In this work, the author employs the quantum hydrodynamic formalism to achieve the geometrization of spacetime for describing the gravitational interaction within the framework of quantum theory. This approach allows for the development of an equation of gravity that is mathematically connected to the fermion and boson fields. This achievement is accomplished by incorporating two fundamental principles: covariance of the quantum field equations and the principle of least action. By considering these principles, a theory is established that enables the calculation of gravitational corrections to Quantum Electrodynamics, and potentially, to the standard model of particle physics as well. The theory also provides an explanation for two phenomena: the existence of a cosmological pressure density similar to quintessence, that is compatible with the small value of the observed cosmological constant, and the breaking of matter-antimatter symmetry at high energies offering insights into why there is an imbalance between the two in the early universe. In the cosmological modeling of the theory, there exists a proposal to account for the formation of supermassive black holes that are accompanied by their own surrounding galaxies, without relying on the process of mass accretion. The model, in accordance with recent observations conducted by the James Webb Space Telescope, supports the notion that galactic configurations were established relatively early in the history of the universe, shortly after the occurrence of the Big Bang.

In this work the author utilizes the quantum geometrization of spacetime for describing the gravitational interaction within the framework of quantum theory. This approach allows for the development of an equation of gravity that is mathematically connected to the fermion and boson fields. This achievement is accomplished by incorporating two fundamental principles: covariance of the quantum field equations and the principle of least action. By considering these principles, a theory is established that enables the calculation of gravitational corrections to Quantum Electrodynamics, and potentially, to the standard model of particle physics as well. The theory also provides an explanation for two phenomena: the existence of a cosmological pressure density similar to quintessence, that is compatible with the small value of the observed cosmological constant, and the breaking of matter-antimatter symmetry at high energies offering insights into why there is an imbalance between the two in the early universe. In the cosmological modeling of the theory, there exists a proposal to account for the formation of supermassive black holes that are accompanied by their own surrounding galaxies, without relying on the process of mass accretion. The model, in accordance with recent observations conducted by the James Webb Space Telescope, supports the notion that galactic configurations were established relatively early in the history of the universe, shortly after the occurrence of the Big Bang.

The paper proposes a theoretical study that investigates the quantum effects on the gravity of black holes. The study utilizes a gravitational model that incorporates quantum mechanics derived from the classical-like quantum hydrodynamic representation. The research calculates the mass density distribution of quantum black holes, specifically in the case of central symmetry. The gravity of the quantum black hole shows contributions coming from the quantum potential energy, which is also sensitive to the presence of the background of gravitational noise. The additional energy, stored in the quantum potential fluctuations and constituting a form of dark energy, leads to a repulsive gravity in the weak gravity limit. This repulsive gravity overcomes the attractive classical Newtonian force at large distances of order of the intergalactic length.

One of the biggest challenges in modern physics is how to unify gravity with quantum theory. There is an absence of a complete quantum theory of gravity, and conventionally it is thought that the effects of quantum gravity occur only at high energies (Planck scale). Here we suggest that certain novel quantum effects of gravity can become significant even at lower energies and could be tested at laboratory scales. We also suggest a few indirect effects of dark energy that can show up at laboratory scales. Using these ideas, we set observational constraints on radio recombination lines of the Rydberg atoms. We further suggest that high-precision measurements of Casimir effects for smaller plate separation could also show some manifestations of the presence of dark energy.

In this article, Planck star and remnant scenario i.e., solution of black hole information paradox in loop quantum gravity (LQG) are elaborated. Since, Black hole is the final fate of collapse scenario in general relativity; firstly, gravitational collapse with two possible final outcomes i.e., black hole and naked singularity, is outlined. Thereafter, black hole thermodynamics along with four laws of black hole thermodynamics, Hawking radiation, brief introduction to information theory and cause of information paradox are given. Then, solution of black hole information paradox outside the LQG are briefly explained. Thereafter, basic concepts of LQG along with loop quantum cosmology (LQC) are described. LQG can solve information paradox by its natural cut off on the value of quantum volume operator. In LQG, a star namely, Planck star is also proposed that is formed at Planck density and resides at so-called singularity point. Since, LQG removes singularity through big bounce and proposes Planck star which provides enough room for information to escape; hence, it can solve information paradox. LQG predicts remnant of black hole of the order of \(10^{-14} m\); which, is under current technological regime. In the remnant scenario, black hole makes quantum transition into white hole and this white hole behaves as a long lived remnants that can solve information paradox. In this quantum transition, a black hole tunnels into a white hole at the end of evaporation.

We continue our recent endeavor in which a time-dependent black hole solution of a one-loop quantum-corrected Einstein-scalar system was obtained and its near-horizon behavior was analyzed. The energy analysis led to a trans-Planckian scaling behavior near the event horizon. In the present work the analysis is extended to a rotating black hole solution of an Einstein-Maxwell-scalar system with a Higgs potential. Although the analysis becomes much more complex compared to that of the previous, we observe the same basic features, including the quantum-gravitational trans-Planckian energy near the horizon.

We propose a cosmological model in which the Big Bang was not the beginning of space and time; there was a previous phase leading up to it, with multiple cycles of contraction and expansion that repeat indefinitely; from big bang to big crunch. The observed accelerated expansion, which relates the change in the space, to change in the stretching of shrink space for the new theory, is derived. As pressure of shrink space decreases, the expansion of space increases, that is although in general, decelerate in the pressure of shrink space leads to accelerate the stretching of space. (pressure of shrink space approaching zero at the end of accelerated expansion, or when all the shrinked space stretches), after that a period of slow contraction begins, thus bringing the universe back to contract to its initial state, ending in a Big Crunch. The universe will not always continue to expanding, no need however, for dark energy. The new definition of eternal space enables us to describe a sequence of events from the Big Bang to the Big Crunch.

This paper gives both a general canonical quantum gravity theory and the general canonical quantum gravity theories of the Universe and general black hole, and discovers the relations reflecting symmetric properties of the standard nonlinear gravitational Lagrangian, which are not relevant to any concrete metric models. This paper concretely shows the general commutation relations of the general gravitational field operators and their zeroth, first, second and third style, respectively, of high order canonical momentum operators for the general nonlinear system of the standard gravitational Lagrangian, and then has finished all the four styles of the canonical quantization of the standard gravity.

The entangled antipodal points on black hole surfaces, recently described by t’Hooft, display an unnoticed relationship with the Borsuk-Ulam theorem. Taking into account this observation and other recent claims, suggesting that quantum entanglement takes place on the antipodal points of a S³ hypersphere, a novel framework can be developed, based on algebraic topological issues: a feature encompassed in an S² unentangled state gives rise, when projected one dimension higher, to two entangled particles. This allows us to achieve a mathematical description of the holographic principle occurring in S². Furthermore, our observations let us to hypothesize that a) quantum entanglement might occur in a four-dimensional spacetime, while disentanglement might be achieved on a motionless, three-dimensional manifold; b) a negative mass might exist on the surface of a black hole.

The thermodynamics of black holes is discussed for the case, when the Newton constant G is not a constant, but is the thermodynamic variable. This gives for the first law of the Schwarzschild black hole thermodynamics: d S BH = − A d K + d M T BH , where the gravitational coupling K = 1 / 4 G , M is the black hole mass, A is the area of horizon, and T BH is Hawking temperature. From this first law it follows that the dimensionless quantity M 2 / K is the adiabatic invariant, which in principle can be quantized if to follow the Bekenstein conjecture. From the Euclidean action for the black hole it follows that K and A serve as dynamically conjugate variables. This allows us to calculate the quantum tunneling from the black hole to the white hole, and determine the temperature and entropy of the white hole.

We delve into nonrelativistic quantum electrodynamics within a background magnetic field, ensuring gauge invariance via a vector potential. Our exploration extends to the Lagrangian, which incorporates electron self-interactions and electromagnetic field interactions. Through the path integral formalism, we elucidate the effective action, with a specific focus on the photon propagator and screening effects. Examining density and current components reveals Laurent expansions in the hydrodynamic limit. The equations of motion in real space are derived, leading to discussions on phenomena such as Poiseuille-like flow and the Navier-Stokes equation. To ground our theoretical framework at practical contexts, we consider applications such as the fluid dynamics at binary star systems. Depending on the velocity of the expelled fluid, our analysis allows for both nonrelativistic and relativistic treatments, providing a versatile tool for understanding the intricacies of fluid behavior at astrophysical scenarios. Additionally, we recognize that at the presence of a magnetic field, magnetohydrodynamics becomes crucial. While our current focus is at nonrelativistic quantum electrodynamics, the insights gained here contribute to a broader understanding, offering a comprehensive foundation for quantum electrodynamics analysis at diverse physical systems.

In this paper only one basic assumption has been made: if we try to describe black holes, their behavior should be understood in the same language as the one we use for particles; black holes should be treated just like atoms. They must be quantum forms of matter, moving in accordance with Schrödinger equations just like everything else. In particular, Rosen’s quantization approach to the gravitational collapse is applied in the simple case of a pressureless “star of dust” by finding the gravitational potential, the Schrödinger equation and the solution for the collapse’s energy levels. By applying the constraints for a Schwarzschild black hole (BH) and by using the concept of BH effective state, previously introduced by one of the authors (CC), the BH quantum gravitational potential, Schrödinger equation and the BH energy spectrum are found. Remarkably, such an energy spectrum is in agreement (in its absolute value) with the one which was conjectured by Bekenstein in 1974 and consistent with other ones in the literature. This approach also permits to find an interesting quantum representation of the Schwarzschild BH ground state at the Planck scale. Moreover, two fundamental issues about black hole quantum physics are addressed by this model: the area quantization and the singularity resolution. As regards the former, a result similar to the one obtained by Bekenstein, but with a different coefficient, has been found. About the latter, it is shown that the traditional classical singularity in the core of the Schwarzschild BH is replaced, in a full quantum treatment, by a two-particle system where the two components strongly interact with each other via a quantum gravitational potential. The two-particle system seems to be non-singular from the quantum point of view and is analogous to the hydrogen atom because it consists of a “nucleus” and an “electron”.

This paper is devoted to investigate charged vector particles tunneling via horizons of a pair of accelerating rotating charged NUT black hole under the influence of quantum gravitational effects. For this purpose, we use the modified Proca equation incorporating generalized uncertainty principle. Using the WKB approximation to the field equation, we obtain a modified tunneling rate and the corresponding corrected Hawking temperature for this black hole. Moreover, we analyze the graphical behavior of corrected Hawking temperature T'_H with respect to the event horizon for the given black hole. By considering quantum gravitational effects on Hawking temperatures, we discuss the stability analysis of this black hole. For a pair of black holes, the temperature T'_H increases with the increase in rotation parameters α and w, correction parameter β, black hole acceleration α and arbitrary parameter k and decreases with the increase in electric e and magnetic charges g.

Various techniques to tackle the black hole information paradox have been proposed. A new way out to tackle the paradox is via the use of pseudo-density operator. This approach has successfully dealt the problem with a two-qubit entangle system for a single black hole. In this paper, we present the interaction with a binary black hole system by using an arrangement of the three-qubit system of Greenberger–Horne–Zeilinger (GHZ) state. We show that our results are in excellent agreement with the theoretical value. We have also studied the interaction between the two black holes by considering the correlation between the qubits in the binary black hole system. The results depict a complete agreement with the proposed model. In addition to the verification, we also propose how modern detection of gravitational waves can be used on our optical setup as an input source, thus bridging the gap with the gravitational wave’s observational resources in terms of studying black hole properties with respect to quantum information and entanglement.

Considering the predictions from the standard model of particle physics coupled with experimental results from particle accelerators, we discuss a scenario in which from the infinite possibilities in the Lie groups we use to describe particle physics, nature needs only the lower dimensional representations - an important phenomenology that we argue indicates nature is code theoretic. We show that the quantum deformation of the SU(2) Lie algebra at the fifth root of unity can be used to address the quantum Lorentz group representation theory through its universal covering group and gives the right low dimensional physical realistic spin quantum numbers confirmed by experiments. In this manner we can describe the spacetime symmetry content of relativistic quantum fields in accordance with the well known Wigner classification. Further connections of the fifth root of unity quantization with the mass quantum number associated with the Poincaré Group and the SU(N) charge quantum numbers are discussed as well as their implication for quantum gravity.

We have recently presented a unified quantum gravity theory [1]. Here we extend on that work and present an even simpler version of that theory. For about hundred years, modern physics has not been able to build a bridge between quantum mechanics and gravity. However, a solution may be found here; we present our quantum gravity theory, which is rooted in indivisible particles where matter and gravity are related to collisions and can be described by collision space-time. In this paper, we also show that we can formulate a quantum wave equation rooted in collision space-time, which is equivalent to mass and energy.The beauty of our theory is that most of the main equations that currently exist in physics are not changed (in terms of predictions), except at the Planck scale. The Planck scale is directly linked to gravity and gravity is, surprisingly, actually a Lorentz symmetry as well as a form of Heisenberg uncertainty break down at the Planck scale. Our theory gives a dramatic simplification of many physics formulas without altering the output predictions. The relativistic wave equation, the relativistic energy momentum relation, and Minkowski space can all be represented by simpler equations when we understand mass at a deeper level. This not attained at a cost, but rather a reflection of the benefit in having gravity and electromagnetism unified under the same theory.

We present a new perspective of the link between QED and Maxwell's equations. We demonstrate that the interpretation of $\mathbf{D}=\varepsilon_{0} \mathbf{E}$ as vacuum polarization is consistent with QED. A free electromagnetic field polarizes the vacuum, but the polarization and magnetization currents cancel giving zero source current. The speed of light is a universal constant, while the fine structure constant, which couples the electromagnetic field to matter, runs as it should.

In our recently proposed theory of quantum gravity, a black hole arises from the spontaneous localisation of an entangled state of a large number of atoms of space-time-matter [STM]. Prior to localisation, the non-commutative curvature of an STM atom is described by the spectral action of non-commutative geometry. By using the techniques of statistical thermodynamics from trace dynamics, we show that the gravitational entropy of a Schwarzschild black hole results from the microstates of the entangled STM atoms and is given (subject to certain assumptions) by the classical Euclidean gravitational action. This action, in turn, equals the Bekenstein-Hawking entropy (Area/$4{L_P}^2$) of the black hole. We argue that spontaneous localisation is related to black-hole evaporation through the fluctuation-dissipation theorem.

We discuss the fate of the correspondence principle beyond quantum mechanics, specifically in quantum field theory and quantum gravity, in connection with the intrinsic limitations of the human ability to observe the external world. We conclude that the best correspondence principle is made of unitarity, locality, proper renormalizability (a refinement of strict renormalizability), combined with fundamental local symmetries and the requirement of having a finite number of fields. Quantum gravity is identified in an essentially unique way. The gauge interactions are uniquely identified in form. Instead, the matter sector remains basically unrestricted. The major prediction is the violation of causality at small distances.

We generalize the dynamical analog of the Berry geometric phase setup to the quaternionic model of Avron et al. In our dynamical quaternionic system, the fast half-integer spin subsystem interacts with a slow two-degrees-of-freedom subsystem. The model is invariant under the 1:1:2 weighted SO(2) symmetry and spin inversion. There is one formal control parameter in addition to four dynamical variables of the slow subsystem. We demonstrate that the most elementary qualitative phenomenon associated with the rearrangement of the energy super-bands of our model consists of the rearrangement of one energy level between two energy superbands which takes place when the formal control parameter takes the special isolated value associated with the conical degeneracy of the semi-quantum eigenvalues. This qualitative phenomenon is of the topological origin, and is characterized by the second Chern class of the associated semi-quantum system. The correspondence between the number of redistributed energy levels and the second Chern number is confirmed through a series of examples.

The phenomenal mathematical efficiency of quantum field theories in modern high-speed information and communication systems has a very simple explanation from the point of view of common sense and higher mathematical logic: all of them – quantum cosmology, quantum physics, quantum metrics and quantum calculus – are the self-informational mathematical systems based on symbolic and numerical functional analysis and elementary recursive calculations of interrelated space and time parameters of matter motion in various states of the material environment.For the first time in scientific and engineering practice, it was clearly shown that the information entropy of both standard symbolic and non-standard numerical functional analysis has absolute exact limits of computational accuracy – 1/10^16 and 1/10^64, respectively. Moreover, the second limit determines the maximum level of accuracy of practical quantum metrics and calculations and fully coordinates four branches of classical physics – thermodynamics, electrodynamics, gravidynamics, chromodynamics with special and general relativity.

We introduce quantum spatio-temporal dynamics (QSD) as modeled by the Nexus Paradigm (NP) of quantum gravity to resolve the problem of energy- momentum localization in a gravitational field. Currently, the gravitational field as described using the language of geometry modeled under General Relativity (GR) fails to provide a generally accepted definition of energy-momentum. Attempts at resolving this problem using geometric methods have resulted in various energy-momentum complexes whose physical meaning remain dubious since the resulting complexes are non-tensorial under a general coordinate transformation. In QSD, the tangential manifold is the affine connection field in which energy-momentum localization is readily defined. We also discover that the positive mass condition is a natural consequence of quantization and that dark energy is a Higgs like field with negative energy density everywhere. Finally, energy-momentum localization in quantum gravity shows that a free falling object will experience large vacuum fluctuations (uncertainties in location) in strong gravity than in weak gravity and that the amplitudes of these oscillations defines the energy of the free falling object.

Black hole collision produce gravitational radiation which is generally thought in a quantum limit to be gravitons. The stretched horizon of a black hole contains quantum information, or a form of quantum hair, which in a coalescence of black holes participates in the generation of gravitons. This may be facilitated with a Bohr-like approach to black hole (BH) quantum physics with quasi-normal mode (QNM) approach to BH quantum mechanics. Quantum gravity and quantum hair on event horizons is excited to higher energy in BH coalescence. The near horizon condition for two BHs right before collision is a deformed AdS spacetime. These excited states of BH quantum hair then relax with the production of gravitons. This is then argued to define RT entropy given by quantum hair on the horizons. These qubits of information from a BH coalescence should then appear in gravitational wave (GW) data. This is a form of the standard AdS/CF T correspondence and the Ryu-Takayanagi (RT) formula [1]. The foundations of physics is proposed to be quantum information and a duality between spacetime observables and quantum fields.

When gravity is quantum, the point structure of space-time should be replaced by a non-commutative geometry. This is true even for quantum gravity in the infra-red. Using the octonions as space-time coordinates, we construct a pre-spacetime, pre-quantum Lagrangian dynamics. We show that the symmetries of this non-commutative space unify the standard model of particle physics with $SU(2)_R$ chiral gravity. The algebra of the octonionic space yields spinor states which can be identified with three generations of quarks and leptons. The geometry of the space implies quantisation of electric charge, and leads to a theoretical derivation of the mysterious mass ratios of quarks and the charged leptons. Quantum gravity is quantisation not only of the gravitational field, but also of the point structure of space-time.

The understanding of black holes in loop quantum gravity is becoming increasingly accurate. This review focuses on the possible experimental or observational consequences of the underlying spinfoam structure of space-time. It adresses both the aspects associated with the Hawking evaporation and the ones due to the possible existence of a bounce. Finally, consequences for dark matter and gravitational waves are considered.

Abstract Using the Pauli algebra version of the Dirac equation six symmetric but non-equivalent copies of the QED Lagrangian are constructed. The group of symmetries is the group of outer automorphisms of the finite quaternion group, isomorphic to the group of permutations on three letters. Solutions to corresponding Dirac equations form six sectors of fermion fields. The intersections between different sectors can only contain massless fields, implying that the sectors are distinct. If the symmetry could be extended to the full Standard Model Lagrangian it would predict the ratio of dark matter to ordinary matter of 5 : 1 which is close to the ratio of 5.2 : 1 according to current observations.

(3+1)D quantum mechanics is a four-dimensional quantum formalism, which is developed neither in a Minkowski spacetime, nor in a purely Hilbert space and not its metric is Lorentzian. This quantum mechanics also yields the quantum Einstein field equation in (3+1)D quantum spacetime. Every observable (3+1)D quantum spacetime can be found to contain internally hidden opposite spin quantum state, that results Supersymmetry. Closed continuous mappings of this hidden quantum state immediately yield more extra hidden dimensions including string. This string is found to be fundamentally eleven-dimensional (rather than lower dimensional) by nature within this quantum spacetime, which is necessarily a natural phenomenon of (3+1)D Quantum Mechanics.

We study the performance of an endoreversible magnetic Otto cycle with a working substance composed of a single quantum dot described using the well-known Fock-Darwin model. We find that tuning the intensity of the parabolic trap (geometrical confinement) impacts the proposed cycle’s performance, quantified by the power, work, efficiency, and parameter region where the cycle operates as an engine. We demonstrate that a parameter region exists where the efficiency at maximum output power exceeds the Curzon-Ahlborn efficiency, the efficiency at maximum power achieved by a classical working substance.

Many experiments and collected data support general relativity as it explains spacetime as a smooth Riemannian manifold. However, general relativity does not explain the chaotic nature of spacetime on the quantum level, where determinism is almost impossible. This is one of the major problems in physics yet it requires a deeper theory to solve this incompatibility. In this research, a derivation made from Newton’s law of gravitation to better explain the behavior of spacetime in the quantum world with the assumption that spacetime is quantized with energy wave-particles and these wave-particles accumulate to form massive wave like particles (hence the standard model of particle physics). In the end, the derivation and the assumption together clearly illustrate general relativity and quantum theory.

In a recent article we showed that the analog of the cosmological constant in two spacetime dimensions for a wide variety of integrable quantum field theories has the form ρvac = −m2/2g where m is a physical mass and g is a generalized coupling, where in the free field limit g → 0, ρvac diverges. We speculated that in four spacetime dimensions ρvac takes a similar form ρvac = −m4/2g, but did not support this idea in any specific model. In this article we study this problem for λφ4theory in d spacetime dimensions. We show how to obtain the exact ρvac for the sinh-Gordon theory in the weak coupling limit by using a saddle point approximation. This calculation indicates that the cosmological constant can be well-defined, positive or negative, without spontaneous symmetry breaking. We also show that ρvac satisfies a Callan-Symanzik type of renormalization group equation. For the most interesting case physically, ρvac is positive and can arise from a marginally relevant negative coupling g and the cosmological constant flows to zero at low energies.

We develop a renormalizable model of Quantum General Relativity (QGR). We do this by building on earlier work with quantum electrodynamics (QED). Working with the Feynman path integral (FPI) approach to QED, we generalize the paths from varying in space to varying in space and time. This gives the standard results plus dispersion in time of order attoseconds or left. Over longer times, the dispersion in time averages out, but at attosecond times it should be detectable with current technology. As an unexpected but welcome side-effect, the approach caused the usual loop integrals to be finite. Since the usual UV divergences are significantly harder to renormalize in QGR than in QED, and since using paths in time plus space is definitely more in keeping with the general spirit of GR, we here apply the same approach to QGR. We show that with an appropriate choice of gauge (trace-reversed de Donder gauge) we can extend the earlier results to include QGR. Sub-attosecond measurements of individual gravitons are not within our reach, but at least the ultraviolet divergences in QGR are contained in the same way. We have therefore a renormalizable model of QGR

Two opposed p–n diodes are connected with another junction that causes cancellation of the electric field in the depletion layer of each diode by the field of the other diode. This derived quantum diode is called the A system. Another dual diode, constructed by the same process but with the p- and n-types positioned as duality, called the B system. When a bias voltage is applied between the A and B systems, Lorentz conservation imparts a momentum (i.e., a wave number) to the carriers in the absence of any internal voltage. Thus, a superconducting bias current density appears without the need for cooling. The reappearances of electron–hole pairs on the junction surfaces are assumed to be described by entire wavefunctions normalized by the band gap. Based on the bias superconducting current, NOT and NAND gates were constructed from the quantum diode systems. Numerical calculations revealed that the constant phases of the entire wavefunctions of the p-and n-types converged. Accordingly, it was clarified that Bose–Einstein condensation and the Meissner effect (described by the London equation) occurred in the quantum diode systems. Moreover, the systems exhibited rectification characteristics and a switching speed of the order of 10^-14 s. Combining this switching property with the large bias superconducting current (of the order of several V), we developed NOT and NAND gates with direct quantum correlations among many qubits, which are unaffected by random and thermal noises. These gates have memorization and initialization properties and are compatible with existing and accumulating programing algorithms. Moreover, when harvesting a divergent current output from these systems, the bias superconducting current and memorization property preserve the formed quantum correlations.

The recently proposed and logically developed paradigm of deep genetical affinity of scientific terms "energy-entropy-information" harmonizes classical and quantum physics with general and special theories of relativity. For the first time in engineering practice, a complex vector-tensor-matrix description of gravitational, thermal and electromagnetic fields in ideal solid, liquid and gaseous media was performed analytically and without preliminary measurements. The basic set of fundamental quantum constants of the standard physical model has been computed with an extreme precision of 1/10^64, which is a natural limit arising due to elementary recursive arithmetic and elementary functional analysis in digital notation.

The purpose of this paper is to find a quantum formulation of entropic gravity, incorporating the bijective theory. In a first part, we will describe the basis of the bijective theory. In a second part, we will incorporate the stress energy quantum tensor defined in the linear approximation of the Einstein’s equation in its quantum version to entropy. In the third part, we will integrate the bijective theory with the newly created relativistic quantum entropy. This will lead us four part where we will formalize quantum entropic gravity.

By this contribution we would like to briefly highlight the problems in conceiving the “Hydrogen Bond” (HB) as a real short-range, directional, electrostatic, attractive interaction and to reframe its nature through the non-approximated view of condensed matter offered by a Quantum Electro-Dynamic (QED) perspective. We focus our attention on water, as the paramount case to show the effectiveness of this 40-years’ old theoretical background, which depicts water as a two-fluid system (where one of the two phases is coherent). The HB emerge to be the result of the electromagnetic field gradient in the coherent phase of water, whose vacuum level is lower than the non-coherent (gas-like) fraction. Thus, the HB can be properly looked at, i.e. no more as a “dipolar force” among molecules, but as the phenomenological effect of their collective thermodynamic tendency to occupy a lower ground-state, compatibly with temperature and pressure. This perspective allows to account for many “anomalous” behaviours of water and to understand why the calculated energy associated to HB should change when considering two molecules (water-dimer), or the liquid state, or the several kinds of ice. The emergence of a condensed, liquid, phase at room temperature is indeed the consequence of the boson condensation as described in the framework of spontaneous symmetry breakings (SSB). The switch from a still semi-classical Quantum Mechanical (QM) in the 1st quantization to a Quantum Field Theory (QFT) view embedded in the 2nd quantization is advocated for a more realistic and authentic description of water, condensed matter and living systems.

The thermocontextual interpretation (TCI) defines the physical state with respect to a system’s actual surroundings at a positive ambient temperature. The TCI provides a clear distinction between the Second Law of thermodynamics and MaxEnt. The Second Law dictates irreversible dissipation of free energy to ambient heat, and it establishes the thermodynamic arrow of time. MaxEnt describes reversible changes in statistical mechanical entropy in response to changes in the system’s boundary constraints. We introduce new TCI postulates that establish the equality of thermal and statistical entropies and MaxEnt as a fundamental physical principle. We then apply MaxEnt to the double-slit experiment. Impacts of multiple particles symmetrically passing through parallel slits record a wave interference pattern over time. However, a which-slit detector eliminates wave interference. Richard Feynman called the double slit experiment the only mystery, at the heart of quantum mechanics. The TCI and MaxEnt offer a simple explanation. The which-slit detector breaks the system’s symmetry, and MaxEnt selects the higher-entropy asymmetrical state, enabling particles to pass through one slit or the other without wave interference.

We consider partition functions, in the form of state sums, and associated probabilistic measures for aperiodic substrates described by model sets and their associated tiling spaces. We propose model set tiling spaces as microscopic models for small scales in the context of quantum gravity. Model sets possess special self-similarity properties that allow us to consider implications on large and observable scales from the underlying (non-ergodic) dynamics. In particular we consider the implication of the underlying aperiodic substrate for the well known problem of time in quantum gravity, and propose a correspondence between small and large scales, the so-called ergodic correspondence, that addresses the emergence of matter properties and spacetime structure. In the process we find a possible bound in the mass spectrum of fundamental particles.

Recently, Bennett et al. [Eur. J. Phys. 37:014001, 2016] presented a physically-motivated and explicitly gauge-independent scheme for the quantisation of the electromagnetic field in flat Minkowski space. In this paper we generalise this field quantisation scheme to curved spacetimes. Working within the standard assumptions of quantum field theory and only postulating the physicality of the photon, we derive the Hamiltonian, $\hat H$, and the electric and magnetic field observables, $\hat {\bf E}$ and $\hat {\bf B}$, without having to invoke a specific gauge. As an example, we quantise the electromagnetic field in the spacetime of an accelerated Minkowski observer, Rindler space, and demonstrate consistency with other field quantisation schemes by reproducing the Unruh effect.

We consider the conjecture of the relationship between the entanglement entropy of spacetime, matter and the action in Einstein's general relativity. Our analysis suggests the possibility of regarding the entanglement entropy of spacetime and matter as the dimensionless action in general relativity by using Planck units. In this case, the action principle originates from the maximization of the entanglement entropy. We also show that the fundamental property of entanglement entropy leads to attractive characteristic of gravitational force for classical particles.

Novel approaches under the extreme conditions of ultra-high gravity of a super massive black hole allow us to assume that the spacetime degrades into the single dimension of time. A unique interpretation of the non-relativistic Schrödinger equation together with the relativistic Klein-Gordon and Dirac equations is presented by swapping the three dimensional space derivatives with the singular time derivative in the D’Alembertian operator. This apparatus reveals a unique time dependent wave equation that results in some implications such as possible time quantization with the intervals of around 3.36 × 10−21 ? which is in the order of uncertainty in time, ∆? = 1.3 × 10−21 ?, calculated from the energy-time version of the Heisenberg uncertainty principle for electrons. As a result of this, an antisymmetric wave function around the edge of the event-horizon zone appears and indicates that the virtual particle-antiparticle pairs of the electron field split into two real components with the spin-up and down states, reconfirming the Hawking radiation. Energy eigenvalues calculated from the application of the Dirac equation satisfies the preservation of energy and charge. The wave equation invoked in this study reduces into the time dependent Dirac equation within the neighborhood of zero-point, ? = 0, insuring the relevance of the evaluations.

Based on a local causal model of the dynamics of curved discrete spacetime, a causal model of quantum field theory in curved discrete spacetime is described. On the elementary level, space(-time) is assumed to consists of interconnected space points. Each space point is connected to a small discrete set of neighboring space points. Density distribution of the space points and the lengths of the space point connections depend on the distance from the gravitational sources. This leads to curved spacetime in accordance with general relativity. Dynamics of spacetime (i.e., the emergence of space and the propagation of space changes) dynamically assigns "in-connections" and "out-connections" to the affected space points. Emergence and propagation of quantum fields (including particles) are mapped to the emergence and propagation of space changes by utilizing identical paths of in/out-connections. Compatibility with standard quantum field theory (QFT) requests the adjustment of the QFT techniques (e.g., Feynman diagrams, Feynman rules, creation/annihilation operators), which typically apply to three in/out connections, to n > 3 in/out connections. In addition, QFT computation in position space has to be adapted to a curved discrete space-time.

Some physicists surmise that gravity lies outside of quantum mechanics. Thus theories like the standard semiclassical theory of quantum to gravity coupling (that of Rosenfeld and Møller) are possible real models of interaction, rather than a mere approximation of a theory of quantum gravity. Unfortunately, semiclassical gravity creates inconsistencies such as superluminal communication. Alternatives by authors such as Diósi, Martin, Penrose, and Wang often use the term 'stochastic' to set themselves apart from the standard semiclassical theory. These theories couple to fluctuations caused by for instance continuous spontaneous localization, hence the term 'stochastic'. This paper looks at stochastic gravity in the framework of a class of emergent or ontological quantum theories, such as those by Bohm, Cetto, and de Broglie. It is found that much or all of the trouble in connecting gravity with a microscopic system falls away, as Einstein's general relativity is free to react directly with the microscopic beables. The resulting continuous gravitational wave radiation by atomic and nuclear systems does not, in contrast to Einstein's speculation, cause catastrophic problems. The small amount of energy exchanged by gravitational waves may have measurable experimental consequences. A very recent experiment by Vinante et al. performed on a small cantilever at mK temperatures shows a surprising non-thermal noise component, the magnitude of which is consistent with the stochastic gravity coupling explored here.

Loop quantum gravity (LQG) quantizes gravity through the quantization of the space-time. It begins with general relativity (GR) and brings some concepts from quantum field theory to quantize the space-time. The conceptual background of GR is necessary to comprehend the LQG framework. Therefore, in this paper, prerequisite concepts such as special relativity, general relativity, covariant electromagnetism, tensor analysis, Lagrangian formulation, Hamiltonian formulation and basics of quantum mechanics are briefly introduced; that, are needed to study loop quantum gravity(LQG).

In this paper we will show that standard physics to a large degree consists of derivatives of a deeper reality. This means standard physics is both overly complex and also incomplete. Modern physics has typically started from working with first understanding the surface of the world, that is typically the macroscopic world, and then forming theories about the atomic and subatomic world. And we did not have much of a choice, as the subatomic world is very hard to observe directly, if not impossible to observe directly at the deepest level. Despite the enormous success of modern physics, it is therefore no big surprise that we at some point have possibly taken a step in the wrong direction. We will claim that one such step came when one thought that the de Broglie wavelength represented a real matter wavelength. We will claim that the Compton wavelength is the real matter wavelength. Based on such a view we will see that many equations in modern physics are only derivatives of much simpler relations. Second, we will claim that in today’s physics one uses two different mass definitions, one mass definition that is complete or at least more complete, embedded in gravity equations without being aware of it, as it is concealed in GM, and the standard, but incomplete, kg mass definition in non-gravitational physics. First, when this is understood, and one uses the more complete mass definition that is embedded in gravity physics, not only in gravity physics, but in all of physics, then one has a chance to unify gravity and quantum mechanics. Our new theory shows that most physical phenomena when observed over a very short timescale are probabilistic for masses smaller than a Planck mass and dominated by determinism at or above Planck mass size. Our findings have many implications. For example, we show that the Heisenberg uncertainty principle is rooted in a foundation not valid for rest-mass particles, so the Heisenberg uncertainty principle can say nothing about rest-masses. When re-formulated based on a foundation compatible with a new momentum that is also compatible with rest-masses, we obtain a re-defined Heisenberg principle that seems to become a certainty principle in the special case of a Planck mass particle. Furthermore, we show that the Planck mass particle is linked to gravity and that we can easily detect the Planck scale from gravity observations. The Planck mass particle is unique as it only lasts the Planck time, and in that very short time period it can only be observed directly from itself, and it therefore closely linked to absolute rest.

The classical Einstein’s Field Equation has been derived previously by demanding that the Clausius relation dS = δQ/T holds. In this letter, we show that the semiclassical Einstein’s Field Equation can be recovered using the generalized entropy Sgen by using the non-equilibrium thermodynamics where the Clausius relation is replaced by the entropy balance relation dS = δQ/T +diS, where diS is some internal entropy. Moreover, since the quantum fields violate the classical focusing, we, therefore, have to use quantum focusing in this case. Using then Jacobson’s idea of thermodynamics of spacetime we recover the semiclassical equation of motion. We, therefore, in a sense also show the validity of the semiclassical approximation, a crucial approach for establishing a number of important ideas such as the Hawking effect.

We argue that the problem of time is not a crucial issue inherent in the quantum picture of the universe evolution. On the minisuperspace model example with the massless scalar field, we demonstrate four approaches to the description of quantum evolution, which give similar results explicitly. The relevance of these approaches to building a quantum theory of gravity is discussed.

Using assembly theory, we investigate the assembly pathways of binary strings of length N formed by joining bits present in the assembly pool and the strings that entered the pool as a result of previous joining operations. We show that the string assembly index is bounded from below by the shortest addition chain for N, and we conjecture about the form of the upper bound. We define the degree of causation for the minimum assembly index and show that for certain N it features regularities that can be used to determine a shortest addition chain. We show that a string with the smallest assembly index for N can be assembled by a binary program of length equal to this index if the length of this string is expressible as a product of Fibonacci numbers. We conjecture that there is no binary program that has a length shorter than the length of the string having the largest assembly index for N that could assemble this string. The results confirm that four Planck areas provide a minimum information capacity that corresponds to a minimum thermodynamic (Bekenstein-Hawking) entropy. Knowing that the problem of determining the assembly index is at least NP-complete, we conjecture that this problem is NP-complete, while the problem of creating the string so that it would have a predetermined largest assembly index is NP-hard. The proof of this conjecture would imply P ≠ NP, since every computable problem and every computable solution can be encoded as a finite binary string. Once the new information is assembled by a dissipative structure or by a human, it is subject to the 2^nd law of thermodynamics, and nature seeks to optimize its assembly pathway.

We report the use of Einstein rings to reveal the quantized and dynamical states of space-time in a region of impressed gravitational field as predicted by the Nexus Paradigm of quantum gravity. This in turn reveals the orbital speeds of objects found therein and the radius of curvature of the quantized space-time. Similarities between the Nexus graviton and the singular isothermal sphere (SIS) in the Cold Dark Matter (CDM) paradigm are highlighted. However unlike the singular isothermal sphere, the Nexus graviton does not contain singularities or divergent integrals. This solves the core cusp problem. In this work, data from a sample of fifteen Einstein rings published on the Cfa-Arizona Space Telescope Lens Survey (CASTLES) website is used to probe the quantized properties of space-time.

It is shown that gravity and quantum physics can be unified upon the basis of a quark description in terms of a recently discovered third type Dirac particle. It requires the awareness of a polarisable second elementary dipole moment next to the angular moment (spin) and the awareness of an (unbroken) omnipresent energetic cosmological background field. The unification has been made explicit by relating the two major gravitational constants of nature (the gravitational constant and Milgrom’s acceleration constant) with the two major nuclear constants of nature (the weak interaction boson and the Higgs boson).

We introduce two symmetric concepts to physics: “distance” (space and time in one) and “wavematter” (electromagnetic wave packet and matter in one). We claim that physics has chosen the wrong concept of time: It is not aware that the time of a moving object flows in a direction other than my time. We provide 15 proofs for our claim by solving 15 mysteries of physics graphically! For example, we prove that length contraction and time dilation are actually geometrical effects in a 4D manifold that we call “Euclidean spacetime” (ES). We prove that the discrepancy in calculating the Hubble constant stems from a systematic error in the redshift measurement. We prove that what I deem wave, deems itself matter, which solves wave–particle duality. We even untangle quantum entanglement without the issue of non-locality. We finally understand why alternative theories of Euclidean relativity have failed: They are all based on four dimensions of space rather than distance. A huge amount of energy was injected into ES at a point that we take as origin. Ever since has this energy been moving radially away at the speed of light. We live in the 3D hypersurface of an expanding 4D hypersphere. Hyperspherical coordinates have the great advantage that they reduce all that is ever happening to just one formula. So, it is the Theory of Everything in these coordinates: “Energy is covering radial distance which, divided by Euclidean time, is equal to the speed of light.” Acceleration and force like gravitation emerge from a rotation of objects in ES and a subsequent projection to 3D space. Matching the symmetry simplifies physics.

For the first time in scientific and engineering practice, it is logically and mathematically substantiated, computationally verified and metrologically confirmed that classic and quantum physics, analytical and quantum chemistry, as well as continuous symbolic and discrete digital mathematical analysis, all have computational limits of information entropy, upper 1/10^16 and lower 1/10^64. Mutual displacement of these limits relatively center of Euclidean three-dimensional and of Cartesian two-dimensional space generate sets of quantum dots of mesh topology and weighted average harmonic units of quantum metrics of internal atomic and outer cosmic space, as well as determines limits of communication speed, clock frequency, calculation power and accuracy for any computing machine with subatomic elements of memory. The matrices of functional density and entropy of energy and information fields reconciles classic and quantum physics with continuous and discrete mathematics of special and general relativity.

In this paper, we investigate the Hawking radiation process by using the quantum tunneling phenomenon of massive spin-1 (W-bosons) and spin-0 particles from (2+1) dimensional Black Hoke with quintessential and magnetic field. For this purpose, using Hamilton-Jacobi ansatz, we apply the WKB approximation to the field equations of massive charged vector particles. We get the required tunneling rate of radiated particles and obtain their corresponding Hawking temperature $T_h$. In order to study the quantum gravity effects, we utilize the generalized Proca and Klein-Gordan equations incorporating the generalized uncertainty principle (GUP) and recover the accompanying quantum corrected temperature $T'_{h}$.

We show that the accelerating expansion phase of the universe can emerge from the group field theory formalism, a candidate theory of quantum gravity. The cosmological evolution can be extracted from condensate states using mean field approximation, in a form of modified FLRW equations. By introducing an effective equation of state w, we can reveal the relevant features of the evolution, and show that with proper choice of parameters, w will approach to −1, corresponds to the behaviour of cosmological constant, results in a late time acceleration and leads to de Sitter spacetime asymptotically.

Here we mathematically model black holes and the early universe following dynamics similar to RLC electrical models, focusing on their similarities at the singularity. We use this mathematically modelling to hypothesize the evolution of an expanding universe as the result of a black hole collapse followed by its evaporation. Or model consists of several steps defined by: (1) the formation of a black hole following general relativity equations; (2) growth of the black hole modelled as a resistance-capacitance-like electrical circuit; (3) expansion of space-time following the disintegration of the black hole, modelled by RLC-like dynamics. In updating this article, version 2, we will expand by presenting three additional examples related to the theory of the generalization Boltzmann's constant in curved space-time and the theory of general and especial relativity. We will calculate the critical mass to produce a black hole in the LHC, the existence of a high temperature Bose-Einstein condensate and finally we will demonstrate the existence of a tangential force to the repulsion force in the disintegration of subatomic particles. In the update of this article, version 3, we will expand to develop two examples. First, we will present the relationship between M-theory, extra dimensions with the theory of the generalization of Boltzmann's constant in curved space-time. Secondly, we will propose the idea of ​​updating the Lambda-CDM model, considering the primordial gravitational waves to correctly describe the evolution of the universe.

Recent advances in the theory of quantum gravity show that the Ricci flow serves as the time evolution operator for the vacuum energy density and that in the presence of baryonic matter, the Ricci flow is analogous to the heat equation in the presence of a heat sink. Here we show using the equations of quantum gravity, that quantum information can be modelled as a thermal fluid consisting of a superposition of weakly excited eigenstates of a quantum field and that each eigenstate vector has an associated eigenstate potential well. The depth of the potential well depends on the amplitude of the eigenstate vector. Measurement is then considered as a selection by tuning process which only allows an eigenstate resonating with the detector to be detected. During the detection process, the resonating eigenstate vector increases in amplitude, deepening its potential well such that the other weakly excited states rapidly drain their small excitation energies into it via the principle of minimum action. This draining process is the act of collapsing the wave function to a specific state. Also, the presence of the eigenstate potential wells is what cancels out the infinities from high energy interactions.

We generalize the idea of quantum clock time to quantum spacetime reference frame via physical realization of a reference system by quantum rulers and clocks. Omitting the internal degrees of freedom (such as spins) of the physical rulers and clocks, only considering their metric properties, the spacetime reference frame is described by a bosonic non-linear sigma model (NLSM). We study the quantum behavior of the system under approximations, and obtain (1) a cosmological constant valued (2/π)ρ_c0 (ρ_c0 the critical density at near current epoch) which is very close to the observations; (2) an effective Einstein-Hilbert term; (3) the ratio of variance to mean-squared of spacetime interval tends to a universal constant 2/π in the infrared region. This effect is testable by observing a linear dependence between the inherent quantum variance and mean-squared of the redshifts from cosmic distant spectral lines. The proportionality is expected to be the observed percentage of the dark energy. The equivalence principle is also generalized to the quantum level.

It is shown that Verlinde’s hypothetical concepts of entropic gravity can be successfully applied to the author’s previous work on the modification of the Newtonian gravity by Einstein’s Cosmological Constant. It allows a theoretical justification for Milgrom’s empirical acceleration constant, thereby revealing some fundamental differences with Verlinde’s conclusions.

We analyze different approaches to quantum gravity. It is stressed that nonperturbative methods to quantise gravity and the usage of diffeomorphism-invariant variables are very important. We pay attention on the Wheeler--DeWitt equation in the framework of canonical quantum gravity. The Wheeler--DeWitt equation is presented in the first order formalism with the hope that this form can solve some problems such as singularities and the ordering. Also, there is a problem of defining the time.

There has been a disconnect between our understanding of the universe's working at the micro and macro scale - that is, disagreement between quantum mechanics (QM) and general relativity (GR). A theory of vacuum-matter equilibrium is presented from scratch to bridge this gap. It is proposed that gravitons are both quanta of matter and gravitation, as every matter entity is believed to interact with gravitation. The vacuum has an energy density that gives rise to virtual-graviton pairs. Upon collision, a virtual-graviton may get stuck to the matter while a graviton from the matter gets ejected. It is possible as all gravitons are identical in mass and size. Equilibrium is thus established where matter erodes in the vacuum, and the vacuum condenses as matter. The probability of graviton exchange depends on the relative energies of the virtual-graviton and matter entity, as calculated in the inertial frame of reference (IFoR) decided by the state motion of vacuum energy at that place. If the rate of matter-vacuum equilibrium is taken as a constant, it leads to the notion of time and time dilation. The force appearing on a matter entity through collision with virtual-gravitons is calculated, and the expression is a hybrid of Newton's and Einstein's equation. It further helps to answer the queries related to phenomena like the flatness of galaxy rotation curves, misconceptions about relativistic mass and length contraction, the relation between time, gravity, and quantum entanglement (QE), and the composite nature of the universal gravitational constant.

We consider the quantum thermodynamic origin of the gravitational force of matter by applying the spacetime entanglement entropy and the Unruh effect originating from vacuum quantum fluctuations. By analyzing both the local thermal equilibrium and quasi-static processes of a system, we may get both the magnitude and direction of Newton's gravitational force in our theoretical model. Our work shows the possibility that the elusive Unruh effect has already shown its manifestation through gravitational force.

The Simulation analogy presented in this work enhances the accessibility of abstract quantum theories, specifically the stochastic hydrodyanimc model (SQHM), by relating them to our daily experiences. The SQHM incorporates the influence of fluctuating gravitational background, resembling dark energy, into quantum equations. This model successfully addresses key aspects of Objective-Collapse Theories, including resolving the 'tails' problem through the definition of quantum potential length in addition to the De Broglie length, beyond which coherent Schrödinger quantum behavior and wavefunction tails cannot be maintained. The SQHM emphasizes that an external environment is unnecessary, asserting that the quantum stochastic behavior leading to wave-function collapse can be an inherent property of a system in a spacetime with fluctuating metrics. Embedded in relativistic quantum mechanics, the theory establishes a coherent link between the uncertainty principle and the constancy of light speed, aligning seamlessly with finite information transmission speed. Within a fluctuating quantum system, the SQHM derives the indeterminacy relation between energy and time, offering insights into measurement processes impossible within a finite time interval in a truly quantum global system. Experimental validation is found in confirming the Lindemann constant for solid lattice melting points and the transition from fluid to superfluid states. The SQHM's self-consistency lies in its ability to describe wavefunction collapse and the measure process. Additionally, the theory resolves the Pre-existing Reality problem by showing that large-scale systems naturally decay into decoherent states stable in time. Continuing, the paper demonstrates that the physical dynamics of SQHM can be analogized to a computer simulation employing optimization procedures for realization. This perspective elucidates the concept of time in contemporary reality and enriches our comprehension of free will. The overall framework introduces an irreversible process impacting the manifestation of macroscopic reality at the present time, asserting that the multiverse exists solely in future states, with the past comprising the formed universe after the current moment. Decoherence at the present time functions as a reduction of the multiverse to a single universe. The macroscopic reality, characterized by fractal consistency where microscopic domains with quantum properties coexist, provides insights into how our consciousness apprehends dynamic reality, the spontaneous emergence of gravity in discrete spacetime evolution, and the attainment of the classical General Relativity limit in Quantum Loop Gravity and Causal Dynamical Triangulation. The Simulation Analogy highlights a strategy focused on minimizing information processing, facilitating the universal simulation in solving its predetermined problem. From within, reality becomes the manifestation of specific physical laws emerging from the inherent structure of the simulation devised to address its particular issue. In this context, the reality simulation appears to employ an entropic optimization strategy, minimizing information loss while efficiently compressing data in line with the simulation's intended purpose.

The nonlocality of entangled quantum mechanical systems is incompatible with the standard interpretation of special relativity as a single 4D Minkowskian metric spacetime. The difficulty is that the definition of a spacetime interval between any pair of events precludes any form of nonlocal interaction, even the relatively benign non-signaling correlations. By an application of the relativity principle, and the use of the space ←→ time symmetry of the Lorentz boost I propose here a reinterpretation of special relativistic spacetime. This new ontology consists of a set of coexisting 3+1D spaces (‘framespaces’), each containing unique content in the form of a complex density. These spaces are related by the Lorentz boost, and coupled pairwise in a manner dictated by the Lorentz transformation. The inter-space coupling acting on the spacetime content gives rise to a nonlocal wave phenomenon, which is identified as quantum wave mechanics. The interspace coupling strength is then inversely proportional to Planck’s constant. The coexistence of multiple spaces is interpreted as momentum superposition, implying that momentum is the fundamental physical basis of quantum superposition. This new spacetime interpretation of quantum mechanics has many consequences, including explanations of quantum non-locality, the spacetime role of Planck’s constant, quantum measurement as a symmetry-breaking process and the redundancy of description of gauge theory.

Recent efforts to conceptually design a technologically meaningful electromagnetic retarded engine indicated that this can only be done using the immense charge and current densities which exist in the atomic scale. However, this scale cannot be described by Newtonian physics, and only a quantum description will suffice to describe the dynamics of an electron on this scale properly. Here we study the retarded field quantum engine and highlight the differences between the quantum and the classical retarded engines.

In the present work, a superlattice structure comprising superconducting and insulator layers is studied. Here, if a magnetic field is applied parallel to the layers, the lack of a pinning center leads to a novel transition; in particular, as the applied magnetic field is reduced, the stationary wave surrounding the magnetic flux quantum in the superconducting layer eventually collides with the superconducting–insulating interfaces on both sides because its radius becomes larger than the width of the superconducting layer. At this instant, the stationary wave will collapse, and a transition will occur: the magnetic quanta are collapsed and thus the uniform magnetic field distribution is achieved, which corresponds to the transition from the superconducting state to the normal state over critical current. Considering a one-dimensional model of the structure, a critical current density equation is derived that indicates an increase in the critical current density for increased applied magnetic field. Subsequently, the same calculation was conducted after changing the direction of the magnetic field component, and the combination of these two calculations expresses the anisotropic property of the structure. The phenomenon is also predicted for anisotropic critical current density. This phenomenon is an important discovery that helps manufacture high-temperature superconducting tape as well as large high-temperature superconducting coils.

In this paper, we consider the formation of quantum black holes (QBHs) through a genuine quantum process. We treat particles at the Planck energy as QBHs. The Hawking temperature and entropy of QBHs are estimated. We also show that a QBH has a discrete energy spectrum. By analogy with supersymmetric theory, the mass of the superpartner of a QBH is estimated.

We derive time evolution equations, namely the Schrodinger-like equations and the Klein-Gordon equations for coherent fields and the Kadanoff-Baym (KB) equations for quantum fluctuations, in Quantum Electrodynamics (QED) with electric dipoles in 2 + 1 dimensions. Next we introduce a kinetic entropy current based on the KB equations in the 1st order of the gradient expansion. We show the H-theorem for the Leading-Order self-energy in the coupling expansion (the Hartree-Fock approximation). We show a conserved energy in the spatially homogeneous systems in the time evolution. We derive aspects of the super-radiance and the equilibration in our single Lagrangian. Our analysis can be applied to Quantum Brain Dynamics, that is QED with water electric dipoles. The total energy consumption to maintain super-radiant states in microtubules seems to be within the energy consumption to maintain the ordered systems in a brain.

The theories of quantum mechanics and relativity dramatically altered our understanding of the universe ushering in the era of modern physics. Quantum theory deals with objects probabilistically at small scales, whereas relativity deals classically with motion in space and time. We show here that the mathematical structures of quantum theory and of relativity follow together from pure thought, defined and uniquely constrained by the same elementary ``combining and sequencing'' symmetries that underlie standard arithmetic and probability. The key is uncertainty, which inevitably accompanies observation of quantity and imposes the use of pairs of numbers. The symmetries then lead directly to the use of complex \sqrt{-1} arithmetic, the standard calculus of quantum mechanics, and the Lorentz transformations of relativistic spacetime. One dimension of time and three dimensions of space are thus derived as the profound and inevitable framework of physics.

A classical origin for the Bohmian quantum potential, as that potential term arises in the quantum mechanical treatment of black holes and Einstein-Rosen (ER) bridges, can be based on 4th-order extensions of Einstein's equations. In Bohm's ontological interpretation, black hole radiation, and the analogous tunneling process of quantum transmission through an ER bridge, are classically allowed if the dynamics are modified to include such a quantum potential. The 4th-order extension of general relativity required to generate the quantum potential is given by adding quadratic curvature terms with coefficients that maintain a fixed ratio, as their magnitudes approach zero. Quantum transmission through the classically non-traversable bridge is replaced by classical transmission through a traversable wormhole. If entangled particles are connected by a Planck-width ER bridge, as conjectured by Maldacena and Susskind, then the classical wormhole transmission effect gives the ontological nonlocal connection between the particles posited in Bohm's interpretation of their entanglement. It is hypothesized that higher-derivative extensions of classical gravity can account for the nonlocal part of the quantum potential generally.

SARS-CoV-2 Omicron variant spike RBD epitopes in complex with spike (S) -protein D614G mutations now predominate globally and increase infectivity by assembling more functional S proteins into the virion. On average, homeopathic medicine contains less than one molecule per dose on average. Single variable SphericalHarmonicY, LaguerreL, WhittakerM, SphericalBesselJ, LegendreP, LegendreQ, LaguerreL, ChebyshevT, and Hypergeometric1F1 Functions pFqarise in connection with the power series solution of the Schrodinger equation or in the summation of perturbation expansions in quantum mechanics. A quantum interpretation of the homeopathic method is presented here through a novel algebraic topology approach to supersymmetry and symmetry breaking in quantum fields and quantum gravity theory with the aim of developing a wide range of physical-based drug design applications in a Small Molecule Quantized Water Memory Network suggesting that the Hidden Black Hole Paradox of Information Loss might be solved under suitable conditions.

This paper results from our investigation into novel means of electromagnetic propulsion. It requires the basis of our claims to be put on a sound theoretical footing regarding the purported momentum exchange with the electromagnetic field. One of these concerns is the huge discrepancy between the energy density of the Zeropoint and its purported manifestation as the Cosmological Constant. Here we state that it is manifestly wrong to introduce the zeropoint at zero order into the stress-energy tensor, because it is something which describes zero particle count. As a fluctuation, it belongs in a higher order Taylor expansion in frequency of the stress-energy tensor. Furthermore in the 3^rd order in the Einstein constant our procedure is some 9 orders of magnitude too small. We make up this difference by suggesting that vacuum energy is much higher still and that more degrees of freedom exist in physics beyond the Standard Model or that there is interaction energy between the modes.

By utilizing a generalized version of the Madelung quantum-hydrodynamic framework that incorporates noise, we derive a solution using the path integral method to investigate how a quantum superposition of states evolves over time. This exploration seeks to comprehend the process through which a stable quantum state ultimately emerges in the presence of fluctuations induced by the noisy gravitational background. The model defines the conditions that give rise to a limited range of interaction for the quantum potential, allowing for the existence of coarse-grained classical descriptions at a macroscopic level. The theory uncovers the smallest attainable level of uncertainty in an open quantum system and examines its consistency with the localized behavior observed in large-scale classical systems. The research delves into connections and similarities with decoherence theory and the Copenhagen interpretation of quantum mechanics. Additionally, it assesses the potential consequences of wave function decay on the measurement of photon entanglement. To validate the proposed theory, an experiment involving entangled photons transmitted between detectors on the Moon and Mars is discussed. Finally, the findings of the theory are applied to the creation of larger Q-bits systems at elevated temperatures.

Despite the successful reconciliation of special relativity and quantum mechanics (QM), a good century ago, general relativity (GR) in its current classical formulation still does not compile with QM. While GR gives precise sensical predictions at large scales, QM is obviously dominated at small scales! We think that the everlasting battle for exploring and understanding the Universe and for privileging a consistent perception of reality is therefore awaiting a consolidator rather than a conqueror. This should be capable of either unifying the two different benchmarks or at least bringing one closer to the other! The latter describes the consolidating approach, which is based on extending QM to relativistic energies and gravitational fields and generalizing Riemann to discretized Finsler geometry. Some properties of the additional geometric structures and curvatures which are disclosed by the proposed quantization and apparently overlooked in Einstein's GR, are analytically and numerically characterized. The analytical analyses introduce dynamics with possible nonlinear connections. We conclude that i) additional geometric structures and curvatures are intrinsic essential and ii) the spacetime at the quantum scale is no longer smooth or continuous. A maximal proper force is predicted, which maximally gravitationally accelerates a test particle and importantly manifests the quantum geometric nature of the generalized spacetime curvature.

Based on a local causal model of the dynamics of curved discrete spacetime, a causal model of quantum field theory in curved discrete spacetime is described. At the elementary level, space(-time) is assumed to consists of interconnected space points. Each space point is connected to a small discrete set of neighbor space points. Density distribution of the space points and the lengths of the space point connections depend on the distance from the gravitational sources. This leads to curved spacetime in accordance with general relativity. Dynamics of spacetime (i.e., the emergence of space and the propagation of space changes) dynamically assigns "in-connections" and "out-connections" to the affected space points. Emergence and propagation of quantum fields (including particles) are mapped to the emergence and propagation of space changes by utilizing identical paths of in/out-connections. Compatibility with standard quantum field theory (QFT) requests the adjustment of the QFT techniques (e.g., Feynman diagrams, Feynman rules, creation/annihilation operators), which typically apply to three in/out connections, to n > 3 in/out connections. In addition, QFT computation in position space has to be adapted to a curved discrete space-time.

Any photon, regardless of its origin, carries the same optical field profile. This feature and the quantum Rayleigh emissions generate temporally discrete groups of several photons in a resonant cavity incorporating one single quantum dot. A periodic stream of single photons is distorted by high-finesse optical cavities and the quantum Rayleigh spontaneous emission in a beam splitter. Groups of photons emerge from interferometric filters because of multiple internal reflections.

On the basis of a limited number of reasonable axioms, we discuss the classification of all the possible universality classes of diffeomorphisms invariant metric theories of quantum gravity. We use the language of the renormalization group and adopt several ideas which originate in the context of statistical mechanics and quantum field theory. Our discussion leads to several ideas that could affect the status of the asymptotic safety conjecture of quantum gravity and give universal arguments towards its proof.

The fact that quantum gravity does not admit a co-variant vacuum state has far-reaching consequences for all physics. It points out that space could not be empty, and we return to the notion of an ether . Such a concept requires a preferred reference frame for, e.g., universe expansion and black holes. Here, we intend to discuss vacuum and quantum gravity from three essential viewpoints: universe expansion, black holes existence, and quantum decoherence.

Black hole temperature T_BH = T_P/2πd as a function of its Planck length real diameter multiplier d is derived from black hole surface gravity and Hawking temperature w.l.o.g. It is conjectured d = 1/2π describes primordial Big Bang singularity as in this case T_BH = T_P. A black hole interacts with the environment and observable black holes have uniquely defined Delaunay triangulations with a natural number of spherical triangles having Planck areas (bits), where a Planck triangle is active and has gravitational potential of -c² if all its vertices have black hole gravitational potential of -c²/2 and is inactive otherwise. As temporary distribution of active triangles on an event horizon tends to maximize Shannon entropy a black hole is a fundamental, one-sided thermodynamic equilibrium limit for a dissipative structure. Black hole blackbody radiation, informational capacity fluctuations, and quantum statistics are discussed. On the basis of the latter, wavelength bounds for BE, MB, and FD statistics are derived as a function of the diameter multiplier d. It is shown that black holes feature wave-particle duality only if d ≤ 8π, which also sets the maximum diameter of a totally collapsible black hole. This outlines the program for research of other nature phenomena that emit perfect blackbody radiation, such as neutron stars and white dwarfs.

In this paper, we investigate the ontological hypothesis, which implies that the spacetime is not the ultimate structure in our universe, and its existence emerges from a deeper physical entity. By using a very simple approach based on a classical problem, regarding the propagation of electromagnetic waves in empty vacuum. We were able to deduce that this deeper entity is just an omnipresent multi-rest states physical structure; aether. After that, we try to see how this aether fits in the universe that we exist in. The outcome is that its existence causes the emergence of some basic phenomena that our universe is built on. At the microscopic scale it turned out to be a source of the essential quantum phenomenon, which is currently known as the wave – particle duality. On the other hand, at the macroscopic scale it causes the emergence of spacetime curvature, around huge, massive objects like Earth, and finally, we try to visualize the prospects of aether, and how it can be a promising alternative for the dark matter.

The correspondence principle made of unitarity, locality and renormalizability has been very successful in quantum field theory. Among the other things, it helped us build the standard model. However, it also showed important limitations. For example, it failed to restrict the gauge group and the matter sector in a powerful way. After discussing its effectiveness, we upgrade it to make room for quantum gravity. The unitarity assumption is better understood, since it allows for the presence of physical particles as well as fake particles (fakeons). The locality assumption is applied to an interim classical action, since the true classical action is nonlocal and emerges from the quantization and a later process of classicization. The renormalizability assumption is refined to single out the special role of the gauge couplings. We show that the upgraded principle leads to an essentially unique theory of quantum gravity. In particular, in four dimensions, a fakeon of spin 2, together with a scalar field, is able to make the theory renormalizable while preserving unitarity. We offer an overview of quantum field theories of particles and fakeons in various dimensions, with and without gravity.

In quantum gravity perturbation theory in Newton's constant $G$ is known to be badly divergent, and as a result not very useful. Nevertheless, some of the most interesting phenomena in physics are often associated with non-analytic behavior in the coupling constant and the existence of nontrivial quantum condensates. It is therefore possible that pathologies encountered in the case of gravity are more likely the result of inadequate analytical treatment, and not necessarily a reflection of some intrinsic insurmountable problem. The nonperturbative treatment of quantum gravity via the Regge-Wheeler lattice path integral formulation reveals the existence of a new phase involving a nontrivial gravitational vacuum condensate, and a new set of scaling exponents characterizing both the running of $G$ and the long-distance behavior of invariant correlation functions. The appearance of such a gravitational condensate is viewed as analogous to the (equally nonperturbative) gluon and chiral condensates known to describe the physical vacuum of QCD. The resulting quantum theory of gravity is highly constrained, and its physical predictions are found to depend only on one adjustable parameter, a genuinely nonperturbative scale $\xi$ in many ways analogous to the scaling violation parameter $\Lambda_{\bar MS} $ of QCD. Recent results point to significant deviations from classical gravity on distance scales approaching the effective infrared cutoff set by the observed cosmological constant. Such subtle quantum effects are expected to be initially small on current cosmological scales, but could become detectable in future high precision satellite experiments.

The purpose of this paper is to show a new approach to unify the theory of general relativity and quantum physics. For this, we rely on thermodynamics, fluid mechanics and the theory of information. We will then see that the Shannon entropy, Boltzmann and Von Neumann can be the source of gravity, which would be a form emerging. For this, we will study at first what is lacking for the unification of general relativity and physics. Secondly, we will explain the concept of entropic gravity by introducing calculations Erik Verlinde. Then we will explain the concept of entropy Boltzmann, Shannon, Von Neumann and the links between them. Then, we will modify Einstein's equations by transforming the tensor of perfect fluid in terms of entropy. Finally, we will link our theory with experience already carried out as part of a link between gravity and quantum theory.

Simulating the non-perturbative and non-Markovian dynamics of open quantum systems is a very challenging many body problem, due to the need to evolve both the system and its environments on an equal footing. Tensor network and matrix product states (MPS) have emerged as powerful tools for open system models, but the numerical resources required to treat finite temperature environments grow extremely rapidly and limit their applications. In this study we use time-dependent variational evolution of MPS to expore the striking theory of Tamescelli et al. that shows how finite temperture open dyanmics can be obtained from zero temperature, i.e. pure wave function, simulations. Using this approach, we produce a benchmark data set for the dynamics of the Ohmic spin-boson model across a wide range of coupling and temperatures, and also present detailed analysis of the numerical costs of simulating non-equilibrium steady states, such as those emerging from the non-perturbative coupling of a qubit to baths at different temperatures. Despite ever growing resource requirements, we find that converged non-perturbative results can be obtained, and we discuss a number of recent ideas and numerical techniques that should allow wide application of MPS to complex open quantum systems.

In this work it is acknowledged that important attempts to devise an emergent quantum (gravity) theory require space-time to be discretized at the Planck scale. It is therefore conjectured that reality is identical to a sub-quantum dynamics of ontological micro-constituents that are connected by a single interaction law. To arrive at a complex system-based toy-model identification of these micro-constituents, two strategies are combined. First, by seeing gravity as an entropic phenomenon and generalizing the dimensional reduction of the associated holographic principle, the universal constants of free space are related to assumed attributes of the micro-constituents. Second, as the effective field dynamics of the micro-constituents must eventually obey Einstein’s field equations, a sub-quantum interaction law is derived from a solution of these equations. A Planck-scale origin for thermodynamic black hole characteristics and novel views on entropic gravity theory result from this approach, which eventually provides a different view on quantum gravity and its unification with the fundamental forces.

The recently proposed Holography-inspired approach to quantum gravity is reviewed and expanded. The approach is based on the foliation of the background spacetime and reduction of the offshell states to the physical states. Careful attention is paid to the boundary conditions. It is noted that the outstanding problems such as the cosmological constant problem and black hole information can be tackled from the common thread of the quantized gravity. One-loop renormalization of the coupling constants and the beta function analysis are illustrated. Active galactic nuclei and gravitational waves are discussed as the potential applications of the present quantization scheme to astrophysics.

At present there is a renewed interest in theories of ”modified” gravity. Here, under a more drastic modification enforced by Galilei group, we obtain a completely new gravitational structure, and which exists in addition to the already available general relativity of today. Correlated with this, we show that in addition, there is a new ”modified” quantum mechanics, in as much as it exists as an independent and new ”pure” non-relativistic quantum me- chanics, and which has no relativistic counterpart. This is in addition to the present quantum mechanics, where the relativistic and non-relativistic structures are counterparts of each other. The above holds, firstly due to the correlation between Galilei group and quantum mechanics. These math- ematical conclusions are consolidated by the fact that there exists a physical Majorana interaction between each neutron- proton pairs in nuclei. Galilei invariance of Majorana exchange in Majorana interaction, shows that the mass here is of pure gravitational nature, and which is immune to the other three forces. This makes an amazing connection between the gravitational force and the quantum mechanics. This pure gravitational mass would man- ifest itself as dark matter of the universe. It is our new modified gravity that generates the dark matter.

In our investigation of the time evolution of energy states Einstein’s interpretation from more than a century ago is found to have greater internal consistency than that of non-relativistic quantum mechanics. We choose to align more closely with his methods by abandoning the non-relativistic Hamiltonian method, which has been the standard for nearly a century, in favor of a relativistically correct Lagrangian method. Integral equations of motion for the absorption and emission of radiation are derived that underlie and anticipate the differentially motivated Schrödinger equation. This new interpretation applies to a large volume of experimental evidence of both classical and quantum mechanical origin. Among the examples discussed in support are Planck’s law describing black body radiation, matrix mechanics, the function of the simplest quantum mechanical system an electron cyclotron, chaos theory, and evolutionary biology.

Affine quantization is a relatively new procedure, and it can solve many new problems. This essay reviews this new, and novel, procedure for particle problems, as well as those of fields and gravity. New quantization tools, which are extremely close to, and even constructed from, the tools of canonical quantization, are able to fully solve selected problems that using the standard canonical quantization would fail. In particular, improvements can even be found with an affine quantization of fields, as well as gravity.

Alena Tensor is a recently discovered class of energy-momentum tensors that provides a mathematical framework in which the description of a physical system in curved spacetime and its description in a flat spacetime with fields are equivalent. As demonstrated in previous publications, in curved spacetime this tensor reproduces Einstein Field Equations and in flat Minkowski spacetime, it describes physical system with fields that can be widely configured. Thanks to the obtained compliance with QM and QED, the use of the discussed tensor may significantly simplify Quantum Field Theory equations and a new interpretation of the Schrödinger equation is possible. In the article it has also been shown that the use of Alena Tensor for the electromagnetic field takes into account effects related to the particle's spin, Abraham–Lorentz effect and, in the curvilinear description, this excludes non-physical phenomena such as the black hole singularity. The article contains a method for verifying Alena Tensor within QM, proposing an explanation for the discrepancy between the Dirac and Klein-Gordon solutions. It also discusses prospects for the application of Alena Tensor in unification theories against the background of existing research directions.

The experiment proposed by Bose et al aims to show the non classicality of gravity through entanglement. This paper seeks to establish optimal conditions under which the entanglement would be maximized. The assumptions made by Bose et al to come to the conclusion of quantized gravity would also be discussed along with alternate conclusions that could arise from the experiment.

We communicate the theoretical results in the study of utilizing the quantum phenomena in optical current for quantum computation in the context of high precision voltage measurements. These results can be used around computation by quantum sampling and quantum communication as the basis for further research and physical implementations. We propose a Main Optical Setup (MOS) for such computation which allows to make a superstructure to implement specific computations and algorithms. To create MOS we used the nonlinear units (e.g., beta- barium borate crystal), arranged in series, powered with pulsed laser pump, and ended with the beam splitter to generate the output state of a number of entangled photon pairs. The computation is made by propagation of entanglement with beam splitters applied crossword and adjustable phase shifters that are tools for parameter steering. We show how to implement the series of cosine-based components on the example of two-component case. The results opens a broad area for future research in the area of building quantum optimizer using the quantum sampling methods and in the area of high precision temporal measurement of voltage, which is the important process for building high-fidelity devices.

Quantum mechanics could be studied through polynomial algebra, as has been demonstrated by a work (“An approach to first-principles electronic structure calculation by symbolic-numeric computation” by A. Kikuchi). We carry forward the algebraic method of quantum mechanics through algebraic number theory; the basic equations are represented by the multivariate polynomial ideals; the symbolic computations process the ideal and disentangle the eigenstates as the algebraic variety; upon which one canbuild the Galois extension of the number field, in analogy with the univariate polynomial case, to investigate the hierarchy of solutions; the Galois extension is accompanied with the group operations, which permute the eigenstates from one to another, and furnish the quantum system with a non-apparent symmetry. Besides, this sort of algebraic quantum mechanics is an embodiment of the class field theory; some of the important consequences of the latter emerge in quantum mechanics. We shall demonstrate these points through simple models; we will see the use of computational algebra facilitates such sort of analysis, which might often be complicated if we try to solve them manually.

The strong coupling between individual quantum emitters and resonant optical micro/nanocavities is beneficial to understand light and matter interactions. Here we propose a plasmonic nanoantenna placed on a metal film to achieve an ultra-high electric field enhancement in the nanogap and ultra-small optical mode volume. The strong coupling between a single quantum dot and the designed structure is investigated in detail by both numerical simulations and theoretical calculations. When a single QD is inserted into the nanogap of the silver nanoantenna, scattering spectra show remarkably large spectral splitting and typical anti-crossing behavior of the vacuum Rabi splitting, which can be realized in the scattering spectra by varying the nanoantenna thickness. Our work shows a possible way to enhance light-matter interaction at a single quantum emitter limit, which can be useful for future quantum and nanophotonic applications.

In this article we presented an application of the quantum cosmological model in teleparallel gravity. Working with a vacuum solution, the gravitational energy density is quantized with the Weyl procedure and we obtain a discrete expression for the gravitational energy. As an immediate consequence the empty space exhibits an expansion for an early universe.

This interdisciplinary work presents a novel patent pending method of inertial electrostatic confinement (IEC) fusion called the Nuclear Electromagnetic Shaping Accelerator Reactor (NESAR) that addresses all of the major failure problems with currently known methods of IEC fusion. A brief background of previous IEC methods that generate a negative potential well to accelerate ions for fusion will be reviewed and compared to the NESAR method of magnetic confinement. In addition, a direct comparison will be presented between the NESAR and the tokamak method of fusion. The NESAR method of fusion obtains the plasma oscillation and compression capabilities of a tokamak without producing the catastrophic magnetic reconnection disruptions that currently plague tokamaks. Since the NESAR can oscillate charged particles comparable to the tokamak, this work will briefly review the history of the tokamak, how sawtooth magnetic reconnection occurs, and how the NESAR precludes the occurrence of magnetic reconnection. This work will also review the beginnings of a novel unified field theory that has obtained interest from the Defense Advanced Research Projects Agency (DARPA). This unified field theory is based upon the trajectory of charged particle movements within the NESAR, which is the only concept of magnetic confinement in the world that may allow charge particles to collectively interact relatively to a solitary location. Due to this possible capability, the confined charged particles have the potential to experience curved trajectories; allowing for the effects of curvature deviation to be placed upon the charged particle within the magnetic confines of the NESAR. If charged particles can experience curvature deviation then deviated acceleration is generated; allowing the electromagnet field to be propelled to a higher spatial dimension that could influence spacetime. Finally, this work will review another theory that explains how magnetic pole reversals are observed by the National Aeronautics and Space Administration’s (NASA) coiled magnetic field detectors. This theory requires little to no postulations to be framed and it is purely based upon the trajectory of charged particles within the NESAR, Michael Faraday’s law of induction, and experimental observations of rotating plasmas.

We generate numerically on a lattice an ensemble of stationary metrics, with spherical symmetry, which have Einstein action S_E « ħ. This is obtained through a Metropolis algorithm with weight exp(-β²S_E²) and β » ħ^-1. The squared action in the exponential allows to circumvene the problem of the non-positivity of S_E. The discretized metrics obtained exhibit a spontaneous polarization in regions of positive and negative scalar curvature. We compare this ensemble with a class of continuous metrics previously found, which satisfy the condition S_E=0 exactly, or in certain cases even the stronger condition R(x)=0 for any x. All these gravitational field configurations are of considerable interest in quantum gravity, because they represent possible vacuum fluctuations and are markedly different from Wheeler's ''spacetime foam''.

Even though materialistic atoms are having independent existence in this current accelerating universe, they are not allowing scientists and engineers to explore the secrets of gravity at atomic scale. This may be due to incomplete unification paradigm, inadequacy of known physics and technological difficulties etc. In this challenging scenario, one fundamental question to be answered is: Is Newtonian gravitational constant having a physical existence? We would like to suggest that, it’s a man created empirical constant and is having no physical existence. Clearly speaking, it’s not real but virtual. For understanding the secrets of large scale gravitational effects, scientists consider it as a physical constant. In the same way, each atomic interaction can be allowed to have its own gravitational constant. With further study, their magnitudes can be refined for a better understanding of the nature. Thinking in this way, we tried to fit the Newtonian gravitational constant. It’s estimated value seems to be 6.679855x10^(-11) m3/kg/sec2. Proceeding further, the famous radiation constants can be shown to be complex or secondary physical constants. By considering proton neutron stability, nuclear binding energy, nuclear charge radii, neutron life time, Fermi’s weak coupling constant and strong coupling constant, we are trying to understand the validity of the proposed three atomic gravitational constants. It needs further study.

We investigate the behavior of thermal quantum coherence in the Heisenberg XXX model for a two-qubit system placed in independently controllable Inhomogeneous magnetic fields applied to two qubits respectively. We discuss the behavior of quantum coherence by systematically varying the coupling parameter, magnetic field, and temperature for both ferromagnetic and antiferromagnetic cases. The results show the interesting behavior of quantum coherence in a certain range of parameters. Generally, it is observed that quantum correlations decay with temperature, but in the ferromagnetic case with uniform magnetic interaction, it rises with temperature up to a certain threshold value and ultimately it decreases its value to zero. Moreover, it is observed that preserving the quantum coherence for small temperatures is very hard with the increasing magnetic field because, at small temperatures, quantum coherence decays sharply with the increase in magnetic field whereas at larger temperatures it decays completely at fairly large values of the magnetic field. The variation of quantum coherence with uniform magnetic field in the antiferromagnetic case is observed to be Gaussian for larger temperature but at zero or nearly zero temperature, it behaves as a constant function for uniform magnetic field up to a threshold value and then decays to zero with an infinite slope. This shows the signature of quantum phase transition from quantum nature to classicality.

The novelty of 21st-century physics is the development of the “superfluid quantum vacuum” model, also named “superfluid quantum space” SQS. This SQS is replacing space-time as the fundamental arena of the universe. It also represents the model that has the potential of unifying four fundamental forces of the universe. SQS in this article is represented as the time-invariant fundamental field of the universe where time is merely the duration of material changes.

Time and space are fundamental concepts for characterizing and understanding our world. Despite of continuous curiosity and extensive studies, the nature of time and space remains elusive, and the underlying quantum structure is unclear. Here we propose a molecular model based on energy space decomposition to incorporate time and space synthetically in a unified framework. In the proposed model, the multipole expansion of action mapped to energy modules in scalar, vector, and matrix forms, results in the generators of time, space, and a material framework, cloud. And the invariance of time, space and cloud transformation corresponds to the conservation of energy, momentum, and mass, respectively. The classification of energy modules reveals a periodicity of energy elements, which constructs a hierarchical world in a molecular framework with dynamics represented by energy transformations. Here the role of time and space could switch from each other, and motion is attributed to the coupling of particle with intermediate bosons, corresponding to energy transformations among different energy modules. The application on Bohr model demonstrates that this picture provides a consistent classical interpretation to the foundation of quantum mechanics, and suggests an atomic model for gravitation.

In quantum field theory (QFT), it is well known that when Feynman diagrams containing loops are evaluated to account for self interactions, probability amplitude comes out to be infinite which is physically not admissible. So, to make the QFT convergent, various renormalization methods are conventionally followed in which an additional (infinite) counter term is postulated which neutralizes the original infinity generated by diagram. The resulting finite values of amplitudes have agreed with experiments with surprising accuracy. However, proponents of renormalization methods acknowledged that this ad-hoc procedure of subtraction of infinity from infinity to reach at a finite value is not at all satisfactory and there is no physical basis for bringing in the counter term. So, it is desirable to establish a method in QFT which does not generate any infinite term (thus not requiring renormalization), but which predicts same results as conventional methods do. In this paper, we describe such a technique taking self interaction quantum electrodynamics diagram representing electron or photon self energy. In our method, no problem of infinity arises and hence renormalization is not necessary. Still, the dependence of calculated probability amplitude on physical variables in our technique comes out to be same as conventional methods. Using similar procedure, we hope, the problem of non-renormalizability of quantum gravity may be solved in future.