Physical Sciences

Abstract: We study a finite effective model for the on-shell mass ratios of the charged leptons. Equal common and relative powers in the square-root mass vector define a circle. Four activation channels give fifteen nonempty states and the response \(\eta(t) = 4\sinh t/(11 + 4\cosh t)\). A three-depth carrier supplies \(q_0 = 2/9\) and \(\Omega = 2667\). On a selected principal-structural pair, a positive self-adjoint lift of the octahedral coupling realizes the prescribed residual stiffness and yields \(h = 1/(3\Omega^2)\). Its isotropic elimination leaves the angular selection to a separately specified shell-activation mean budget. Under this budget and the identification of the natural parameter with the mass angle, \(\theta_* = \eta^{-1}[\eta(q_0) - h]\) is the unique entropy-projection solution and the globally attracting equilibrium of a Fisher natural-gradient flow. The mass ratios remain \(m_\mu/m_e = 206.768285719792\ldots\) and \(m_\tau/m_e = 3477.441682622933\ldots\), with residuals of \(0.66\) and \(0.43\) standard deviations against the fixed CODATA and PDG references. A separate two-step history construction realizes the same score multiplicities and, with an explicitly prepared three-mode readout, the same mass amplitudes. These conditional realizations specify which operator, history, and readout choices a microscopic model must supply.

Abstract: The dilemma of most upcoming researchers in the field of fiber reinforced polymer (FRP) composite processing is not the lack or accessibility to relevant background literature but rather their comprehensive nature, or their applicability to the specific needs of the researcher. Most existing literature either target just a specific modeling aspect or present high-level overview of the overall FRP process which lacks necessary underlying physics, coupling across hierarchical physics scales and computational techniques needed to improve on existing process simulation tools without necessarily reinventing the wheel. The current review article presents detailed understanding of the overall FRP composite process, the relevant transport phenomena and underlying physics across various scales and current trends in computational solution techniques used to predict FRP composite melt-flow phenomena in order to develop well equipped process-structure-property (PSP) maps for improved process monitoring and optimized print properties and performance. The overall position of potential research opportunities from survey of existing simulation efforts includes (i) the refinement of existing and development of new quantitative and qualitative multiscale models for predicting transport phenomena, (ii) development of new closed-form tensor evolution equations and constitutive relations with new information of the bulk fiber and melt-flow field states, and (iii) proper model benchmarking with experimental observation from in-situ process monitoring, and development of machine learning tools for the creation of a robust PSP map.

Abstract: Bohmian pilot wave theory and super determinism are not found satisfactory in explaining spooky non local action of quantum entanglement. Consciousness interpreted by film theory of the universe has provided an alternative solution for an appropriate reason for quantum entanglement. Mechanism of consciousness applied to explain entanglement. During the process it is found that there may exist a symmetry between conscious process of brain and universe. Further the symmetry has been analyzed to provide a model in which Planck constant ‘h’ is a variable rather than a constant. The model is a closed quantum system defining the reality and the purpose of application of quantum mechanics to interpret physical universe. It substantiates the concept that whole universe as a single quantum state and all quantum systems in this universe are subsystems of the universe. With the quantum system described in this model, a quantum AI system can generate consciousness which must be a practical proof for ‘consciousness as an emerging phenomenon’ in quantum systems with a specific arrangement. A design for a pilot model or a thought experiment resembling quantum consciousness system connected to the universe has been suggested for the purpose of experimental verification.

Abstract: This paper develops a geometric framework for causality and quantum observation within four-dimensional real spacetime, without invoking additional degrees of freedom or external measurement mechanisms. Promoting the bounded Lorentz angle to an intrinsic kinematic flow activates a spatial-vector ↔ temporal-bivector duality linking the Euclidean and Minkowski domains. Complementary manifolds, tangent spaces, and spinors become geometrically reciprocal, forming a closed, self-sustained intrinsic cyclic symmetry. Anchoring this flow to an observer’s local rest frame, without privileging any admissible timelike direction, establishes past-to-future causal ordering within a finite causal interaction volume whose boundary is double-covered by reflection symmetry. The geometric product of momentum and causal separation yields a Lorentz-invariant action defining a dynamical phase, motivating a 4π-periodic causal-boundary standing-wave interpretation. Spacetime event reflections generate four Dirac-related boundary eigenstates with geometric CPT closure, weighted by causal-boundary amplitudes to form a generalized wavefunction. Under semiclassical uncertainty and gravitational stability constraints, the Planck length emerges as a conditional minimum causal distance scale. Quantum observation is formulated as relational causal-boundary mode selection, registering spin orientation and matter–antimatter identity, rather than as wavefunction collapse.

Abstract:

Dynamic Theory is a five-dimensional theory in which geometry comes from thermodynamics: the three laws give a Lorentzian Weyl geometry whose fifth coordinate measures mass density. General relativity and particle physics were said to follow, but the derivations stop short. We complete them under conservation of mass, the vanishing of the fifth velocity component, imposed on the geometry as well as on matter. For gravity, an adopted action of Weyl’s form gives the five-dimensional Einstein equations, and conservation of mass picks out surfaces on which, with the mass axis orthogonal and of fixed scale, they reduce exactly to Einstein’s, with γ_PPN = β_PPN = 1, geodesic motion and gravitational radiation matching the orbital decay of PSR B1913+16 to 0.2%. For particles, it is a no-flux boundary at the end of the mass axis. As in domain-wall constructions, it binds one chiral zero mode of the five-dimensional Dirac field, on which an adopted charged current has the V−A form, and two such fields form a lepton doublet; the hand is chosen. The gauge fields are four-dimensional, and gauge dynamics and the Higgs sector are adopted from the Standard Model. The quantum condition makes the charge of every colour singlet an integer multiple of the electron’s; with the measured neutron charge selecting zero, neutrons and neutrinos are exactly neutral. Heavy partners along the mass axis are bounded.

Abstract: Modern science is barely four centuries old, although attempts to understand the material world go back much further. This paper explores the idea that many of the most fundamental scientific laws were born in so-called Eureka moments: In a very simple way, the essence of the law is grasped, before it is formulated in mathematical equations; extremely difficult to solve, sometimes. A number of landmark episodes are selected: Galileo’s celebrated “Dialogue”; Einstein’s “happiest thought”; Planck’s discovery of a constant comparable to Newton’s; Meitner and Frisch’s decisive winter walk; and several other. Also discussed is the recent experimental confirmation of the equivalence principle in the quantum domain. These historical examples will be examined in perspective, while addressing through them some enduring questions: Do we really understand classical physics better than quantum physics? Is “physical reality” still a meaningful concept? We have discovered fundamental laws and learned how to use them to accomplish an extraordinary range of things. But, do we truly understand everything we know how to do? It is often said that nobody understands quantum mechanics. We shall argue that nobody understands classical physics either, if we define “understanding” as: “having a clear idea of why”.

Abstract: This paper presents a clock‑synchronisation procedure equivalent to the Poincaré–Einstein convention, treating time coordinates as ensembles of intrinsic proper‑time indications of abstract clocks distributed throughout space. Starting from Einstein’s postulates and an isolated moving inertial frame, the synchronisation rule is expressed as a sequence of operations on clocks and light signals rather than as an abstract algebraic construction. Under initial conventional synchronisation t'=x'/c the propagation time from the origin to the synchronised point emerges as a function of a derived parameter c+, that depends on the system’s relative velocity, yielding an expression algebraically equivalent to the one‑way light velocity associated with the Tangherlini transformation. The analysis suggests that the Lorentz transformation implicitly contains the structural components of the Tangherlini transformation, making the two operationally equivalent under general covariance. The Lorentz transformation remains intact and is necessary for the appearance of c+. It is shown that Lorentz‑transformed coordinates coincide with the intrinsic coordinates of an event in the moving system only for a unique stationary‑frame velocity, indicating a condition for coordinate consistency rather than a constraint on the underlying physics. In this formulation, relative simultaneity arises as a coordinate artefact tied to the synchronisation convention rather than a physical effect.

Abstract: We propose a zeroth law of time: good clocks keep step, whatever they are made with and without being directly coupled to each other. No exception is known within the accuracy reached. Thermometers agree because they have exchanged heat; clocks agree although they have exchanged nothing. They are linked only indirectly, through the web of physical laws, which are mutually induced and mutually constraining. We state the law within a picture in which classical time is made with records: each record-making event, a time grain, costs at least k_Bln 2 of entropy per bit over a full cycle. The result is classical time, a coarse-grained quantity accumulated from many grains and shared by all good clocks. Keeping step has a price: two stochastic clocks agree to a relative precision ε only after producing at least 8k_B/ε² of entropy together. Where the law meets the zeroth law of thermodynamics, it gains a test: near equilibrium, thermal clocks at different heights read one common time exactly when heat falls like all other energy. An erasure–Szilard cycle shows that energy conservation and local position invariance enforce this, and free-fall data imply that their readings agree to within about one percent of the gravitational redshift between them. Many grains, one flow.

Abstract: Global preservation does not determine what a finite observer can recover. Observer-Dependent En-tropy Retrieval (ODER) makes the passage from preserved encoding to retained possession calculable through causal collection, joint access, and receiving dynamics. For finite Hayden–Preskill sources cou-pled to Schwarzschild propagation and a causal detector, we hold the source, late-radiation apparatus, and collection lifetime fixed. Across all 32 source states, optimal deterministic entanglement-recovery fidelity is at most 0.3308 without early radiation and at least 0.8476 with it. The upper bound applies to every decoder on the available registers, even when decoding computation is unrestricted. A controlled catcher carries this separation into memory; a separate two-site receiver retains a certified separation with finite switching and lossy storage. Independent identical zero-mean Gaussian rail noise admits an exact Pauli–erasure reduction at a specified coherent one-photon interface, yielding deterministic recovery certificates. A separate effective outgoing-field model shows how observer ordering depends on the matched time, incident stream, and receiver controls. Matched spectral trans-mission and mean delay leave finite-window access undetermined. A finite tensor-network (MERA) comparison likewise finds different reference information at identical collection size and individual inclusion probabilities. Removing disentanglers increases mean acquisition under both protocols while reducing their mean difference. Sharp access envelopes and an exact calibration-sufficiency criterion identify the missing information; an additional joint-collection statistic supplies a uniform recovery guarantee. In a five-carrier code, independently erasing collected shares reverses the ranking of two access protocols whose individual efficiencies remain matched. A reference-assisted verification construction shows that preserved encoding and reference erasure induce identical channels below its joint-access threshold and become distinguishable with sufficient access. Once collected, the diary correlations must enter memory and remain there. Uniform capture of an arbitrary collected register gives an exact conditional-mutual-information transfer law in the presence of early side information. Recorded progressive collection extends that channel to randomly admitted registers, with exact infor-mation dynamics and a finite-memory deadline certificate. A centered modular preparation attains the sharp strip-holomorphic activation envelope, and a finite receiver approximates its trajectory with explicit resource requirements. Programmable receiver tests and a staged BEC program connect these constructions to controlled measurements. The resulting standard is physical: the stated data must suffice to establish the claimed recovery or verification performance. The channel constructions determine when that standard is met and which additional measurement can settle an otherwise undetermined claim.

Abstract: Quantum interpretations differ in their accounts of reality while often predicting identical observations. We examine their relative plausibility under eight alternative judgments emphasizing economy of universal dynamics, definite physical configurations, physical selection of outcomes, states and events relative to interacting systems, quantum states as expectations, time symmetry and dependence on future boundary conditions, correlations between measurement settings and underlying variables, or a balance of these considerations. For each judgment, we retrospectively assign illustrative prior probabilities across ten accounts according to their perceived explanatory merits. Bayesian updating multiplies these weights by experimental evidence factors and rescales each distribution to total 100%.Discrimination requires different probabilities for common observable records, with noise and calibration uncertainties sufficiently constrained. The calculations show that different Bohmian entry times can yield identical detector probabilities, identify conditions for distinguishing collapse from environmental dephasing, and derive a spatial test separating two specified collapse laws. A likelihood reconstructed from published radiation summaries of the XENONnT experiment gives an approximate evidence factor of 0.3245, relative to ordinary quantum predictions, for an equal mixture of specified white-noise continuous spontaneous localization and regularized Diósi–Penrose models. Under the stated parameter priors, a starting collapse benchmark weight of 45% falls to 20.98%, while Bohm's rises from 20% to 28.73%. Accounts with matched observable predictions and parameter assumptions retain their relative odds. Three entries without calculated likelihoods receive assumed neutral evidence factors. The estimates depend on the initial judgments, model coverage, parameter priors, and likelihood reconstruction.

Abstract: Entropic corrections within the scope of the Generalized Uncertainty Principle are applied to the apparent Universe with zero curvature in a study of inflation models. It is demonstrated that the corresponding quantum-gravity deformation of the inflation potential is also the inflation potential that, within low energies far from the Planck energies, is coincident with the initial one. With the inflation pattern, in slow roll regime this leads to an increase of the number of e-foldings as compared to the semi-classical consideration. It is shown that in this case for hybrid inflation the probability of the origination of primordial black holes (pbhs) decreases at the last stage of inflation. In conclusion it is noted that the derived formulae may be used to compute the quantum-gravity corrections for pbhs originating in the De Sitter space during the pre-inflation era as well the corresponding quantities, specifically for the scale-invariant power spectrum of a scalar field from small pbhs. Briefly, further steps associated with application of the methods considered are discussed.

Abstract: The Topological Relational Field Theory (TRFT) series [1–3] previously elevated the finite observation window to a thermodynamic coordinate and, in TRFT III, proposed a candidate fourth law based on the time-conjugate field \( Φ \). In this paper, within the frameworks of standard quantum estimation and open-system theory, we perform a rigorous independent test and boundary delimitation of this candidate law, and complete three substantive developments of cross-scale significance. The core conclusions are fully testable independently of the framework (dual-track independence). First, we establish the precise domains of kinematics and thermodynamics. By introducing the Scaled Reference Point Relation (SRPR) and the quantum Cramér–Rao bound (CRB), we prove that in the macroscopic reality regime (\( r \) > 1), the CRB strictly takes over statistical precision, and the candidate law degenerates into a conditional constraint on bandwidth; whereas in the extremely short, few-body attosecond limit (\( r \) ≪ 1), the original law again becomes an absolutely tight upper bound, thereby precisely delimiting the valid territory of the law. Second, we reveal the "third class of irreversibility" of the arrow of time (the cosmic resource barrier). The derivation shows that the number of independent measurements required for reverse recovery of decoherence explodes exponentially as \( e^{2\varGamma t} \). Combined with the upper bound on baryonic matter in the observable universe, this gives a resource barrier \( Γt≈91.8 \). Even approaching the Bremermann limit, the barrier is delayed only logarithmically to about 139. This establishes an extremely hard physical limit based on the total capacity of the universe, opening a new paradigm independent of statistical probability and local energy consumption. Third, we reveal the microscopic origin of topological decoherence and the prerequisite for an engineering breakthrough. Within the SSH + Lindblad model, we rigorously prove that uniform environment coupling (\( P=I \)) locks the loss rate due to wavefunction normalization; only by "screening the edges and coupling solely to the bulk region" (\( P ≠ I \)) can the topological decoherence rate be exponentially suppressed by wavefunction overlap (\( {\varGamma }_{\mathrm{topo}}\propto e^{-cN} \)). This mechanism connects with the macroscopic barrier and establishes the core spatial-geometric prerequisite that must be satisfied for topological quantum device design in the NISQ era.

Abstract: Cold-atom experiments now control the exchange phase of strongly interacting one-dimensional gases and resolve the asymmetric momentum distribution of a driven impurity together with its relaxation after trap release. We introduce a finite-memory closure from Viscous Time Theory (VTT) for the preparation-history dependence of this observable. The prepared exchange phase remains the experimental control variable; a causal reduced coordinate follows it with a finite response time, and the mismatch between the two is the VTT state variable. Under an odd-response condition on the impurity momentum distribution, the momentum skewness acquires a linear, history-resolved correction. We test the closure in a microscopic reference model, a spinful Bose–Hubbard ring with exact time evolution, using protocols that end at the same exchange phase and differ only in their history. Interacting systems develop a history-dependent skewness that is small and oscillatory for slow preparation and of order one for fast preparation. An oscillatory generalization of the closure, calibrated on monotonic ramps alone and then frozen, predicts the held-out reversal protocols and reduces the mean-square error of the memoryless adiabatic baseline in the slow regime by 30 to 45% at fixed interaction strength and by 12% after averaging over a 20% spread of interaction strength. The response persists at a larger system size, where its frequency follows the lower level spacing of the system. The results define a quantitative experimental programme: calibrate on monotonic pulses, predict reversal pulses, and compare with a full microscopic baseline supplied with the same pulse history.

Abstract: This paper presents a quantum-mechanical model of rotating dipoles in perovskite crystals that exhibit ferroelectric properties. The symmetric rotator model accounts for both the displacement of a crystal lattice site—which lowers its symmetry—and the deformation of electron density within the unit cell. Matrices for the projection operators of dipole moments are calculated, incorporating a transformation from a rotating "molecular" coordinate system to the laboratory frame. In the limit of minimal rotation, these matrices—up to a numerical factor—correspond to the projection operator matrices for angular momentum (for j=1) in both spherical (cyclic) and Cartesian coordinates. Furthermore, by accounting for the coupling with the intrinsic spin of the electron associated with the dipole, the total angular momentum of the dipole is found to correspond to j=1/2. It is shown that two rotating dipoles, subject to dipole-dipole interaction, can "pair up"—either antiparallel (resulting in a minimal total dipole moment) or parallel (increasing the total dipole moment). In the latter case, a system of N dipoles can generate a macroscopic dipole moment within a domain. A variational model is proposed to explain the possibility of a second-order phase transition characterized by the onset of an ordered state. A general estimate is provided for the critical temperature at which the system undergoes a phase transition into a polarized state.

Abstract: In quantum mechanics energy is an observable, whereas time is a parameter; Pauli's theorem and the problem of time in canonical quantum gravity reflect this asymmetry. We define the time operator \( \hat{t}=\hat{x}/c \) and form, with the relativistic energy \( \hat{E}_R \), Einstein's constant \( \kappa \) and the time \( \hat{t}_0 \) in the rest system, operators of gravitational-field and curvature type, and derive their commutation relations, wave equations and spectra. The commutator \( [\hat{t},\hat{E}_R]=\tfrac{i\hbar}{c}\hat{v}_x \) is bounded with norm \( \hbar \) and is not a multiple of the identity, so Pauli's theorem is not contradicted. The sum \( c\,\hat{t}+\kappa\hat{E}_R \) is unitarily equivalent to the time operator and has a continuous spectrum. A postulated field equation, \( \hat{G}_0+\hat{\Lambda}=\kappa\hat{E}_R \), has the structure of Einstein's equation; for small velocities it becomes the Schrödinger equation of a particle in a homogeneous field. The metric tensor of this scalar model is not quantized. A metric operator is constructed from commuting position operators; in the vacuum sector it reproduces the Schwarzschild line element, which serves as a consistency test, and in general it is obtained only under an explicit correspondence condition, which is a postulate and not derived.

Abstract: We present a phenomenological effective framework for dynamical dark energy based on the macroscopic elastic response of the cosmological background. By formulating an effective scalar field action \(S_\phi\) under a spatial zero-mode constraint (\(\nabla_i \phi = 0\)), we show that the temporal strain mode \(\phi(t) = \ln(a/a_0)\) emerges as an exact solution to the Euler--Lagrange equations. Within the homogeneous and isotropic approximation, the strain variable is restricted to a temporal mode with vanishing spatial gradients (\(\nabla_i \phi = 0\)). Consequently, the construction introduces no additional propagating spatial scalar degrees of freedom at the background level, avoiding long-range fifth forces without invoking screening mechanisms. Cosmologically, the kinetic strain rate drives a smooth transition toward an effective dark energy equation of state \(w_{\mathrm{el}} \to -1\) at late times. By matching the stored strain energy within the causal boundary to the Bekenstein--Hawking horizon scaling, we adopt the natural normalization \(\kappa = 1\). This framework provides a physically transparent, background-effective alternative to standard scalar-tensor theories, offering dynamic signatures testable by next-generation cosmological surveys.

Abstract: We derive a geometric mechanism for magnetic interaction within anisotropic spatial dynamics (ASD). The transverse length vector effect identifies the physical interaction distance of two charges moving with a common transverse velocity as r_T=γr, where r is the reference separation and γ is the Lorentz factor. Applying Coulomb’s inverse-square law to this distance gives F_T=(1-β² ) F₀ and the magnetic interaction difference ΔF_m=-β² F₀, with β=v/c. These relations are exact throughout the subluminal interval for this configuration. Magnetism is thus represented as the motion-induced geometric reduction of a single Coulomb interaction. A virtual-work analysis distinguishes the physical force conjugate to r_T from the generalized force Q_r=F₀/γ conjugate to r. This supplies an ASD interpretation of the inverse-Lorentz-factor scaling while preserving the different physical roles of the two force variables. We further prove that rotational and reflection covariance, separate linearity in the source and test velocities, and zero magnetic power determine a unique bilinear quasistatic kernel once its normalization is fixed by the transverse result. Superposition recovers the Biot–Savart representation and the Ampère force between parallel steady currents. Comparison with conventional electrodynamics identifies differences in spatial interpretation, force decomposition, and exact velocity dependence.

Abstract: This study introduces a mathematical formulation, termed the causal recording (CR) framework, to elucidate propagating dissipative open systems such as surface waves. In this framework, spatiotemporally independent local states deterministically transition via an operator and irreversibly register force information. By sequentially recording these states from previously registered causal steps, the model inherently incorporates time-irreversibility and physical stability regardless of spatial domain boundaries. The coherence of the CR formulation with natural patterns is confirmed through direct comparison with real-time water ripple experiments. Numerical reconstructions reveal that the emergent macroscopic wave evolution is autonomously driven by the sequential accumulation of localized Newtonian force events. Furthermore, dynamic analysis reveals that dissipative Lagrangian trajectories emerge from the collective history of these local force events. Based on the difference between localized internal force depletion and external propagation, a dual dynamic structure for propagating open systems is proposed, suggesting a total-energy formulation: U_prop = U_i + U_e. Finally, by correlating these emergent dynamics during propagation with entropic force, the entropy at the initial force source is offset by the continuous forward energy flux. When the continuous external energy flows are included, the total entropy of the propagating dissipative system continuously increases.

Abstract: What is the minimum structure needed to describe spacetime? In general relativity spacetime is described by a metric, and light reveals its most fundamental property, the causal boundary between events that can influence one another and events that cannot. Four Null spacetime theory reverses this approach: rather than positing a smooth metric manifold through which light moves, it takes balanced null connections as the structural primitives, from which spacetime geometry, clocks, field strengths and the spinors of matter are reconstructed. It proposes that spacetime is built from microscopic cells, each spanned by four balanced lightlike vectors, the null generators, whose spatial directions point to the corners of a regular tetrahedron. The four generators and the six bivectors formed by their pairs, \(q_a\wedge q_b\), are the foundational structure of the theory. The generators carry the geometry: the metric is reconstructed exactly from their mutual products, and each cell has a unique relational clock. The six bivectors are the channels in which field strengths and curvature live: they split exactly three plus three into electric and magnetic sectors, exchanged by the Hodge star, just as the six edges of the tetrahedron join its four vertices. With the four triples and the four volume, a cell carries the complete graded structure \(1,4,6,4,1\) of spacetime forms, and the same generators carry the spinors and the Dirac operator of spin \(\tfrac{1}{2}\) matter. The dynamics rests on this kinematic core. On null fronts the scalar and vector parts of gravity act as constraints, the Raychaudhuri and Damour equations, while its two shear modes propagate. Under the composition postulate a single Huygens law is selected as the unique fixed point of free propagation: Kirchhoff's exact formula over one cell tick, with free waves on the light cone and one finite cell coefficient, \(a_4=1/12\). The Maxwell and Dirac equations, each with its own gauge or Clifford structure, propagate their physical solutions on the same shell, with \(g=2\) as a consistency result. Under the integrability postulate, the response of this law to curvature gives the Einstein coupling \(\kappa=1\) and, within the stated transverse traceless basis through order \(\mathcal{L}_c^2\), a unique finite cell completion with exact rational coefficients. On the F4 lattice, used as a Euclidean quantum regulator, the quadratic kinetic terms studied are protected against Lorentz violation, a chiral fermion without doublers exists, the photon is transverse and kept massless by an exact Ward identity, and two healthy low energy graviton modes are found; a candidate improvement \(c_{\rm imp}=1/18\) removes their order \(\mathcal{L}_c^2\) birefringence but loses positivity at the cutoff. For massless fields carried by the selected law, and provided the cone is protected quantum mechanically, the theory predicts no energy dependent speed of light or gravity at order \((k\mathcal{L}_c)^2\), and horizon entropy may be counted in cells. For neighboring cells sharing a face the transport is fixed by geometry, and exact balance makes their gluing discrete, with primitive hinge deficits in units of \(\pi/3\). The principal open problems are the rule selecting and evolving the discrete face identifications, causal adjacency and topology of the balanced cell complex, and whether this dynamics fixes the last coefficient of the gravitational interaction beyond the transverse traceless sector; nonlinear constraint preservation in 3D; a physical real time realization of the cells that keeps the regulator's Lorentz protection; the decoupling of cutoff states, unitarity and interacting quantum gravity; the dynamical origin of balance; and the size of the cell.

Abstract: Building on a famous idea by Hawking, Vaz won second prize in the Gravity Research Foundation essay contest in 2014 by demonstrating that quantum gravitational collapse does not lead to a singularity hidden by the event horizon, but rather to the formation of a thin spherical shell of condensed matter on the Schwarzschild surface. This surface was therefore revealed to be an apparent rather than a real horizon. This completely new view of black holes (BHs) was also consistent with Einstein’s 1939 idea of the localization of collapsing particles within a thin spherical shell. This "gravitational atom" is not supported by any degeneracy pressure, but by quantum gravity, just as ordinary atoms are supported by quantum mechanics. After determining the potential energy for these thin spherical shells of condensed matter at the apparent horizon in the theory of general relativity, one demonstrates here that these BHs are quantum objects obeying Schrödinger theory in the non-relativistic case and Dirac theory in the relativistic case, generalizing previous results. On the one hand, the results obtained have profound implications for the BH information paradox; on the other, they also seem consistent with astrophysical observations of rotating BHs. In fact, data from 20 rotating BHs, whether of stellar origin, located at the hearts of certain galaxies, or identified through gravitational wave astronomy, are analyzed. All 20 were found to be highly excited quantum states, gravitational spinor solutions of the Dirac equation for particular values of the principal quantum number and the total angular momentum quantum number.