11 pages, 2 figures. To appear in the Proceedings of the 4th International Workshop DICE2008: "From Quantum Mechanics through Complexity to Spacetime", Castiglioncello (Tuscany, Italy), September 22-26, 2008
We raise the issue whether conventional quantum mechanics, which is not a hidden variable theory in the usual Jauch-Piron's sense, might nevertheless be a hidden variable theory in the sense recently conjectured by G. 't Hooft in his pre-quantization scheme. We find that quantum mechanics might indeed have a fully deterministic underpinning by showing that Born's rule naturally emerges (i.e., it is not postulated) when 't Hooft's Hamiltonian for be-ables is combined with the Koopmann - von Neumann operatorial formulation of classical physics.
We consider non minimal coupling between matters and gravity in modified theories of gravity. In contrary to the current common sense, we report that quantum mechanics can effectively emerge when the space-time geometry is sufficiently flat. In other words, quantum mechanics might play no role when and where the space-time geometry is highly curved. We study the first two simple models of Effectively Emergent Quantum Mechanics(EEQM): R-dependent EEQM and G-dependent EEQM where R is the Ricci scalar and G is the Gauss-Bonnet Lagrangian density. We discuss that these EEQM theories might be fine …
Recently 't Hooft demonstrated that ``For any quantum system there exists at least one deterministic model that reproduces all its dynamics after prequantization''. An extension is presented here which covers quantum systems that are characterized by a complete set of mutually commuting Hermitian operators (``beables''). We introduce the symmetry of beables: any complete set of beables is as good as any other one which is obtained through a real general linear group transformation. The quantum numbers of a specific set are related to symmetry breaking initial and boundary conditions in a deter…
There ought to exist a reformulation of quantum theory which does not depend on classical time. To achieve such a reformulation, we introduce the concept of an atom of space-time-matter (STM). An STM atom is a classical non-commutative geometry, based on an asymmetric metric, and sourced by a closed string. Different such atoms interact via entanglement. The statistical thermodynamics of a large number of such atoms gives rise, at equilibrium, to a theory of quantum gravity. Far from equilibrium, where statistical fluctuations are large, the emergent theory reduces to classical general relativ…
In Stephen Adler's book, "Quantum theory as an emergent phenomenon," the author starts from a classical mechanics structure and "derives" the formalism of quantum theory, together with wave function collapse dynamics, the latter providing the interpretation of quantum theory. A detailed outline of the author's argument is presented in this book review.
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.
Several experimental groups reported the evidence of multiple periodic modulations of nuclear decay constants which amplitudes are of the order .1% and periods of one year, 24 hours or about one month. We argue that such deviations from radioactive decay law can be described in nonlinear quantum mechanics framework, in which decay process obeys to nonlinear Shroedinger equation with Doebner-Goldin terms. Proposed corrections to Hamiltonian of quantum system interaction with gravitation field correspond to some emergent gravity theories, in particular, bilocal gravity model. Decay parameter var…
We present an explicit correspondence between quantum mechanics and the classical theory of irreversible thermodynamics as developed by Onsager, Prigogine et al. Our correspondence maps irreversible Gaussian Markov processes into the semiclassical approximation of quantum mechanics. Quantum-mechanical propagators are mapped into thermodynamical probability distributions. The Feynman path integral also arises naturally in this setup. The fact that quantum mechanics can be translated into thermodynamical language provides additional support for the conjecture that quantum mechanics is not a fund…
The role of probability in quantum mechanics is reviewed, with a discussion of the ``orthodox'' versus the statistical interpretive frameworks, and of a number of related issues. After a brief summary of sources of unease with quantum mechanics, a survey is given of attempts either to give a new interpretive framework assuming quantum mechanics is exact, or to modify quantum mechanics assuming it is a very accurate approximation to a more fundamental theory. This survey focuses particularly on the issues of whether probabilities in quantum mechanics are postulated or emergent.
We show the emergence of Berry phase in a forced harmonic oscillator system placed in the quantum space-time of Moyal type, where the time 't' is also an operator. An effective commutative description of the system gives a time dependent generalised harmonic oscillator system with perturbation linear in position and momentum. The system is then diagonalised to get a generalised harmonic oscillator and then its adiabatic evolution over time-period $\mathcal{T}$ is studied in Heisenberg picture to compute the expression of geometric phase-shift.
The transition from the quantum to the classical is governed by randomizing devices (RD), i.e., dynamical systems that are very sensitive to the environment. We show that, in the presence of RDs, the usual arguments based on the linearity of quantum mechanics that lead to the measurement problem do not apply. RDs are the source of probabilities in quantum mechanics. Hence, the reason for probabilities in quantum mechanics is the same as the reason for probabilities in other parts of physics, namely our ignorance of the state of the environment. This should not be confused with decoherence. The…
The classical thermostatics of equilibrium processes is shown to possess a quantum-mechanical dual theory with a finite-dimensional Hilbert space of quantum states. Specifically, the kernel of a certain Hamiltonian operator becomes the Hilbert space of quasistatic quantum mechanics. The relation of thermostatics to topological field theory is also discussed in the context of the emergent approach to quantum theory, where the concept of entropy plays a key role.
We present our model of an Emergent Quantum Mechanics which can be characterized by "realism without pre-determination". This is illustrated by our analytic description and corresponding computer simulations of Bohmian-like "surreal" trajectories, which are obtained classically, i.e. without the use of any quantum mechanical tool such as wave functions. However, these trajectories do not necessarily represent ontological paths of particles but rather mappings of the probability density flux in a hydrodynamical sense. Modelling emergent quantum mechanics in a high-low intesity double slit scena…
The question whether global entanglement of a multiparticle quantum system can be inferred from local properties is of great relevance for the theory of quantum correlations as well as for experimental implementations. We present a method to systematically find quantum states, for which the two- or three-body marginals do not contain any entanglement, nevertheless, the knowledge of these reduced states is sufficient to prove genuine multiparticle entanglement of the global state. With this, we show that the emergence of global entanglement from separable local quantum states occurs frequently …
A geometric interpretation for quantum correlations and entanglement according to a particular framework of emergent quantum mechanics is developed. The mechanism described is based on two ingredients: 1. At an hypothetical sub-quantum level description of physical systems, the dynamics has a regime where it is partially ergodic and 2. A formal projection from a two-dimensional time mathematical formalism of the emergent quantum theory to the usual one-dimensional time formalism of quantum dynamics. Observable consequences of the theory are obtained. Among them we show that quantum correlation…
We introduce a new and conceptually simple interpretation of quantum mechanics based on reduced density matrices of sub-systems from which the standard Copenhagen interpretation emerges as an effective description of macroscopically large systems. Wave function collapse is seen to be a useful but fundamentally unnecessary piece of prudent book keeping which is only valid for macro-systems. The new interpretation lies in a class of modal interpretations in that it applies to quantum systems that interact with a much larger environment. However, we show that it does not suffer from the problems …
We analyze the emergence of diffractive focusing in the transition from discrete to continuous space-time variables. Three types of dynamical equations are studied in a top-to-bottom approach, starting with the most general system. First we solve a linear cellular automaton of two species, then a nearest neighbour tight-binding array and finally the time-dependent Schrödinger equation. All models are shown to produce diffractive solutions for square packet distributions. The main result of this paper is that in discrete variables, the nature of the solutions depends strongly on the size of wav…
It has been argued that gravity acts dissipatively on quantum-mechanical systems, inducing thermal fluctuations that become indistinguishable from quantum fluctuations. This has led some authors to demand that some form of time irreversibility be incorporated into the formalism of quantum mechanics. As a tool towards this goal we propose a thermodynamical approach to quantum mechanics, based on Onsager's classical theory of irreversible processes and on Prigogine's nonunitary transformation theory. An entropy operator replaces the Hamiltonian as the generator of evolution. The canonically conj…
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 Copenhagen interpretation has been remarkably successful but seems at odds with the underlying linearity of quantum mechanics. We show how it can emerge in a simple way from the underlying microscopic quantum world governed by Schrodinger's equation without the need for observers or their brains. In order to achieve this, we assemble pieces of various pre-existing ideas. Firstly, we adopt a relational approach and use the eigenvectors of the reduced density matrix of a quantum sub-system, or equivalently the Schmidt decomposition, to define the `internal state' of a sub-system. Previous wo…
Since the advent of quantum mechanics we have mainly been concerned with its predictions from the perspective of an external observer. This is in strong contrast to the theory of general relativity, where the physics is governed by the intrinsic properties of space-time. At the same time, the precise relation between space-time and quantum mechanics is still one of the greatest problems of theoretical physics. This immediately raises the question on the completeness of our understanding of quantum mechanics. Here we address the problem by making an intrinsic analysis of observables in generic …
The nature of time in quantum mechanics is closely related to the use of a complex, rather than say real, Hilbert space. This becomes particularly clear when considering quantum field theory in time dependent backgrounds, such as in cosmology, when the notion of positive frequency ceases to be well defined. In spacetimes lacking time orientation, i.e without the possibility of defining an arrow of time, one is forced to abandon complex quantum mechanics. One also has to face this problem in quantum cosmology. I use this to argue that this suggests that, at a fundamental level, quantum mechanic…
We describe a nano-electromechnical system that exhibits the "retroactive" quantum jumps discovered by Mabuchi and Wiseman [Phys. Rev. Lett. 81, 4620 (1998)]. This system consists of a Cooper-pair box coupled to a nano-mechanical resonator, in which the latter is continuously monitored by a single-electron transistor or quantum point-contact. Further, we show that these kinds of jumps, and the jumps that emerge in a continuous quantum non-demolition measurement are one and the same phenomena. We also consider manipulating the jumps by applying feedback control to the Cooper-pair box.
Using the linear local induction approximation, we investigated the self-induced motion of a vortex line that corresponds to the motion of a particle in quantum mechanics. Concerning Kelvin waves, the effective Schrödinger equation, physical quantities operators, and the corresponding path-integral formula are obtained. The vortex line-particle mapping may help in understanding particle motion in quantum mechanics.
Equilibrium statistical mechanics rests on the assumption of ergodic dynamics of a system modulo the conservation laws of local observables: extremization of entropy immediately gives Gibbs' ensemble (GE) for energy conserving systems and a generalized version of it (GGE) when the number of local conserved quantities (LCQ) is more than one. Through the last decade, statistical mechanics has been extended to describe the late-time behaviour of periodically driven (Floquet) quantum matter starting from a generic state. The structure built on the fundamental assumptions of ergodicity and identifi…
The algebraic properties of a strict deformation quantization are analysed on the classical phase space $\bR^{2n}$. The corresponding quantization maps enable us to take the limit for $\hbar \to 0$ of a suitable sequence of algebraic vector states induced by $\hbar$-dependent eigenvectors of several quantum models, in which the sequence converges to a probability measure on $\bR^{2n}$, defining a classical algebraic state. The observables are here represented in terms of a Berezin quantization map which associates classical observables (functions on the phase space) to quantum observables (ele…
Emergent supersymmetry in a time-space inverted quantum mechanics
Universidade Federal do Paraná（巴拉那联邦大学）；Centro Interdisciplinar de Ciência, Tecnologia e Inovação (CICTI)（跨学科科学与技术创新中心）；Max-Planck Institute for the Physics of Complex Systems（马克斯·普朗克复杂系统物理研究所）
What defines an emergent quantum mechanics (EmQM)? Can new insight be advanced into the nature of quantum nonlocality by seeking new links between quantum and emergent phenomena as described by self-organization, complexity, or emergence theory? Could the development of a future EmQM lead to a unified, relational image of the cosmos? One key motivation for adopting the concept of emergence in relation to quantum theory concerns the persistent failure in standard physics to unify the two pillars in the foundations of physics: quantum theory and general relativity theory (GRT). The total contrad…
It has been argued that the existence of time crystals requires a spontaneous breakdown of the continuous time translation symmetry so to account for the unexpected non-stationary behavior of quantum observables in the ground state. Our point is that such effects do emerge from position ($\hat{q}_i$) and/or momentum ($\hat{p}_i$) noncommutativity, i.e., from $[\hat{q}_i,\,\hat{q}_j]\neq 0$ and/or $[\hat{p}_i,\,\hat{p}_j]\neq 0$ (for $i\neq j$). In such a context, a predictive analysis is carried out for the $2$-dim noncommutative quantum harmonic oscillator through a procedure supported by the…
The "problem of time" in present physics substantially consists in the fact that a straightforward quantization of the general relativistic evolution equation and constraints generates for the Universe wave function the Wheeler-De Witt equation, which describes a static Universe. Page and Wootters considered the fact that there exist states of a system composed by entangled subsystems that are stationary, but one can interpret the component subsystems as evolving: this leads them to suppose that the global state of the universe can be envisaged as one of this static entangled state, whereas th…
Can physical concepts and laws emerge in a neural network as it learns to predict the observation data of physical systems? As a benchmark and a proof-of-principle study of this possibility, here we show an introspective learning architecture that can automatically develop the concept of the quantum wave function and discover the Schrödinger equation from simulated experimental data of the potential-to-density mappings of a quantum particle. This introspective learning architecture contains a machine translator to perform the potential to density mapping, and a knowledge distiller auto-encoder…
There are various reasons to believe that quantum theory could be an emergent phenomenon. Trace Dynamics is an underlying classical dynamics of non-commuting matrices, from which quantum theory and classical mechanics have been shown to emerge, in the thermodynamic approximation. However, the time that is used to describe evolution in quantum theory is an external classical time, and is in turn expected to be an emergent feature - a relic of an underlying theory of quantum gravity. In this essay we borrow ideas from Trace Dynamics to show that classical time is a thermodynamic approximation to…
A general theory of dynamics is formulated with the aim of its application in emergent quantum mechanics. In such a framework it is argued that the fundamental dynamics of emergent quantum mechanics must be non-reversible.
The origin of the nonlocal nature of quantum mechanics is investigated in the context of Everett's formulation of quantum mechanics. EPR phenomenon can fully be explained without introducing any kind of decoherence.
The study of generic properties of quantum states has led to an abundance of insightful results. A meaningful set of states that can be efficiently prepared in experiments are ground states of gapped local Hamiltonians, which are well approximated by matrix product states. In this work, we introduce a picture of generic states within the trivial phase of matter with respect to their non-equilibrium and entropic properties: We do so by rigorously exploring non-translation-invariant matrix product states drawn from a local i.i.d. Haar-measure. We arrive at these results by exploiting techniques …
We obtain Schroedinger quantum mechanics from Perelman's functional and from the Ricci flow equations of a conformally flat Riemannian metric on a closed 2-dimensional configuration space. We explore links with the recently discussed "emergent quantum mechanics".
We report on an "anti-Gleason" phenomenon in classical mechanics: in contrast with the quantum case, the algebra of classical observables can carry a non-linear quasi-state, a monotone functional which is linear on all subspaces generated by Poisson-commutative functions. We present an example of such a quasi-state in the case when the phase space is the 2-sphere. This example lies in the intersection of two seemingly remote mathematical theories - symplectic topology and the theory of topological quasi-states. We use this quasi-state to estimate the error of the simultaneous measurement of no…
When an interaction quench by a factor of four is applied to an attractive Bose-Einstein condensate, a higher-order quantum bright soliton exhibiting robust oscillations is predicted in the semiclassical limit by the Gross-Pitaevskii equation. Combining matrix-product state simulations of the Bose-Hubbard Hamiltonian with analytical treatment via the Lieb-Liniger model and the eigenstate thermalization hypothesis, we show these oscillations are absent. Instead, one obtains a large stationary soliton core with a small thermal cloud, a smoking-gun signal for non-semiclassical behavior on macrosc…
In this paper, proceeding from the recently developed way of deriving the quantum-mechanical equations from the classical ones, the complete system of hydrodynamical equations, including the quantum Euler equation, is derived for a perfect fluid and an imperfect fluid with pairwise interaction between the particles. For the Bose-Einstein condensate of the latter one the Bogolyubov spectrum of elementary excitations is easily reproduced in the acoustic approximation.
We introduce functional degrees of freedom by a new gauge principle related to the phase of the wave functional. Thereby, quantum mechanical systems are seen as dissipatively embedded part of a nonlinear classical structure producing universal correlations. There are a fundamental length and an entropy/area parameter, besides standard couplings. For states that are sufficiently spread over configuration space, quantum field theory is recovered.
Elements of a "deeper level" explanation of the deBroglie-Bohm (dBB) version of quantum mechanics are presented. Our explanation is based on an analogy of quantum wave-particle duality with bouncing droplets in an oscillating medium, the latter being identified as the vacuum's zero-point field. A hydrodynamic analogy of a similar type has recently come under criticism by Richardson et al., because despite striking similarities at a phenomenological level the governing equations related to the force on the particle are evidently different for the hydrodynamic and the quantum descriptions, respe…
We consider the classical dynamics of bosonic and fermionic matrix variables in complex Hilbert space, defined by a trace action, assuming cyclic invariance under the trace and the presence of a global unitary invariance. With plausible and explicitly stated assumptions, including the existence of a large hierarchy of scale between the underlying dynamics and observed physics, we show that (1) the equilibrium statistical mechanics of this matrix dynamics, in the canonical ensemble, gives rise to an emergent quantum mechanics for many degrees of freedom, including the standard canonical commuta…
We map the dynamics of entanglement in random unitary circuits, with finite on-site Hilbert space dimension $q$, to an effective classical statistical mechanics, and develop general diagrammatic tools for calculations in random unitary circuits. We demonstrate explicitly the emergence of a `minimal membrane' governing entanglement growth, which in 1+1D is a directed random walk in spacetime (or a variant thereof). Using the replica trick to handle the logarithm in the definition of the $n$th Rényi entropy $S_n$, we map the calculation of the entanglement after a quench to a problem of interact…
Emergent Non-Biorthogonal Born Rule at Dynamical Quantum Phase Transitions
Asia Pacific Center for Theoretical Physics（亚太理论物理中心）；Beijing National Laboratory for Condensed Matter Physics and Institute of Physics, Chinese Academy of Sciences（北京凝聚态物理国家实验室和中国科学院物理研究所）；School of Physics and Astronomy, Lancaster University（兰开斯特大学物理与天文学院）；New Cornerstone Science Laboratory（新基石科学实验室）；Department of Physics, Xiamen University（厦门大学物理系）
A profound quest of statistical mechanics is the origin of irreversibility - the arrow of time. New stimulants have been provided, thanks to unprecedented degree of control reached in experiments with isolated quantum systems and rapid theoretical developments of manybody localization in disordered interacting systems. The proposal of (many-body) eigenstate thermalization (ET) for these systems reinforces the common belief that either interaction or extrinsic randomness is required for thermalization. Here, we unveil a quantum thermalization mechanism challenging this belief. We find that, pro…
In this paper we present 'Quantum Model Theory' (QMod), a theory we developed to model entities that entail the typical quantum effects of 'contextuality', 'superposition', 'interference', 'entanglement' and 'emergence'. The aim of QMod is to put forward a theoretical framework that is more general than standard quantum mechanics, in the sense that, for its complex version it only uses this quantum calculus locally, i.e. for each context corresponding to a measurement, and for its real version it does not need the property of 'linearity of the set of states' to model the quantum effect. In thi…
