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Search Results (247)

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18 pages, 382 KB  
Article
Self-Organized Criticality and Quantum Coherence in Tubulin Networks Under the Orch-OR Theory
by José Luis Díaz Palencia
AppliedMath 2025, 5(4), 132; https://doi.org/10.3390/appliedmath5040132 - 2 Oct 2025
Abstract
We present a theoretical model to explain how tubulin dimers in neuronal microtubules might achieve collective quantum coherence, resulting in wavefunction collapses that manifest as avalanches within a self-organized criticality (SOC) framework. Using the Orchestrated Objective Reduction (Orch-OR) theory as inspiration, we propose [...] Read more.
We present a theoretical model to explain how tubulin dimers in neuronal microtubules might achieve collective quantum coherence, resulting in wavefunction collapses that manifest as avalanches within a self-organized criticality (SOC) framework. Using the Orchestrated Objective Reduction (Orch-OR) theory as inspiration, we propose that microtubule subunits (tubulins) become transiently entangled via dipole–dipole couplings, forming coherent domains susceptible to sudden self-collapse. We model a network of tubulin-like nodes with scale-free (Barabási–Albert) connectivity, each evolving via local coupling and stochastic noise. Near criticality, the system exhibits power-law avalanches—abrupt collective state changes that we identify with instantaneous quantum wavefunction collapse events. Using the Diósi–Penrose gravitational self-energy formula, we estimate objective reduction times TOR=/Eg for these events in the 10–200 ms range, consistent with the Orch-OR conscious moment timescale. Our results demonstrate that quantum coherence at the tubulin level can be amplified by scale-free critical dynamics, providing a possible bridge between sub-neuronal quantum processes and large-scale neural activity. Full article
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12 pages, 1025 KB  
Article
Detecting Event-Related Spectral Perturbations in Right-Handed Sensorimotor Cortical Responses Using OPM-MEG
by Hao Lu, Yong Li, Min Xiang, Yuyu Ma, Yang Gao and Xiaolin Ning
Bioengineering 2025, 12(10), 1022; https://doi.org/10.3390/bioengineering12101022 - 25 Sep 2025
Abstract
The optically pumped magnetometer, OPM-MEG, has the potential to replace the traditional low-temperature superconducting quantum interference device, SQUID-MEG. Event-related spectral perturbations (ERSPs) can be used to examine the temporal- and frequency-domain characteristics of a signal. In this paper, a finger-tapping movement paradigm based [...] Read more.
The optically pumped magnetometer, OPM-MEG, has the potential to replace the traditional low-temperature superconducting quantum interference device, SQUID-MEG. Event-related spectral perturbations (ERSPs) can be used to examine the temporal- and frequency-domain characteristics of a signal. In this paper, a finger-tapping movement paradigm based on auditory cues is adopted, and OPM-MEG is used to measure the functional signals of the brain. The event-related spectral perturbation values of the right and left hands of right-handed people were calculated and compared. The results showed that there was a significant difference in the event-related spectral perturbations between the right and left hands of right-handed people. In summary, OPM-MEG has the ability to measure the event-related spectral perturbations of the brain during finger movements and verify the asymmetry of motor skills. Full article
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14 pages, 596 KB  
Article
Quantum Security Multi-Party Extremum Protocol with Greenberger–Horne–Zeilinger States
by Ping Wang, Gong-De Guo, Shu-Xin Lin, Xin Zhang and Song Lin
Technologies 2025, 13(10), 431; https://doi.org/10.3390/technologies13100431 - 24 Sep 2025
Viewed by 29
Abstract
Secure multi-party extremum, as a significant offshoot of secure multi-party computation, has extensive applications in various domains, including healthcare, financial transactions, market analysis, sports events, etc. Nevertheless, most existing secure multi-party extremum protocols rely on computational hard problems and are thus vulnerable to [...] Read more.
Secure multi-party extremum, as a significant offshoot of secure multi-party computation, has extensive applications in various domains, including healthcare, financial transactions, market analysis, sports events, etc. Nevertheless, most existing secure multi-party extremum protocols rely on computational hard problems and are thus vulnerable to quantum algorithms. This paper presents a quantum secure multi-party extremum protocol that is built upon the correlations of Greenberger–Horne–Zeilinger (GHZ) states. Within this protocol, multiple participants, with the aid of a semi-honest third party, can obtain the maximum and minimum values of their secret inputs. GHZ states act as the information carriers and are transmitted among the participants and the third party. Their unique correlations ensure the secure transmission of quantum particles. The analysis demonstrates that the proposed protocol is capable of not only warding off common external attacks but also resisting internal attacks launched by dishonest participants and the semi-honest third party. Moreover, the protocol boasts correctness and high scalability. Full article
(This article belongs to the Section Quantum Technologies)
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35 pages, 638 KB  
Article
On the Relativity of Quantumness as Implied by Relativity of Arithmetic and Probability
by Marek Czachor
Entropy 2025, 27(9), 922; https://doi.org/10.3390/e27090922 - 2 Sep 2025
Viewed by 580
Abstract
A hierarchical structure of isomorphic arithmetics is defined by a bijection gR:RR. It entails a hierarchy of probabilistic models, with probabilities pk=gk(p), where g is the restriction of [...] Read more.
A hierarchical structure of isomorphic arithmetics is defined by a bijection gR:RR. It entails a hierarchy of probabilistic models, with probabilities pk=gk(p), where g is the restriction of gR to the interval [0,1], gk is the kth iterate of g, and k is an arbitrary integer (positive, negative, or zero; g0(x)=x). The relation between p and gk(p), k>0, is analogous to the one between probability and neural activation function. For k1, gk(p) is essentially white noise (all processes are equally probable). The choice of k=0 is physically as arbitrary as the choice of origin of a line in space, hence what we regard as experimental binary probabilities, pexp, can be given by any k, pexp=gk(p). Quantum binary probabilities are defined by g(p)=sin2π2p. With this concrete form of g, one finds that any two neighboring levels of the hierarchy are related to each other in a quantum–subquantum relation. In this sense, any model in the hierarchy is probabilistically quantum in appropriate arithmetic and calculus. And the other way around: any model is subquantum in appropriate arithmetic and calculus. Probabilities involving more than two events are constructed by means of trees of binary conditional probabilities. We discuss from this perspective singlet-state probabilities and Bell inequalities. We find that singlet state probabilities involve simultaneously three levels of the hierarchy: quantum, hidden, and macroscopic. As a by-product of the analysis, we discover a new (arithmetic) interpretation of the Fubini–Study geodesic distance. Full article
(This article belongs to the Special Issue Quantum Measurement)
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19 pages, 1865 KB  
Article
Bayesian Analysis of the Nexus Paradigm Predictions for Supermassive Black Hole Observations by the Event Horizon Telescope
by Stuart Marongwe, Moletlanyi Tshipa and Christian Corda
Universe 2025, 11(9), 289; https://doi.org/10.3390/universe11090289 - 26 Aug 2025
Viewed by 760
Abstract
We present a Bayesian statistical analysis to evaluate the Nexus Paradigm (NP) of quantum gravity, using horizon-scale observations of supermassive black holes (SMBHs) Sagittarius A* (Sgr A*) and M87* from the Event Horizon Telescope (EHT). The NP predicts angular diameters for the dark [...] Read more.
We present a Bayesian statistical analysis to evaluate the Nexus Paradigm (NP) of quantum gravity, using horizon-scale observations of supermassive black holes (SMBHs) Sagittarius A* (Sgr A*) and M87* from the Event Horizon Telescope (EHT). The NP predicts angular diameters for the dark depression, emission ring, and base diameter, which we compare to EHT measurements. Employing Gaussian likelihoods and priors informed by mass-to-distance ratio uncertainties, we compute the posterior distribution for the angular scale parameter θg, achieving a combined χ20.0062 (four degrees of freedom) corresponding to a 4.37 σ (99.9972%) confidence level. Individual features show deviations <0.1 σ supporting the NP’s claim of 99th percentile agreement. Compared to General Relativity (GR), which predicts a shadow diameter inconsistent with the observed dark depression (χ2168, ~12.97 σ) the NP is favored with a Bayes factor of ~1036. These results validate the NP’s predictions and highlight its potential as a quantum gravity framework, though refined uncertainties and broader model comparisons are recommended. Full article
(This article belongs to the Special Issue Quantum Gravity Phenomenology: Insights and Advances)
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36 pages, 6171 KB  
Review
Atomistic Modeling of Microstructural Defect Evolution in Alloys Under Irradiation: A Comprehensive Review
by Yue Fan
Appl. Sci. 2025, 15(16), 9110; https://doi.org/10.3390/app15169110 - 19 Aug 2025
Viewed by 737
Abstract
Developing structural materials capable of maintaining integrity under extreme irradiation conditions is a cornerstone challenge for advancing sustainable nuclear energy technologies. The complexity and severity of radiation-induced microstructural changes—spanning multiple length and timescales—pose significant hurdles for purely experimental approaches. This review critically evaluates [...] Read more.
Developing structural materials capable of maintaining integrity under extreme irradiation conditions is a cornerstone challenge for advancing sustainable nuclear energy technologies. The complexity and severity of radiation-induced microstructural changes—spanning multiple length and timescales—pose significant hurdles for purely experimental approaches. This review critically evaluates recent advancements in atomistic modeling, emphasizing its transformative potential to decipher fundamental mechanisms driving microstructural evolution in irradiated alloys. Atomistic simulations, such as molecular dynamics (MD), have successfully unveiled initial defect formation processes at picosecond scales. However, the inherent temporal limitations of conventional MD necessitate advanced methodologies capable of exploring slower, thermally activated defect kinetics. We specifically traced the development of powerful potential energy landscape (PEL) exploration algorithms, which enable the simulation of high-barrier, rare events of defect evolution processes that govern long-term material degradation. The review systematically examines point defect behaviors in various crystal structures—BCC, FCC, and HCP metals—and elucidates their characteristic defect dynamics, respectively. Additionally, it highlights the pronounced effects of chemical complexity in concentrated solid-solution alloys and high-entropy alloys, notably their sluggish diffusion and enhanced defect recombination, underpinning their superior radiation tolerance. Further, the interaction of extended defects with mechanical stresses and their mechanistic implications for material properties are discussed, highlighting the critical interplay between thermal activation and strain rate in defect evolution. Special attention is dedicated to the diverse mechanisms of dislocation–obstacle interactions, as well as the behaviors of metastable grain boundaries under far-from-equilibrium environments. The integration of data-driven methods and machine learning with atomistic modeling is also explored, showcasing their roles in developing quantum-accurate potentials, automating defect analysis, and enabling efficient surrogate models for predictive design. This comprehensive review also outlines future research directions and fundamental questions, paving the way toward autonomous materials’ discovery in extreme environments. Full article
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17 pages, 310 KB  
Article
Statistical Entropy Based on the Generalized-Uncertainty-Principle-Induced Effective Metric
by Soon-Tae Hong, Yong-Wan Kim and Young-Jai Park
Universe 2025, 11(8), 256; https://doi.org/10.3390/universe11080256 - 2 Aug 2025
Viewed by 299
Abstract
We investigate the statistical entropy of black holes within the framework of the generalized uncertainty principle (GUP) by employing effective metrics that incorporate leading-order and all-order quantum gravitational corrections. We construct three distinct effective metrics induced by the GUP, which are derived from [...] Read more.
We investigate the statistical entropy of black holes within the framework of the generalized uncertainty principle (GUP) by employing effective metrics that incorporate leading-order and all-order quantum gravitational corrections. We construct three distinct effective metrics induced by the GUP, which are derived from the GUP-corrected temperature, entropy, and all-order GUP corrections, and analyze their impact on black hole entropy using ’t Hooft’s brick wall method. Our results show that, despite the differences in the effective metrics and the corresponding ultraviolet cutoffs, the statistical entropy consistently satisfies the Bekenstein–Hawking area law when expressed in terms of an invariant (coordinate-independent) distance near the horizon. Furthermore, we demonstrate that the GUP naturally regularizes the ultraviolet divergence in the density of states, eliminating the need for artificial cutoffs and yielding finite entropy even when counting quantum states only in the vicinity of the event horizon. These findings highlight the universality and robustness of the area law under GUP modifications and provide new insights into the interplay between quantum gravity effects and black hole thermodynamics. Full article
(This article belongs to the Collection Open Questions in Black Hole Physics)
8 pages, 306 KB  
Proceeding Paper
Constraints on the Equation of State of Quark Stars from Compact Object Observations
by Shu-Peng Wang, Zhi-Jun Ma, Jian-Feng Xu and Zhen-Yan Lu
Proceedings 2025, 123(1), 3; https://doi.org/10.3390/proceedings2025123003 - 29 Jul 2025
Viewed by 539
Abstract
Introducing an additional term into the thermodynamic potential density of the quark matter system, as required for thermodynamic consistency, resolves the inconsistency that arises in the conventional perturbative quantum chromodynamics (QCD) model. In this work, we use a revised, thermodynamically consistent perturbative QCD [...] Read more.
Introducing an additional term into the thermodynamic potential density of the quark matter system, as required for thermodynamic consistency, resolves the inconsistency that arises in the conventional perturbative quantum chromodynamics (QCD) model. In this work, we use a revised, thermodynamically consistent perturbative QCD model to compute the stability window and equation of state of up-down (ud) quark matter at zero temperature. Our results indicate that the measured tidal deformability for GW170817 places an upper limit on the maximum mass of ud quark stars, but does not rule out the possibility of such stars with a mass of about two solar masses. However, when the maximum mass of ud quark stars significantly exceeds two solar masses, such as the compact object with a mass in the range of 2.50–2.67 M observed in the GW190814 event, it cannot be identified as a ud quark star according to the revised perturbative QCD model. Full article
(This article belongs to the Proceedings of The 5th International Conference on Symmetry (Symmetry 2025))
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15 pages, 1019 KB  
Article
Genotypic Variability in Growth and Leaf-Level Physiological Performance of Highly Improved Genotypes of Pinus radiata D. Don Across Different Sites in Central Chile
by Sergio Espinoza, Marco Yáñez, Carlos Magni, Eduardo Martínez-Herrera, Karen Peña-Rojas, Sergio Donoso, Marcos Carrasco-Benavides and Samuel Ortega-Farias
Forests 2025, 16(7), 1108; https://doi.org/10.3390/f16071108 - 4 Jul 2025
Viewed by 361
Abstract
Pinus radiata D. Don is planted in South Central Chile on a wide range of sites using genetically improved genotypes for timber production. As drought events are expected to increase with ongoing climatic change, the variability in gas exchange, which could impact growth [...] Read more.
Pinus radiata D. Don is planted in South Central Chile on a wide range of sites using genetically improved genotypes for timber production. As drought events are expected to increase with ongoing climatic change, the variability in gas exchange, which could impact growth and water use, needs to be evaluated. In this study, we assessed the genotypic variability of leaf-level light-saturated photosynthesis (Asat), stomatal conductance (gs), transpiration (E), intrinsic water use efficiency (iWUE), and Chlorophyll a fluorescence (OJIP-test parameters) among 30 P. radiata genotypes (i.e., full-sib families) from third-cycle parents at age 6 years on three sites in Central Chile. We also evaluated tree height (HT), diameter at breast height (DBH), and stem index volume (VOL). Families were ranked for HT as top-15 and bottom-15. In the OJIP-test parameters we observed differences at the family level for the maximum quantum yield of primary PSII photochemistry (Fv/Fm), the probability that a photon trapped by the PSII reaction center enters the electron transport chain (ψEo), and the potential for energy conservation from photons captured by PSII to the reduction in intersystem electron acceptors (PIABS). Fv/Fm, PIABS, and ψEo ranged from 0.82 to 0.87, 45 to 95, and 0.57 to 0.64, respectively. Differences among families for growth and not for leaf-level physiology were detected. DBT, H, and VOL were higher in the top-15 families (12.6 cm, 8.4 m, and 0.10 m3, respectively) whereas Asat, gs, E, and iWUE were similar in both the top-15 and bottom-15 families (4.0 μmol m−2 s−1, 0.023 mol m−2 s−1, 0.36 mmol m−2 s−1, and 185 μmol mol m−2 s−1, respectively). However, no family by site interaction was detected for growth and leaf-level physiology. The results of this study suggest that highly improved genotypes of P. radiata have uniformity in leaf-level physiological rates, which could imply uniform water use at the stand-level. The family variation found in PIABS suggests that this parameter could be incorporated to select genotypes tolerant to environmentally stressful conditions. Full article
(This article belongs to the Special Issue Water Use Efficiency of Forest Trees)
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23 pages, 337 KB  
Article
A Spacetime Metric for the 4 + 1 Formalism
by Martin Land
Sci 2025, 7(3), 86; https://doi.org/10.3390/sci7030086 - 1 Jul 2025
Viewed by 477
Abstract
In his foundational work on classical and quantum electrodynamics, Stueckelberg introduced an external evolution parameter, τ, in order to overcome difficulties associated with the problem of time in relativity. Stueckelberg particle trajectories are described by the evolution of spacetime events under the [...] Read more.
In his foundational work on classical and quantum electrodynamics, Stueckelberg introduced an external evolution parameter, τ, in order to overcome difficulties associated with the problem of time in relativity. Stueckelberg particle trajectories are described by the evolution of spacetime events under the monotonic advance of τ, the basis for the Feynman–Stueckelberg interpretation of particle–antiparticle interactions. An event is a solution to τ-parameterized equations of motion, which, under simple conditions, including the elimination of pair processes, can be reparameterized by the proper time of motion. The 4+1 formalism in general relativity (GR) extends this framework to provide field equations for a τ-dependent local metric γμν(x,τ) induced by these Stueckelberg trajectories, leading to τ-parameterized geodesic equations in an evolving spacetime. As in standard GR, the linearized theory for weak fields leads to a wave equation for the local metric induced by a given matter source. While previous attempts to solve the wave equation have produced a metric with the expected features, the resulting geodesic equations for a test particle lead to unreasonable trajectories. In this paper, we discuss the difficulties associated with the wave equation and set up the more general ADM-like 4+1 evolution equations, providing an initial value problem for the metric induced by a given source. As in the familiar 3+1 formalism, the metric can be found as a perturbation to an exact solution for the metric induced by a known source. Here, we propose a metric, ansatz, with certain expected properties; obtain the source that induces this metric; and use them as the initial conditions in an initial value problem for a general metric posed as a perturbation to the ansatz. We show that the ansatz metric, its associated source, and the geodesic equations for a test particle behave as required for such a model, recovering Newtonian gravitation in the nonrelativistic limit. We then pose the initial value problem to obtain more general solutions as perturbations of the ansatz. Full article
22 pages, 323 KB  
Article
Mathematical Formalism and Physical Models for Generative Artificial Intelligence
by Zeqian Chen
Foundations 2025, 5(3), 23; https://doi.org/10.3390/foundations5030023 - 24 Jun 2025
Viewed by 583
Abstract
This paper presents a mathematical formalism for generative artificial intelligence (GAI). Our starting point is an observation that a “histories” approach to physical systems agrees with the compositional nature of deep neural networks. Mathematically, we define a GAI system as a family of [...] Read more.
This paper presents a mathematical formalism for generative artificial intelligence (GAI). Our starting point is an observation that a “histories” approach to physical systems agrees with the compositional nature of deep neural networks. Mathematically, we define a GAI system as a family of sequential joint probabilities associated with input texts and temporal sequences of tokens (as physical event histories). From a physical perspective on modern chips, we then construct physical models realizing GAI systems as open quantum systems. Finally, as an illustration, we construct physical models realizing large language models based on a transformer architecture as open quantum systems in the Fock space over the Hilbert space of tokens. Our physical models underlie the transformer architecture for large language models. Full article
(This article belongs to the Section Physical Sciences)
47 pages, 700 KB  
Review
Probes for String-Inspired Foam, Lorentz, and CPT Violations in Astrophysics
by Chengyi Li and Bo-Qiang Ma
Symmetry 2025, 17(6), 974; https://doi.org/10.3390/sym17060974 - 19 Jun 2025
Cited by 1 | Viewed by 1508
Abstract
Lorentz invariance is such a basic principle in fundamental physics that it must be constantly tested and any proposal of its violation and breakdown of CPT symmetry that might characterize some approaches to quantum gravity should be treated with care. In this review, [...] Read more.
Lorentz invariance is such a basic principle in fundamental physics that it must be constantly tested and any proposal of its violation and breakdown of CPT symmetry that might characterize some approaches to quantum gravity should be treated with care. In this review, we examine, among other scenarios, such instances in supercritical (Liouville) string theory, particularly in some brane models for “quantum foam”. Using the phenomenological formalism introduced here, we analyze the observational hints of Lorentz violation in time-of-flight lags of cosmic photons and neutrinos which fit excellently stringy space–time foam scenarios. We further demonstrate how stringent constraints from other astrophysical data, including the recent first detections of multi-TeV events in γ-ray burst 221009A and PeV cosmic photons by the Large High Altitude Air Shower Observatory (LHAASO), are satisfied in this context. Such models thus provide a unified framework for all currently observed phenomenologies of space–time symmetry breaking at Planckian scales. Full article
(This article belongs to the Special Issue Lorentz Invariance Violation and Space–Time Symmetry Breaking)
19 pages, 1355 KB  
Article
Mathematical Evaluation of Classical and Quantum Predictive Models Applied to PM2.5 Forecasting in Urban Environments
by Jesús Cáceres-Tello and José Javier Galán-Hernández
Mathematics 2025, 13(12), 1979; https://doi.org/10.3390/math13121979 - 16 Jun 2025
Cited by 1 | Viewed by 435
Abstract
Air quality modeling has become a strategic area within data science, particularly in urban contexts where pollution exhibits high variability and nonlinear dynamics. This study provides a mathematical and computational comparison between two predictive paradigms: the classical Long Short-Term Memory (LSTM) model, designed [...] Read more.
Air quality modeling has become a strategic area within data science, particularly in urban contexts where pollution exhibits high variability and nonlinear dynamics. This study provides a mathematical and computational comparison between two predictive paradigms: the classical Long Short-Term Memory (LSTM) model, designed for sequential analysis of time series, and the quantum model Quantum Support Vector Machine (QSVM), based on kernel methods applied in Hilbert spaces. Both approaches are applied to real PM2.5 concentration data collected at the Plaza Castilla monitoring station (Madrid) over the period 2017–2024. The LSTM model demonstrates moderate accuracy for smooth seasonal trends but shows limited performance in detecting extreme pollution events. In contrast, the QSVM achieves perfect binary classification through a quantum kernel based on angle encoding, with significantly lower training time and computational cost. Beyond the empirical results, this work highlights the growing potential of Quantum Artificial Intelligence as a hybrid paradigm capable of extending the boundaries of classical models in complex environmental prediction tasks. The implications point toward a promising transition to quantum-enhanced predictive systems aimed at advancing urban sustainability. Full article
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19 pages, 291 KB  
Article
Prolegomena to Agapeology: Reflections on Love as Panexperiential Phenomenon
by Lenart Škof
Religions 2025, 16(6), 733; https://doi.org/10.3390/rel16060733 - 6 Jun 2025
Viewed by 996
Abstract
This paper is an attempt to reflect upon the hidden or mysterious logic of love as an ontological and panexperiential phenomenon. In our attempt, we are crossing the fields of philosophy, spirituality, and contemporary research in psi phenomena (also known as paranormal phenomena) [...] Read more.
This paper is an attempt to reflect upon the hidden or mysterious logic of love as an ontological and panexperiential phenomenon. In our attempt, we are crossing the fields of philosophy, spirituality, and contemporary research in psi phenomena (also known as paranormal phenomena) and investigating some historical conditions of margins and disputes between the disciplines based on David Ray Griffin’s work, Parapsychology, Philosophy, and Spirituality. In the main part of this paper, we present the aesthetic theory of force by Christoph Menke and follow his rich analyses on the hidden, obscure layers of the soul. Based on these analyses, we present our own thesis on agapeology as being related both to psi phenomena and aesthetic phenomena. Throughout the history of religion and Western science, magical and miraculous events were too often relegated to the domain of faith or superstition and dismissed almost entirely. In the final parts of this paper, we aim to show that using the approaches of synchronicity (C.G. Jung) and ontology of the ground (F.W.J., Schelling) and acknowledging the phenomena known as quantum entanglement (C. Keller), we can postulate an underlying nexus, providing us with an access to the agapeistic effects of what we idiosyncratically call the phenomenon of dark love. Full article
(This article belongs to the Special Issue Between Philosophy and Theology: Liminal and Contested Issues)
18 pages, 251 KB  
Article
Complex Riemannian Spacetime: Removal of Black Hole Singularities and Black Hole Paradoxes
by John W. Moffat
Axioms 2025, 14(6), 440; https://doi.org/10.3390/axioms14060440 - 4 Jun 2025
Viewed by 564
Abstract
An approach is presented to resolve key paradoxes in black hole physics through the application of complex Riemannian spacetime. We extend the Schwarzschild metric into the complex domain, employing contour integration techniques to remove singularities while preserving the essential features of the original [...] Read more.
An approach is presented to resolve key paradoxes in black hole physics through the application of complex Riemannian spacetime. We extend the Schwarzschild metric into the complex domain, employing contour integration techniques to remove singularities while preserving the essential features of the original solution. A new regularized radial coordinate is introduced, leading to a singularity-free description of black hole interiors. Crucially, we demonstrate how this complex extension resolves the long-standing paradox of event horizon formation occurring only in the infinite future of distant observers. By analyzing trajectories in complex spacetime, we show that the horizon can form in finite complex time, reconciling the apparent contradiction between proper and coordinate time descriptions. This approach also provides a framework for the analytic continuation of information across event horizons, resolving the Hawking information paradox. We explore the physical interpretation of the complex extension versus its projection onto real spacetime. The gravitational collapse of a dust sphere with negligible dust is explored in the complex spacetime extension. The approach offers a mathematically rigorous framework for exploring quantum gravity effects within the context of classical general relativity. Full article
(This article belongs to the Special Issue Complex Variables in Quantum Gravity)
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