T. Grandou, J. L. Rubin
After pointing out the historical avatar at the origin of a would be twin or clock paradox, we argue that, at least on a local scale, the (re-qualified) paradox is but a necessary consequence of the sole principle of causality.
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We discuss the twin paradox or the clock paradox under the small velocity approximation of special relativity. In this paper the traveller twin of the standard twin parable sets out with a non-relativistic speed for the trip leaving behind the stay-at-home one on earth and continues up to a distance and finally returns home with the same speed when the siblings can compare their ages or their initially synchronized wrist watches. The common knowledge that at small velocities the length contraction and time dilation effects of special relativity can be ignored so that the world becomes essentia…
Conventional wisdom, based on kinematic (flat-space) intuition, tell us that a static twin is aging faster than his traveling twin brother. However, such a situation could be exactly inverted if the two twins are embedded in an external gravitational field, and if the (dynamical) distortion of the space-time geometry, due to gravity, is strong enough to compensate the kinematic effect of the relative twin motion.
The "twin paradox" of special relativity offers the possibility to make interstellar flights within a lifetime. For very long journeys with velocities close to the speed of light, however, we have to take into account the expansion of the universe. Inspired by the work of Rindler on hyperbolic motion in curved spacetime, we study the worldline of a uniformly accelerated observer in de Sitter spacetime and the communication between the traveling observer and an observer at rest.
We consider the twin paradox of special relativity in a universe with a compact spatial dimension. Such topology allows two twin observers to remain inertial yet meet periodically. The paradox is resolved by considering the relationship of each twin to a preferred inertial reference frame which exists in such a universe because global Lorentz invariance is broken. The twins can perform "global" experiments to determine their velocities with respect to the preferred reference frame (by sending light signals around the cylinder, for instance). Here we discuss the possibility of doing so with loc…
The twin paradox in the vicinity of rotating black holes
研究旋转黑洞附近双生子佯谬，通过基于残差图和优化的数值框架识别轨迹，发现固有时与方位距离、加速度负相关，经数值雅可比场分析得出特定测地线无共轭点，为初学者提供理解广义相对论概念的可视化工具。
Despite being a major component in the teaching of special relativity, the twin `paradox' is generally not examined in courses on general relativity. Due to the complexity of analytical solutions to the problem, the paradox is often neglected entirely, and students are left with an incomplete understanding of the relativistic behaviour of time. This article outlines a project, undertaken by undergraduate physics students at the University of Sydney, in which a novel computational method was derived in order to predict the time experienced by a twin following a number of paths between two given…
Motivated by a conjecture put forward by Abramowicz and Bajtlik we reconsider the twin paradox in static spacetimes. According to a well known theorem in Lorentzian geometry the longest timelike worldline between two given points is the unique geodesic line without points conjugate to the initial point on the segment joining the two points. We calculate the proper times for static twins, for twins moving on a circular orbit (if it is a geodesic) around a centre of symmetry and for twins travelling on outgoing and ingoing radial timelike geodesics. We show that the twins on the radial geodesic …
We discuss a rather surprising version of the twin paradox in which (contrary to the familiar classical version) the twin who accelerates is older on the reunion than his never accelerating brother.
Relativistic rigid motion suggests a new version for the so-called `twin paradox', comparing the ages of two astronauts on a very long spaceship. Although there is always an instantaneous inertial frame in which the whole spaceship, being rigid, is simultaneously at rest, the twins' ages, measured as the proper-times along their individual world lines, are different when they are located at remote parts of the spaceship. The age, or proper-time, difference depends on the distance at rest between the astronauts and the rapidity difference between start to end. The relation of the age difference…
The black hole information paradox is really a combination of two problems: the causality paradox and the entanglement problem. The causality paradox arises because in the semiclassical approximation infalling matter gets causally trapped inside its own horizon; it is therefore unable to send its information back to infinity if we disallow propagation outside the light cone. We show how the causality paradox is resolved in the fuzzball paradigm. One needs to distinguish between two kinds of Rindler spaces: (a) Rindler space obtained by choosing accelerating coordinates in Minkowski space and (…
The Classical Twin Paradox is widely dealt in literature and neatly resolved. In addition, it is also well known that, when looking at two systems which are boosted relative to each other, the concept of the simultaneous effect of a quantum measurement in space-time causes some discrepancies in the cause-effect behavior. However, these discrepancies have been thought not to cause any apparent paradox except for violating the Free-Will postulate. In this paper we suggest that using the local t axis, all over space, as the axis in which the quantum measurement is thought to be simultaneous, we d…
The twin paradox, which evokes from the the idea that two twins may age differently because of their relative motion, has been studied and explained ever since it was first described in 1906, the year after special relativity was invented. The question can be asked: "Is there anything more to say?" It seems evident that acceleration has a role to play, however this role has largely been brushed aside since it is not required in calculating, in a preferred reference frame, the relative age difference of the twins. Indeed, if one tries to calculate the age difference from the point of the view o…
The problem of absolute motion in the context of the twin paradox is discussed. It is shown that the various versions of the clock paradox feature some aspects which Mach might have been appreciated. However, the ultimate cause of the behavior of the clocks must be attributed to the autonomous status of spacetime, thereby proving the relational program advocated by Mach as impracticable.
The twin paradox is the best known thought experiment associated with Einstein's theory of relativity. An astronaut who makes a journey into space in a high-speed rocket will return home to find he has aged less than a twin who stayed on Earth. This result appears puzzling, since the situation seems symmetrical, as the homebody twin can be considered to have done the travelling with respect to the traveller. Hence it is called a "paradox". In fact, there is no contradiction and the apparent paradox has a simple resolution in Special Relativity with infinite flat space. In General Relativity (d…
We consider a new version of the twin paradox. The twins move along the same circular free photon path around the Schwarzschild center. In this case, despite their different velocities, all twins have the same non-zero acceleration. On the circular photon path, the symmetry between the twins situations is broken not by acceleration (as it is in the case of the classic twin paradox), but by the existence of an absolute standard of rest (timelike Killing vector). The twin with the higher velocity with respect to the standard of rest is younger on reunion. This closely resembles the case of perio…
In this paper we apply the concept of radar time (popularised by Bondi in his work on k-calculus) to the well-known relativistic twin `paradox'. Radar time is used to define hypersurfaces of simultaneity for a class of travelling twins, from the `Immediate Turn-around' case, through the `Gradual Turn-around' case, to the `Uniformly Accelerating' case. We show that this definition of simultaneity is independent of choice of coordinates, and assigns a unique time to any event (with which the travelling twin can send and receive signals), resolving some common misconceptions.
Twin-paradox and Entanglement
本文研究了量子探测器在狭义相对论中的双生子悖论，并探讨了加速度方向变化对探测器响应和纠缠的影响，可能对黑洞时空有相关性。
Twins travelling at constant relative velocity will each see the other's time dilate leading to the apparent paradox that each twin believes the other ages more slowly. In a finite space, the twins can both be on inertial, periodic orbits so that they have the opportunity to compare their ages when their paths cross. As we show, they will agree on their respective ages and avoid the paradox. The resolution relies on the selection of a preferred frame singled out by the topology of the space.
The channel capacity between two users is affected by relativistic effects. Under the presence of a fixed noise at the receiver, there appears an asymmetry between "slowly aging" and "fast aging" observers which can be used to have private communication transmission. We discuss some models for users inside gravitational wells and in the twin paradox scenario.
In a multiply connected space, the two twins of the special relativity twin paradox move with constant relative speed and meet a second time without acceleration. The twins' situations appear to be symmetrical despite the need for one to be younger due to time dilation. Here, the suggestion that the apparent symmetry is broken by homotopy classes of the twins' worldlines is reexamined using space-time diagrams. It is found that each twin finds her own spatial path to have zero winding index and that of the other twin to have unity winding index, i.e. the twins' worldlines' relative homotopy cl…
On Spavieri's conundrum or the shadow of the twin paradox -- A submission to the One-Way Linear Effect (OWLE) Award
本文探讨了线性萨格纳克效应中的相对论不一致性问题，指出双生子悖论的常规解是关键，任何对同时性的调整都无法解决该问题。
We study the role of acceleration in the twin paradox. From the coordinate transformation that relates an accelerated and an inertial observer we find that, from the point of view of the accelerated observer, the rate of the differential lapses of time depends not only on the relative velocity, but also on the product of the acceleration and the distance between the observers. However, this result does not have a direct operational interpretation because an observer at a certain position can measure only physical quantities that are defined at the same position. For local measurements, the asy…
The aim of this paper is to provide a logic-based conceptual analysis of the twin paradox (TwP) theorem within a first-order logic framework. A geometrical characterization of TwP and its variants is given. It is shown that TwP is not logically equivalent to the assumption of the slowing down of moving clocks, and the lack of TwP is not logically equivalent to the Newtonian assumption of absolute time. The logical connection between TwP and a symmetry axiom of special relativity is also studied.
We investigate local and global properties of timelike geodesics in three static spherically symmetric spacetimes. These properties are of its own mathematical relevance and provide a solution of the physical `twin paradox' problem. The latter means that we focus our studies on the search of the longest timelike geodesics between two given points. Due to problems with solving the geodesic deviation equation we restrict our investigations to radial and circular (if exist) geodesics. On these curves we find general Jacobi vector fields, determine by means of them sequences of conjugate points an…
Recently Abramowicz and Bajtlik [ArXiv: 0905.2428 (2009)] have studied the twin paradox in Schwarzschild spacetime. Considering circular motion they showed that the twin with a non-vanishing 4-acceleration is older than his brother at the reunion and argued that in spaces that are asymptotically Minkowskian there exists an absolute standard of rest determining which twin is oldest at the reunion. Here we show that with vertical motion in Schwarzschild spacetime the result is opposite: The twin with a non-vanishing 4-acceleration is younger. We also deduce the existence of a new relativistic ti…
We propose an implementation of a twin paradox scenario in superconducting circuits, with velocities as large as a few percent of the speed of light. Ultrafast modulation of the boundary conditions for the electromagnetic field in a microwave cavity simulates a clock moving at relativistic speeds. Since our cavity has a finite length, the setup allows us to investigate the role of clock size as well as interesting quantum effects on time dilation. In particular, our theoretical results show that the time dilation increases for larger cavity lengths and is shifted due to quantum particle creati…
Inertial-to-Rindler Coordinates, with applications to the Twin Paradox, Radar Time and the Unruh Temperature
本文提出了一种惯性到兰德勒坐标的变换，用于解决双生悖论、雷达时间和Unruh温度问题，并推导了速度依赖的Unruh温度修正。
We discuss the Sagnac effect in standard Minkowski coordinates and with an alternative synchronization convention. We find that both approaches lead to the same result without any contradictions. When applying standard coordinates to the complete rim of the rotating disk, a time-lag has to be taken into account which accounts for the global anisotropy. We propose a closed Minkowski space-time as an exact equivalent to the rim of a disk, both in the rotating and non-rotating case. In this way the Sagnac effect can be explained as being purely topological, neglecting the radial acceleration alto…
This is a consecutive paper on the timelike geodesic structure of static spherically symmetric spacetimes. First we show that for a stable circular orbit (if it exists) in any of these spacetimes all the infinitesimally close to it timelike geodesics constructed with the aid of the general geodesic deviation vector have the same length between a pair of conjugate points. In Reissner--Nordström black hole metric we explicitly find the Jacobi fields on the radial geodesics and show that they are locally (and globally) maximal curves between any pair of their points outside the outer horizon. If …
Interference of Clocks: A Quantum Twin Paradox
本文提出量子时钟干涉仪，证明闭合光脉冲干涉仪不受引力时间膨胀影响，但能实现量子孪生子悖论，并设计实验隔离该效应。
Finite-size clocks in quantum field theory and the twin paradox
本文通过量子场论中的真空涨落模型，研究了微观尺度上时间测量受轨迹和真空涨落相互作用影响的双生悖论问题。
We study the foundation of space-time theory in the framework of first-order logic (FOL). Since the foundation of mathematics has been successfully carried through (via set theory) in FOL, it is not entirely impossible to do the same for space-time theory (or relativity). First we recall a simple and streamlined FOL-axiomatization SpecRel of special relativity from the literature. SpecRel is complete with respect to questions about inertial motion. Then we ask ourselves whether we can prove usual relativistic properties of accelerated motion (e.g., clocks in acceleration) in SpecRel. As it tur…
Discussions on the Langevin Twins 'paradox' are most often based on a "triangular" diagram which outlines the twins spacetime travels. It won't be our way, avoiding what we think to be a problem at the basis of numerous controversies. Our approach relies on a fundamentally different Equivalence Principle, namely the so-called "Punctual Equivalence Principle", from which we think that a very conformal aspect proceeds. We present a resolution of this paradox in the framework of the so-called "scale gravity". This resolution hinges on a clear determinism of the Twins proper times, in some definit…
Special relativity and the twins: a review and a new approach
本文针对双生子悖论，提出了一种仅基于狭义相对论和等效原理的简单精确解决方案，并综述了早期近似解与背景，旨在适用于课堂教学。
We propose a resolution to the black-hole information-loss paradox: in one formulation of physical theory, information is preserved and macroscopic causality is violated; in another, causality is preserved and pure states evolve to mixed states. However, no experiments can be performed that would distinguish these two descriptions. We explain how this could work in practice; a key ingredient is the suggested quantum-chaotic nature of black holes.
The circular twin paradox and Thomas Precession are presented in a way that makes both accessible to students in introductory relativity courses. Both are discussed by examining what happens during travel around a polygon and then in the limit as the polygon tends to a circle. Since relativistic predictions based on these examples can be verified in experiments with macroscopic objects such as atomic clocks and the gyroscopes on Gravity Probe B, they are particularly convincing to introductory students.
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