Showing papers on "Four-force published in 2012"
TL;DR: Optical sensors find various applications in all fields of scientific research, instrumentation and practical applications as mentioned in this paper, and are widely used in physics, chemistry, biology and medicine, and also have a great impact on today's technological advances in telecommunications, photolithography on semiconductor chips, particle detection or object tracking to name a few.
Abstract: Optical sensors find various applications in all fields of scientific research, instrumentation and practical applications. Optical techniques are widely used in physics, chemistry, biology and medicine. They also have a great impact on today’s technological advances in telecommunications, photolithography on semiconductor chips, particle detection or object tracking to name a few. A book that would provide a summary of all optical sensors and their practical applications would be attractive to many readers across the board. The author’s intent to give an overview on this topic is well suited to meet this goal. This book serves as a good introduction to optical sensors. It covers the basics of light sources, detectors, various optical elements, and goes through some concepts about optical sensors and techniques. Optical sensors may refer to devices for light detection, e.g. CCD or CMOS cameras or PIN photodiodes. The author expands this concept and defines an optical sensor as a system consisting of a light source, a photodetector and optical elements for light delivery. He then describes the basic properties of incoherent and coherent light followed by numerous examples of optical sensors and their applications. Rigorous mathematical treatment, details about experimental arrangements and device architecture are beyond the scope of the book. However, the author provides an extended list of references on any given topic. Some of the references may be unfamiliar to the English speaking audiences. A comprehensive description of many modern optical sensor concepts is provided. The reader will find general coverage on how the humans and insects differ in their vision. The material touches upon the Purkinje effect on the shift of human eye’s spectral sensitivity. The reader will also find an extensive coverage about switches, rain sensors, displacement, velocity and distance measurement concepts, and laser vibrometers. A good discussion on optical techniques for temperature measurement is given. The reader will find examples about pyrometers and microbolometers as well as other thermal sensors used in different wavelength ranges. Microscopy and holography techniques are also discussed among the others. Various interferometric techniques and their applications are provided along with interesting examples. The reader will also find the basic concept of fluorescence detection and its applications. The reader will not find discussion on the state-of-the-art ultrafast techniques, e.g. laser induced fluorescence or four-wavemixing-based methods and their wide range of applications in science and technologies. Concepts and applications in the deep and extreme ultraviolet range, important for the photolithography, are not discussed either. The next editions of the book will hopefully include these important topics. The book is a good start for beginners who want to learn about optical sensors. An experimentalist may use this book as a reference. Engineering undergraduate students may find the material useful to jump start their projects and can use the references provided therein for more in-depth studies. A reader interested in biological applications of optical sensors, e.g. photodynamic therapy or fibre-optic based diagnostic techniques, will not find relevant material in this book. Teachers and general readers may find the material useful in preparing for classroom presentations and for general understanding of the optical sensor principles.
267 citations
Book•
02 Apr 2012
TL;DR: In this article, Malament presents the basic logical-mathematical structure of general relativity and considers a number of special topics concerning the foundations of general relativistic and its relation to Newtonian gravitation theory.
Abstract: In "Topics in the Foundations of General Relativity and Newtonian Gravitation Theory", David B. Malament presents the basic logical-mathematical structure of general relativity and considers a number of special topics concerning the foundations of general relativity and its relation to Newtonian gravitation theory. These special topics include the geometrized formulation of Newtonian theory (also known as Newton-Cartan theory), the concept of rotation in general relativity, and Godel spacetime. One of the highlights of the book is a no-go theorem that can be understood to show that there is no criterion of orbital rotation in general relativity that fully answers to our classical intuitions. "Topics" is intended for both students and researchers in mathematical physics and philosophy of science.
222 citations
TL;DR: In this article, it was shown that general relativity is invariant with respect to Weyl transformations in an arbitrary Weyl frame, and that WIST gravity theories are mathematically equivalent to Brans-Dicke theory when viewed in a particular Weyl framework.
Abstract: We show that the general theory of relativity can be formulated in the language of Weyl geometry. We develop the concept of Weyl frames and point out that the new mathematical formalism may lead to different pictures of the same gravitational phenomena. We show that in an arbitrary Weyl frame general relativity, which takes the form of a scalar–tensor gravitational theory, is invariant with respect to Weyl transformations. A key point in the development of the formalism is to build an action that is manifestly invariant with respect to Weyl transformations. When this action is expressed in terms of Riemannian geometry we find that the theory has some similarities with Brans–Dicke gravitational theory. In this scenario, the gravitational field is not described by the metric tensor only, but by a combination of both the metric and a geometrical scalar field. We illustrate this point by examining how distinct geometrical and physical pictures of the same phenomena may arise in different frames. To give an example, we discuss the gravitational spectral shift as viewed in a general Weyl frame. We further explore the analogy of general relativity with scalar–tensor theories and show how a known Brans–Dicke vacuum solution may appear as a solution of general relativity theory when reinterpreted in a particular Weyl frame. Finally, we show that the so-called WIST gravity theories are mathematically equivalent to Brans–Dicke theory when viewed in a particular frame.
108 citations
TL;DR: This work presents a streamlined axiom system of special relativity in first-order logic and “derive” an axiomSystem of general relativity in two natural steps to make general relativity more accessible for the non-specialist.
Abstract: We present a streamlined axiom system of special relativity in first-order logic. From this axiom system we “derive” an axiom system of general relativity in two natural steps. We will also see how the axioms of special relativity transform into those of general relativity. This way we hope to make general relativity more accessible for the non-specialist.
53 citations
TL;DR: In this article, the authors derived the constraints that the relativity principle imposes between coefficients of a deformed (but rotational invariant) composition law, dispersion relation, and transformation laws, at first order in the power expansion.
Abstract: In the context of departures from special relativity written as a momentum power expansion in the inverse of an ultraviolet energy scale M, we derive the constraints that the relativity principle imposes between coefficients of a deformed (but rotational invariant) composition law, dispersion relation, and transformation laws, at first order in the power expansion. In particular, we find that at that order the consistency of a modification of the energy-momentum composition law fixes the modification in the dispersion relation. We therefore obtain the most generic modification of special relativity which is rotational invariant and that preserves the relativity principle at leading order in 1/M. © 2012 American Physical Society.
46 citations
01 Jan 2012
TL;DR: The geodesic principle can be recovered as a theorem in general relativity as mentioned in this paper, but it is not a consequence of Einstein's equation (or the conservation principle) alone, and other assumptions are needed to drive the theorems in question.
Abstract: It is often claimed that the geodesic principle can be recovered as a theorem in general relativity. Indeed, it is claimed that it is a consequence of Einstein’s equation (via the conservation principle that is, itself, a consequence of that equation). These claims are certainly correct, but it may be worth drawing attention to one small qualification. Though the geodesic principle can be recovered as theorem in general relativity, it is not a consequence of Einstein’s equation (or the conservation principle) alone. Other assumptions are needed to drive the theorems in question. My goal in this short note is to make this claim precise.
41 citations
TL;DR: In this paper, a simple formula was proposed to characterize the probability of detecting non-general-relativistic corrections of a given magnitude, which can be applied to all tests that embed General Relativity in a larger theory, including tests of individual theories such as Brans-Dicke gravity.
Abstract: The observations of gravitational-wave signals from astrophysical sources such as binary inspirals will be used to test General Relativity for self consistency and against alternative theories of gravity. I describe a simple formula that can be used to characterize the prospects of such tests, by estimating the matched-filtering signal-to-noise ratio required to detect non-General-Relativistic corrections of a given magnitude. The formula is valid for sufficiently strong signals; it requires the computation of a single number, the fitting factor between the General-Relativistic and corrected waveform families; and it can be applied to all tests that embed General Relativity in a larger theory, including tests of individual theories such as Brans-Dicke gravity, as well as the phenomenological schemes that introduce corrections and extra terms in the post-Newtonian phasing expressions of inspiral waveforms. The formula suggests that the volume-limited gravitational-wave searches performed with second-generation ground-based detectors would detect alternative-gravity corrections to General-Relativistic waveforms no smaller than 1-10% (corresponding to fitting factors of 0.9 to 0.99).
37 citations
TL;DR: In this paper, the authors explore modifications of general relativity that retain the same graviton degrees of freedom, and therefore explicitly break Lorentz covariance, and apply it to a realistic class of theories.
Abstract: General relativity is a generally covariant, locally Lorentz covariant theory of two transverse, traceless graviton degrees of freedom. According to a theorem of Hojman, Kucha\ifmmode \check{r}\else \v{r}\fi{}, and Teitelboim, modifications of general relativity must either introduce new degrees of freedom or violate the principle of local Lorentz covariance. In this paper, we explore modifications of general relativity that retain the same graviton degrees of freedom, and therefore explicitly break Lorentz covariance. Motivated by cosmology, the modifications of interest maintain explicit spatial covariance. In spatially covariant theories of the graviton, the physical Hamiltonian density obeys an analogue of the renormalization group equation which encodes invariance under flow through the space of conformally equivalent spatial metrics. This paper is dedicated to setting up the formalism of our approach and applying it to a realistic class of theories. Forthcoming work will apply the formalism more generally.
34 citations
TL;DR: In this paper, the authors show how a Brownian motion on a short scale can originate a relativistic motion on scales that are larger than particle's Compton wavelength, which can be described in terms of polycrystalline vacuum.
Abstract: Building on our previous work [Phys.Rev.D82,085016(2010)], we show in this paper how a Brownian motion on a short scale can originate a relativistic motion on scales that are larger than particle's Compton wavelength. This can be described in terms of polycrystalline vacuum. Viewed in this way, special relativity is not a primitive concept, but rather it statistically emerges when a coarse graining average over distances of order, or longer than the Compton wavelength is taken. By analyzing the robustness of such a special relativity under small variations in the polycrystalline grain-size distribution we naturally arrive at the notion of doubly-special relativistic dynamics. In this way, a previously unsuspected, common statistical origin of the two frameworks is brought to light. Salient issues such as the role of gauge fixing in emergent relativity, generalized commutation relations, Hausdorff dimensions of representative path-integral trajectories and a connection with Feynman chessboard model are also discussed.
TL;DR: In this paper, the authors reassess the notion of spacetime transformations between inertial frames in the absence of the relativity principle, arguing that significant and nontrivial physics can still be extracted as long as the transformations are at least linear.
Abstract: Ever since the work of von Ignatowsky circa 1910 it has been known (if not always widely appreciated) that the relativity principle, combined with the basic and fun- damental physical assumptions of locality, linearity, and isotropy, leads almost uniquely to either the Lorentz transformations of special relativity or to Galileo’s transformations of classical Newtonian mechanics. Consequently, if one wishes (for whatever reason) to entertain the possibility of Lorentz symmetry breaking within the context of the class of local physical theories, then it seems likely that one will have to abandon (or at the very least grossly modify) the relativity principle. Working within the framework of local physics, we reassess the notion of spacetime transformations between inertial frames in the absence of the relativity principle, arguing that significant and nontrivial physics can still be extracted as long as the transformations are at least linear. An interesting technical aspect of the analysis is that the transformations now form a groupoid /pseudo-group — it is this technical point that permits one to evade the von Ignatowsky argument. Even in the absence of a relativity principle we can (assuming locality and linearity) nevertheless deduce clear and compelling rules for the transformation of space and time, rules for the composition of 3-velocities, and rules for the transformation of energy and momentum. Within this framework, the energy-momentum transformations are in general affine, but may be chosen to be linear, with the 4-component vector P = (E, −p
T
) trans- forming as a row vector, while the 4-component vector of space-time position X = (t, x
T
)
T
transforms as a column vector. As part of the analysis we identify two particularly elegant and physically compelling models implementing “minimalist” violations of Lorentz invariance — in the first of these minimalist models all Lorentz violations are confined to carefully delineated particle physics sub-sectors, while the second minimalist Lorentz-violating model depends on one free func- tion of absolute velocity, but otherwise preserves as much as possible of standard Lorentz invariant physics.
TL;DR: In this paper, the authors study the thermodynamics of an ideal gas in doubly special relativity and derive a series solution for the partition function and derive thermodynamic quantities, which they use to obtain a stiffer equation of state.
Abstract: We study thermodynamics of an ideal gas in doubly special relativity. A new type of special functions (which we call ``incomplete modified Bessel functions'') emerge. We obtain a series solution for the partition function and derive thermodynamic quantities. We observe that doubly special relativity thermodynamics is nonperturbative in the special relativity and massless limits. A stiffer equation of state is found.
TL;DR: In this article, the authors proposed a non-commutative special relativity in which space-time and matter degrees of freedom are treated as classical matrices with arbitrary commutation relations, and a space time line element is defined using a trace.
Abstract: There ought to exist a description of quantum field theory which does not depend on an external classical time. To achieve this goal, in a recent paper we have proposed a non-commutative special relativity in which space-time and matter degrees of freedom are treated as classical matrices with arbitrary commutation relations, and a space-time line element is defined using a trace. In the present paper, following the theory of Trace Dynamics, we construct a statistical thermodynamics for the non-commutative special relativity, and show that one arrives at a generalized quantum dynamics in which space and time are non-classical and have an operator status. In a future work, we will show how standard quantum theory on a classical space-time background is recovered from here.
TL;DR: Within an axiomatic framework of kinematics, it was shown in this article that the existence of faster than light particles is logically independent of Einstein's special theory of relativity.
Abstract: Within an axiomatic framework of kinematics, we prove that the existence of faster than light particles is logically independent of Einstein's special theory of relativity. Consequently, it is consistent with the kinematics of special relativity that there might be faster than light particles.
TL;DR: It is shown how conformal relativity is related to Brans–Dicke theory and to low-energy-effective superstring theory and that like in ekpyrotic/cyclic models, the transition through the singularity in conformal cosmology in the string frame takes place in the weak coupling regime.
Abstract: We show how conformal relativity is related to Brans–Dicke theory and to low-energy-effective superstring theory. Conformal relativity or the Hoyle–Narlikar theory is invariant with respect to conformal transformations of the metric. We show that the conformal relativity action is equivalent to the transformed Brans–Dicke action for ω = -3/2 (which is the border between standard scalar field and ghost) in contrast to the reduced (graviton-dilaton) low-energy-effective superstring action which corresponds to the Brans–Dicke action with ω = -1. We show that like in ekpyrotic/cyclic models, the transition through the singularity in conformal cosmology in the string frame takes place in the weak coupling regime. We also find interesting self-duality and duality relations for the graviton-dilaton actions.
Posted Content•
TL;DR: In this article, a local version of Shape Dynamics that is equivalent to General Relativity is constructed, in the sense that the algebras of Dirac observables weakly coincide.
Abstract: In this conceptual paper we construct a local version of Shape Dynamics that is equivalent to General Relativity in the sense that the algebras of Dirac observables weakly coincide. This allows us to identify Shape Dynamics observables with General Relativity observables, whose observables can now be interpreted as particular representative functions of observables of a conformal theory at fixed York time. An application of the observable equivalence of General Relativity and Shape Dynamics is to define the quantization of General Relativity through quantizing Shape Dynamics and using observable equivalence. We investigate this proposal explicitly for gravity in 2+1 dimensions.
TL;DR: In this article, an approximate coordinate transformation to an accelerated frame was proposed, which turns out to be closely related to Rindler coordinates, widely used in modern general relativity, leading him directly to interpret gravitation in terms of spacetime curvature.
Abstract: On his way to general relativity, Einstein used the equivalence principle to formulate a theory of the static gravitational field. In this context he introduced an approximate coordinate transformation to an accelerated frame which turns out to be closely related to Rindler coordinates, widely used in modern general relativity. This work, published in the Annalen, led him directly to interpret gravitation in terms of spacetime curvature.
TL;DR: The authors provided an historical account of the main steps (experimental as well as theoretical) which led Poincare to contribute to the theory of relativity, starting from the optical experiments which led to the inconsistency of the classical (Galilean) composition law for velocities to explain light propagation.
Abstract: Often considered as the last ‘encyclopedist’, Henri Poincare died one hundred years ago. If he was a prominent man in 1900 French Society, his heritage is not so clearly recognised, particularly in France. Among his too often misunderstood works is his contribution to the theory of relativity, mainly because it is almost never presented within Poincare's general approach to science, including his philosophical writings. Our aim is therefore to provide an historical account of the main steps (experimental as well as theoretical) which led Poincare to contribute to the theory of relativity. Starting from the optical experiments which led to the inconsistency of the classical (Galilean) composition law for velocities to explain light propagation, we introduce the FitzGerald and Lorentz contraction which was viewed as the ‘sole hypothesis’ to explain the Michelson and Morley experiment. We then show that Poincare's contribution starts with a discussion of the principles governing the mechanics and was built s...
Posted Content•
TL;DR: In this article, the equivalence of General Relativity and Shape Dynamics can be extended to a theory, that respects the BRST-symmetries of general Relativity as well as the ones of an extended version of Shape Dynamics.
Abstract: We show that the equivalence of General Relativity and Shape Dynamics can be extended to a theory, that respects the BRST-symmetries of General Relativity as well as the ones of an extended version of Shape Dynamics. This version of Shape Dynamics implements local spatial conformal transformations as well as a local an abstract analogue of special conformal transformations. Standard effective field theory arguments suggest that the definition of a gravity theory should implement this duality between General Relativity and Shape Dynamics, thus the name “Doubly General Relativity.” We briefly discuss several consequences: bulk/bulk- duality in classical gravity, experimental falsification of Doubly General Relativity and possible implications for the renormalization of quantum gravity in the effective field theory framework.
TL;DR: In this paper, the OPERA data were examined in the framework of special relativity with de Sitter spacetime symmetry (dS-SR) and it was shown that the ICARUS anomaly is in agreement with the prediction of dS- SR with R≃1.95×1012 l.y.
Abstract: We explore the recent OPERA experiment of superluminal neutrinos in the framework of special relativity with de Sitter spacetime symmetry (dS-SR). According to Einstein, a photon is treated as a massless particle in the framework of special relativity. In special relativity (SR) we have the universal parameter c, the photon velocity cphoton and the phase velocity of a light wave in vacuum cwave = λν. Due to the null experiments of Michelson–Morley we have c = cwave. The parameter cphoton is determined by the Noether charges corresponding to the spacetime symmetries of SR. In Einstein's special relativity (E-SR) we have c = cphoton. In dS-SR, i.e. the special relativity with SO(4, 1) de Sitter spacetime symmetry, we have cphoton > c. In this paper, the OPERA datum are examined in the framework of dS-SR. We show that OPERA anomaly is in agreement with the prediction of dS-SR with R≃1.95×1012 l.y. Based on the p-E relation of dS-SR, we also prove that the Cohen and Glashow's argument of possible superluminal neutrino's Cherenkov-like radiation is forbidden. We conclude that OPERA and ICARUS results are consistent and they are explained in the dS-SR framework.
TL;DR: In this article, a new deformed Poisson bracket was proposed, which leads to the Fock coordinate transformation by using an analogous procedure as in Deformed Special Relativity, and a canonical transformation with which the new coordinates and momentum satisfy the usual Poisson brackets and therefore transform like the usual Lorentz vectors.
Abstract: In this paper, we propose a new deformed Poisson brackets which leads to the Fock coordinate transformation by using an analogous procedure as in Deformed Special Relativity. We therefore derive the corresponding momentum transformation which is revealed to be different from previous results. Contrary to the earlier version of Fock's nonlinear relativity for which plane waves cannot be described, our resulting algebra keeps invariant for any coordinate and momentum transformations the four dimensional contraction $p_{\mu} x^{\mu} $, allowing therefore to associate plane waves for free particles. As in Deformed Special Relativity, we also derive a canonical transformation with which the new coordinates and momentum satisfy the usual Poisson brackets and therefore transform like the usual Lorentz vectors. Finally, we establish the dispersion relation for Fock's nonlinear relativity.
Book•
28 Jan 2012
TL;DR: In this article, the authors presented the hypothesis that there is no speed barrier in the universe -thus refuting the speed of light postulate, and they obtained a Parameterized Special Theory of Relativity (PSTR) for the same thought experiment, i.e. considering non-constant accelerations and arbitrary 3D-curves.
Abstract: In this book we present the hypothesis that there is no speed barrier in the universe - thus refuting the speed of light postulate. While Einstein considered a relative space and relative time but the ultimate speed of light, we do the opposite: we consider an absolute time and absolute space but no ultimate speed, and we call it the Absolute Theory of Relativity (ATR). We then parameterize Einstein’s thought experiment with atomic clocks, supposing that we know neither if the space and time are relative or absolute, nor if the speed of light is ultimate speed or not. We obtain a Parameterized Special Theory of Relativity (PSTR). Our PSTR generalizes not only Einstein’s Special Theory of Relativity, but also our ATR, and introduces three more possible Relativities to be studied in the future. Afterwards, we extend our research considering not only constant velocities but constant accelerations too. Eventually we propose a Noninertial Multirelativity for the same thought experiment, i.e. considering non-constant accelerations and arbitrary 3D-curves.
Book•
02 Mar 2012
TL;DR: In this article, the Atom and Brownian Motion were used to set the stage for the development of quantum mechanics, and the evolution of Quantum Mechanics was discussed. But the main focus of the paper was on the evolution and history of quantum physics.
Abstract: 1. Setting the Stage for 1905 2. Radiation and the Quanta 3. The Atom and Brownian Motion 4. The Special Theory of Relativity 5. The General Theory of Relativity 6. Einstein and the Evolution of Quantum Mechanics 7. Epilogue
TL;DR: The covariant optimality conditions for rocket trajectories in general relativity are derived, with and without a bound on the magnitude of the proper acceleration, to solve two specific problems: the minimum fuel consumption transfer between two galaxies in a FLRW model and between two stable circular orbits in the Schwarzschild spacetime.
Abstract: We derive the covariant optimality conditions for rocket trajectories in general relativity, with and without a bound on the magnitude of the proper acceleration. The resulting theory is then applied to solve two specific problems: the minimum fuel consumption transfer between two galaxies in a FLRW model, and between two stable circular orbits in the Schwarzschild spacetime.
09 Feb 2012
TL;DR: In this article, a return to the mothers theorem of the Schwarzschild metric of general relativity is proposed to better understand the gothic-R theorem of GRS, which is already implicit in Einstein's equivalence principle of 1907 and hence in special relativity (with acceleration included).
Abstract: General relativity is notoriously difficult to interpret. A "return to the mothers" is proposed to better understand the gothic-R theorem of the Schwarzschild metric of general relativity. It is shown that the new finding is already implicit in Einstein's equivalence principle of 1907 and hence in special relativity (with acceleration included). The TeLeMaCh theorem, named onomatopoetically after Telemachus, is bound to transform metrology if correct.
Key words: Equivalence principle, Telemach theorem, Schwarzschild metric, metrology, Large Hadron Collider (LHC).
TL;DR: In the 20th century, physics has understood space and time as being coupled into a “space-time” manifold, a fundamental arena in which everything takes place as discussed by the authors, which allows description of electromagnetic phenomena in a three-dimensional Euclid space.
Abstract: In the 20 th century, physics has understood space and time as being coupled into a “space-time” manifold, a fundamental arena in which everything takes place. Space-time was considered to have three spatial dimensions and one temporal dimension. Out of the experimental facts one can conclude that time t we measure with clocks is only a numerical order of duration of motion, i.e. material change in a threedimensional space. This view allows description of electromagnetic phenomena in a three-dimensional Euclid space. Résumé: Au cours du 20ème siècle, la physique comprenait l'espace et le temps comme étant jumelés en “espace-temps” variés, une arène fondamentale où tout prend place. On croyait espace-temps avoir trois dimensions spatiales et une dimension temporelle. A partir des données expérimentales on peut conclure que le temps t mesuré au moyen d'horloges – n'est qu'un ordre numérique de durée de motion, c'est-à-dire changement matériel dans un espace tridimensionnel. Ce point de vue rend possible la description de phénomènes électromagnétiques dans un espace d'Euclide tridimensionnel.
TL;DR: In this article, the relativistic field equations for a gas in special and general relativity are determined from the Boltzmann equation, and constitutive equations are obtained from the Chapman-Enskog methodology applied to a relativism model equation proposed by Anderson and Witting.
Abstract: Relativistic field equations for a gas in special and general relativity are determined from the Boltzmann equation The constitutive equations are obtained from the Chapman-Enskog methodology applied to a relativistic model equation proposed by Anderson and Witting Two applications in general relativity are considered: one refers to a gas in a homogeneous and isotropic Universe where irreversible processes are present during its evolution; in the other it is analyzed a gas under the influence of a spherically symmetrical non-rotating and uncharged source of the gravitational field
TL;DR: In this paper, a complete and realistic solution to the problem of twin paradox in the frame work of general relativity has been provided, starting with inertial motion in flat space time, going through hyperbolic motion inflat space time and ending with the treatment for curved space time.
Abstract: We have provided a complete and realistic solution to the problem of Twin Paradox, for the first time, in the frame work of general relativity. Some of the inspiration for this paper has come from the well known papers by Linet and Teyssandier (Phys Rev D 66:024045, 2002) discussing objects moving on geodesics for more general metrics than Schwarzschild. The subject of the “Twin paradox” is encountered frequently in relativity classes but a complete solution in the general relativity framework is not being taught. Our approaches have covered all the cases, starting with inertial motion in flat space time, going through hyperbolic motion in flat space time and ending with the treatment for curved space time.