The project concerns the interplay among quantum mechanics, statistical mechanics and thermodynamics, in isolated quantum systems. The underlying goal is to improve our understanding of the concept of thermal equilibrium in quantum systems. First, I investigated the role played by observables and measurements in the emergence of thermal behaviour. This led to a new notion of thermal equilibrium which is specific for a given observable, rather than for the whole state of the system. The equilibrium picture that emerges is a generalization of statistical mechanics in which we are not interested in the state of the system but only in the outcome of the measurement process. I investigated how this picture relates to one of the most promising approaches for the emergence of thermal behaviour in isolated quantum systems: the Eigenstate Thermalization Hypothesis. Then, I applied the results to study some equilibrium properties of many-body localised systems. Despite the localization phenomenon, which prevents thermalization of subsystems, I was able to show that we can still use the predictions of statistical mechanics to describe the equilibrium of some observables. Moreover, the intuition developed in the process led me to propose an experimentally accessible way to unravel the interacting nature of many-body localised systems. Second, I exploited the "Concentration of Measure" phenomenon to study the macroscopic properties of the basis states of Loop Quantum Gravity. These techniques were previously used to explain why the thermal behaviour in quantum systems is such an ubiquitous phenomenon, at the macroscopic scale. I focused on the local properties, their thermodynamic behaviour and interplay with the semiclassical limit. This was motivated by the necessity to understand, from a quantum gravity perspective, how and why a classical horizon exhibits thermal properties.
On the base of years of experience of working on the problem of the physical foundation of quantum mechanics the author offers principles of solving it. Under certain pressure of mathematical formalism there has raised a hypothesis of complexity of space and time by Minkovsky, being significant mainly for quantum objects. In this eight-dimensional space and time with six space and two time dimensions all the problems and peculiarities of quantum mechanical formalism disappear, the reasons of their appearance become clear, and there comes a clear and physically transparent picture of the founda…
The old cosmological-constant (CC) problem indicates an inconsistency of the usual formulation of semiclassical gravity. The usual formulation of semiclassical gravity also seems to be inconsistent with the conventional interpretation of quantum mechanics based on the discontinuous wave-function collapse. By reformulating semiclassical gravity in terms of Bohmian deterministic particle trajectories, the resulting semiclassical theory avoids both the old CC problem and the discontinuous collapse problem of the usual semiclassical theory. The relevance to the new CC problem and to particle creat…
We discuss foundation of quantum mechanics (interpretations, superposition, principle of complementarity, locality, hidden variables) and quantum information theory.
This paper proposes a basic theory on physical reality and a new foundation for quantum mechanics and classical mechanics. It presents a scenario not only to solve the problem of the arbitrariness on the operator ordering for the quantization procedure, but also to clarify how the classical-limit occurs. This paper is the first of the three papers into which the previous paper quant-ph/9906130 has been separated for readability.
We consider an alternative approach to the foundations of statistical mechanics, in which subjective randomness, ensemble-averaging or time-averaging are not required. Instead, the universe (i.e. the system together with a sufficiently large environment) is in a quantum pure state subject to a global constraint, and thermalisation results from entanglement between system and environment. We formulate and prove a "General Canonical Principle", which states that the system will be thermalised for almost all pure states of the universe, and provide rigorous quantitative bounds using Levy's Lemma.
Quantum computation teaches us that quantum mechanics exhibits exponential complexity. We argue that the standard scientific paradigm of "predict and verify" cannot be applied to testing quantum mechanics in this limit of high complexity. We describe how QM can be tested in this regime by extending the usual scientific paradigm to include {\it interactive experiments}.
The authors of the recent paper [1] boldly claim to discover a new fully quantum approach to foundation of statistical mechanics: "Our conceptually novel approach is free of mathematically ambiguous notions such as probability, ensemble, randomness, etc." The aim of this note is to show that this approach is neither specific for quantum systems nor really conceptually different from the standard textbook arguments supporting microcanonical or canonical ensembles in statistical mechanics.
Foundational investigations in quantum mechanics, both experimental and theoretical, gave birth to the field of quantum information science. Nevertheless, the foundations of quantum mechanics themselves remain hotly debated in the scientific community, and no consensus on essential questions has been reached. Here, we present the results of a poll carried out among 33 participants of a conference on the foundations of quantum mechanics. The participants completed a questionnaire containing 16 multiple-choice questions probing opinions on quantum-foundational issues. Participants included physi…
This is a collection of references (papers, books, preprints, book reviews, Ph. D. thesis, patents, web sites, etc.), sorted alphabetically and (some of them) classified by subject, on foundations of quantum mechanics and quantum information. Specifically, it covers hidden variables (``no-go'' theorems, experiments), interpretations of quantum mechanics, entanglement, quantum effects (quantum Zeno effect, quantum erasure, ``interaction-free'' measurements, quantum ``non-demolition'' measurements), quantum information (cryptography, cloning, dense coding, teleportation), and quantum computation…
We point out that a new mechanism for radiation should exist if the Bohm theory of quantum mechanics is taken seriously. By traversing a quantum potential, an electron will necessarily be accelerated and radiate. For an illustration, we show that in the double-slit experiment this radiation yields a characteristic spectrum and a distinct pattern on the screen that is complementary to the pattern of the electrons. Experimentally, either the existence or the nonexistence of such a radiation would have important implications for the foundations of quantum mechanics.
Reimann [Phys. Rev. Lett. 101, 190403 (2008)] claimed that generic isolated macroscopic quantum system will equilibrate under experimentally realistic conditions by proving a theorem. We here show that the proof is invalid for most many-body systems and is unable to demonstrate equilibration in realistic experiment.
The foundations of non-linear quantum mechanics are based on six postulates and five propositions. On a first quantised level, these approaches are built on non-linear differential operators, non-linear eigenvalue equations, and the notion of non-linear observables and non-linear states. The present theory predicts that the non-linear function solution of a non-linear partial differential equation for a free particle is correct and that the commutator of the position operator and the non-linear momentum operator does not commute. Moreover, the implicit wave function of linear quantum mechanics…
The pure state space of Quantum Mechanics is investigated as Hermitian Symmetric Kaehler manifold. The classical principles of Quantum Mechanics (Quantum Superposition Principle, Heisenberg Uncertainty Principle, Quantum Probability Principle) and Spectral Theory of observables are discussed in this non linear geometrical context.
Even though quantum mechanics has existed for almost 100 years, questions concerning the foundation and interpretation of the theory still remain. These issues have gathered more attention in recent years, but does this mean that physicists are more aware of foundational issues concerning quantum mechanics? A survey was sent out to 1234 physicists affiliated to 8 different universities. 149 responded to the questions, which both concerned foundational issues related to quantum mechanics, specifically, as well as questions concerning interpretations of physical theories in general. The answers …
The Weltanschauung emerging from quantum theory clashes profoundly with our classical concepts. Quantum characteristics like superposition, entanglement, wave-particle duality, nonlocality, contextuality are difficult to reconcile with our everyday intuition. In this article I survey some aspects of quantum foundations and discuss intriguing connections with the foundations of mathematics.
Bohmian trajectories have been used for various purposes, including the numerical simulation of the time-dependent Schroedinger equation and the visualization of time-dependent wave functions. We review the purpose they were invented for: to serve as the foundation of quantum mechanics, i.e., to explain quantum mechanics in terms of a theory that is free of paradoxes and allows an understanding that is as clear as that of classical mechanics. Indeed, they succeed in serving that purpose in the context of a theory known as Bohmian mechanics, to which this article is an introduction.
The unification of Quantum Mechanics and General Relativity remains the primary goal of Theoretical Physics, with string theory appearing as the only plausible unifying scheme. In the present work, in a search of the conceptual foundations of string theory, we analyze the relational logic developed by C. S. Peirce in the late nineteenth century. The Peircean logic has the mathematical structure of a category with the relation $R_{ij}$ among two individual terms $S_i$ and $S_j$, serving as an arrow (or morphism). We introduce a realization of the corresponding categorical algebra of composition…
A survey probing respondents' views on various foundational issues in quantum mechanics was recently created by Schlosshauer, Kofler, and Zeilinger [arXiv:1301.1069] and then given to 33 participants at a quantum foundations conference. Here we report the results of giving this same survey to the attendees at another recent quantum foundations conference. While it is rather difficult to conclude anything of scientific significance from the poll, the results do strongly suggest several interesting cultural facts -- for example, that there exist, within the broad field of "quantum foundations", …
The foundational ideas of quantum mechanics continue to give rise to counterintuitive theories and physical effects that are in conflict with a classical description of Nature. Experiments with light at the single photon level have historically been at the forefront of tests of fundamental quantum theory and new developments in photonics engineering continue to enable new experiments. Here we review recent photonic experiments to test two foundational themes in quantum mechanics: wave-particle duality, central to recent complementarity and delayed-choice experiments; and Bell nonlocality where…
For time-dependent systems the wavefunction depends explicitly on time and it is not a pure state of the Hamiltonian. We construct operators for which the above wavefunction is a pure state. The method is based on the introduction of conserved quantities $Q$ and the pure states are defined by ${\hat Q}ψ=qψ$. The conserved quantities are constructed using parametrised mechanics and the Noether theorem.
Symmetries are widely used in modeling quantum systems but they do not contribute in postulates of quantum mechanics. Here we argue that logical, mathematical, and observational evidence require that symmetry should be considered as a fundamental concept in the construction of physical systems. Based on this idea, we propose a series of postulates for describing quantum systems, and establish their relation and correspondence with axioms of standard quantum mechanics. Through some examples we show that this reformulation helps better understand some of ambiguities of standard description. None…
In-principle restrictions on the amount of information that can be gathered about a system have been proposed as a foundational principle in several recent reconstructions of the formalism of quantum mechanics. However, it seems unclear precisely why one should be thus restricted. We investigate the notion of paradoxical self-reference as a possible origin of such epistemic horizons by means of a fixed-point theorem in Cartesian closed categories due to F. W. Lawvere that illuminates and unifies the different perspectives on self-reference.
We present an axiomatization of non-relativistic Quantum Mechanics for a system with an arbitrary number of components. The interpretation of our system of axioms is realistic and objective. The EPR paradox and its relation with realism is discussed in this framework. It is shown that there is no contradiction between realism and recent experimental results.
Although it has been almost 100 years since the beginnings of quantum mechanics, the discussions about its interpretation still do not cease. Therefore, a survey of opinions regarding this matter is of particular interest. This poll was conducted following an idea and using the methodology of Schlosshauer et al. (arXiv:1301.1069 [quant-ph]), but among a slightly different group. It is supposed to give another snapshot of attitudes towards the interpretation of quantum mechanics and keep discourse about this topic alive.
As it is well known, classical mechanics consists of several basic features like determinism, reductionism, completeness of knowledge and mechanicism. In this article the basic assumptions are discussed which underlie those features. It is shown that these basic assumptions - though universally assumed up the beginnings of the XX century - are far from being obvious. Finally it is shown that - to a certain extent - there is nothing wrong in assuming these basic postulates. Rather, the error lies in the epistemological absolutization of the theory, which was considered as a mirroring of Nature.
We formulate statistical mechanics based on a pure quantum state, which we call a ``thermal pure quantum (TPQ) state''. A single TPQ state gives not only equilibrium values of mechanical variables, such as magnetization and correlation functions, but also those of genuine thermodynamic variables and thermodynamic functions, such as entropy and free energy. Among many possible TPQ states, we discuss the canonical TPQ state, the TPQ state whose temperature is specified. % We also propose there are other TPQ states. In the TPQ formulation of statistical mechanics, thermal fluctuations are complet…
In order to arrive at Bohmian mechanics from standard nonrelativistic quantum mechanics one need do almost nothing! One need only complete the usual quantum description in what is really the most obvious way: by simply including the positions of the particles of a quantum system as part of the state description of that system, allowing these positions to evolve in the most natural way. The entire quantum formalism, including the uncertainty principle and quantum randomness, emerges from an analysis of this evolution. This can be expressed succinctly---though in fact not succinctly enough---by …
Recently, Olavo has proposed several derivations of the Schrodinger equation from different sets of hypothesis ("axiomatizations") [Phys. Rev. A 61, 052109 (2000)]. One of them is based on the infinitesimal inverse Weyl transform of a classically evolved phase space density. We show however that the Schrodinger equation can only be obtained in that manner for linear or quadratic potential functions.
Boltzmann's ergodic hypothesis furnishes a possible explanation for the emergence of statistical mechanics in the framework of classical physics. In quantum mechanics, the Eigenstate Thermalization Hypothesis (ETH) is instead generally considered as a possible route to thermalization. This is because the notion of ergodicity itself is vague in the quantum world and it is often simply taken as a synonym for thermalization. Here we show, in an elementary way, that when quantum ergodicity is properly defined, it is, in fact, equivalent to ETH. In turn, ergodicity is equivalent to thermalization, …
Focusing on isolated macroscopic systems, described either in terms of a quantum mechanical or a classical model, our two key questions are: In how far does an initial ensemble (usually far from equilibrium and largely unknown in detail) evolve towards a stationary long-time behavior ("equilibration")? In how far is this steady state in agreement with the microcanonical ensemble as predicted by Statistical Mechanics ("thermalization")? In the first part of the paper, a recently developed quantum mechanical treatment of the problem is briefly summarized, putting particular emphasis on the reali…
Karl Popper and Paul Feyerabend have been among the most influential philosophers of science of the twentieth century. Extensive studies have been dedicated to the development of their controversial relationship, which saw Feyerabend turning from a student and supporter of Popper to one of his harshest critics. Yet, it is not as well known that the rift between Popper and Feyerabend generated mainly in the context of their studies on the foundation of quantum mechanics, which has been the main subject of their discussions for about two decades. This paper reconstructs in detail their diatribe …
This thesis is a contribution to the debate on the implications of quantum information theory for the foundations of quantum mechanics. In Part 1, the logical and conceptual status of various notions of information is assessed. It is emphasized that the everyday notion of information is to be firmly distinguished from the technical notions arising in information theory; however it is maintained that in both settings `information' functions as an abstract noun, hence does not refer to a particular or substance (the worth of this point is illustrated in application to quantum teleportation). The…
A thermal equilibrium state of a quantum many-body system can be represented by a typical pure state, which we call a thermal pure quantum (TPQ) state. We construct the canonical TPQ state, which corresponds to the canonical ensemble of the conventional statistical mechanics. Only a single realization of the TPQ state gives all variables of statistical-mechanical interest. We show that TPQ states corresponding to different ensembles give identical thermodynamic results, and they are related by simple analytic transformations. We have thus completed the TPQ formulation of statistical mechanics.…
In this paper we review Castagnino's contributions to the foundations of quantum mechanics. First, we recall his work on quantum decoherence in closed systems, and the proposal of a general framework for decoherence from which the phenomenon acquires a conceptually clear meaning. Then, we introduce his contribution to the hard field of the interpretation of quantum mechanics: the modal-Hamiltonian interpretation solves many of the interpretive problems of the theory, and manifests its physical relevance in its application to many traditional models of the practice of physics. In the third part…
The superposition principle forms the very backbone of quantum theory. The resulting linear structure of quantum theory is structurally so rigid that tampering with it may have serious, seemingly unphysical, consequences. This principle has been succesful at even the highest available accelerator energies. Is this aspect of quantum theory forever then? The present work is an attempt to understand the attitude of the founding fathers, particularly of Bohr and Dirac, towards this principle. The Heisenberg matrix mechanics on the one hand, and the Schrodinger wave mechanics on the other, are crit…
The nRules are empirical regularities that were discovered in macroscopic situations where the outcome is known. When they are projected theoretically into the microscopic domain they predict a novel ontology including the frequent collapse of an atomic wave function, thereby defining an nRule based foundation theory. Future experiments can potentially discriminate between this and other foundation theories of (non-relativistic) quantum mechanics. Important features of the nRules are: (1) they introduce probability through probability current rather than the Born rule, (2) they are valid indep…
Alain Aspect's three experiments on Bell's theorem, published in the early 1980s, were a turning point in the history of the research on the foundations of quantum mechanics not only because they corroborated entanglement as the distinctive quantum signature but also because these experiments brought wider recognition to this field of research and Aspect himself. These experiments may be considered the most direct precursors of the research on quantum information, which would blossom a decade later.
This paper provides theorems aimed at shedding light on issues in the foundations of quantum mechanics. These theorems can be used to propose new interpretations to the theory, or to better understand, evaluate and improve current interpretations. Some of these applications include: (1) A proof of the existence of pilot-wave theories that are fully equivalent to standard quantum mechanics in a path-wise sense. This equivalence is stronger than what is entailed from the more traditional requirements of equivariance, or good mixing properties, and is necessary to assure proper correlations acros…
A realistic axiomatic formulation of nonrelativistic quantum mechanics for a single microsystem with spin is presented, from which the most important theorems of the theory can be deduced. In comparison with previous formulations, the formal aspect has been improved by the use of certain mathematical theories, such as the theory of equipped spaces, and group theory. The standard formalism is naturally obtained from the latter, starting from a central primitive concept: the Galilei group.
This paper presents the thermal interpretation of quantum physics. The insight from Part I of this series that Born's rule has its limitations -- hence cannot be the foundation of quantum physics -- opens the way for an alternative interpretation -- the thermal interpretation of quantum physics. It gives new foundations that connect quantum physics (including quantum mechanics, statistical mechanics, quantum field theory and their applications) to experiment. The thermal interpretation resolves the problems of the foundations of quantum physics revealed in the critique from Part I of this seri…
The foundations of statistical mechanics, namely how equilibrium hypothesis emerges microscopically from quantum theory, is explored through investigating the environment-induced quantum decoherence processes. Based on the recent results on non-Markovian dynamics [Phys. Rev. Lett. 109, 170402 (2012)], we find that decoherence of quantum states manifests unexpected complexities. Indeed, an arbitrary given initial quantum state, under the influence of different reservoirs, can evolve into four different steady states: thermal, thermal-like, quantum memory and oscillating quantum memory states. T…
I present a reconstruction of general Hamiltonian action mechanics that eliminates all foundational problems of quantum mechanics. The key advance is the completion of Hamiltonian mechanics to the universal mechanics of particles based on action-waves, consistent with the inclusive validity of the principle of stationary action. It is found that irreducible indeterminism is intrinsic and universal at all scales of dynamics. The new action-wave equation is the complete description of single dynamical histories, dissolving the classical-quantum divide. The statistical theory of quantum mechanics…
'Tis said, to know others is to be learned, to know oneself, wise - I demonstrate that it could be more fundamental than knowing the rest of nature, by applying classical computational principles and engineering hindsight to derive and explain quantum entanglement, state space formalism and the statistical nature of quantum mechanics. I show that an entangled photon pair is literally no more than a 1-bit hologram, that the quantum state formalism is completely derivable from general considerations of representation of physical information, and that both the probabilistic aspects of quantum the…
We attempt to contribute some novel points of view to the "foundations of quantum mechanics", using mathematical tools from "quantum probability theory" (such as the theory of operator algebras). We first introduce an abstract algebraic framework for the formulation of mathematical models of physical systems that is general enough to encompass classical and quantum mechanical models. After a short discussion on the properties of classical systems (realism and determinism), we move on to the study of a general class of quantum-mechanical models of physical systems and explain what some of the k…
In this thesis, we have proposed some novel thought experiments involving foundations of quantum mechanics and quantum information theory, using quantum entanglement property. Concerning foundations of quantum mechanics, we have suggested some typical systems including two correlated particles which can distinguish between the two famous theories of quantum mechanics, i.e. the standard and Bohmian quantum mechanics, at the individual level of pair of particles. Meantime, the two theories present the same predictions at the ensemble level of particles. Regarding quantum information theory, two …
Chapter 3 of S. Lloyd's 1988 Ph.D. thesis, `Black Holes, Demons, and the Loss of Coherence: How complex systems get information and what they do with it,' supervisor Heinz Pagels. Reformulates statistical mechanics in terms of pure states and shows that (a) quantum statistics of typical pure states are very close to the mechanics of statistical mechanical ensembles; (b) if a system is in a typical state with energy E, then the reduced density matrix of a subsystem is very close to a thermal state. (A similar result was derived using Levy's lemma some years later by S. Popescu, A.J. Short, A.Wi…
Quasi-set theory provides us a mathematical background for dealing with collections of indistinguishable elementary particles. In this paper, we show how to obtain the usual statistics (Maxwell-Boltzmann, Bose-Einstein, and Fermi-Dirac) into the scope of quasi-set theory. We also show that, in order to derive Maxwell-Boltzmann statistics, it is not necessary to assume that the particles are distinguishable. In other words, Maxwell-Boltzmann statistics is possible even in an ensamble of indistinguishable particles, at least from the theoretical point of view. The main goal of this paper is to p…
We review a recent approach to the foundations of quantum mechanics inspired by quantum information theory. The approach is based on a general framework, which allows one to address a large class of physical theories which share basic information-theoretic features. We first illustrate two very primitive features, expressed by the axioms of causality and purity-preservation, which are satisfied by both classical and quantum theory. We then discuss the axiom of purification, which expresses a strong version of the Conservation of Information and captures the core of a vast number of protocols i…
Envariance -- entanglement assisted invariance -- is a recently discovered symmetry of composite quantum systems. We show that thermodynamic equilibrium states are fully characterized by their envariance. In particular, the microcanonical equilibrium of a system $\mathcal{S} $ with Hamiltonian $H_\mathcal{S}$ is a fully energetically degenerate quantum state envariant under every unitary transformation. The representation of the canonical equilibrium then follows from simply counting degenerate energy states. Our conceptually novel approach is free of mathematically ambiguous notions such as e…
We propose a discrete path integral formalism over graphs fundamental to quantum mechanics (QM) based on our interpretation of QM called Relational Blockworld (RBW). In our approach, the transition amplitude is not viewed as a sum over all field configurations, but is a mathematical machine for measuring the symmetry of the discrete differential operator and source vector of the discrete action. Therefore, we restrict the path integral to the row space of the discrete differential operator, which also contains the discrete source vector, in order to avoid singularities. In this fashion we obta…
We argue that Anton Zeilinger's "foundational conceptual principle" for quantum mechanics according to which an elementary system carries one bit of information is an idealistic principle, which should be replaced by a realistic principle of contextuality. Specific properties of quantum systems are a consequence of impossibility to speak about them without reference to the tools of their observation (identification) and, consequently, context in which these tools are applied. In particular, the assumption of non-locality is not required to explain quantum correlation. Correlated quantum events…
In this proceeding I review the main experimental results obtained at IENGF (Turin, Italy) by using a source of entangled photons realised superposing, by means of an optical condenser, type I PDC produced in two crystals. More in details, after having described how this source is built, I will report on a Bell inequalities test obtained with it. Then I describe a recent innovative double slit experiment realised with a similar scheme. Finally, I hint about future developments of this activity at IENGF and in particular about a quantum cryptographic scheme in d=4.
Based on the concept of ensemble, it is proved in the manuscript that the probability amplitude function can also been used to describe the classical statistical system. The motion equations of probability amplitude functions of classical statistical system are obtained, which are similar to that in quantum mechanics. It is also proved in the meantime that microsystems that obey quantum mechanics can also be described in the forms of classical statistical mechanics and deterministic classical mechanics. The quantum revised formula of classical interaction force and the revised Liouville's equa…
An intricate quantum statistical effect guides us to a deterministic, non-causal quantum universe with given fixed initial and final state density matrix. A concept is developed on how and where something like macroscopic physics can emerge. The concept does not allow to incorporate philosophically indispensable free will decisions. If the quantum world and its conjugate evolve independently one can replace both fixed final states by a matching common one. This allows for external manipulations done in the quantum world and its conjugate which do not otherwise alter the basic structure. In a b…
The broad debate on foundational issues in quantum mechanics, which took place at the famous 1957 Chapel Hill conference on \textit{The Role of Gravitation in Physics}, is here critically analyzed with an emphasis on Richard Feynman's contributions. One of the most debated questions at Chapel Hill was whether the gravitational field had to be quantized and its possible role in wave function collapse. Feynman's arguments in favor of the quantization of the gravitational field, based essentially on a series of gedanken experiments, are here discussed. Then the related problem of the wave functio…
The ZX-calculus is a graphical calculus for reasoning about quantum systems and processes. It is known to be universal for pure state qubit quantum mechanics, meaning any pure state, unitary operation and post-selected pure projective measurement can be expressed in the ZX-calculus. The calculus is also sound, i.e. any equality that can be derived graphically can also be derived using matrix mechanics. Here, we show that the ZX-calculus is complete for pure qubit stabilizer quantum mechanics, meaning any equality that can be derived using matrices can also be derived pictorially. The proof rel…
