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La Teoria Quàntica de Camps en Espais Corbats ha demostrat ser una teoria semi-clàssica molt útil per a l'estudi de fenòmens físics que combinen gravetat i efectes quàntics. En particular, prediu que la dinàmica d'un camp gravitacional de fons pot excitar espontàniament partícules a partir del buit quàntic. El procés de producció de partícules té una importància especial en l'estudi de l'univers primerenc en cosmologia i és la base de la radiació de Hawking en la física dels forats negres. Físicament, aquest efecte quàntic és anàleg a l'efecte Schwinger ben conegut en l'electrodinàmica quàntica. L'objectiu d'aquesta Tesi és estudiar aquest fenomen general de producció de partícules, així com altres aspectes fonamentals relacionats, com ara els efectes de “backreaction”, les anomalies quàntiques i les tècniques de renormalització. Una de les principals contribucions d'aquesta Tesi és el desenvolupament i la transferència de tècniques típicament utilitzades en la Teoria Quàntica de Camps en Espais Corbats a camps quàntics acoblats a “backgrounds” electromagnètics intensos. Per exemple, l'estudi inclou l'exploració de si l'anomalia gravitatòria per a camps de Weyl també està present en “backgrounds” elèctrics. A més, aquesta Tesi aborda si la propietat d’invariància adiabàtica del nombre de partícules creades en un univers en expansió es manté en el cas d'un background purament electromagnètic. Finalment, el mètode de renormalització adiabàtica, particularment útil per a camps quàntics en universos en expansió, es desenvolupa aquí per a camps de Dirac de 4 dimensions que estan acoblats a un background elèctric general. Aquesta Tesi també proporciona contribucions rellevants en l'àrea de la Gravitació. D'una banda, ampliem un mètode de regularització i renormalització reeixit que s'ha proposat recentment en la literatura, anomenat “pragmatic mode-sum method”. Aquest mètode es va desenvolupar originalment per a forats negres, i en aquesta Tesi l'hem adaptat per a universos en expansió. D'altra banda, la Tesi inclou un estudi detallat de les correccions quàntiques a la mètrica de Schwarzschild, originades pels efectes de “backreaction” dels camps quàntics que viuen en aquest “background”. L’argument conductor en l'anàlisi és l'anomalia conforme i la suposició d'estaticitat. També s'analitzen les propietats geomètriques i les aplicacions del nou espai-temps (sense horitzó). Tots aquests resultats milloren considerablement la nostra comprensió del comportament dels camps quàntics acoblats a “backgrounds” gravitacionals i electromagnètics externs. El paper de les anomalies quàntiques ha estat fonamental per aconseguir-ho. Quantum Field Theory in Curved Spacetimes has proven to be a very useful semiclassical theory for studying physical phenomena that combine gravity and quantum effects. In particular, it predicts that the dynamics of a background gravitational field can spontaneously excite particles out of the quantum vacuum. The process of particle production is of particular importance in the study of the very early universe in Cosmology, and it is the basis of Hawking radiation in black hole physics. Physically, this quantum effect is analogous to the well-known Schwinger effect in quantum electrodynamics. The goal of this Thesis is to study this general phenomenon of particle production, as well as other related fundamental aspects, such as backreaction effects, quantum anomalies, and renormalization techniques. One of the main contributions of this Thesis is the development and transfer of techniques typically used in QFT in curved spacetimes to quantum fields coupled to strong electrodynamics backgrounds. For instance, the study includes the exploration of whether the gravitational anomaly for Weyl fields is also present for electric backgrounds. Moreover, this Thesis also addresses if the fundamental property of the adiabatic invariance of the number of created particles in an expanding universe is maintained in the case of a pure electric background. Finally, the method of adiabatic renormalization, which is particularly useful for quantum fields in expanding universes, is developed here for 4-dimensional Dirac fields that are coupled to a general, electric background. This Thesis also provides relevant contributions in the area of Gravitation. On the one hand, we extend a successful regularization and renormalization method recently communicated in the literature, called pragmatic mode-sum regularization. This method was originally developed for black holes, and in this Thesis we adapted it for expanding universes. On the other hand, the Thesis includes a detailed study of quantum corrections to the Schwarzschild metric, originated from the back-reaction effects of quantum fields living in this black hole background. As we will see in more detail below, the driving argument in the analysis is the conformal anomaly and the assumption of staticity. The geometrical properties and applications of the new (horizonless) spacetime are also analyzed. All these results improve considerably our understanding of the behavior of quantum fields coupled to external gravitational and electromagnetic backgrounds. The role of quantum anomalies has been fundamental to achieve this.

Engineering lattice models with tailored inter-site tunnelings and onsite energies could synthesize essentially arbitrary Riemannian surfaces with highly tunable local curvatures. Here, we point out that discrete synthetic Poincare half-planes and Poincare disks, which are created by lattices in flat planes, support infinitely degenerate eigenstates for any nonzero eigenenergies. Such Efimov-like states exhibit a discrete scaling symmetry and imply an unprecedented apparatus for studying quantum anomaly using hyperbolic surfaces. Furthermore, all eigenstates are exponentially localized in the hyperbolic coordinates, signifying the first example of quantum funneling effects in Hermitian systems. As such, any initial wave packet travels towards the edge of the Poincare half-plane or its equivalent on the Poincare disk, delivering an efficient scheme to harvest light and atoms in two dimensions. Our findings unfold the intriguing properties of hyperbolic spaces and suggest that Efimov states may be regarded as a projection from a curved space with an extra dimension.

Progress in understanding quantum systems has been driven by the exploration of the geometry, topology, and dimensionality of ultracold atomic systems. The NASA Cold Atom Laboratory (CAL) aboard the International Space Station has enabled the study of ultracold atomic bubbles, a terrestrially-inaccessible topology. Proof-of-principle bubble experiments have been performed on CAL with an rf-dressing technique; an alternate technique (dual-species interaction-driven bubbles) has also been proposed. Both techniques can drive discovery in the next decade of fundamental physics research in microgravity., 17 pages, 2 figures

Fracton phases of matter feature local excitations with restricted mobility. Despite the substantial theoretical progress they lack conclusive experimental evidence. We discuss a simple and experimentally available realization of fracton physics. We note that superfluid vortices form a Hamiltonian system that conserves total dipole moment and trace of the quadrupole moment of vorticity; thereby establishing a relation to a traceless scalar charge theory in two spatial dimensions. Next we consider the limit where the number of vortices is large and show that emergent vortex hydrodynamics also conserves these moments. Finally, we show that on curved surfaces, the motion of vortices and that of fractons agree; thereby opening a route to experimental study of the interplay between fracton physics and curved space. Our conclusions also apply to charged particles in a strong magnetic field. Fractons are phases of matter featuring particles with restricted mobility and represent a new paradigm of quantum condensed matter physics; but observing them experimentally is a challenge. Here, the authors demonstrate a simple platform for the realisation of fracton physics with vortices of a two-dimensional superfluid.

General $\mathcal{N}=(1,0)$ supergravity-matter systems in six dimensions may be described using one of the two fully fledged superspace formulations for conformal supergravity: (i) $\mathsf{SU}(2)$ superspace; and (ii) conformal superspace. With motivation to develop rigid supersymmetric field theories in curved space, this paper is devoted to the study of the geometric symmetries of supergravity backgrounds. In particular, we introduce the notion of a conformal Killing spinor superfield $\epsilon^\alpha$, which proves to generate extended superconformal transformations. Among its cousins are the conformal Killing vector $\xi^a$ and tensor $\zeta^{a(n)}$ superfields. The former parametrise conformal isometries of supergravity backgrounds, which in turn yield symmetries of every superconformal field theory. Meanwhile, the conformal Killing tensors of a given background are associated with higher symmetries of the hypermultiplet. By studying the higher symmetries of a non-conformal vector multiplet we introduce the concept of a Killing tensor superfield. We also analyse the problem of computing higher symmetries for the conformal d'Alembertian in curved space and demonstrate that, beyond the first-order case, these operators are defined only on conformally flat backgrounds., Comment: 62 pages

This paper deals with the generalization of the linear theory of the unification of gravitational and electromagnetic fields using 4-dimensional gauge symmetry in order to solve the contradictions from the Kaluza-Klein theory’s unification of the gravitational and electromagnetic fields. The unification of gravitational and electromagnetic fields in curved space-time starts from the Bianchi identity, which is well known as a mathematical generalization of the gravitational equation, and by using the existing gauge symmetry condition, equations for the gravitational and electromagnetic fields can be obtained. In particular, the homogeneous Maxwell’s equation can be obtained from the first Bianchi identity, and the inhomogeneous Maxwell’s equation can be obtained from the second Bianchi identity by using Killing’s equation condition of the curved space-time. This paper demonstrates that gravitational and electromagnetic fields can be derived from one equation without contradiction even in curved space-time, thus proving that the 4-dimensional metric tensor using the gauge used for this unification is more complete. In addition, geodesic equations can also be derived in the form of coordinate transformation, showing that they are consistent with the existing equations, and as a result, they are consistent with the existing physical equations.

We consider travelling times of billiard trajectories in the exterior of an obstacle K on a two-dimensional Riemannian manifold M. We prove that given two obstacles with almost the same travelling times, the generalised geodesic flows on the non-trapping parts of their respective phase-spaces will have a time-preserving conjugacy. Moreover, if M has non-positive sectional curvature, we prove that if K and L are two obstacles with strictly convex boundaries and almost the same travelling times then K and L are identical.

This paper is devoted to the proper-time method and describes a model case that reflects the subtleties of constructing the heat kernel, is easily extended to more general cases (curved space, manifold with a boundary), and contains two interrelated parts: an asymptotic expansion and a path integral representation. We discuss the significance of gauge conditions and the role of ordered exponentials in detail, derive a new nonrecursive formula for the Seeley–DeWitt coefficients on the diagonal, and show the equivalence of two main approaches using the exponential formula.

The article formulates the classical three-body problem in conformal-Euclidean space (Riemannian manifold), and its equivalence to the Newton three-body problem is mathematically rigorously proved. It is shown that a curved space with a local coordinate system allows us to detect new hidden symmetries of the internal motion of a dynamical system, which allows us to reduce the three-body problem to the 6th order system. A new approach makes the system of geodesic equations with respect to the evolution parameter of a dynamical system (internal time) fundamentally irreversible. To describe the motion of three-body system in different random environments, the corresponding stochastic differential equations (SDEs) are obtained. Using these SDEs, Fokker-Planck-type equations are obtained that describe the joint probability distributions of geodesic flows in phase and configuration spaces. The paper also formulates the quantum three-body problem in conformal-Euclidean space. In particular, the corresponding wave equations have been obtained for studying the three-body bound states, as well as for investigating multichannel quantum scattering in the framework of the concept of internal time. This allows us to solve the extremely important quantum-classical correspondence problem for dynamical Poincar&eacute, systems.

The T T ¯ $$ T\overline{T} $$ deformation of a 2 dimensional field theory living on a curved space- time is equivalent to coupling the undeformed field theory to 2 dimensional ‘ghost-free’ massive gravity. We derive the equivalence classically, and using a path integral formulation of the random geometries proposal, which mirrors the holographic bulk cutoff picture. We emphasize the role of the massive gravity Stückelberg fields which describe the diffeomorphism between the two metrics. For a general field theory, the dynamics of the Stückelberg fields is non-trivial, however for a CFT it trivializes and becomes equivalent to an additional pair of target space dimensions with associated curved target space geometry and dynamical worldsheet metric. That is, the T T ¯ $$ T\overline{T} $$ deformation of a CFT on curved spacetime is equivalent to a non-critical string theory in Polyakov form, with a non-zero B-field. We give a direct proof of the equivalence classically without relying on gauge fixing, and determine the explicit form for the classical Hamiltonian of the T T ¯ $$ T\overline{T} $$ deformation of an arbitrary CFT on a curved spacetime. When the QFT action is a sum of a CFT plus an operator of fixed scaling dimension, as for example in the sine-Gordon model, the equivalence to a non-critical theory string holds with a modified target space metric and modified B-field. Finally we give a stochastic path integral formulation for the general T T ¯ + J T ¯ + T J ¯ $$ T\overline{T}+J\overline{T}+T\overline{J} $$ deformation of a general QFT, and show that it reproduces a recent path integral proposal in the literature.

This theory assumes the universe it is a closed sphere inside a “shell” which holds it still preventing it from expanding or collapsing. Before big bang, the universe must have been filled with linear radiation and no mass, space was flat and time was zero (empty set). An initial big bang took place everywhere inside the shell having as purpose to curve flat space and to create mass and time. At initial moment mass got created along with all existing physical laws. Later on, stars and planets formed by gathering of mass, and then accumulated into galaxies which move randomly by curved trajectories. Inside the universe there are no lines and even light travels on long distances by curved trajectory. It cannot be an expansion of the universe since the “shell” doesn’t allow that to happen. Behaviour of curved space at subatomic level generated by the initial big bang is still happening today and this prevents all spheres of mass inside the universe from stop moving. Light coming from far distance galaxies is being curved by the behaviour of space at subatomic level at a constant linear rate with distance and time. If more time and space is given to a star, light reaching us it will shift to red even more, do to a much more curved trajectory. The universe is fixed with a constant diameter, space itself doesn’t move in any linear direction, it just curves onto itself

Мы изучаем, как модифицируются модели квантовой теории при перепараметризации координат пространства-времени и одновременно некоторых преобразований полевой функции. Предъявлены преобразования, которые превращают действие массивного поля в пространстве-времени Минковского в действие безмассового поля в некотором искривлённом пространстве.

We apply the functional renormalization group equation to a massive Fierz-Pauli action in curved space and find that, even though a massive term is a modification in the infrared sector, the mass term modifies the value of the non-gaussian fixed point in the UV sector.We obtained the beta function for the scale dependent mass parameter and found that the massive Fierz-Pauli case still seems to be an asymptotically safe theory., Comment: 7 pages, 4 figures

The paper belongs to the sphere of quantum physics, physics of waves and physical fields, in particular—to the gravitation. Their study provides a better understanding of the problems of natural sciences at all levels, from elementary particles, to Universe as a whole. Therefore, the solution of these problems is an urgent and important task, which to the works of many generations of scientists of the world was dedicated. However, they have not been fully resolved. In well-known works, including general relativity, determination of the wave and energy parameters of the gravitational field of the Universe and their numerical values are absent. Solutions found are limited to tensor equations of a general form, which allows their interpretation of over a wide range. Other disadvantages of famous models are: 1) the voluminous world of the Universe reduced to the planes on which space objects and other objects move, sagging planes due to their own mass; 2) signs of “top” and “bottom” of the system, which are not in the real Universe, just as they are not on Earth and not in the Solar system; 3) the formation of “voids” between the object and the curved space and others. Main goals of the work to identify these contradictions and find ways to resolve them are performed. The main difference and the scientific novelty of the work performed are the justification of the gravity model based on a rigorous determination of the wave and energy parameters of the gravitational field of the Universe and their numerical values. The initial parameters of this worked—is the frequency oscillation νG of the waves of the gravitational field (Nastasenko’s constant) found in 2011. Research Results: Knowing νG can find all wave parameters of the gravitational field and their numerical values. The proposed new spatial-wave model of the action of gravity is based on the wave parameters of the gravitational fields of material objects. In the framework of their unity with electromagnetic fields, it reduces their structures to similar ones and eliminates the drawbacks of the previous model—of replaced gravity on curvature of space.

Plank quantum and classical string energy relations seem to be uncorrelated. This work correlated them. The relativistic energy-momentum relation has been used together with plank and de Brogglie hypothesis to prove that the wave group velocity is equal to the particle velocity in both ordinary and curved space. The plank energy relation is shown also to be related to the classical energy relation of an oscillating string. Starting from plank energy relation for n photons and performing integration, the expression of classical string energy was obtained. This means that one can treat electromagnetic waves as a collection of continuous photons having frequencies ranging from zero to w. Conversely, starting from classical string energy relation by differentiating it with respect to angular frequency, the plank quantum energy for n photons has been found. This means that the quanta results from separation of electromagnetic waves to single isolated waves. Each wave consists of n photons or quanta.

The quantum tunneling radiation of arbitrarily dimensional Reissner–Nordstrom black hole is corrected by beyond semiclassical theory and Lorentz symmetry violation theory, resulting in new expressions for the tunneling rate of scalar particles and the Hawking temperature at the horizon of the black hole. The physical significance of our results and the thermodynamic evolution characteristics of the black hole are also discussed.

As an analog model of general relativity, optics on some two-dimensional (2D) curved surfaces has received increasing attention in the past decade. Here, in light of the Huygens–Fresnel principle, we propose a theoretical frame to study light propagation along arbitrary geodesics on any 2D curved surfaces. This theory not only enables us to solve the enigma of “infinite intensity” that existed previously at artificial singularities on surfaces of revolution but also makes it possible to study light propagation on arbitrary 2D curved surfaces. Based on this theory, we investigate the effects of light propagation on a typical surface of revolution, Flamm’s paraboloid, as an example, from which one can understand the behavior of light in the curved geometry of Schwarzschild black holes. Our theory provides a convenient and powerful tool for investigations of radiation in curved space.

We consider two scalar fields interacting through a $$\chi ^*\chi \phi ^*\phi $$ term in the presence of a Reissner–Nordstrom black hole. Initially, only $$\chi $$ particles are present. We find that the produced $$\phi $$ particles are localized in a region around the black hole and have a tendency toward condensation provided that $$\phi $$ particles are much heavier than the $$\chi $$ particles. We also find that such a configuration is phenomenologically viable only if the scalars and the black hole have dark electric charges.

We study the self-gravitating Abrikosov vortex in curved space with and without a (negative) cosmological constant, considering both singular and non-singular solutions with an eye to hairy black holes. In the asymptotically flat case, we find that non-singular vortices round off the singularity of the point particle's metric in 3 dimensions, whereas singular solutions consist of vortices holding a conical singularity at their core. There are no black hole vortex solutions. In the asymptotically AdS case, in addition to these solutions there exist singular solutions containing a BTZ black hole, but they are always hairless. So we find that in contrast with 4-dimensional 't Hooft-Polyakov monopoles, which can be regarded as their higher-dimensional analogues, Abrikosov vortices cannot hold a black hole at their core. We also describe the implications of these results in the context of AdS/CFT and propose an interpretation for their CFT dual along the lines of the holographic superconductor., 30 pages, 7 figures

In this paper we have investigated the general condition of self-adjointness of the generalised momentum operators and we have shown that it highly depends on the metric of the space. We have also discussed the domain of the generalised momentum operators at boundary conditions.

This paper examines the possibility that space is intrinsically curved and the conse- quences of this to measurements involving time. I begin by demonstrating an error in the way we construct our clocks and how this error invalidates the theories of Special and General Relativity. I further demonstrate how this error may be rectified using curved space geometry and the implications of curved space on the constancy of the speed of light. I propose a hypothesis of 4 spatial dimensions that describes our universe and extend this idea to a model of a curved space multiverse where particles in a recursive structure of concentric shells cast their shadows into the dimensions within. I then present existing evidence that supports the hypothesis of intrinsically curved space. Finally, I suggest a method to begin unifying Quantum Mechanics and General Relativity and discuss the uncertainties in constructing a simulation of our universe.

This paper examines the possibility that space is intrinsically curved and the consequences of this to measurements involving time. If you would like to see an easy-to-understand video walk through of this paper, follow this url: https://youtu.be/SelZZPr42bs Or for a more technical presentation of the material, use this link : https://youtu.be/1p-uYSsiys0 I begin by demonstrating an error in the way we construct our clocks and how this error invalidates the theories of Special and General Relativity. I further demonstrate how this error may be rectified using curved space geometry and the implications of curved space on the constancy of the speed of light. I propose a hypothesis of 4 spatial dimensions that describes our universe and extend this idea to a model of a curved space multiverse where particles in a recursive structure of concentric shells cast their shadows into the dimensions within. I then present existing evidence that supports the hypothesis of intrinsically curved space. Finally, I suggest a method to begin unifying Quantum Mechanics and General Relativity and discuss the uncertainties in constructing a simulation of our universe.

The decoupling of heavy fields as required by the Appelquist-Carazzone theorem plays a fundamental role in the construction of any effective field theory. However, it is not a trivial task to implement a renormalization prescription that produces the expected decoupling of massive fields, and it is even more difficult in curved spacetime. Focused on this idea, we consider the renormalization of the one-loop effective action for the Yukawa interaction with a background scalar field in curved space. We compute the beta functions within a generalized DeWitt-Schwinger subtraction procedure and discuss the decoupling in the running of the coupling constants. For the case of a quantized scalar field, all the beta function exhibit decoupling, including also the gravitational ones. For a quantized Dirac field, decoupling appears almost for all the beta functions. We obtain the anomalous result that the mass of the background scalar field does not decouple., Comment: New references and comments added

Jiménez and Maroto [Phys. Rev. D 83, 023514 (2011)] predicted free-space, longitudinal electrodynamic waves in curved space-time, if the Lorenz condition is relaxed. A general-relativistic extension of Woodside’s electrodynamics [Am. J. Phys. 77, 438 (2009)] includes a dynamical, scalar field in both the potential- and electric/magnetic-field formulations without mixing the two. We formulate a longitudinal-wave theory, eliminating curvature polarization, magnetization density, and scalar field in favor of the electric/magnetic fields and the metric tensor. We obtain a wave equation for the longitudinal electric field for a spatially flat, expanding universe with a scale factor. This work is important, because: (i) the scalar- and longitudinal-fields do not cancel, as in classical quantum electrodynamics; and (ii) this new approach provides a first-principles path to an extended quantum theory that includes acceleration and gravity.

In this work, we investigate the behaviour of Dirac particles in a class of Gödel-type space-time backgrounds in the presence of non-minimal coupling of the gravitational field with background curvature. We obtain the allowed energies for this relativistic system by solving analytically the Dirac equation in flat and curved space in a topologically trivial flat Gödel-type metric, and analyze the effects on the energy eiegnvalues.

Topological defects have received much attention due to their stability against perturbations and potential applications in nonvolatile high-density memory. Topologically non-trivial textures can be compelled by constraints on boundary condition, geometrical structure, and curved space. Ferroelectric vortices have been realized in various finite-sized nanostructures that allow such constraints to be produced. However, manipulation of topological excitations in otherwise topologically trivial flat ferroelectrics remains a tantalizing challenge. Here we show that a vortex–antivortex pair can be produced by a momentary electric pulse using a tip in a usual Kittel’s stripe domain of a BiFeO3 thin film. Moreover, we demonstrate that the distance between the paired vortex and antivortex can be controlled by dragging the biased tip. The spatial distribution of the local piezoresponse vectors is directly mapped using angle-resolved piezoresponse force microscopy and analyzed by local winding number calculation. Our findings offer a useful concept for the control of topological defects in ferroelectrics.

We discuss consistency at the quantum level in the rigid $\mathcal N=1$ supersymmetric field theories with a $U(1)_R$ symmetry in four-dimensional curved space which are formulated via coupling to the new-minimal supergravity background fields. By analyzing correlation functions of the current operators in the $\mathcal{R}$-multiplet, we show that the quantum consistency with the (unbroken) supersymmetry requires the $U(1)_R$ anomaly coefficient, which depends only on the field content of the theory, to vanish. This consistency condition is obtained under the assumption that the supercurrent Ward identity is non-anomalous and that the vacuum is supersymmetric., 15 pages plus 2 appendices, published version in JHEP, minor changes, references added

We consider the leading order perturbative renormalization of the multicritical $\phi^{2n}$ models and some generalizations in curved space. We pay particular attention to the nonminimal interaction with the scalar curvature $\frac{1}{2}\xi \phi^2 R$ and discuss the emergence of the conformal value of the coupling $\xi$ as the renormalization group fixed point of its beta function at and below the upper critical dimension as a function of $n$. We also examine our results in relation with Kawai and Ninomiya's formulation of two dimensional gravity., Comment: 13 pages, 3 figures; v3: matches the published version

The theory of general relativity is related to the concept of curvature of space- time induced by the presence of the massive objects. We will see through this paper that the general relativity can be linked with linear Algebra and Vector Analysis without the need for concept of space-time. This is important for the unification of general relativity with quantum mechanics, gravity with electromagnetic, and a better understanding of the universe, gravity, black holes. The most important is the separation between the space-time and the big bang theory, which prove the existence of space-time before that, which leads to the existence of the creator of the universe.

A model of the Universe is proposed in which three-dimensional space consists of positive and negative charges which are exactly equal and opposite. The charges are separated by a distance d, which is a random variable of the order of 0.1 nm. The charges are produce by continuous creation from nothing and the Universe doubles in volume every 2 to 3 billion years. Vast tracts of space move relative to each other and they meet whirlpools that are produced in which the charges are forced together producing protons and neutrons. Each proton and each neutron consume a pair of charges every 917 seconds and this creates the force of gravity in which space physically contracts around large objects. This concept of gravity is consistent with Newton’s and Einstein’s equations and allows one to visualize curved space and space-time. Focal areas in which the charges are ordered create information and energy. Electromagnetic radiation is a wave of energy in which order forms at the front and dissolves at the rear. Large objects move in a straight line because their electrons order adjacent space and the object moves with a surrounding wave. The quantum world and the world of large objects are not dissimilar and we can construct physical models of the Universe that all intelligent humans can understand. This includes a physical understanding of Schrodinger’s equation and its parameters. Everything in the Universe is composed ultimately of positive and negative charges, which can be combined in an infinite number of ways. This applies to abstract concepts as well as concrete objects. The only difference is that the former is four dimensional and involves complex information flow. Thus human consciousness, behavior, religious beliefs and spiritual experience are just as real and susceptible to scientific study as are anatomy and physiology.