Pub Date : 2023-07-05DOI: 10.12988/astp.2023.92005
Krish Jhurani, T. McMaken
This paper examines the issue of the existence and nature of time-like geodesics in asymptotically flat spacetimes and proposes a novel generalized topological criterion for the existence of time-like geodesics. Its validity is proved using theorems such as the Jordan-Brouwer Separation Theorem, the Raychaudhuri Equation, and key elements of Differential Geometry. More specifically, the proof primarily hinges on a closed, simply-connected subset of the spacetime manifold and a continuous map, causing a non-trivial induction on the first homology groups, from the boundary of this subset to a unit circle. The mathematical analysis conclusively affirms the presence of these geodesics, intersecting transversally within the said subset of spacetime. Findings underscore these geodesics' significant implications for the structure of asymptotically flat spacetimes, including stability, and hypothetical existence of wormholes. The generalized topological criterion also has implications on the problem of obstructions for the existence of Lorentzian metrics, and Einstein's Constraint Equations. Future research should extend this topological criterion to other classes of spacetimes, including those with non-trivial topologies or non-zero cosmological constants. Also, the criterion's application to study complex dynamical systems, such as gravitational waves or rotating black holes, could offer significant insights.
{"title":"Existence of time-like geodesics in asymptotically flat spacetimes: a generalized topological criterion","authors":"Krish Jhurani, T. McMaken","doi":"10.12988/astp.2023.92005","DOIUrl":"https://doi.org/10.12988/astp.2023.92005","url":null,"abstract":"This paper examines the issue of the existence and nature of time-like geodesics in asymptotically flat spacetimes and proposes a novel generalized topological criterion for the existence of time-like geodesics. Its validity is proved using theorems such as the Jordan-Brouwer Separation Theorem, the Raychaudhuri Equation, and key elements of Differential Geometry. More specifically, the proof primarily hinges on a closed, simply-connected subset of the spacetime manifold and a continuous map, causing a non-trivial induction on the first homology groups, from the boundary of this subset to a unit circle. The mathematical analysis conclusively affirms the presence of these geodesics, intersecting transversally within the said subset of spacetime. Findings underscore these geodesics' significant implications for the structure of asymptotically flat spacetimes, including stability, and hypothetical existence of wormholes. The generalized topological criterion also has implications on the problem of obstructions for the existence of Lorentzian metrics, and Einstein's Constraint Equations. Future research should extend this topological criterion to other classes of spacetimes, including those with non-trivial topologies or non-zero cosmological constants. Also, the criterion's application to study complex dynamical systems, such as gravitational waves or rotating black holes, could offer significant insights.","PeriodicalId":127314,"journal":{"name":"Advanced Studies in Theoretical Physics","volume":"7 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-07-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"133426667","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2023-01-01DOI: 10.12988/astp.2023.92008
Riadh Al Rabeh
Present day astronomy is highly complex and multi-disciplinary. It relies on the presumed existence of dark matter, dark energy, expanding universe, a big bang starting point, and many singularity blackholes dotted in the picture. We propose to simplify this using Mach’s principle of the effect of distant masses, Einstein equivalence and gravity phase-shit idea, and the author’s idea regarding the radiation origin of matter [1]. We only use simple and well-known facts to do this. The effect of distant masses solves the problem of terminal rotation curves in galaxies. Dark matter and dark energy problems are explained via Einstein equivalence principle and the gravity phase-shift, and the radiation origin of matter is used to understand the nature of stars and blackholes excluding any singularity solution. The universe is perceived as an eternal dynamic structure, ruled by familiar forces and concepts in which the gravity can cause limitless mass accumulation to form stars that subsequently and a result of external and internal factors, disintegrate and eject some or all of their accumulated matter. In the process we obtain formulae for calculating Newton’s universal constant of gravitation, the condition for forming a blackhole, the pressure level inside stars, a formula for the Hubble constant via gravitational redshift, and a formula for the terminal condition of the rotation curves of galaxies-helped by Mach’s principle regarding the effect of distant masses. We also point to supporting statements to our results in published literature.
{"title":"Simplifying astronomy via Mach's principle, Einstein's equivalence principle, and the gravity-phase-shift","authors":"Riadh Al Rabeh","doi":"10.12988/astp.2023.92008","DOIUrl":"https://doi.org/10.12988/astp.2023.92008","url":null,"abstract":"Present day astronomy is highly complex and multi-disciplinary. It relies on the presumed existence of dark matter, dark energy, expanding universe, a big bang starting point, and many singularity blackholes dotted in the picture. We propose to simplify this using Mach’s principle of the effect of distant masses, Einstein equivalence and gravity phase-shit idea, and the author’s idea regarding the radiation origin of matter [1]. We only use simple and well-known facts to do this. The effect of distant masses solves the problem of terminal rotation curves in galaxies. Dark matter and dark energy problems are explained via Einstein equivalence principle and the gravity phase-shift, and the radiation origin of matter is used to understand the nature of stars and blackholes excluding any singularity solution. The universe is perceived as an eternal dynamic structure, ruled by familiar forces and concepts in which the gravity can cause limitless mass accumulation to form stars that subsequently and a result of external and internal factors, disintegrate and eject some or all of their accumulated matter. In the process we obtain formulae for calculating Newton’s universal constant of gravitation, the condition for forming a blackhole, the pressure level inside stars, a formula for the Hubble constant via gravitational redshift, and a formula for the terminal condition of the rotation curves of galaxies-helped by Mach’s principle regarding the effect of distant masses. We also point to supporting statements to our results in published literature.","PeriodicalId":127314,"journal":{"name":"Advanced Studies in Theoretical Physics","volume":"110 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135550665","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2023-01-01DOI: 10.12988/astp.2023.92009
R. Alvarado
Two exact solutions to Einstein equations were obtained; whose difference is the kind of initial expansion (greater on an axis or on a plane) in an anisotropic and homogeneous symmetry of Petrov type D. In these solutions, a mixture of dark energy and a ”standard” attractive Bose-Einstein Condensate (BEC) were considered. The initial singularity problem was studied and is only present in one of these models. Also, the study of temperature allowed to determine that it is null at the start of the universe and as time increases asymptotically, it tends to a constant value, hence a BEC is essential in the first expansion phase and, for this work, with 8 / 9 parts of the total early universe energy. Hubble and deceleration parameters were studied as well and it was determined that the Hubble parameter initially gets indefinite in t = 0, but tends to a constant value when time increases; for the deceleration parameter, it was stated that the universe initially expands in a decelerated form, but from a certain value, it starts continuously to expand fast towards a constant value. As time increases asymptotically, models tend to a one of FRWL flat type of dark energy.
{"title":"Anisotropic cosmological exact solutions of Petrov type D of a mixture of dark energy and an attractive Bose-Einstein condensate","authors":"R. Alvarado","doi":"10.12988/astp.2023.92009","DOIUrl":"https://doi.org/10.12988/astp.2023.92009","url":null,"abstract":"Two exact solutions to Einstein equations were obtained; whose difference is the kind of initial expansion (greater on an axis or on a plane) in an anisotropic and homogeneous symmetry of Petrov type D. In these solutions, a mixture of dark energy and a ”standard” attractive Bose-Einstein Condensate (BEC) were considered. The initial singularity problem was studied and is only present in one of these models. Also, the study of temperature allowed to determine that it is null at the start of the universe and as time increases asymptotically, it tends to a constant value, hence a BEC is essential in the first expansion phase and, for this work, with 8 / 9 parts of the total early universe energy. Hubble and deceleration parameters were studied as well and it was determined that the Hubble parameter initially gets indefinite in t = 0, but tends to a constant value when time increases; for the deceleration parameter, it was stated that the universe initially expands in a decelerated form, but from a certain value, it starts continuously to expand fast towards a constant value. As time increases asymptotically, models tend to a one of FRWL flat type of dark energy.","PeriodicalId":127314,"journal":{"name":"Advanced Studies in Theoretical Physics","volume":"102 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"136207551","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2023-01-01DOI: 10.12988/astp.2023.92010
R. Alvarado
Two exact solutions to Einstein equations, which differ because of its type of initial expansion, are obtained to a nonlinear scalar field with a potential type V = Λ (cid:16) 1 − tanh ( √ 6 φ 2 ) 4 (cid:17) . It is determined that the energy density of solutions is not singular for any time value and for which at the beginning in t = 0, the space-time is a vacuum of Kasner type ( a 1 = a 2 = − 2 a 3 = 2 / 3) for one solution and the flat world for the other. By having studied the temperature, it is established that it is null at the beginning and that once it increases up to a maximum value, it stops increases and asymptotically goes down to zero in respect to time. The Hubble and deceleration parameters were studied, it is showed that the Hubble parameter is indefinite in t = 0 and tends to have a constant value as time increases; then, the deceleration parameter indicates an initial process of a decelerated expansion that continuously changes into an accelerated one as time increases. By the study of the Jacobi stability of the solutions, it is obtained that the solutions are initially unstability but cease to be so in a determined time. The space-time of both solutions transforms into the equivalent of dark energy for FRWL as time increases.
{"title":"From vacuum to dark energy. Exact anisotropic cosmological solution of Petrov type D for a nonlinear scalar field","authors":"R. Alvarado","doi":"10.12988/astp.2023.92010","DOIUrl":"https://doi.org/10.12988/astp.2023.92010","url":null,"abstract":"Two exact solutions to Einstein equations, which differ because of its type of initial expansion, are obtained to a nonlinear scalar field with a potential type V = Λ (cid:16) 1 − tanh ( √ 6 φ 2 ) 4 (cid:17) . It is determined that the energy density of solutions is not singular for any time value and for which at the beginning in t = 0, the space-time is a vacuum of Kasner type ( a 1 = a 2 = − 2 a 3 = 2 / 3) for one solution and the flat world for the other. By having studied the temperature, it is established that it is null at the beginning and that once it increases up to a maximum value, it stops increases and asymptotically goes down to zero in respect to time. The Hubble and deceleration parameters were studied, it is showed that the Hubble parameter is indefinite in t = 0 and tends to have a constant value as time increases; then, the deceleration parameter indicates an initial process of a decelerated expansion that continuously changes into an accelerated one as time increases. By the study of the Jacobi stability of the solutions, it is obtained that the solutions are initially unstability but cease to be so in a determined time. The space-time of both solutions transforms into the equivalent of dark energy for FRWL as time increases.","PeriodicalId":127314,"journal":{"name":"Advanced Studies in Theoretical Physics","volume":"135 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"136207546","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2022-07-17DOI: 10.12988/astp.2022.91866
Huailong Wang
In evaluating differential cross section of elastic scattering, different theories were applied to low-momentum and relativistic particles. For low-momentum motion, Lippmann-Schwinger scattering equation was applied, called fundamental formula; while for relativistic particles, a general scattering theory was used which calculates S matrix. In this paper, Lippmann-Schwinger equation is applied uniformly to both low-momentum and relativistic particles. The cross sections are valuated to the first order of Born approximation. One-body time-independent Green’s functions for relativistic free particles are given. Compared to the general scattering theory, the fundamental theory has a clearer physical picture and the approximations made are more explicit.
{"title":"Evaluation of cross section of elastic scattering for non-relativistic and relativistic particles by means of fundamental scattering formulas","authors":"Huailong Wang","doi":"10.12988/astp.2022.91866","DOIUrl":"https://doi.org/10.12988/astp.2022.91866","url":null,"abstract":"In evaluating differential cross section of elastic scattering, different theories were applied to low-momentum and relativistic particles. For low-momentum motion, Lippmann-Schwinger scattering equation was applied, called fundamental formula; while for relativistic particles, a general scattering theory was used which calculates S matrix. In this paper, Lippmann-Schwinger equation is applied uniformly to both low-momentum and relativistic particles. The cross sections are valuated to the first order of Born approximation. One-body time-independent Green’s functions for relativistic free particles are given. Compared to the general scattering theory, the fundamental theory has a clearer physical picture and the approximations made are more explicit.","PeriodicalId":127314,"journal":{"name":"Advanced Studies in Theoretical Physics","volume":"5 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2022-07-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"122385146","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2021-10-28DOI: 10.12988/astp.2022.91844
I. Oda
We consider a generic scale invariant scalar quantum field theory and its symmetry breakdown. Based on the dimension counting identity, we give a concise proof that dilaton is exactly massless at the classical level if scale invariance is broken spontaneously. On the other hand, on the basis of the generalized dimension counting identity, we prove that the dilaton becomes massive at the quantum level if scale invariance is explicitly broken by quantum anomaly. It is pointed out that a subtlety occurs when scale invariance is spontaneously broken through a scale invariant regularization method where the renormalization scale is replaced with the dilaton field. In this case, the dilaton remains massless even at the quantum level after spontaneous symmetry breakdown of scale symmetry, but when the massless dilaton couples non-minimally to the Einstein-Hilbert term and is applied for cosmology, it is phenomenologically ruled out by solar system tests unless its coupling to matters is much suppressed compared to the gravitational interaction.
{"title":"Scale invariance and dilaton mass","authors":"I. Oda","doi":"10.12988/astp.2022.91844","DOIUrl":"https://doi.org/10.12988/astp.2022.91844","url":null,"abstract":"We consider a generic scale invariant scalar quantum field theory and its symmetry breakdown. Based on the dimension counting identity, we give a concise proof that dilaton is exactly massless at the classical level if scale invariance is broken spontaneously. On the other hand, on the basis of the generalized dimension counting identity, we prove that the dilaton becomes massive at the quantum level if scale invariance is explicitly broken by quantum anomaly. It is pointed out that a subtlety occurs when scale invariance is spontaneously broken through a scale invariant regularization method where the renormalization scale is replaced with the dilaton field. In this case, the dilaton remains massless even at the quantum level after spontaneous symmetry breakdown of scale symmetry, but when the massless dilaton couples non-minimally to the Einstein-Hilbert term and is applied for cosmology, it is phenomenologically ruled out by solar system tests unless its coupling to matters is much suppressed compared to the gravitational interaction.","PeriodicalId":127314,"journal":{"name":"Advanced Studies in Theoretical Physics","volume":"1 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2021-10-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"134353699","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2021-04-29DOI: 10.21203/RS.3.RS-475105/V1
N. Matjelo
In this paper, we consider modeling measurement as part of the overall system dynamics in a way that allows a dynamic interaction between the target system and the measuring system/device. For example, the interaction between the target system and the measuring system can be modeled as a form of collision, scattering process, or some coupling between the two systems depending on how they interact with each other. We show that following this line of thinking about the two systems as intertwined/coupled, in the classical picture, naturally leads to the general dynamics analogous to Schrodinger's wave dynamics.
{"title":"Considering Measurement Dynamics In Classical Mechanics","authors":"N. Matjelo","doi":"10.21203/RS.3.RS-475105/V1","DOIUrl":"https://doi.org/10.21203/RS.3.RS-475105/V1","url":null,"abstract":"\u0000 In this paper, we consider modeling measurement as part of the overall system dynamics in a way that allows a dynamic interaction between the target system and the measuring system/device. For example, the interaction between the target system and the measuring system can be modeled as a form of collision, scattering process, or some coupling between the two systems depending on how they interact with each other. We show that following this line of thinking about the two systems as intertwined/coupled, in the classical picture, naturally leads to the general dynamics analogous to Schrodinger's wave dynamics.","PeriodicalId":127314,"journal":{"name":"Advanced Studies in Theoretical Physics","volume":"11 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2021-04-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"127594196","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2020-03-17DOI: 10.12988/astp.2020.91464
I. Oda
We discuss spontaneous symmetry breakdown (SSB) of both global and local scale symmetries in scalar-tensor gravity with two scalar fields, one of which couples nonminimally to scalar curvature while the other is a normal scalar field. In case of a global scale symmetry, by moving from the Jordan frame to the Einstein frame, a normal scalar field becomes massive while the dilaton remains massless after the SSB. In case of a local scale symmetry, we take a gauge fixing condition for the local scale invariance, $a R + b phi^2 = k$, which was found in our previous study of a Weyl's quadratic gravity. Together with locally scale invariant potential terms in a classical action, this gauge condition generates a Higgs potential whose vacuum expectation value (VEV) produces the Einstein-Hilbert action with an $R^2$ term in the lowest level of approximation. One interesting aspect in this model is that a massless Nambu-Goldstone boson associated with a scale invariance is absorbed into the metric tensor field and consequently an $R^2$ term is induced in the action.
讨论了标量张量引力中具有两个标量场的全局和局部尺度对称性的自发对称击穿(SSB)，其中一个标量场与标量曲率非最小耦合，另一个是标准标量场。在全局尺度对称的情况下，通过从约当坐标系移动到爱因斯坦坐标系，标准标量场变得有质量，而膨胀在SSB之后保持无质量。在局部尺度对称的情况下，我们对局部尺度不变性取一个规范固定条件，$a R + b phi^2 = k$，这是我们在之前的Weyl二次引力研究中发现的。与经典作用中的局部尺度不变势项一起，该规范条件产生希格斯势，其真空期望值(VEV)产生在最低近似水平上具有$R^2$项的爱因斯坦-希尔伯特作用。该模型中一个有趣的方面是，与尺度不变性相关的无质量nambugoldstone玻色子被吸收到度量张量场中，因此在作用中产生了一个R^2$项。
{"title":"Spontaneous symmetry breakdown of scale symmetries","authors":"I. Oda","doi":"10.12988/astp.2020.91464","DOIUrl":"https://doi.org/10.12988/astp.2020.91464","url":null,"abstract":"We discuss spontaneous symmetry breakdown (SSB) of both global and local scale symmetries in scalar-tensor gravity with two scalar fields, one of which couples nonminimally to scalar curvature while the other is a normal scalar field. In case of a global scale symmetry, by moving from the Jordan frame to the Einstein frame, a normal scalar field becomes massive while the dilaton remains massless after the SSB. In case of a local scale symmetry, we take a gauge fixing condition for the local scale invariance, $a R + b phi^2 = k$, which was found in our previous study of a Weyl's quadratic gravity. Together with locally scale invariant potential terms in a classical action, this gauge condition generates a Higgs potential whose vacuum expectation value (VEV) produces the Einstein-Hilbert action with an $R^2$ term in the lowest level of approximation. One interesting aspect in this model is that a massless Nambu-Goldstone boson associated with a scale invariance is absorbed into the metric tensor field and consequently an $R^2$ term is induced in the action.","PeriodicalId":127314,"journal":{"name":"Advanced Studies in Theoretical Physics","volume":"29 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2020-03-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"132567329","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2020-03-03DOI: 10.12988/astp.2021.91707
I. Oda
It is shown that in a quadratic gravity based on Weyl's conformal geometry, not only the Einstein-Hilbert action emerges but also a Weyl gauge field becomes massive in the Weyl gauge condition, $tilde R = k$, for a Weyl gauge symmetry within the framework of the BRST formalism. We also consider a more general gravitational theory with a scalar field in the Weyl geometry and see that the Einstein-Hilbert action can be induced from spontaneous symmetry breakdown of the Weyl gauge symmetry. Thus, it turns out that Weyl's conformal gravity is quantum mechanically equivalent to Einstein's general relativity plus a massive Weyl gauge field, and the Weyl geometry is free from an infamous ``second clock problem'' in quantum regime.
证明了在基于Weyl共形几何的二次重力中，对于BRST形式体系框架内的Weyl规范对称，在Weyl规范条件下$tilde R = k$，不仅出现了Einstein-Hilbert作用，而且Weyl规范场变得有质量。我们还考虑了在Weyl几何中具有标量场的更一般的引力理论，并看到爱因斯坦-希尔伯特作用可以由Weyl规范对称的自发对称性破坏引起。因此，事实证明，Weyl的共形引力在量子力学上等同于爱因斯坦的广义相对论加上一个巨大的Weyl规范场，并且Weyl几何免于量子制度中臭名昭著的“秒钟问题”。
{"title":"Emergence of Einstein gravity from Weyl gravity","authors":"I. Oda","doi":"10.12988/astp.2021.91707","DOIUrl":"https://doi.org/10.12988/astp.2021.91707","url":null,"abstract":"It is shown that in a quadratic gravity based on Weyl's conformal geometry, not only the Einstein-Hilbert action emerges but also a Weyl gauge field becomes massive in the Weyl gauge condition, $tilde R = k$, for a Weyl gauge symmetry within the framework of the BRST formalism. We also consider a more general gravitational theory with a scalar field in the Weyl geometry and see that the Einstein-Hilbert action can be induced from spontaneous symmetry breakdown of the Weyl gauge symmetry. Thus, it turns out that Weyl's conformal gravity is quantum mechanically equivalent to Einstein's general relativity plus a massive Weyl gauge field, and the Weyl geometry is free from an infamous ``second clock problem'' in quantum regime.","PeriodicalId":127314,"journal":{"name":"Advanced Studies in Theoretical Physics","volume":"154 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2020-03-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"115895169","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{This paper is a comparison of the Minkowski, Einstein and Einstein dual theories of relativity. The dual is based on an identity relating the observer time and the proper time as a contact transformation on configuration space, which leaves phase space invariant. The theory is dual in that, for a system of $n$ particles, any inertial observer has two unique sets of global variables $({bf{X}}, t)$ and $({bf{X}}, tau)$ to describe the dynamics. Where ${bf{X}}$ is the (unique) canonical center of mass. In the $({bf{X}}, t)$ variables, time is relative and the speed of light is unique, while in the $({bf{X}}, tau)$ variables, time is unique and the speed of light is relative with no upper bound. The two sets of particle and Maxwell field equations are mathematically equivalent, but the particle wave equations are not. The dual version contains an additional longitudinal radiation term that appears instantaneously with acceleration, does not depend on the nature of the force and the Wheeler-Feynman absorption hypothesis is a corollary. The homogenous and isotropic nature of the universe is sufficient to prove that a unique definition of Newtonian time exists with zero set at the big bang. The isotopic dual of $R$ is used to improve the big bang model, by providing an explanation for the lack of antimatter in our universe, a natural arrow for time, conservation of energy, momentum and angular momentum. This also solves the flatness and horizon problems without inflation. We predict that radiation from a betatron (of any frequency) will not produce photoelectrons, that matter and antimatter are gravitationally repulsive and that data from distant sources does not have a unique physical interpretation. We provide a table showing the differences between the Minkowski, Einstein and dual versions of the special theory.}
{"title":"The Einstein dual theory of relativity","authors":"T. Gill, G. A. D. Parga","doi":"10.12988/astp.2019.9312","DOIUrl":"https://doi.org/10.12988/astp.2019.9312","url":null,"abstract":"{This paper is a comparison of the Minkowski, Einstein and Einstein dual theories of relativity. The dual is based on an identity relating the observer time and the proper time as a contact transformation on configuration space, which leaves phase space invariant. The theory is dual in that, for a system of $n$ particles, any inertial observer has two unique sets of global variables $({bf{X}}, t)$ and $({bf{X}}, tau)$ to describe the dynamics. Where ${bf{X}}$ is the (unique) canonical center of mass. In the $({bf{X}}, t)$ variables, time is relative and the speed of light is unique, while in the $({bf{X}}, tau)$ variables, time is unique and the speed of light is relative with no upper bound. The two sets of particle and Maxwell field equations are mathematically equivalent, but the particle wave equations are not. The dual version contains an additional longitudinal radiation term that appears instantaneously with acceleration, does not depend on the nature of the force and the Wheeler-Feynman absorption hypothesis is a corollary. \u0000The homogenous and isotropic nature of the universe is sufficient to prove that a unique definition of Newtonian time exists with zero set at the big bang. The isotopic dual of $R$ is used to improve the big bang model, by providing an explanation for the lack of antimatter in our universe, a natural arrow for time, conservation of energy, momentum and angular momentum. This also solves the flatness and horizon problems without inflation. \u0000We predict that radiation from a betatron (of any frequency) will not produce photoelectrons, that matter and antimatter are gravitationally repulsive and that data from distant sources does not have a unique physical interpretation. We provide a table showing the differences between the Minkowski, Einstein and dual versions of the special theory.}","PeriodicalId":127314,"journal":{"name":"Advanced Studies in Theoretical Physics","volume":"68 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2020-01-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"133398922","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
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