as a Complex Network and the Cosmological Constant Problem

We propose a promising model of discrete spacetime based on nonassociative geometry and complex networks. Our approach treats space as a simplicial 3-complex (or complex network), built from “atoms” of spacetime and entangled states forming n-dimensional simplices (n=1,2,3). At large scales, a highly connected network is a coarse, discrete representation of a smooth spacetime. We show that, for high temperatures, the network describes disconnected discrete space. At the Planck temperature, the system experiences phase transition, and for low temperatures, the space becomes a triangulated discrete space. We show that the cosmological constant depends on the Universe’s topology. The “foamy” structure, analogous to Wheeler’s “spacetime foam”, significantly contributes to the effective cosmological constant, which is determined by the Euler characteristic of the Universe.

A unified model of inflation and dark energy based on the holographic spacetime foam

I present a model of inflation and dark energy in which the inflaton potential is constructed by imposing that a scalar field representing the classical energy of the spacetime foam inside the Hubble horizon is an exact solution to the cosmological equations. The resulting potential has the right properties to describe both the early and late expansion epochs of the universe in a unified picture.

Measuring the homogeneity of the quantum universe

There are not many tools to quantitatively monitor the emergence of classical geometric features from a quantum spacetime, whose microscopic structure may be a highly quantum-fluctuating ``spacetime foam''. To improve this situation, we introduce new quantum observables that allow us to measure the absolute and relative homogeneity of geometric properties of a nonperturbative quantum universe, as function of a chosen averaging scale. This opens a new way to compare results obtained in full quantum gravity to descriptions of the early Universe that assume homogeneity and isotropy at the outset. Our construction is purely geometric and does not depend on a background metric. We illustrate the viability of the quantum homogeneity measures by a nontrivial application to two-dimensional Lorentzian quantum gravity formulated in terms of a path integral over causal dynamical triangulations, and find some evidence of quantum inhomogeneity.

Lorentz and CPT breaking in gamma-ray burst neutrinos from string theory

Previous studies on high-energy gamma-ray burst neutrinos from IceCube suggest a neutrino speed variation at the Lorentz violation (LV) scale of ~6.4 × 1017 GeV, with opposite velocity variances between neutrinos and antineutrinos. Within a spacetime foam model, inspired by string theory, we develop an approach to describe the suggested neutrino/antineutrino propagation properties with both Lorentz invariance and CPT symmetry breaking. A threshold analysis on the bremsstrahlung of electron-positron pair (ν → νee+) for the superluminal (anti)neutrino is performed. We find that, due to the energy violation caused by the quantum foam, such reaction may be restricted to occur at sufficient high energies and could even be kinematically forbidden. Constraints on neutrino LV from vacuum ee+ pair emission are naturally avoided. Future experiments are appealed to test further the CPT violation of cosmic neutrinos and/or neutrino superluminality.

Lorentz- and CPT-violating neutrinos from string/D-brane model

We show that the space-time foam model from string/D-brane theory predicts a scenario in which neutrinos can possess linearly energy dependent speed variation, together with an asymmetry between neutrinos and antineutrinos, indicating the possibility of Lorentz and CPT symmetry violation for neutrinos. Such a scenario is supported by a phenomenological conjecture from the possible associations of IceCube ultrahigh-energy neutrino events with the gamma-ray bursts. It is also consistent with the constraints set by the energy-losing decay channels (e.g., e+e− pair emission, or neutrino splitting) upon superluminal neutrino velocities. We argue that the plausible violations of energy-momentum conservation during decay may be responsible for the stable propagation of these neutrinos, and hence for the evasion of relevant constraints.

Probing Spacetime Foam with Extragalactic Sources of High-Energy Photons

Quantum fluctuations can endow spacetime with a foamy structure. In this review article, we discuss our various proposals to observationally constrain models of spacetime foam. One way is to examine if the light wave-front from a distant quasar or GRB can be noticeably distorted by spacetime-foam-induced phase incoherence. As the phase fluctuations are proportional to the distance to the source but inversely proportional to the wavelength, ultra-high energy photons (>1 TeV) from distant sources are particularly useful. We elaborate on several proposals, including the possibility of detecting spacetime foam by observing “seeing disks” in the images of distant quasars and active galactic nuclei. We also discuss the appropriate distance measure for calculating the expected angular broadening. In addition, we discuss our more recent work in which we investigate whether wave-front distortions on small scales (due to spacetime foam) can cause distant objects become undetectable because the phase fluctuations have accumulated to the point at which image formation is impossible. Another possibility that has recently become accessible is to use interferometers to observe cosmologically distant sources, thereby giving a large baseline perpendicular to the local wave vector over which the wave front could become corrugated and thus distorted, reducing or eliminating its fringe visibility. We argue that all these methods ultimately depend on the availability of ways (if any) to carry out proper averaging of contributions from different light paths from the source to the telescope.

Discretization and de-geometrization (II): Quantizing Minkowski's spacetime continuum

A path toward quantizing gravity is suggested by describing the emergence of the spacetime continuum and its curvature using a mechanistic substratum model of discrete entities. By fusing pregeometry and the new mathematics of endo-geometry, a concept of a dynamically changing hyperspherical “quantized bubble” replaces the conventional geometric point. A quantum foam is an assemblage of these interacting bubbles. The structure of the cosmos, particles, and black holes are treated as naturally emerging four-dimensional hyperspheres. An insight into dark energy is considered.

Testing Lorentz invariance of electrons with LHAASO observations of PeV gamma-rays from the Crab Nebula

The Large High Altitude Air Shower Observatory (LHAASO) recently reported the detection of gamma-ray emissions with energies up to 1.1PeV from the Crab Nebula. Using the absence of vacuum Cherenkov effect by inverse-Compton electrons, we improve previous bounds to linear-order Lorentz invariance violation (LV) in the dispersion relations of electrons by 104 times. We show that the LV effect on electrons is severely constrained, compatible with certain type of LV as expected by some models of quantum gravity (QG), such as the string/D-brane inspired space-time foam. We argue that such models are supported by the Crab Nebula constraints from the LHAASO observations, as well as various LV phenomenologies for photons to date.

Searching new particles at neutrino telescopes with quantum-gravitational decoherence

We discuss the interplay of wave packet decoherence and decoherence induced by quantum gravity via interactions with spacetime foam for high-energy astrophysical neutrinos. In this context, we point out a compelling consequence of the expectation that quantum gravity should break global symmetries, namely that quantum-gravity induced decoherence may not only be the most sensitive probe for quantum properties of spacetime but also can provide both a powerful tool for the search for new particles, including totally decoupled backgrounds interacting only gravitationally, and at the same time a window into the intricacies of black hole information processing.

A Unified Model of Inflation and Dark Energy Based on the Holographic Spacetime Foam

A Unified Model of Inflation and Dark Energy Based on the Holographic Spacetime Foam

Midisuperspace foam and the cosmological constant

Wheeler’s conjectured ‘spacetime foam’—large quantum fluctuations of spacetime at the Planck scale—could have important implications for quantum gravity, perhaps even explaining why the cosmological constant seems so small. Here I explore this problem in a midisuperspace model consisting of metrics with local spherical symmetry. Classically, an infinite class of ‘foamy’ initial data can be constructed, in which cancellations between expanding and contracting regions lead to a small average expansion even if Λ is large. Quantum mechanically, the model admits corresponding stationary states, for which the probability current is also nearly zero. These states appear to describe a self-reproducing spacetime foam with very small average expansion, effectively hiding the cosmological constant.

Dispersion of light traveling through the interstellar space, induced and intrinsic Lorentz invariance violation

Theoretical models and experimental observations suggest that gamma-ray bursts (GRB) and high-energy neutrino bursts travelling through the interstellar space may reach the Earth at different speeds. We propose and study in details the mechanism (i), which always exists, where GRB are slowed down due to the dispersion of light in the interstellar medium. In addition to the standard media such as electrons and photons as CMB, we consider the medium with invisible axions. The amount of GRB delays in different media are calculated in details utilizing a novel technique in QFT by using the hitherto known or estimated densities of particles in the space without introducing any arbitrary parameter. Previously, the GRB delays have been interpreted as a sign of Lorentz invariance violation by modifying the dispersion relation of Special Relativity, which relates the energy, the momentum and the mass of a particle, based on different mechanisms (ii), such as a stringy spacetime foam, coming from a quantum gravity effect and using an adjustable parameter. Obviously, all the above-mentioned mechanisms (i) and (ii) are induced (seeming) Lorentz invariance violations but not an intrinsic (genuine) one. The amount of GRB delay due to the two aforementioned interpretations can be distinguished by observing the time of arrival of light with different frequencies. Namely, dispersion of light (i) predicts that the higher energy GRB arrive the Earth earlier, while in the other interpretations (ii), they arrive later. We notice that the needed amount for delay due to the dispersion of light shall have the potential power to shed additional light on the microstructure of interstellar media with respect to the densities of constituent particles and the origins of their sources. Finally, we indicate the ways to detect the intrinsic Lorentz invariance violation and to interpret them theoretically.