Minoru Omote, Susumu Kamefuchi
On the basis of a manifestly covariant formalism of non-relativistic quantum mechanics in general coordinate systems, proposed by us recently, we derive general expressions for inertial forces. The results enable us further to discuss, and to explain the validity of, the equivalence principle in non-relativistic quantum mechanics.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
继续探索
The equivalence principle and inertial-gravitational decoherence
本文从布朗斯坦反对意见出发，论证惯性-引力退相干会破坏量子引力探测，并推测通过关联函数广义协变性在有效场论中实现等价原理的可能性。
After a review of the existing theory of non-inertial frames and mathematical observers in Minkowski space-time we give the explicit expression of a family of such frames obtained from the inertial ones by means of point-dependent Lorentz transformations as suggested by the locality principle. These non-inertial frames have non-Euclidean 3-spaces and contain the differentially rotating ones in Euclidean 3-spaces as a subcase. Then we discuss how to replace mathematical accelerated observers with dynamical ones (their world-lines belong to interacting particles in an isolated system) and of how…
We present a formalism of Galilean quantum mechanics in non-inertial reference frames and discuss its implications for the equivalence principle. This extension of quantum mechanics rests on the Galilean line group, the semidirect product of the real line and the group of analytic functions from the real line to the Euclidean group in three dimensions. This group provides transformations between all inertial and non-inertial reference frames and contains the Galilei group as a subgroup. We construct a certain class of unitary representations of the Galilean line group and show that these repre…
In an ideal test of the equivalence principle, the test masses fall in a common inertial frame. A real experiment is affected by gravity gradients, which introduce systematic errors by coupling to initial kinematic differences between the test masses. We demonstrate a method that reduces the sensitivity of a dual-species atom interferometer to initial kinematics by using a frequency shift of the mirror pulse to create an effective inertial frame for both atomic species. This suppresses the gravity-gradient-induced dependence of the differential phase on initial kinematic differences by a facto…
We explore the interplay between the equivalence principle and a generalization of the Heisenberg uncertainty relations known as extended uncertainty principle, that comprises the effects of spacetime curvature at large distances. Specifically, we observe that, when the modified uncertainty relations hold, the weak formulation of the equivalence principle is violated, since the inertial mass of quantum systems becomes position-dependent whilst the gravitational mass is left untouched. To obtain the above result, spinor and scalar fields are separately analyzed by considering the non-relativist…
We show that in complete agreement with classical mechanics, the dynamics of any quantum mechanical wave packet in a linear gravitational potential involves the gravitational and the inertial mass only as their ratio. In contrast, the spatial modulation of the corresponding energy wave function is determined by the third root of the product of the two masses. Moreover, the discrete energy spectrum of a particle constrained in its motion by a linear gravitational potential and an infinitely steep wall depends on the inertial as well as the gravitational mass with different fractional powers. Th…
We determine the quantum mechanical limits to inertial mass-sensing based on nanomechanical systems. We first consider a harmonically oscillating cantilever whose vibration frequency is changed by mass accretion at its surface. We show that its zero-point fluctuations limit the mass sensitivity, for attainable parameters, to about an electron mass. In contrast to the case of a classical cantilever, we find the mass sensitivity of the quantum mechanical cantilever is independent of its resonant frequency in a certain parameter regime at low temperatures. We then consider an optomechanical setup…
Quantum Mechanics of Open Systems in Non-Inertial Motion
本文提出基于耗散子的框架，分析非惯性运动下开放量子系统的动力学，并以旋转环形腔体中的Lamb位移为例，揭示非惯性效应、退相干、耗散与系统—浴盆纠缠的相互作用。
Einstein`s equivalence principle states the complete physical equivalence of a gravitational field and corresponding inertial field in an accelerated reference frame. However, to what extent the equivalence principle remains valid in non-relativistic quantum mechanics is a controversial issue. To avoid violation of the equivalence principle, Bargmann`s superselection rule forbids a coherent superposition of states with different masses. Here we suggest a quantum simulation of non-relativistic Schrödinger particle dynamics in non-inertial reference frames, which is based on propagation of polar…
In a recent paper (arXiv:1701.04298 [quant-ph]) Toroš, Großardt and Bassi claim that the potential necessary to support a composite particle in a gravitational field must necessarily cancel the relativistic coupling between internal and external degrees of freedom. As such a coupling is responsible for the gravitational redshift measured in numerous experiments, the above statement is clearly incorrect. We identify the simple mistake in the paper responsible for the incorrect claim.
We combine linear response theory and dimensional regularization in order to derive the dynamical Casimir force in the low frequency regime. We consider two parallel plates moving along the normal direction in $D-$dimensional space. We assume the free-space values for the mass of each plate to be known, and obtain finite, separation-dependent mass corrections resulting from the combined effect of the two plates. The global mass correction is proportional to the static Casimir energy, in agreement with Einstein's law of equivalence between mass and energy for stressed rigid bodies.
Gauge field theories may quite generally be defined as describing the coupling of a matter-field to an interaction-field, and they are suitably represented in the mathematical framework of fiber bundles. Their underlying principle is the so-called gauge principle, which is based on the idea of deriving the coupling structure of the fields by satisfying a postulate of local gauge covariance. The gauge principle is generally considered to be sufficient to define the full structure of gauge-field theories. This paper contains a critique of this usual point of view: firstly, by emphazising an gaug…
An atom attached to a micrometer-scale wire that is vibrating at a frequency of 100 MHz and with displacement amplitude 1 nm experiences an acceleration magnitude 10^9 ms^-2, approaching the surface gravity of a neutron star. As one application of such extreme non-inertial forces in a mesoscopic setting, we consider a model two-path atom interferometer with one path consisting of the 100 MHz vibrating wire atom guide. The vibrating wire guide serves as a non-inertial reference frame and induces an in principle measurable phase shift in the wave function of an atom traversing the wire frame. We…
This is the fourth in a series of papers on developing a formulation of quantum mechanics in non-inertial reference frames. This formulation is grounded in a class of unitary cocycle representations of what we have called the Galilean line group, the generalization of the Galilei group to include transformations amongst non-inertial reference frames. These representations show that in quantum mechanics, just as the case in classical mechanics, the transformations to accelerating reference frames give rise to fictitious forces. In previous work, we have shown that there exist representations of…
Our recent paper (arXiv:1701.04298 [quant-ph]) discussed the occurrence of a coupling of centre of mass and internal degrees of freedom for complex quantum systems in non-inertial frames. There, we pointed out that an external force supporting the system against gravity plays a crucial role for the coupling between center of mass position to the internal degrees of freedom. In a comment (arXiv:1702.06670 [quant-ph]) to our paper, Pikovski et al. question our conclusion and present the argument that the lack of the coupling term would be in contradiction with the observation of gravitational ti…
The formula for the correlation function of spin measurements of two particles in two moving inertial frames is derived within Lorentz-covariant quantum-mechanics formulated in the absolute synchronization framework. The results are the first exact Einstein-Podolsky-Rosen correlation functions obtained for Lorentz-covariant quantum-mechanical system in moving frames under physically acceptable conditions, i.e., taking into account the localization of the particles during the detection and using the spin opeartor with proper transformation properties under the action of the Lorentz group. Some …
In previous work we have developed a formulation of quantum mechanics in non-inertial reference frames. This formulation is grounded in a class of unitary cocycle representations of what we have called the Galilean line group, the generalization of the Galilei group that includes transformations amongst non-inertial reference frames. These representations show that in quantum mechanics, just as is the case in classical mechanics, the transformations to accelerating reference frames give rise to fictitious forces. A special feature of these previously constructed representations is that they al…
A recent concept in theoretical physics, motivated in string duality and M-theory, is the notion that not all quantum theories arise from quantising a classical system. Also, a given quantum model may possess more than just one classical limit. In view of these developments, we analyse some general properties that quantum mechanics must satisfy, if it is not to be formulated as a quantisation of a given classical mechanics. Instead, our approach to quantum mechanics is modelled on a statement that is close in spirit to the equivalence principle of general relativity, thus bearing a strong rese…
In this paper we develop a discussion about PT Symmetric Quantum Mechanics, working with basics elements of this theory. In a simple case of two body system, we developed the Quantum Brachistochrone problem. Comparing the results obtained through the PT Symmetric Quantum Mechanics with that ones obtained using the standard formalism, we conclude that this new approach is not able to reveal any new effect.
We use the Feynman path integral approach to nonrelativistic quantum mechanics twofold. First, we derive the lagrangian for a spinless particle moving in a uniformly but not necessarily constantly accelerated reference frame; then, applying the strong equivalence principle (SEP) we obtain the Schroedinger equation for a particle in an inertial frame and in the presence of a uniform and constant gravity field. Second, using the associated Feynman propagator, we propagate an initial gaussian wave packet, with the final wave function and probability density depending on the ratio m/hbar, where m …
Einstein's Equivalence Principle in Nonrelativistic Quantum Mechanics
本文在非相对论量子力学中精确表述爱因斯坦等效原理，证明自由落体与惯性观测者等价，推导引力红移，并应用于受限系统揭示量子隧穿，确认等效原理在量子领域的有效性。
A recent analysis by Pikovski et al. [Nat. Phys. 11, 668 (2015)] has triggered interest in the question of how to include relativistic corrections in the quantum dynamics governing many-particle systems in a gravitational field. Here we show how the center-of-mass motion of a quantum system subject to gravity can be derived more rigorously, addressing the ambiguous definition of relativistic center-of-mass coordinates. We further demonstrate that, contrary to the prediction by Pikovski et al., external forces play a crucial role in the relativistic coupling of internal and external degrees of …
On the emergent origin of the inertial mass
本研究在特定涌力量子力学框架下论证物理系统惯性质量的涌现起源，并得出惯性定律的涌现诠释与能量-时间不确定关系推导两项理论推论。
A quantum particle moving in a gravitational field may penetrate the classically forbidden region of the gravitational potential. This raises the question of whether the time of flight of a quantum particle in a gravitational field might deviate systematically from that of a classical particle due to tunnelling delay, representing a violation of the weak equivalence principle. I investigate this using a model quantum clock to measure the time of flight of a quantum particle in a uniform gravitational field, and show that a violation of the equivalence principle does not occur when the measurem…
Photon interference and bunching are widely studied quantum effects that have also been proposed for high precision measurements. Here we construct a theoretical description of photon-interferometry on rotating platforms, specifically exploring the relation between non-inertial motion, relativity, and quantum mechanics. On the basis of this, we then propose an experiment where photon entanglement can be revealed or concealed solely by controlling the rotational motion of an interferometer, thus providing a route towards studies at the boundary between quantum mechanics and relativity.
Unitary equivalence of Schrödinger and Heisenberg pictures survives in nonlinear quantum mechanics
本文证明在非线性量子力学中，当哈密顿量依赖于瞬时期望值时，薛定谔绘景与海森堡绘景的幺正等价性仍成立，尽管交织算子依赖初始状态，但物理预言一致。
It has been demonstrated, using variational methods, that quantum vacuum energy gravitates according to the equivalence principle, at least for the finite Casimir energies associated with perfectly conducting parallel plates. This conclusion holds independently of the orientation of the plates. We review these arguments and add further support to this conclusion by considering parallel semitransparent plates, that is, $δ$-function potentials, acting on a massless scalar field, in a spacetime defined by Rindler coordinates. We calculate the force on systems consisting of one or two such plates …
Testing the Quantum Equivalence Principle with Gravitational Waves
本研究通过分析LIGO/Virgo引力波事件，利用波振幅和频率的修正，约束了量子等效原理的破坏，并适用于未来探测器。
We argue that in a framework for emergent quantum mechanics, the weak equivalence principle is a consequence of concentration of measure in large dimensional spaces of $1$-Lipshitz functions. Furthermore, as a consequence of the emergent framework and the properties that we assume for the fundamental dynamics, it is argued that gravity must be a classical, emergent interaction.
A Newtonian mechanics model is essentially the model of a point body in an inertial reference frame. How to describe extended bodies in non-inertial (vibrational) reference frames with the random initial conditions? One of the most general description (known as the higher derivatives formalism) consists in taking into account the infinite number of the higher order temporal derivatives of the coordinates in the Lagrange function. Such formalism describes physical objects in the infinite dimensional space does not contradict quantum mechanics and infinite dimensional Hilbert space.
We consider the two main theorems in the derivation of the Quantum Hamilton--Jacobi Equation from the Equivalence Postulate (EP) of quantum mechanics. The first one concerns a basic cocycle condition, which holds in any dimension with Euclidean or Minkowski metrics and implies a global conformal symmetry underlying the Quantum Hamilton--Jacobi Equation. In one dimension such a condition fixes the Schwarzian equation. The second theorem concerns energy quantization which follows rigorously from consistency of the equivalence postulate.
With an eye on developing a quantum theory of gravity, many physicists have recently searched for quantum challenges to the equivalence principle of general relativity. However, as historians and philosophers of science are well aware, the principle of equivalence is not so clear. When clarified, we think quantum tests of the equivalence principle won't yield much. The problem is that the clash/not-clash is either already evident or guaranteed not to exist. Nonetheless, this work does help teach us what it means for a theory to be geometric.
The three-tangle-dependence of $S_{max} = \max <S>$, where $S$ is Svetlichny operator, are explicitly derived when one party moves with an uniform acceleration with respect to other parties in the generalized Greenberger-Horne-Zeilinger and maximally slice states. The $π$-tangle-dependence of $S_{max}$ are also derived implicitly. From the dependence we conjecture that the multipartite entanglement is not the only physical resource for quantum mechanical multipartite non-locality.
We consider an unexplored aspect of the mass equivalence principle in the quantum realm, its connection with atomic stability. We show that if the gravitational mass were different from the inertial one, a Hydrogen atom placed in a constant gravitational field would become unstable in the long term. In contrast, independently of the relation between the two masses, the atom does not become ionized in an uniformly accelerated frame. This work, in the line of previous analyses studying the properties of quantum systems in gravitational fields, contributes to the extension of that programme to in…
In his sixth problem, Hilbert called for an axiomatic approach to theoretical physics with an aim to achieve precision and rigour in scientific reasoning, where logic and language (semantics) of physics play the pivotal role. It is from such a point of view, we investigate the scientific value of the modern experiments to perform quantum tests of equivalence principle. Determination of Planck constant involves the use of acceleration due to gravity of the earth $(g)$ that results in the force on a test mass. The equivalence between inertial mass and gravitational mass of a test object is assum…
Generating quantum non-local entanglement with mechanical rotations
本文提出一种类似萨格纳克的干涉仪，利用光子干涉仪的机械旋转产生纠缠态，违反Bell-CHSH不等式直至Tsirelson界，表明机械旋转可作为控制量子非局域性的资源。
The aim of this short Note is to show that the Schrödinger and Heisenberg pictures of quantum mechanics are not equivalent unless one uses a quantization rule clearly stated by Born and Jordan in their famous 1925 paper. This rule is sufficient and necessary to ensure energy conservation in Heisenberg's matrix mechanics. It follows, in particular, that Schrödinger and Heisenberg mechanics are not equivalent if one quantizes observables using the Weyl prescription.
A general argument is presented against relativistic, unitary, single-outcome quantum mechanics. This is achieved by combining the Wigner's Friend thought experiment with measurements on a Greenberger-Horne-Zeilinger (GHZ) state, and describing the evolution of the quantum state in various inertial frames. Assuming unitary quantum mechanics and single outcomes, the result is that the Born rule must be violated in some inertial frame: in that frame, outcomes are obtained for which no corresponding term exists in the pre-measurement wavefunction.
A Matter-Wave Quantum Superposition of Inertial and Constant Acceleration Motions
本研究提出三种计算惯性与加速运动叠加态量子物质波非相对论动力学的方法，验证了经典不可观测的相对相位可通过干涉实验探测，揭示海森堡绘景的适用性及与相对论处理的一致性，为等效原理相关研究提供支撑。
We postulate that physical states are equivalent under coordinate transformations. We then implement this equivalence principle first in the case of one-dimensional stationary systems showing that it leads to the quantum analogue of the Hamilton-Jacobi equation which in turn implies the Schroedinger equation. In this context the Planck constant plays the role of covariantizing parameter. The construction is deeply related to the GL(2,C)-symmetry of the second-order differential equation associated to the Legendre transformation which selects, in the case of the quantum analogue of the Hamilton…
The supposed equivalence of the conventional interpretation of quantum mechanics with Bohm's interpretation is generally demonstrated only in the coordinate representation. It is shown, however, that in the momentum representation this equivalence is not valid.
We consider the problem of whether the canonical and microcanonical ensembles are locally equivalent for short-ranged quantum Hamiltonians of $N$ spins arranged on a $d$-dimensional lattices. For any temperature for which the system has a finite correlation length, we prove that the canonical and microcanonical state are approximately equal on regions containing up to $O(N^{1/(d+1)})$ spins. The proof rests on a variant of the Berry--Esseen theorem for quantum lattice systems and ideas from quantum information theory.
Recently we showed that the postulated diffeomorphic equivalence of states implies quantum mechanics. This approach takes the canonical variables to be dependent by the relation p=\partial_q S_0 and exploits a basic GL(2,C)-symmetry which underlies the canonical formalism. In particular, we looked for the special transformations leading to the free system with vanishing energy. Furthermore, we saw that while on the one hand the equivalence principle cannot be consistently implemented in classical mechanics, on the other it naturally led to the quantum analogue of the Hamilton-Jacobi equation, …
We study the effect of large acceleration of an uniformly accelerated frame on the validity of weak equivalence principle. Specifically we demonstrate how the behaviour of free quantum particle, as observed by an observer with large uniform acceleration, completely changes from that of a quantum particle emmarsed in a uniform gravitational field. We also extend our analysis to the simplest noncommutative space scenario to show that while spatial noncommutativity does not affect the quantum particle in a gravitational field, it does alter the energy eigenvalues of a quantum particle as seen fro…
The operational approach to time is a cornerstone of relativistic theories, as evidenced by the notion of proper time. In standard quantum mechanics, however, time is an external parameter. Recently, many attempts have been made to extend the notion of proper time to quantum mechanics within a relational framework. Here, we use similar ideas combined with the relativistic mass-energy equivalence to study an accelerating massive quantum particle with an internal clock system. We show that the ensuing evolution from the perspective of the particle's internal clock is non-Hermitian. This result d…
The equivalence principle is a perennial subject of controversy, especially in connection with radiation by a uniformly accelerated classical charge, or a freely falling charge observed by a supported detector. Recently, related issues have been raised in connection with the Unruh radiation associated with accelerated detectors (including two-level atoms and resonant cavities). A third type of system, very easy to analyze because of conformal invariance, is a two-dimensional scalar field interacting with perfectly reflecting boundaries (mirrors). After reviewing the issues for atoms and caviti…
We demonstrate that optomechanical non-reciprocity is equivalent to the anti-resonance, often discussed in the context of coupled driven harmonic oscillators. We show that that suitable phase-difference between the cavity driving fields make the relevant optomechanical couplings complex, which leads to non-reciprocity in the field fluctuations and anti-resonance in average field amplitudes. This analogy with anti-resonance demonstrates that only for a particular frequency (the so-called isolation frequency) of input signal, maximum non-reciprocity can be achieved. In contrast to the previous s…
Operator formulation of Classical mechanics: Levi-Civita map and equivalence of central forces in 2-dimensions
本文在经典力学算符表述下求解二维开普勒势与谐振子势的类薛定谔方程及经典波函数，并利用 Levi-Civita 映射和 Sundman 时间重参数化证明了两类中心力模型的等价性。
The propagation of the wave function of a particle is characterised by a group and a phase velocity. The group velocity is associated with the particle's classical velocity, which is always smaller than the speed of light, and the phase velocity is associated with the propagation speed of the wave function phase and is treated as being unphysical, since its value is always greater than the speed of light. Here we show, using Sciama's Machian formulation of rest mass energy, that this physical interpretation, for the group and the phase velocity of the wave function, is only valid if the weak e…
Gravitation, according to General Relativity, is an attribute of space-time's geometry and hence not a force in the Newtonian sense. This is a consequence of Einstein's equivalence principle, which so far passed all experimental tests with high precision. However, the search for possible violations continues, for they, as the case may be, are expected to point towards more fundamental theoretical extensions of General Relativity. In particular, it is expected that useful insights are gained by studying the interaction between gravitational fields and genuine quantum-mechanical systems, like at…
That gravitation can be understood as purely metric phenomenon depends crucially on the validity of a number of hypotheses which are summarised by the Einstein Equivalence Principle, the least well tested part of which being the Universality of Gravitational Redshift. A recent and currently widely debated proposal (Nature 463 (2010) 926-929) to re-interpret some 10-year old experiments in atom interferometry would imply, if tenable, substantial reductions on upper bounds for possible violations of the Universality of Gravitational Redshift by four orders of magnitude. This interpretation, howe…
The aim of the famous Born and Jordan 1925 paper was to put Heisenberg's matrix mechanics on a firm mathematical basis. Born and Jordan showed that if one wants to ensure energy conservation in Heisenberg's theory it is necessary and sufficient to quantize observables following a certain ordering rule. One apparently unnoticed consequence of this fact is that Schrödinger's wave mechanics cannot be equivalent to Heisenberg's more physically motivated matrix mechanics unless its observables are quantized using this rule, and not the more symmetric prescription proposed by Weyl in 1926, which has…
扫码添加微信好友，提出您的宝贵建议 👇
💡 备注请填写：网站反馈
发表机构由 AI 从论文文本抽取，如发现错误，欢迎反馈修正建议。