Alexander R. H. Smith
A novel quantum time dilation effect is shown to arise when a clock moves in a quantum superposition of two relativistic velocities. This effect is argued to be measurable using existing atomic interferometry techniques, potentially offering a new test of relativistic quantum theory.
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Time dilation of quantum clocks in a relativistic gravitational potential
本文通过 Page 和 Wootters 量子时间形式，研究了相对论引力势中两个量子时钟的动力学演化，发现其时间膨胀效应与广义相对论 Schwarzschild 解一致，并探讨了引力红移。
On the feasibility of detecting quantum delocalization effects on relativistic time dilation in optical clocks
本文推导光学晶格中离域原子钟在量子相对论主导阶的时间膨胀，提出实验与噪声分析，指出²⁴Mg钟有望探测该效应，而现有⁸⁷Sr钟尚不能。
The irreversibility of relativistic time-dilation
该研究针对相对论纳入涨落关系时存在的问题，通过分析特定类时空探究时间膨胀效应与涨落关系的关联，得出正熵产由狭义相对论和引力时间膨胀效应共同导致的结论。
The theory of relativity associates a proper time with each moving object via its world line. In quantum theory however, such well-defined trajectories are forbidden. After introducing a general characterisation of quantum clocks, we demonstrate that, in the weak-field, low-velocity limit, all "good" quantum clocks experience time dilation as dictated by general relativity when their state of motion is classical (i.e. Gaussian). For nonclassical states of motion, on the other hand, we find that quantum interference effects may give rise to a significant discrepancy between the proper time and …
Dirac particle dynamics is encoded as a unitary path summation rule and implemented on a qubit array, where the qubit array represents both spacetime and the fermions contained therein. The unitary path summation rule gives a quantum algorithm to model a many-body system of Dirac particles in a gauge field with Lorentz invariance down to the grid scale (Planck scale)--the lattice-based model neither suffers the Fermi-sign problem nor breaks Lorentz invariance. Yet, for the Dirac Hamiltonian to generate the unitary evolution of the 4-spinor field at the Planck scale, there is time dilation betw…
The relativistic quantum decay laws of moving unstable particles are analyzed for a general class of mass distribution densities which behave as power laws near the (non-vanishing) lower bound $μ_0$ of the mass spectrum. The survival probability $\mathcal{P}_p(t)$, the instantaneous mass $M_p(t)$ and the instantaneous decay rate $Γ_p(t)$ of the moving unstable particle are evaluated over short and long times for an arbitrary value $p$ of the (constant) linear momentum. The ultrarelativistic and non-relativistic limits are studied. Over long times, the survival probability $\mathcal{P}_p(t)$ is…
Time Dilation in Quantum Systems and Decoherence: Questions and Answers
最近的研究表明，相对论性时间膨胀导致粒子内部和外部自由度之间的相关性，导致后者的退相干。在本说明中，我们简要总结了结果，并解决了对这些发现提出的评论和关切。除了对评论的简短答复外，我们还对这项工作的一些基本原则进行了教学讨论。这一注释旨在澄清当这两个理论被共同考虑时所产生的一些违反直觉的方面。
General relativistic effects in quantum interference of photons
量子力学和广义相对论已经在许多实验中得到广泛而独立的证实。然而，这两个理论的相互作用从未被测试过：所有测量引力对量子系统影响的实验都与非相对论性牛顿引力相一致。另一方面，广义相对论的所有检验都可以在经典物理学的框架内描述。在这里，我们讨论了一个量子干涉实验与单光子，可以探测量子力学在弯曲的时空。我们考虑一个光子在干涉仪中沿两条路径叠加运动，每条路径经历不同的引力时间膨胀。如果时间膨胀的差异与光子的相干时间相当，量子干涉的可见性预计会下降，而对于较短的时间膨胀，重力的影响将只会导致两臂之间的相对相移。我们讨论了量子力学和广义相对论之间的相互作用的哪些方面在这样的实验中被探索，并分析了实验的可行性。
Although time is one of the fundamental notions in physics, it does not have a unique description. In quantum theory time is a parameter ordering the succession of the probability amplitudes of a quantum system, while according to relativity theory each system experiences in general a different proper time, depending on the system's world line, due to time to time dilation. It is therefore of fundamental interest to test the notion of time in the regime where both quantum and relativistic effects play a role, for example, when different amplitudes of a single quantum clock experience different…
The possibility of using retrocausality to obtain a fundamentally relativistic account of the Bell correlations has gained increasing recognition in recent years. It is not known, however, the extent to which these models can make use of their relativistic properties to account for relativistic effects on entangled systems. We consider here a hypothetical relativistic Bell experiment, where one of the wings experiences time-dilation effects. We show that the retrocausal Brans model (Found. Phys, 49(2), 2019) can be easily generalised to analyse this experiment, and that it predicts less separa…
At the intersection of quantum theory and relativity lies the possibility of a clock experiencing a superposition of proper times. We consider quantum clocks constructed from the internal degrees of relativistic particles that move through curved spacetime. The probability that one clock reads a given proper time conditioned on another clock reading a different proper time is derived. From this conditional probability distribution, it is shown that when the center-of-mass of these clocks move in localized momentum wave packets they observe classical time dilation. We then illustrate a quantum …
Relativistic time dilation from a quantum mechanism
本文提出放弃光速普适性假设，通过量子态在伽利略参考系外的畸变机制推导出洛伦兹变换，从而从量子力学出发重建狭义相对论，并以此解释超光速粒子不可观测及暗物质现象。
Atom interferometer as a freely falling clock for time-dilation measurements
提出利用单光子跃迁原子干涉仪作为自由下落时钟，直接测量相对论时间膨胀，可在MAGIS-100或10米原型机实现，突破原子钟极限。
Ab initio quantum theory of mass defect and time dilation in trapped-ion optical clocks
本文从头推导了电磁束缚两粒子系统的相对论哈密顿量，应用于Paul阱冷离子，系统量子力学地处理了离子钟中的相对论频移，澄清了时间膨胀与质量亏损的作用。
Quantum time dilation occurs when a clock moves in a superposition of relativistic momentum wave packets. We utilize the lifetime of an excited hydrogen-like atom as a clock to demonstrate how quantum time dilation manifests in a spontaneous emission process. The resulting emission rate differs when compared to the emission rate of an atom prepared in a mixture of momentum wave packets at order $v^2/c^2$. This effect is accompanied by a quantum correction to the Doppler shift due to the coherence between momentum wave packets. This quantum Doppler shift affects the spectral line shape at order…
By associating a binary signal with the relativistic worldline of a particle, a binary form of the phase of non-relativistic wavefunctions is naturally produced by time dilation. An analog of superposition also appears as a Lorentz filtering process, removing paths that are relativistically inequivalent. In a model that includes a stochastic component, the free-particle Schrödinger equation emerges from a completely relativistic context in which its origin {\em and function} is known. The result establishes the fact that the phase of wavefunctions in Schrödinger's equation and the attendant su…
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。
Relativistic implications of entropy and purity
本文提出量子物体的不确定性导致其在引力下经历相对论效应，需用非黎曼几何描述，并推导出含量子参数的时间膨胀修正律。
Atomic clock interferometers are a valuable tool to test the interface between quantum theory and gravity, in particular via the measurement of gravitational time dilation in the quantum regime. Here, we investigate whether gravitational time dilation may be also used as a resource in quantum information theory. In particular, we show that for a freely falling interferometer and for a Mach-Zehnder interferometer, the gravitational time dilation may enhance the precision in estimating the gravitational acceleration for long interferometric times. To this aim, the interferometric measurements sh…
Rigorous Comparison of Gravimetry Employing Atom Interferometers and the Measurement of Gravitational Time Dilation
我们提出了一个严格的引力和明确的答案，在否定的问题，是否重力与原子干涉仪是等价的测量的相对引力时间膨胀的两个时钟在空间中分离。虽然物质和光波，量子态和振荡器时钟通过普朗克-爱因斯坦-德布罗意关系和等效原理是量子同义词，但在引力理论的测试背景下存在关键差异。
Interplays between quantum physics and gravity have long inspired exciting studies, which reveal subtle connections between quantum laws and the general notion of curved spacetime. One important example is the uniqueness of free-falling motions in both quantum and gravitational physics. In this work, we re-investigate the free-falling motions of quantum test wave packets that are distributed over weakly curved spacetime backgrounds. Except for the de Broglie relations, no assumption of priori given Hamiltonians or least actions satisfied by the quantum system is made. We find that the mean mot…
The recently proposed centre of mass decoherence of composite objects due to gravitational time-dilation [Pikovski et al., Nat.Phys. 15. June (2015); arXiv:1311.1095] is confronted with the principle of equivalence between gravity and observer's acceleration. In the laboratory frame, a positional superposition $\vert x_1\rangle+\vert x_2\rangle$ can quickly decohere whereas in the free-falling frame, as I argue, the superposition can survive for almost arbitrary long times. The paradoxical result is explained by the so far unappreciated feature of the proposed model: the centre of mass canonic…
The Instability of a Quantum Superposition of Time Dilations
本文利用相对论时间膨胀概念，证明引力势叠加导致非幺正演化，探针粒子产生退相干，并提出微波干涉仪实验以研究量子-经典边界。
Universal decoherence due to gravitational time dilation
低能量子系统的物理学研究通常没有明确考虑背景时空。弯曲时空的量子理论所固有的现象，如霍金辐射，通常被认为只在极端的物理条件下才相关：在高能量和强引力场中。在这里，我们考虑低能量子力学在引力时间膨胀的存在下，并表明，后者导致量子叠加的退相干。时间膨胀导致复合粒子内部自由度和质心之间的普遍耦合。由此产生的相关性导致粒子位置的退相干，即使没有任何外部环境。我们还表明，地球上的弱时间膨胀已经足以使微米级的物体退相干。因此，引力可以解释经典性的出现，而这种效应原则上可以在未来的物质波实验中得到检验。
Time Dilation and center of Mass Normalization in the Page-Wootters Formalism
该研究在Page-Wootters量子力学框架下，揭示复合量子钟的相对论效应，发现内部能量对质心的反作用会引发时间非局域的薛定谔方程，还得到干涉可见度的二次方能量修正项，可通过差分测量分离。
The Hong-Ou-Mandel (HOM) effect is analyzed for photons in a modified Mach-Zehnder setup with two particles experiencing different gravitational potentials, which are later recombined using a beam-splitter. It is found that the HOM effect depends directly on the relativistic time dilation between the arms of the setup. This temporal dilation can be used to estimate the $γ$ and $β$ parameters of the parameterized post-Newtonian formalism. The uncertainty in the parameters $γ$ and $β$ are of the order $ 10^{-8}-10^{-12}$, depending on the quantum state employed.
Quantum mechanics and general relativity have been each successfully tested in numerous experiments. However, the regime where both theories are jointly required to explain physical phenomena remains untested by laboratory experiments, and is also not fully understood by theory. This contribution reviews recent ideas for a new type of experiments: quantum interference of "clocks", which aim to test novel quantum effects that arise from time dilation. "Clock" interference experiments could be realised with atoms or photons in near future laboratory experiments.
Survival acceleration
本文提出并分析了一个相对论量子效应：激发态原子处于动量叠加态时，因时间膨胀导致未衰变条件下高动量分量概率增大，从而产生可计算的加速度。
Bootstrapping Time Dilation Decoherence
本文提出了一个广义相对论性的球壳物质模型，球壳物质表面有一个理想流体，球壳物质与一个内振子耦合，它推广了作者最近提出的一个模型，用于构造一个自引力干涉仪[1]。内部振子的演化是相对于壳层的本地固有时间来定义的，允许振子作为本地时钟，根据壳层的位置和动量以不同的方式滴答作响。对系统进行了哈密顿约化，并对约化后的相空间给出了近似的量子描述。如果我们只关注外部动力学，我们必须追踪时钟的自由度，这将导致一种内禀退相干的形式，这种退相干与引力时间膨胀引起的“普遍”退相干机制有一些共同的特征[2]。我们注意到，在平坦时空的（无引力）极限中，退相干仍然存在，强调这种效应可以完全归因于适当的时间差，因此不一定与引力有关。虽然[2]中描述的效应在没有外部引力场的情况下消失，但我们的方法通过包括自相互作用来引导引力对时间膨胀退相干的贡献，从而产生根本上的引力内禀退相干效应。
We investigate the Hong-Ou-Mandel (HOM) effect $-$ a two-photon quantum-interference effect $-$ in the space-time of a rotating spherical mass. In particular, we analyze a common-path HOM setup restricted to the surface of the earth and show that, in principle, general-relativistic frame-dragging induces observable shifts in the HOM dip. For completeness and correspondence with current literature, we also analyze the emergence of gravitational time-dilation effects in HOM interference, for a dual-arm configuration. The formalism thus presented establishes a basis for encoding general-relativis…
The motivation for this thesis was to recast quantum self-testing [MY98,MY04] in operational terms. The result is a category-theoretic framework for discussing the following general question: How do different implementations of the same input-output process compare to each other? In the proposed framework, an input-output process is modelled by a causally structured channel in some fixed theory, and its implementations are modelled by causally structured dilations formalising hidden side-computations. These dilations compare through a pre-order formalising relative strength of side-computation…
Quantum signatures of proper time in optical ion clocks
本文研究了光学离子钟中量子时间效应，通过哈密顿形式推导了谐振子中时间膨胀效应，并展示了真空能量、压缩和量子修正对二次多普勒移位的影响，证明了量子时间干涉测量的可能性。
Frequency shifts due to relativistic effects and retardation in continuous variable quantum key distribution
本文系统分解星基量子通信中的频率偏移来源，发现迟滞效应与相对论贡献同量级，并通过连续变量量子密钥分发密钥率分析证明这些修正会显著影响通信性能，需纳入考虑。
Wigner dynamics of quantum semi-relativistic oscillator
用Monte-Carlo方法和分子动力学方法相结合，精确求解了描述半相对论量子一维谐振子时间演化的积分Wigner-Liouwille方程.研究了相对论效应对动量、速度和坐标维格纳分布函数以及量子算符平均值随时间演化的强烈影响。意外的“突起”的时间演化的分布函数进行了观察。计算了振子的相对论本征时间膨胀。
On relativistic particle creation in Bose-Einstein condensates
我们表明，粒子创建的Bogoliubov模式的玻色-爱因斯坦凝聚体由于加速运动的陷阱是一个真正的相对论效应。为此，我们表明，Bogoliubov模式可以描述的闵可夫斯基度量的时间重新缩放。这样做的结果是，声子将林德勒变换视为广义的林德勒变换，其中光速被声速取代，从而增强了小速度下的粒子生成。由于Rindler变换的非相对论极限只是一个不需要长度收缩或时间膨胀的伽利略变换，我们证明了这种效应在非相对论极限下消失。
The Computational Power of Minkowski Spacetime
连接经典计算的两个端点的类时曲线的洛伦兹长度是通过闵可夫斯基时空的路径的函数。相关的运行时间差异是由于时间膨胀：观察者发现另一个物理上相同的理想时钟以不同的速度比自己的时钟滴答的现象。使用出现在计算复杂性理论的框架中的想法，时间膨胀被量化为一个算法资源，通过相关的相对论能量的$n$第阶多项式时间减少在完成观察者的旅程。这些结果使得量子计算的最佳二次\emph{Grover speedup}和使用经典计算机和相对论效应的$n=2$加速之间的比较成为可能。我们的目标不是提出一个实用的计算模型，而是探索物理学对计算的最终限制。
Relativistic approach to thermodynamic irreversibility
针对弯曲时空中的局域化量子系统，通过转换量子统计力学的两点测量方案，证明量子涨落定理的相对论版本，揭示熵产生具观察者依赖性，相关思想已发表于两篇论文。
Geometry and proper time of a relativistic quantum clock
针对量子时钟时间描述缺乏几何性的问题，提出将量子自由度纳入修正黎曼几何的路径长度微扰框架，并预言 Schwarzschild 时空中与 Compton 波长和波包尺度之比相关的可检验引力时间膨胀修正。
The Aharonov-Bohm effect is considered by most authors as a quantum effect, but a generally accepted explanation does not seem to be available. The phenomenon is studied here under the assumption that hypothetical electric dipole distributions configured by moving charges in the solenoid act on the electrons as test particles. The relative motions of the interacting charged particles introduce relativistic time dilations. The massless dipoles are postulated as part of an impact model that has recently been proposed to account for the far-reaching electrostatic forces between charged particles …
Twin paradox with macroscopic clocks in superconducting circuits
我们提出了一个双胞胎悖论的超导电路的情况下，与几个百分点的光速的速度大的实现。微波腔中电磁场边界条件的超快调制模拟了以相对论速度运动的时钟。由于我们的腔有一个有限的长度，设置允许我们调查的作用，时钟的大小以及有趣的量子效应的时间膨胀。特别是，我们的理论结果表明，时间膨胀增加较大的腔长，并转移由于量子粒子的创建。
Quantum Reference Frames for Lorentz Symmetry
本研究提出量子参考系下的洛伦兹对称性变换框架，引入量子洛伦兹变换与推进叠加，预测时间膨胀与长度收缩的叠加效应，并探讨通过波包扩展观测这些效应的方法。
Quantum Error-Corrected Memories Keep Proper Time
该研究证明量子纠错不会消除时间膨胀效应，而是将固有时间差编码为相对相位旋转，并可在特定离散相位下转化为确定性逻辑门，为连接容错量子信息与相对论时钟提供了平台。
Einstein's Cat -- A Thought Experiment Against Anti-Relativist Claims
本文通过“爱因斯坦的猫”思想实验，利用“同步或死亡时钟”检验光钟与机械钟的同步性，证明时间膨胀同样适用于机械钟，从而反驳时间膨胀仅适用于光钟的反相对论观点，揭示相对论性时间膨胀的普适性。
Robust self-test of the maximally entangled state of two-qubits without assuming unitary observables
研究不假设酉可观测量的两量子比特最大纠缠态的稳健自测试问题，通过规避测量装置的扩张，对物理非投影算子进行正则化并得出解析稳健性界限。
On the Derivation of Equations of Motion from Symmetries in Quantum-Mechanical Systems via Heisenberg's Uncertainty
本文提出以海森堡不确定性原理为基础，利用量子力学系统中的对称性构建运动方程，通过引入对称性-膨胀算符并构建李代数，推导出相对论、非相对论及超相对论情形，为理解对称性和推导运动方程提供了新方法。
Gravitational and Relativistic Deflection of X-Ray Superradiance
在量子系统中探索爱因斯坦的相对论，例如使用高速运行的原子钟，可以加深我们的物理学知识。然而，在寻找新的方法来探测引力和狭义相对论的影响以及它们在光-物质相互作用中的作用方面仍然存在许多挑战。在这里，我们介绍了一个计划的X射线量子光学，允许毫米尺度的相对论红移的调查，直接探测一个固定的核晶体在地球的引力场与X射线。或者，可以使用紧凑的旋转晶体来迫使相互作用的X射线在晶体中经历不均匀的时钟滴答速率。我们发现，引力或特殊相对论时间膨胀与量子干涉的关联将通过X射线光子的偏转表现出来。我们的协议提出了一个新的和可行的桌面解决方案，在量子世界中探测引力和狭义相对论的影响。
A quantum mechanical interpretation for the relativity of the space-time
在狭义相对论中，物理量一般表示为速度的函数。在延伸物体的特定情况下，其在运动方向上的长度的洛伦兹收缩的因子1/γ被写为延伸物体的速度的函数。运动时钟的时间间隔膨胀的洛伦兹因子伽马也是如此。在本文中，我们表明，当伽马被写入作为一个函数的相对论能量的考虑对象的长度和时间间隔的表达式表明，长度的收缩以及时间间隔的膨胀是表现的波动行为的物质。
We present in this paper that the CHSH game admits one and only one optimal state and so remove all ambiguity of representations. More precisely, we use the well-known universal description of quantum commuting correlations as state space on the universal algebra for two player games, and so allows us to unambigiously compare quantum strategies as states on this common algebra. As such we find that the CHSH game leaves a single optimal state on this common algebra. In turn passing to any non-minimal Stinespring dilation for this unique optimal state is the only source of ambiguity (including s…
Using quantum nonlocality for device-independent confirmation of relativistic effects
针对经典时钟同步易受延迟攻击的问题，提出利用量子非定域性的设备无关认证实现高安全时钟同步，并扩展至设备无关地观测相对论时间膨胀。
Which is the Quantum Decay Law of Relativistic Particles?
我们讨论了运动中不稳定系统的量子力学生存概率与静止系统的量子力学生存概率之间的关系。通常的生存概率的定义只考虑了不稳定系统的时间演化，导致运动系统的生存概率与静止系统的生存概率之间的关系不同于基于相对论时间膨胀的标准关系。这种方法导致其他作者声称非标准的量子力学效应与狭义相对论明显矛盾。我们表明，一个适当的相对论定义的生存概率，也考虑到空间演化的不稳定系统导致标准的生存概率之间的关系的系统在运动和系统在休息，符合狭义相对论。我们提出了一个严格的推导这个结果的基础上的波包治疗。
Electron acceleration due to photon absorption: A possible origin of the infinity problems in relativistic quantum fields
基于最近提出的扩展粒子的概念，我们进行了一个用适当低频率的光子加速单电子的Gedanken实验。考虑到由于获得的速度和无限重复的单次吸收过程引起的相对论时间膨胀，可以表明无限极限的动能等于m_{e} c^{2}/2。然而，电子的惯性质量似乎增强了，并且可以确定这种增强是由相对论质量效应描述的。因此，看来虽然在相互作用中存在奇点--使粒子加速到c的极限附近所需的频率变成无穷大--粒子本身的能量却接近一个有限的极限。与Bethe对兰姆位移的计算相比，这一结果似乎为所采用的重整化方法提供了最终的依据。
Quantum channel tomography and estimation by local test
本文通过局部测试方法，在不同条件下提出了量子通道体素和估计的最优查询复杂度，展示了海森堡缩放的实现条件。
We study the survival probability of moving relativistic unstable particles with definite momentum $\vec{p} \neq 0$. The amplitude of the survival probability of these particles is calculated using its integral representation. We found decay curves of such particles for the quantum mechanical models considered. These model studies show that late time deviations of the survival probability of these particles from the exponential form of the decay law, that is the transition times region between exponential and non-expo\-nen\-tial form of the survival probability, should occur much earlier than …
In this paper we propose an experiment designed to observe a general-relativistic effect on single photon interference. The experiment consists of a folded Mach-Zehnder interferometer, with the arms distributed between a single Earth orbiter and a ground station. By compensating for other degrees of freedom and the motion of the orbiter, this setup aims to detect the influence of general relativistic time dilation on a spatially superposed single photon. The proposal details a payload to measure the required effect, along with an extensive feasibility analysis given current technological capab…
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