Distance and the conventionality of simultaneity in special relativity

The conventionality of simultaneity within inertial frames is presented in a general formalism that clarifies the relationship of spatial measures to the choice of simultaneity. A number of claims that such measures undermine the conventional nature of simultaneity are presented and shown to be unfounded. In particular, a recent claim by Coleman and Korte [9] that such measures empirically establish a unique simultaneity relationship is shown to be in error. In addition, the general formalism enables the empirical status of simultaneity within an inertial frame to be clarified by presenting the choice of simultaneity as a gauge choice.1. Recent introductions to the literature have been given by Redhead [35], Ungar [47], Havas [21], and Vetharaniam and Stedman [48].2. The conventionalist position is by no means a uniform one, and in particular, it is worth noting an important distinction exemplified in the respective positions of Reichenbach and Grünbaum. For Reichenbach [37, p. 144f.] we have no empirical access to the one-way speed of light due to the nature of light as a first signal, and the conventionality comes from our absence ofknowledge about the one-way speed of light. For Grünbaum the one-way speed of light is actually objectively undetermined, and the physical attributes that sustain a speed in a given direction are non-existent. See, for example, [16, p. 87] and [17, p. 352]. Discussions of the differences between the positions of Reichenbach and Grünbaum may be found in [14] and [35]. Naturally, one may adhere to a position espoused by Reichenbach without the added ontological commitment of Grünbaum.3. Our is equivalent to (1 - 2), where is the symbol introduced by Reichenbach and customarily used in the discussions of the conventionality of simultaneity.4. An exposition of this argument may be found in the recent text by Lucas and Hodgson [28].5. Schrödinger [42, p. 78] has aptly labeled this quantity the distance of simultaneity.6. Examples of previous uses space-dependent synchrony parameters may be found in studies by Clifton [8], Havas [21], Anderson and Stedman [1], and Stedman [43; 44, § 2].7. This approach has been reviewed by Basri in [4] and [3].8. A number of faulty assessments of the empirical status of the conventionality of simultaneity may be similarly traced at least in part to overly simplistic assumptions on the nature of as Havas [21] and Clifton [8], for example, have had occasion to point out.9. See, for example, [1]. Kinematic formula relating other quantities in a treatment of STR without the standard convention on the one-way speed of light were first derived by Winnie [53].10. In comparison to other space dependent treatments of the synchrony parameter, ourh is analogous to defined by Clifton in Eq. (15) of [8], and equivalent to -f defined by Havas in Eq. (A1) of [21] and to defined in Eq. (6) of our earlier treatment in [1]. We take this opportunity to mention that the irrotational property ofh was inadvertently referred to as solenoidal in this work.11. Equation (26) is equivalent to Møller's expression in § 8.8 of [32] for the speed of light in terms of the metric components where our-h _i is equivalent to Møller's _i (g _i0)/ .12. Note as well, the expression of this operation in standard texts on STR by Rindler [38, pp. 27–28] and Mermin [30, p. 79] respectively: To measure the rod's length in any inertial frame in which it moves longitudinally, its end-point must be observed simultaneously... and, ...a measurement of the length of a moving meter stick involves determining how far apart the two ends areat the same time. In the same context of determining the length of moving rods, Mermin [30, p. 185] proposes that the sense of length entailing the concept of being determined at simultaneous times is inherent in the notion of rods: ...it is precisely the lines of constant time that determine whatA orB means by the stick. For the notion of the stick includes implicitly the assumption that all the points of matter making up the stick exist at the same moment.13. In many ways the claim that the special properties of proper lengths with Einstein synchronization undermines the conventionality of simultaneity is analogous to the claim that the correspondence of the slow-clock transport method of synchronization with that of Einstein synchronization provides an empirical determination of synchronization. The use of clock transport as a means for synchronization was discussed by Reichenbach [37, p. 133f], while the proposal that slow transport of clocks provides a unique form of synchronization was first argued for by Eddington [10]. Arguments that it undermines any significant sense of the conventionality in the one-way speed of light have been given by Ellis and Bowman [13] with responses by Grünbaum [19] and Salmon [41, 40].14. Coleman and Korte [9, pp. 423–425] claim their method is free from any assumptions on the one-way speed of light; however, they assume that is a constant 3-vector.15. Reichenbach explicitly mentioned in [36, § 43] that a condition equivalent to Eq. (13) is a sufficient condition for a constant roundtrip speed of light.16. The remarks of one of the referees have served to alert us to the need to emphasize both of these points.17. The manner in which gravity may be viewed as a gauge theory has been the subject of considerable discussion (see, for example, the discussion in [23] and [24]). We note that the manner in which we are takingh as a potential differs from the sense in which the Christoffel symbols as affine connections may be seen to play a role of gauge potentials in GTR.18. A discussion of the significance of Weyl's work and the importance of the round-trip measurements may be found in works by Yang [56] and Mills [31].19. In the context only of time orthogonal coordinates, an example of the fiber structure we are imposing on space and time may be found in [26, p. 71f]. Again we note that in a more general treatment, where the Christoffel symbols are considered as connections, the fiber structure instead consists of a bundle of linear frames of Riemannian spacetime (see, for example, the presentations in [46] and [23]).20. Our position is not unlike Göckeler and Schücker's [15, p. 75] claim that Einstein's particular choice of coordinates in GTR masks the general gauge structure of the theory.     

On attempts to rescue the conventionality thesis of distant simultaneity in str

Recently, some conventionalists have tried to rescue the conventionality of distant simultaneity by introducing a spatially dependent (x,y,z), where {1,2,3}. In this paper, we show that this attempt fails by providing a detailed analysis of the coordinate independent and non-conventional procedure for directly measuring the metricd _M ² on eventspace with respect to a physical radar coordinate system. The measuredd _M ² in turn provides the empirical basis for uniquely determining the hyperplanes of space for a given inertial observer in a way that makes absolutely no reference whatsoever to any kind of synchrony, whether spatially dependent or not except for the sole purpose of assigning physical coordinates to events.     

Zeroth law of thermodynamics and transitivity of simultaneity

The transitivity of thermal equilibrium is equivalent to the transitivity of clock rate synchronization. The condition of clock rate synchronization in general relativity is shown, which is weaker than time-orthogonality.     

LiNbO_3和LiTaO_3拉曼光谱中的反复转馈现象

ＬｉＮｂＯ＿３和ＬｉＴａＯ＿３拉曼光谱中的反复转馈现象张昊（中国科学院物理所北京１０００８０）郝伟，廖理几（北京工业大学应用物理系北京１０００２２）Ｒｏｕｎｄ－ｔｒｉｐＦｅｅｄｔｈｒｏｕｇｈＥｆｆｅｃｔｓｉｎＲａｍａｎＳｐｅｃｔｒａｏｆＬｉｎｂＯ＿３...     

双光子阵列点激发同时多维荧光信息的处理

五维同时荧光信息显微成像方法是一种新的荧光信息获取技术，它采用了双光子阵列点激发方式.这一方法可同时获取激发阵列点每点荧光的位置信息、荧光光谱信息和荧光寿命信息，弥补了现有荧光检测技术的不同功能信息不具有同时性的缺陷.给出了从这种技术的复合信息中提取复合光谱几何强度结构图像、不同光谱几何强度结构图像、不同光谱寿命图像的方法.提出了一种激发荧光强度修正系数矩阵方法，消除阵列点激发光强不均匀对激发荧光强弱产生的不利影响，取得明显效果.实验对实际样品做了数据采集和处理，给出图像结果，表明处理的效果良好.对存在的问题也作了讨论. 关键词： 荧光信息处理 双光子 荧光光谱 荧光寿命     

Lightlike simultaneity,comoving observers and distances in general relativity

We state a condition for an observer to be comoving with another observer in general relativity, based on the concept of lightlike simultaneity. Taking into account this condition, we study relative velocities, Doppler effect and light aberration. We obtain that comoving observers observe the same light ray with the same frequency and direction, and so gravitational redshift effect is a particular case of Doppler effect. We also define a distance between an observer and the events that it observes, called lightlike distance, obtaining geometrical properties. We show that lightlike distance is a particular case of radar distance in the Minkowski space-time and generalizes the proper radial distance in the Schwarzschild space-time. Finally, we show that lightlike distance gives us a new concept of distance in Robertson–Walker space-times, according to Hubble law.     

Can Einstein's definition of simultaneity be considered a convention?

We give an easy way of falsifying the Reichenbach-Grümbaum conventionalist interpretation of the definition of simultaneity of distant events.     

Limitations of the geometrodynamic clock

We examine sources of error in the geometrodynamic (or Marzke-Wheeler) clock, and choose parameters to minimize the total error. In theories with time-varying masses, there is an unavoidable minimum error. For a human-scale clock, the dominant error is from quantum uncertainty in the photon location.     

Crux of the clock paradox

The central riddle or crux of the relativistic clock paradox is studied with methods that are familiar from thermodynamics and hamiltonian mechanics, but which are not usually used, as here, to relate theory to phenomenology in the context of relativistic chronometry. Contrasting ramifications of the special and general theory are considered.     

环程光程随机扰动时光纤环形腔的有效带宽

对由环境引起的环程光程扰动对光纤环形腔的影响作了详细的理论分析,在扰动为各态历经扰动假设下的理论分析表明：小的慢与快变化扰动的影响是不同的。慢变化扰动影响与人射光时间相干性相同,使有效带宽增大;而快变化扰动对有效带宽的影响很小。然而对大的慢或快变化扰动,都会使环形腔失去它的带通和带阻特性。实验结果证实了一结论。     

基于同时的相对性对钟慢尺缩效应的再认识

同时的相对性、钟慢效应和尺缩效应是狭义相对论时空观的主要内容.鉴于同时性是时空测量的基础,本文从同时的相对性出发详述了对钟慢效应和尺缩效应的再认识:钟慢效应是运动时钟走时率变慢和校表问题的综合表现,其实质是同时的相对性在时间量度上的直接反映;尺缩效应的实质是同时的相对性在空间量度上的反映,也是不同观测者对同一客观事实的不同时空描述.     

Atomic and gravitational clock

Atomic and gravitational clocks are governed by the laws of electrodynamics and gravity, respectively. While the strong equivalence principle (SEP) assumes that the two clocks have been synchronous at all times, recent planetary data seem to suggest a possible violation of the SEP. Our past analysis of the implications of an SEP violation on different physical phenomena revealed no disagreement. However, these studies assumed that the two different clocks can be consistently constructed within the framework. The concept of scale invariance, and the physical meaning of different systems of units, are now reviewed and the construction of two clocks that do not remain synchronous—whose rates are related by a nonconstant function _a—is demonstrated. The cosmological character of _a is also discussed.This paper is reprinted with minor editorial modifications fromNature,296, 709 (1982).     

Noncommutative geometry of the quantum clock

We introduce a model of noncommutative geometry that gives rise to the uncertainty relations recently derived from the discussion of a quantum clock. We investigate the dynamics of a free particle in this model from the point of view of doubly special relativity and discuss the geodesic motion in a Schwarzschild background.     

A note on Lorentz transformations and simultaneity in classical physics and special relativity

Since early models of wave propagation in both stationary and moving media during the nineteenth century, the Lorentz transformation (LT) has played a key role in describing characteristic wave phenomena, e.g., the Doppler shift effect. In these models LT connects two different events generated by wave propagations, as observed in two reference systems and the synchronism is absolute. In relativistic physics LT implements the relativity principle. As a consequence, it connects two space-time event coordinates that both correspond to the same physical event and “absolute synchronization” is not allowed. The relativistic interpretation started from Einstein’s early criticism of the notion of “simultaneity” and Minkowski’s invariance of the space-time interval. In this paper, the two different roles of LT, i.e., in classical wave propagation theories and in relativistic physics, are discussed. Einstein’s early criticism is also re-examined with respect to LT in view of its significance for the notion of simultaneity. Indeed, that early criticism is found to be defective. Our analysis is also useful for general readers in view of its impact on modern speculations about the existence of a preferred system of reference Σ, where light propagation is isotropic, and related implications.

     

锶原子光晶格钟自旋极化谱线的探测

87Sr原子存在核自旋,在磁场作用下原子能级会分裂成不同塞曼子能级.通过光抽运对原子进行自旋极化,其自旋极化谱线的探测为锶光钟系统的闭环锁定提供精确的频率参考.本文对~(87)Sr原子钟跃迁能级5s~2~1S_0→5s5p~3P_0中的m_F=+9/2和m_F=-9/2的塞曼磁子能级自旋极化谱线进行了探测.经过一级宽带冷却和二级窄线宽冷却与俘获后,锶冷原子温度为3.9μK,原子数目为3.5×10~6.利用邻近"魔术波长"的813.426 nm半导体激光光源实现水平方向的一维光晶格装载.采用归一化探测方法用线宽为Hz量级的698 nm钟激光对~1S_0→~3P_0偶极禁戒跃迁进行探测,在150 ms的探测时间下获得线宽为6.7 Hz的钟跃迁简并谱.在磁光阱竖直方向施加一个300 mGs的偏置磁场获得塞曼分裂谱,并通过689 nm的圆偏振自旋极化光进行光抽运,最终在探测时间为150 ms时,获得左右旋极化谱线线宽分别为6.2 Hz和6.8 Hz.     

Progress on the optical lattice clock

Optical lattice clocks have made significant leaps forward in recent years, demonstrating the ability to measure time/frequency at unprecedented levels. Here we highlight this progress, with a particular focus on research efforts at NIST and JILA. We discuss advances in frequency instability and the characterization of key systematic effects, with a brief outlook to the future.     

A simple variation of the Marzke-Wheeler clock

The Marzke-Wheeler clock is based on the back-and-forth passage of a light signal between two observers who remain at rest with respect to one another. It differs from earlier photon clocks by providing a specific method based on the properties of free particles and light signals for establishing the relative rest of the two observers. The present paper provides an alternative and more straightforward method also based on the properties of free particles and light signals for accomplishing this result.     

Salecker-Wigner-Peres clock and average tunneling times

The quantum clock of Salecker-Wigner-Peres is used, by performing a post-selection of the final state, to obtain average transmission and reflection times associated to the scattering of localized wave packets by static potentials in one dimension. The behavior of these average times is studied for a Gaussian wave packet, centered around a tunneling wave number, incident on a rectangular barrier and, in particular, on a double delta barrier potential. The regime of opaque barriers is investigated and the results show that the average transmission time does not saturate, showing no evidence of the Hartman effect (or its generalized version).     

Mean-field theory of the three-state chiral clock model

The phase diagram of the three-state chiral clock model, which is known to exhibit commensurate and incommensurate ordered modulated structures, is investigated in the mean-field approximation. First a numerical analysis of the mean-field equations is presented. It is based in the main on the observation that these equations define a non-linear mapping in a four dimensional space. This method of analyzing the mean-field theory proves particularly useful in the determination of the pinning transition of the incommensurate structures. Next the phase diagram is investigated analytically by means of a Landau expansion modified such as to include domain walls. It is found that in the vicinity of the order-disorder transition most features of the phase diagram can be explained quantitatively by this expansion. Finally we present a systematic lowtemperature expansion of the mean-field theory, showing that the low-temperature phase diagram obtained in the mean-field approximation is different from that of the full model.Dedicated to B. Mühlschlegel on the occasion of his 60th birthday