Uncertainty principle in larmor clock

It is well known that the spin operators of a quantum particle must obey uncertainty relations. We use the uncertainty principle to study the Larmor clock. To avoid breaking the uncertainty principle, Larmor time can be defined as the ratio of the phase difference between a spin-up particle and a spin-down particle to the corresponding Larmor frequency. The connection between the dwell time and the Larmor time has also been confirmed. Moreover, the results show that the behavior of the Larmor time depends on the height and width of the barrier.     

Larmor precession and dwell time of a particle scattered by a quantum well

The Larmor precession of a neutral spin- particle in a uniform constant magnetic field confined to the region of a one-dimensional rectangular potential well is investigated. The spin precession serves as a clock to measure the time spent by a quantum particle dwelling at a potential well. With the help of a general spin coherent state it is explicitly shown that the spin precession time is equal to the dwell time. The comparison of the time in a potential well with that in free space shows apparent superluminality.     

Measurement of the neutron interaction time with quantum objects

The first experiments aimed at measuring neutron tunneling time in a quasi-bound resonance and Bragg diffraction time were carried out by the Larmor clock method.     

On the measure of proper time in general relativity

The theoretical measure of proper time on a moving particle in general relativity is the aggregate of infinitesimal clock readings in successive inertial frames along its space-time path. This raises the question of whether the proper time can be satisfactorily measured by a clock permanently located with the particle. An investigation is made of the likely effects of acceleration, or equivalently of a gravitational field, on atomic, nuclear, and particle clocks. The orders of magnitude of such effects are compared with those of other classical influences such as the Einstein redshift and transverse Doppler effects.     

Dirac particle with memory: Proper time non-locality

A generalization of the standard model of Dirac particle in external electromagnetic field is proposed. In the generalization we take into account interactions of this particle with environment, which is described by the memory function. This function takes into account that the behavior of the particle at proper time can depend not only at the present time, but also on the history of changes on finite time interval. In this case the Dirac particle can be considered an open quantum system with non-Markovian dynamics. The violation of the semigroup property of dynamic maps is a characteristic property of dynamics with memory. We use the Fock-Schwinger proper time method and derivatives of non-integer orders with respect to proper time. The fractional differential equation, which describes the Dirac particle with memory, and the expression of its exact solution are suggested. The asymptotic behavior of the proposed solutions is described.     

Transmission time of a particle in the reflectionless Sech-squared potential: Quantum clock approach

We investigate the time for a particle to pass through the reflectionless Sech-squared potential. Using the Salecker-Wigner and Peres quantum clock an average transmission time of a Gaussian wave packet representing the particle is explicitly evaluated in terms of average momentum and travel distance. The average transmission time is shown to be shorter than the time of free-particle motion and very close to the classical time for wave packets with well-localized momentum states. Since the clock measures the duration of scattering process the average transmission time can be interpreted as the average dwell time.     

Proper time synchronization

A clock-transport method of synchronization employing proper time is described that yields in any given inertial system the same result as slow transport, but that imposes no limit on transport proper speed. It is argued that because the method involves only the empirically validated kinematic invariant proper time, on which all observers must agree, there exists an option to synchronize clocks in such a way that thesimultaneity of spatially separated events is agreed upon by all observers, hence is absolute. Such agreement refers only to phase equality of members (present at the events judged simultaneous) of comoving clock sets, not to clock rates or clock phase numerical values in different inertial systems. The demonstration employs only the on-worldline assertions of Einstein's kinematics. It thus depends on a limited subset of his ideas and allows a different identification of the spacelike invariant.     

Larmor spin precession and neutron optics

We consider the neutron-optical phenomena that emerge during the coherent interaction of a neutron with a sample when the neutron spin precesses in a magnetic field. As follows from general considerations, such an interaction gives rise to an extra precession phase, which is added to the Larmor precession phase. This phenomenon can be interpreted as a manifestation of the time delay due to a finite time of the neutron-sample interaction. The Larmor neutron spin precession with a constant frequency serves as a clock for measuring this time delay. We used such a clock to directly measure the difference between the neutron velocity in matter and its vacuum value. We also present the results of the first experiments in which Larmor clocks were used to measure the neutron tunneling time in the resonance of a quasi-bound state and the Bragg diffraction time. Prospects for further applications of the method are discussed.     

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.     

Light Clocks and the Clock Hypothesis

The clock hypothesis of relativity theory equates the proper time experienced by a point particle along a timelike curve with the length of that curve as determined by the metric. Is it possible to prove that particular types of clocks satisfy the clock hypothesis, thus genuinely measure proper time, at least approximately? Because most real clocks would be enormously complicated to study in this connection, focusing attention on an idealized light clock is attractive. The present paper extends and generalized partial results along these lines with a theorem showing that, for any timelike curve in any spacetime, there is a light clock that measures the curve’s length as accurately and regularly as one wishes.     

一维复合势垒中的Larmor钟

利用Larmor钟方法计算了一维复合势垒系统中的隧穿时间．从计算结果，对由Larmor钟所定义的Larmor时间在复合势垒中的有效性、可加性，以及它们与透射时间τ_T、反射时间τ_R、逗留时间τ_D的关系作了讨论．6个Larmor时间中，τ_xT,τ_xR,τ_yT和τ_yR都不是有效的时间量，它们不能为隧穿时间提供有效的描述，只有τ_yT和τ_yR满足可加性和判据τ_D＝Tτ_yT+Rτ_yR，它们最有可能给出透射时间τ_T、反射时间τ_R．τ_yT,τ_yR与势垒的对称性有关，等式τ_yT＝τ_yR是否成立与势垒是否对称有关． 关键词：     

The case of escape probability as linear in short time

We derive rigorously the short-time escape probability of a quantum particle from its compactly supported initial state, which has a discontinuous derivative at the boundary of the support. We show that this probability is linear in time, which seems to be a new result. The novelty of our calculation is the inclusion of the boundary layer of the propagated wave function formed outside the initial support. This result has applications to the decay law of the particle, to the Zeno behaviour, quantum absorption, time of arrival, quantum measurements, and more.     

On the behavior of an oscillator clock near the singularity of a gravitational field

In 1975 Møller tried to show that the general relativistic concept of standard time or proper time would lose its physical meaning in the vicinity of singularities of a gravitational field [1]. His treatment of a classical harmonic oscillator clock falling into a singularity is checked in the present paper and is found to be insufficient to prove the above statement. A relativistic clock model is given to ensure the reasonable physical meaning of proper time.     

New approach to the quantum tunneling process: Characteristic times for transmission and reflection

In [1] we have demonstrated that scattering of a quantum particle on a one-dimensional potential barrier should be considered as a combined process involving two alternative elementary transmission and reflection processes. For symmetric potential barriers, we have found solutions of the Schrödinger equation which describe the transmission and reflection processes in all stages of scattering. The present work studies time aspects of both processes. The local and asymptotic group tunneling times, dwell time, and Larmor tunneling time are determined for each process. Among these time characteristics, the group tunneling times should be considered as auxiliary. As to the dwell and Larmor tunneling times, they are the best estimates (of the expected values) of times the quantum particle in stationary and localized nonstationary states dwells in the barrier region. Moreover, the Larmor time is simply the dwell time averaged over the corresponding ensemble of particles. This characteristic can be measured experimentally and hence the suggested model of scattering can be verified.     

对自由落体的诺维科夫时间与牛顿绝对时间关系讨论

文章首先将史瓦西黑洞场中自由下落质点的固有时(诺维科夫坐标时)公式,由自然单位制化成了国际单位制中的形式.然后,根据牛顿第二定律和万有引力定律,推导出了自由下落质点经历的绝对时间公式,进而证明了广义相对论中自由落体经历的固有时,恰好等于牛顿力学给出的绝对时间.最后,对自由下落质点在黑洞内外经历的时间进行了特例计算.     

Simulations of single charged particle motion in external magnetic and electric fields

In this paper we present a software package for computational modeling of single particle motion in static and dynamic external magnetic and electric fields and show applications of our package to general cases and particular cases of space, laboratory and fusion plasmas. In addition we further elaborate on the properties of a new concept named Larmor Center Trajectory that we introduced in our previous work [D. Erzen, J.P. Verboncoeur, J. Duhovnik, N. Jeli, Int. J. Multiphys. 1, 419 (2007)] as a generalization of the well known guiding center approximation, and show the ranges of applicability of this concept, especially in strongly inhomogeneous fields when adiabatic approximations break.     

超高精度空间站共视时间比对新方法

随着科学技术的进步和发展,许多基础前沿领域要求时间比对的精度为几十皮秒甚至更高.空间站上的原子钟系统比地面钟性能更优,但传统的共视时间比对方法应用于空间站共视存在一定的局限性.本文基于广义相对论分析了精度为几十皮秒的空间站共视时间比对原理,考虑了所有的皮秒级以上的时延项;结合空间站共视时间比对原理,仿真分析了空间站对于中国几大主要地理城市的可见性,分析结果表明部分地区存在共视时间比对的工作盲区.结合理论和仿真研究了空间站轨道误差对传统共视时间比对方法的影响,研究结果表明传统共视时间比对方法不能有效地抵消轨道误差,其对共视时间比对的影响在几百皮秒量级.提出了空间站分时共视时间比对新方法,介绍了该方法的主要原理和优势.通过仿真实验验证了新方法的有效性,能够实现几十皮秒精度的两地面站远距离共视时间比对,同时解决了传统共视方法的工作盲区问题.     

On Relativistic Generalization of Gravitational Force

In relativistic theories, the assumption of proper mass constancy generally holds. We study gravitational relativistic mechanics of point particle in the novel approach of proper mass varying under Minkowski force action. The motivation and objective of this work are twofold: first, to show how the gravitational force can be included in the Special Relativity Mechanics framework, and, second, to investigate possible consequences of the revision of conventional proper mass concept (in particular, to clarify a proper mass role in the divergence problem). It is shown that photon motion in the gravitational field can be treated in terms of massless refracting medium, what makes the gravity phenomenon compatible with SR Mechanics framework in the variable proper mass approach. Specifically, the problem of point particle in the spherical symmetric stationary gravitational field is studied in SR-based Mechanics, and equations of motion in the Lorentz covariant form are obtained in the relativistic Lagrangean problem formulation. The dependence of proper mass on potential field strength is derived from the Euler-Lagrange equations as well. One of new results is the elimination of conventional 1/r divergence, which is known to be not removable in Schwarzschild gravitomechanics. Predictions of particle and photon gravitational properties are in agreement with GR classical tests under weak-field conditions; however, deviations rise with potential field strength. The conclusion is made that the approach of field-dependent proper mass is perspective for development of SR gravitational mechanics and further studies of gravitational problems.     

A new synchronization scheme based on time division multiplexing and wavelength division multiplexing technology for practical quantum key distribution system

Three clock synchronization schemes for a quantum key distribution system are compared experimentally through the outdoor fibre and the interaction physical model of the the clock signal and the the quantum signal in the quantum key distribution system is analysed to propose a new synchronization scheme based on time division multiplexing and wavelength division multiplexing technology to reduce quantum bits error rates under some transmission rate conditions.The proposed synchronization scheme can not only completely eliminate noise photons from the bright background light of the the clock signal,but also suppress the fibre nonlinear crosstalk.     

The analysis of time: Is the relativistic time unique?

Time is analyzed by considering the actual setup of clock system within the four-dimensional framework. We find that both relativistic time and universal time can be embedded in such a symmetry framework. Although Poincaré and Einstein both understood the meaning of Lorentz's local time in terms of sending light signals to calibrate clocks, they differed on a basic point: Einstein believed local time to be the necessary and unique time, while Poincaré admitted flexibility in the definitions of time and regarded local time as only a convention. The results of our analysis shed light on Poincaré's original idea concerning conventions of time and provide the conceptual basis for the formulation of a new four-dimensional symmetry with a universal time. We demonstrate that the one-way speeds of light measured by stable atomic clocks in rockets may not be isotropic, in contrast to the two-way speeds of light. Furthermore, atomic clocks can be used to set up a clock system which reads a universal (but not absolute) time.I dedicate this paper to the memory of my beloved father Hsu Mau-Yuen (1903–1977), whose understanding helped me to choose to work on physical problems. Part of the research was accomplished while I held an NRC Senior Resident Research Associateship.