Jaroslav Hruby
In the paper it is shown the connection between spacetime and quantum information using an information spacetime as superspace. The connection of quantum information with anticommuting variables is given . Also a solitonic bag is presented where the information is confined.
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The quantum mechanical motion of a relativistic particle in a non-continuous spacetime is investigated. The spacetime model is a dense, rationale subset of two-dimensional Minkowski spacetime. Solutions of the Dirac equation are calculated using a generalized version of Feynman's checkerboard model. They turn out to be closely related to the continuum propagator.
The Clifford spacetime algebraic description of Maxwell's equations is reviewed and shown to give a unified picture of recently published versions of photon quantum mechanics. Photon wave equations and a conserved four-current are derived from the complexified standard Lagrangian. The equations of motion and scalar product are found to be in good agreement with those obtained from Fourier transformation of momentum space wave function and scalar product [Phys. Rev. A 102, 042201 (2020)].
Everett's interpretation of quantum mechanics was proposed to avoid problems inherent in the prevailing interpretational frame. It assumes that quantum mechanics can be applied to any system and that the state vector always evolves unitarily. It then claims that whenever an observable is measured, all possible results of the measurement exist. This assertion of multiplicity has been understood in many ways by proponents of Everett's theory. Here we shall illustrate how different views on multiplicity carry onto different views on spacetime.
We propose measurement-based quantum computation (MBQC) as a quantum mechanical toy model for spacetime. Within this framework, we discuss the constraints on possible temporal orders enforced by certain symmetries present in every MBQC. We provide a classification for all MBQC temporal relations compatible with a given initial quantum state and measurement setting, in terms of a matroid. Further, we find a symmetry transformation related to local complementation that leaves the temporal relations invariant. After light cones and closed time-like curves have previously been found to have MBQC c…
What ontology does realism about the quantum state suggest? The main extant view in contemporary philosophy of physics is wave-function realism. We elaborate the sense in which wave-function realism does provide an ontological picture; and defend it from certain objections that have been raised against it. However, there are good reasons to be dissatisfied with wave-function realism, as we go on to elaborate. This motivates the development of an opposing picture: what we call spacetime state realism; a view which takes the states associated to spacetime regions as fundamental. This approach en…
Quantum field theory is the traditional solution to the problems inherent in melding quantum mechanics with special relativity. However, it has also long been known that an alternative first-quantized formulation can be given for relativistic quantum mechanics, based on the parametrized paths of particles in spacetime. Because time is treated similarly to the three space coordinates, rather than as an evolution parameter, such a spacetime approach has proved particularly useful in the study of quantum gravity and cosmology. This paper shows how a spacetime path formalism can be considered to a…
This paper presents a simple model that mimics quantum mechanics (QM) results in terms of probability fields of free particles subject to self-interference, without using Schroedinger equation or complex wavefunctions. Unlike the standard QM picture, the proposed model only uses integer-valued quantities and arithmetic operations. In particular, it assumes a discrete spacetime under the form of an euclidean lattice. The proposed approach describes individual particle trajectories as random walks. Transition probabilities are simple functions of a few quantities that are either randomly associa…
We argue that the flat spacetime with inexact quantum mechanics in it is dual to the de Sitter spacetime with exact quantum mechanics in it, and the positive cosmological constant of this de Sitter spacetime is in the second order of the degree of the violation of the bulk quantum mechanics in the flat spacetime. The flat spacetime is holographic and has a dual time-contracted boundary conformal field theory with two redefined central charges at null infinity. The vanishing smallness of the observed positive cosmological constant suggests the extraordinary exactness of the bulk quantum mechani…
This paper presents a simple model that mimics quantum mechanics (QM) results in terms of probability fields of free particles subject to self-interference, without using Schrödinger equation or wavefunctions. Unlike the standard QM picture, the proposed model only uses integer-valued quantities and arithmetic operations. In particular, it assumes a discrete spacetime under the form of an euclidean lattice. The proposed approach describes individual particle trajectories as random walks. Transition probabilities are simple functions of a few quantities that are either randomly associated to th…
This paper presents a realistic, stochastic, and local model that reproduces nonrelativistic quantum mechanics (QM) results without using its mathematical formulation. The proposed model only uses integer-valued quantities and operations on probabilities, in particular assuming a discrete spacetime under the form of a Euclidean lattice. Individual (spinless) particle trajectories are described as random walks. Transition probabilities are simple functions of a few quantities that are either randomly associated to the particles during their preparation, or stored in the lattice nodes they visit…
Three postulates are discussed: first that well-defined properties cannot be assigned to an isolated system, secondly that quantum unitary evolution is atemporal, and thirdly that some physical processes are never reversed. It is argued that these give useful insight into quantum behaviour. The first postulate emphasizes the fundamental role in physics of interactions and correlations, as opposed to internal properties of systems. Statements about physical interactions can only be framed in a context of further interactions. This undermines the possibility of objectivity in physics. However, q…
In this paper we will analyze the the status of gauge freedom in quantum mechanics (QM) and quantum field theory (QFT). Along with this analysis comparison with ordinary QFT will be given. We will show how the gauge freedom problem is connected with the spacetime coordinates status - the very point at which the difficulties of QM begin. A natural solution of the above mentioned problem will be proposed in which we give a slightly more general form of QM and QFT (in comparison to the ordinary QFT) with noncommutative structure of spacetime playing fundamental role in it. We achieve it by reinte…
This note is an addendum to quant-ph/0507115. In that paper, I present a formalism for relativistic quantum mechanics in which the spacetime paths of particles are considered fundamental, reproducing the standard results of the traditional formulation of relativistic quantum mechanics and quantum field theory. Now, it is well known that there are issues with the ability to localize the position of particles in the usual formulation of relativistic quantum mechanics. The present note shows how, in the spacetime path formalism, the natural representation of on-shell 3-momentum states is effectiv…
Feynman's sum-over-histories formulation of quantum mechanics is reviewed as an independent statement of quantum theory in spacetime form. It is different from the usual Schrödinger-Heisenberg formulation that utilizes states on spacelike surfaces because it assigns probabilities to different sets of alternatives. Sum-over-histories quantum mechanics can be generalized to deal with spacetime alternatives that are not "at definite moments of time". An example in field theory is the set of alternative ranges of values of a field averaged over a spacetime region. An example in particle mechanics …
Following our discussion [Physica A, 375 (2007) 123] to associate an analogous probabilistic description with spacetime geometry in the Schwarzschild metric from the macro- to the micro-domain, we argue that there is a possible connection among normalized probabilities, spacetime geometry (in the form of Schwarzschild radii) and quantum mechanics (in the form of complex wave functions). We show how this association along different (n)-nested surfaces --representing curve space due to an inhomogeneous density of matter-- preserves the postulates of quantum mechanics at different geometrical sca…
Entangled in Spacetime
本文基于量子叠加、纠缠与非局域波函数坍缩，分析延迟选择量子擦除实验中测量对粒子行为的逆向影响，揭示量子力学如何调和延迟选择悖论。
We construct a world model consisting of a matter field living in 4 dimensional spacetime and a gravitational field living in 11 dimensional spacetime. The seven hidden dimensions are compactified within a radius estimated by reproducing the particle - wave characteristic of diffraction experiments. In the presence of matter fields the gravitational field develops localized modes with elementary excitations called gravonons which are induced by the sources (massive particles). The final world model treated here contains only gravonons and a scalar matter field. The solution of the Schroedinger…
This paper surveys the application of geometric algebra to the physics of electrons. It first appeared in 1996 and is reproduced here with only minor modifications. Subjects covered include non-relativistic and relativistic spinors, the Dirac equation, operators and monogenics, the Hydrogen atom, propagators and scattering theory, spin precession, tunnelling times, spin measurement, multiparticle quantum mechanics, relativistic multiparticle wave equations, and semiclassical mechanics.
A quantum mechanical path integral derivation is given of a thermal propagator in non-static Gui spacetime. The thermal nature of the propagator is understood in terms of homotopically non-trivial paths in the configuration space appropriate to tortoise coordinates. The connection to thermal emission from collapsing black holes is discussed.
General relativistic particle trajectories via quantum mechanical weak values and the Schwarzschild-Alcubierre spacetime
该研究发现史瓦西时空中相对论量子粒子的弱测量平均轨迹、弯曲时空量子理论概率流流线与混合史瓦西-阿库别瑞时空经典类光测地线三者等价，为弯曲时空量子理论的构建与确定性诠释提供了新路径。
It has earlier been argued that there should exist a formulation of quantum mechanics which does not refer to a background spacetime. In this paper we propose that, for a relativistic particle, such a formulation is provided by a noncommutative generalisation of the Hamilton-Jacobi equation. If a certain form for the metric in the noncommuting coordinate system is assumed, along with a correspondence rule for the commutation relations, it can be argued that this noncommutative Hamilton-Jacobi equation is equivalent to standard quantum mechanics.
We propose an optomechanics experiment that can search for signatures of a fundamentally classical theory of gravity and in particular of the many-body Schroedinger-Newton (SN) equation, which governs the evolution of a crystal under a self-gravitational field. The SN equation predicts that the dynamics of a macroscopic mechanical oscillator's center of mass wavefunction differ from the predictions of standard quantum mechanics. This difference is largest for low-frequency oscillators, and for materials, such as Tungsten or Osmium, with small quantum fluctuations of the constituent atoms aroun…
Hartman Effect from a Geometrodynamic Extension of Bohmian Mechanics
本文通过几何动力学扩展布雷姆-玻姆力学，揭示量子隧穿与时空几何的联系，解释哈特曼效应的几何自调节机制。
The formalism for histories-based generalized quantum mechanics developed in two earlier papers is applied to the treatment of histories (of particles or fields or more general objects) in curved spacetimes (which need not admit foliation in spacelike hypersurfaces). The construction of the space of temporal supports (a partial semigroup generalizing the space of finite time sequences employed in traditional temporal description of histories) employs spacelike subsets of spacetime having dimensionality less than or equal to three. Definition of symmetry is sharpened by the requirement of conti…
We consider electrodynamics on a noncommutative spacetime using the enveloping algebra approach and perform a non-relativistic expansion of the effective action. We obtain the Hamiltonian for quantum mechanics formulated on a canonical noncommutative spacetime. An interesting new feature of quantum mechanics formulated on a noncommutative spacetime is an intrinsic electric dipole moment. We note however that noncommutative intrinsic dipole moments are not observable in present experiments searching for an EDM of leptons or nuclei such as the neutron since they are spin independent. These exper…
Familiar textbook quantum mechanics assumes a fixed background spacetime to define states on spacelike surfaces and their unitary evolution between them. Quantum theory has changed as our conceptions of space and time have evolved. But quantum mechanics needs to be generalized further for quantum gravity where spacetime geometry is fluctuating and without definite value. This paper reviews a fully four-dimensional, sum-over-histories, generalized quantum mechanics of cosmological spacetime geometry. This generalization is constructed within the framework of generalized quantum theory. This is …
The ontology proposed in this paper is aimed at demonstrating that it is possible to understand the counter-intuitive predictions of quantum mechanics while still retaining much of the framework underlying classical physics, the implication being that it is better to avoid wandering into unnecessarily speculative realms without the support of conclusive evidence. In particular, it is argued that it is possible to interpret quantum mechanics as simply describing an external world consisting of familiar physical entities (e.g., particles or fields) residing in classical 3-dimensional space (not …
The propagator of a spinless particle is calculated from the quantum mechanical path integral formalism in static curved spacetimes endowed with event-horizons. A toy model, the Gui spacetime, and the 2D and 4D Schwarzschild black holes are considered. The role of the topology of the coordinates configuration space is emphasised in this framework. To cover entirely the above spacetimes with a single set of coordinates, tortoise coordinates are extended to complex values. It is shown that the homotopic properties of the complex tortoise configuration space imply the thermal behaviour of the pro…
Relativistic quantum mechanics of a Proca (spin-1) particle in Riemannian spacetimes is constructed. Covariant equations defining electromagnetic interactions of a Proca particle with the anomalous magnetic moment and the electric dipole moment in Riemannian spacetimes are formulated. The relativistic Foldy-Wouthuysen transformation with allowance for terms proportional to the zero power of the Planck constant is performed. The Hamiltonian obtained agrees with the corresponding Foldy-Wouthuysen Hamiltonians derived for scalar and Dirac particles and with their classical counterpart. The unific…
Usual quantum mechanics requires a fixed, background, spacetime geometry and its associated causal structure. A generalization of the usual theory may therefore be needed at the Planck scale for quantum theories of gravity in which spacetime geometry is a quantum variable. The elements of generalized quantum theory are briefly reviewed and illustrated by generalizations of usual quantum theory that incorporate spacetime alternatives, gauge degrees of freedom, and histories that move forward and backward in time. A generalized quantum framework for cosmological spacetime geometry is sketched. T…
We present a spacetime setting for non-relativistic quantum mechanics that deflates "quantum mysteries" and relates non-relativistic quantum mechanics to special relativity. This is achieved by assuming spacetime symmetries are fundamental in a blockworld setting, i.e., by interpreting spacetime relations as fundamental to relata. To justify this Relational Blockworld (RBW), we adopt a result due to G. Kaiser whereby the relativity of simultaneity, stemming from the Poincare algebra of special relativity, is responsible for the canonical commutation relations of non-relativistic quantum mechan…
The rules of quantum mechanics require a time coordinate for their formulation. However, a notion of time is in general possible only when a classical spacetime geometry exists. Such a geometry is itself produced by classical matter sources. Thus it could be said that the currently known formulation of quantum mechanics pre-assumes the presence of classical matter fields. A more fundamental formulation of quantum mechanics should exist, which avoids having to use a notion of time. In this paper we discuss as to how such a fundamental formulation could be constructed for single particle, non-re…
The mathematical similarities between non-relativistic wavefunction propagation in quantum mechanics and image propagation in scalar diffraction theory are used to develop a novel understanding of time and paths through spacetime as a whole. It is well known that Feynman's original derivation of the path integral formulation of non-relativistic quantum mechanics uses time-slicing to calculate amplitudes as sums over all possible paths through space, but along a definite curve through time. Here, a 3+1D spacetime wave distribution and its 4-momentum dual are formally developed which have no ext…
We introduce superdensity operators as a tool for analyzing quantum information in spacetime. Superdensity operators encode spacetime correlation functions in an operator framework, and support a natural generalization of Hilbert space techniques and Dirac's transformation theory as traditionally applied to standard density operators. Superdensity operators can be measured experimentally, but accessing their full content requires novel procedures. We demonstrate these statements on several examples. The superdensity formalism suggests useful definitions of spacetime entropies and spacetime qua…
We use a generalized scheme of supersymmetric quantum mechanics to obtain the energy spectrum and wave function for Dirac equation in (1+1)-dimensional spacetime coupled to a static scalar field.
Earlier work presented a spacetime path formalism for relativistic quantum mechanics arising naturally from the fundamental principles of the Born probability rule, superposition, and spacetime translation invariance. The resulting formalism can be seen as a foundation for a number of previous parameterized approaches to relativistic quantum mechanics in the literature. Because time is treated similarly to the three space coordinates, rather than as an evolution parameter, such approaches have proved particularly useful in the study of quantum gravity and cosmology. The present paper extends t…
The canonical answer to the question posed is "Yes." -- tacitly assuming that quantum theory and the concept of spacetime are to be unified by `quantizing' a theory of gravitation. Yet, instead, one may ponder: Could quantum mechanics arise as a coarse-grained reflection of the atomistic nature of spacetime? -- We speculate that this may indeed be the case. We recall the similarity between evolution of classical and quantum mechanical ensembles, according to Liouville and von Neumann equation, respectively. The classical and quantum mechanical equations are indistinguishable for objects which …
Quantum mechanics in its presently known formulation requires an external classical time for its description. A classical spacetime manifold and a classical spacetime metric are produced by classical matter fields. In the absence of such classical matter fields, quantum mechanics should be formulated without reference to a classical time. If such a new formulation exists, it follows as a consequence that standard linear quantum mechanics is a limiting case of an underlying non-linear quantum theory. A possible approach to the new formulation is through the use of noncommuting spacetime coordin…
In a recent paper we have suggested that a formulation of quantum mechanics should exist, which does not require the concept of time, and that the appropriate mathematical language for such a formulation is noncommutative differential geometry. In the present paper we discuss this formulation for the free point particle, by introducing a commutation relation for a set of noncommuting coordinates. The sought for background independent quantum mechanics is derived from this commutation relation for the coordinates. We propose that the basic equations are invariant under automorphisms which map o…
Many theories of quantum gravity can be understood as imposing a minimum length scale the signatures of which can potentially be seen in precise table top experiments. In this work we inspect the capacity for correlated many body systems to probe non-classicalities of spacetime through modifications of the commutation relations. We find an analytic derivation of the dynamics for a single mode light field interacting with a single mechanical oscillator and with coupled oscillators to first order corrections to the commutation relations. Our solution is valid for any coupling function as we work…
Thermal Spacetime, Part I: Relativistic Bohmian Mechanics
本文将Klein-Gordon方程正能解的未来管域解释为包含逆平衡温度的扩展相空间，提出相对论玻姆力学的新表述，以相空间经典轨迹作为隐变量，并通过全纯规范理论引入相互作用。
The conserved probability densities (attributed to the conserved currents derived from relativistic wave equations) should be non-negative and the integral of them over an entire hypersurface should be equal to one. To satisfy these requirements in a covariant manner, the foliation of spacetime must be such that each integral curve of the current crosses each hypersurface of the foliation once and only once. In some cases, it is necessary to use hypersurfaces that are not spacelike everywhere. The generalization to the many-particle case is also possible.
We study the behaviour of a nonrelativistic quantum particle interacting with different potentials in the spacetimes of topological defects. We find the energy spectra and show how they differ from their free-space values.
The complementarity between signaling and randomness in any communicated resource that can simulate singlet statistics is generalized by relaxing the assumption of free will in the choice of measurement settings. We show how to construct an ontological extension for quantum mechanics (QM) through the oblivious embedding of a sound simulation protocol in a Newtonian spacetime. Minkowski or other intermediate spacetimes are ruled out as the locus of the embedding by virtue of hidden influence inequalities. The complementarity transferred from a simulation to the extension unifies a number of res…
It is shown that, with some reasonable assumptions, the theory of general relativity can be made compatible with quantum mechanics by using the field equations of general relativity to construct a Robertson-Walker metric for a quantum particle so that the line element of the particle can be transformed entirely to that of the Minkowski spacetime, which is assumed by a quantum observer, and the spacetime dynamics of the particle described by a Minkowski observer takes the form of quantum mechanics. Spacetime structure of a quantum particle may have either positive or negative curvature. However…
The state-of-the-art physics consists of two irreconcilable branches, i.e., the quantum theory and the general relativity, which work well in their own territories, independently. However, what are quantum and spacetime after all? The key question was never addressed, satisfactorily. In this work, we describe a possibility to reformulate the quantum theory in the Minkowski spacetime from the viewpoint of classic physics in the Euclidean spacetime, i.e., classic mechanics and stochastic process theory. We show that quantum theory and Minkowski spacetime may connect with each other and emerge fr…
Controlling Photon Entanglement with Mechanical Rotation
本研究通过在旋转平台的HOM干涉仪臂中加入Sagnac干涉仪，发现机械旋转引发的非惯性运动可改变纠缠双光子态的对称性，为研究时空对量子系统的影响及卫星量子通信相关研究提供支撑。
Unifying spacetime approaches to quantum mechanics
本文通过时空态统一了多种时空量子力学方法，揭示了路径积分、量子态随时间演化、伪密度矩阵等方案的内在联系，并探讨了其在量子基础、相对论量子场论等领域的应用。
Bosonic and fermionic particle currents can be introduced in a more unified way, with the cost of introducing a preferred spacetime foliation. Such a unified treatment of bosons and fermions naturally emerges from an analogous superstring current, showing that the preferred spacetime foliation appears only at the level of effective field theory, not at the fundamental superstring level. The existence of the preferred spacetime foliation allows an objective definition of particles associated with quantum field theory in curved spacetime. Such an objective definition of particles makes the Bohmi…
It is argued that the quantum correlations are not maximally nonlocal to make it possible to control local outcomes from outside spacetime, and quantum mechanics emerges from timeless nonlocality and biased local randomness. This rules out a world described by NL (nonlocal) boxes. A new type of experiments is suggested.
Quantum gravitational decoherence of a mechanical oscillator from spacetime fluctuations
本文研究时空涨落（源于变形对易关系或度规张量涨落）导致的机械振子动量基退相干，并用实验数据约束模型参数，同时为其他量子引力模型提供界限。
Curved spacetimes from quantum mechanics
本文推广了 Penrose 自旋几何定理，证明仅利用抽象 Poincaré 不变量子力学系统的可观测量，即可在经典极限下恢复弯曲 Lorentzian 4-流形的局部度规与曲率结构。
It is proposed that the Schrodinger equation for a free point particle has non-linear corrections which depend on the mass of the particle. It is assumed that the corrections become extremely small when the mass is much smaller or much larger than a critical value (the critical value being related to but smaller than Planck mass). The corrections become significant when the mass is close to this critical value and could play a role in explaining wave-function collapse. It appears that such corrections are not ruled out by present day experimental tests of the Schrodinger equation. Corrections …
We formulate quantum mechanics in spacetimes with real-order fractional geometry and more general factorizable measures. In spacetimes where coordinates and momenta span the whole real line, Heisenberg's principle is proven and the wave-functions minimizing the uncertainty are found. In spite of the fact that ordinary time and spatial translations are broken and the dynamics is not unitary, the theory is in one-to-one correspondence with a unitary one, thus allowing us to employ standard tools of analysis. These features are illustrated in the examples of the free particle and the harmonic osc…
Spacetime quantum mechanics for bosonic and fermionic systems
本文提出了一种将时空对称结构应用于量子力学的新方法，统一了时空分离的公理，并为路径积分和费米子系统提供了新的视角。
From Mass-Shell Factorisation to Spin: An Attempt at a Matrix-Valued Liouville Framework for Relativistic Classical and Quantum Phase-Spacetime
本文探讨了在相空间上直接构建相对论统计力学如何自然产生旋量结构，并提出了一种矩阵值李群框架，用于连接相对论经典和量子相空间，其中自旋代数作为任何包含质量和壳分支和角动量维度的相对论统计理论所必需的内部结构出现。
Many phenomena and fundamental predictions, ranging from Hawking radiation to the early evolution of the Universe rely on the interplay between quantum mechanics and gravity or more generally, quantum mechanics in curved spacetimes. However, our understanding is hindered by the lack of experiments that actually allow us to probe quantum mechanics in curved spacetime in a repeatable and accessible way. Here we propose an experimental scheme for a photon that is prepared in a path superposition state across two rotating Sagnac interferometers that have different diameters and thus represent a su…
`How do our ideas about quantum mechanics affect our understanding of spacetime?' This familiar question leads to quantum gravity. The complementary question is also important: `How do our ideas about spacetime affect our understanding of quantum mechanics?' This short abstract of a talk given at the Gafka2004 conference contains a very brief summary of some of the author's papers on generalizations of quantum mechanics needed for quantum gravity. The need for generalization is motivated. The generalized quantum theory framework for such generalizations is described and illustrated for usual q…
Quantum mechanics introduces the concept of probability at the fundamental level, yielding the measurement problem. On the other hand, recent progress in cosmology has led to the "multiverse" picture, in which our observed universe is only one of the many, bringing an apparent arbitrariness in defining probabilities, called the measure problem. In this paper, we discuss how these two problems are intimately related with each other, developing a complete picture for quantum measurement and cosmological histories in the quantum mechanical universe. On one hand, quantum mechanics eliminates the a…
In classical relativistic mechanics, a "preferred" proper direction in spacetime for each particle is determined by the direction of its 4-momentum. Analogously, for each quantum particle we find a local direction uniquely determined by the many-particle wave function, which for each particle defines the proper foliation of spacetime. This can be used to formulate a relativistic-covariant version of Bohmian mechanics, with equivariant probability density on proper hypersurfaces.
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