Epistemological consequences of quantum nonlocality (entanglement) are discussed under the assumption of a universally valid Schrödinger equation in the absence of hidden variables. This leads inevitably to a {\it many-minds interpretation}. The recent foundation of quasi-classical neural states in the brain (based on environmental decoherence) permits in principle a formal description of the whole chain of measurement interactions, including the {\it behavior} of conscious observers, without introducing any intermediate classical concepts (for macroscopic "pointer states") or "observables" (for microscopic particle positions and the like) --- thus consistently formalizing Einstein's {\it ganzer langer Weg} from the observed to the observer in quantum mechanical terms.
This paper aims to invalidate the hypothesis that consciousness is necessary for the quantum measurement process. To achieve this target, I propose a considerable modification of the Schroedinger cat and the Dead-Alive Physicist thought experiments, called 'PIAR', short for Physicist Inside the Ambiguous Room. A specific strategy has enabled me to plan the experiment in such a way as to logically justify the inconsistency of the above hypothesis and to oblige its supporters to rely on an alternative interpretation of quantum mechanics in which the real-world phenomena exist independently of ou…
This paper elaborates on four previously proposed rules of engagement between conscious states and physiological states. A new rule is proposed that applies to a continuous model of conscious brain states that cannot precisely resolve eigenvalues. If two apparatus states are in superposition, and if their eigenvalues are so close together that they cannot be consciously resolved on this model, then it is shown that observation will not generally reduce the superposition to just one of its member eigenstates. In general, the observation of a quantum mechanical superposition results in another s…
We examine the role of a conscious observer in a typical quantum mechanical measurement. Four rules are given that govern stochastic choice and state reduction in several cases of continuous and intermittent observation. It is found that consciousness always accompanies a state reduction leading to observation, but its presence is not sufficient to 'cause' a reduction. The distinction is clarified and codified by the rules that are given below. This is the first of several papers that lead to an experimental test of the rules, and of the "parallel principle" that is described elsewhere. Key wo…
Preciously given rules allow conscious systems to be included in quantum mechanical systems. There rules are derived from the empirical experience of an observer who witnesses a quantum mechanical interaction leading to the capture of a single particle. In the present paper it is shown that purely classical changes experienced by an observer are consistent with these rules. Three different interactions are considered, two of which combine classical and quantum mechanical changes. The previously given rules support all of these cases. Key Words: brain states, conscious observer, detector, measu…
In a previous paper, the author proposed a quantum mechanical interaction that would insure that the evolution of subjective states would parallel the evolution of biological states, as required by von Neumann's theory of measurement. The particular model for this interaction suggested an experiment that the author has now performed wih negative results. A modified model is outlined in this paper that preserves the desirable features of the original model, and is consistent with the experimental results. This model will be more difficult to verify. However, some strategies are suggested.
If conscious observers are to be included in the quantum mechanical universe, we need to find the rules that engage observers with quantum mechanical systems. The author has proposed five rules that are discovered by insisting on empirical completeness; that is, by requiring the rules to draw empirical information from Schrodinger's solutions that is more complete than is currently possible with the (Born) probability interpretation. I discard Born's interpretation, introducing probability solely through probability current. These rules tell us something about brains. They require the existenc…
Contemporary quantum mechanical description of nature involves two processes. The first is a dynamical process governed by the equations of local quantum field theory. This process is local and deterministic, but it generates a structure that is not compatible with observed reality. A second process is therefore invoked. This second process somehow analyzes the structure generated by the first process into a collection of possible observable realities, and selects one of these as the actually appearing reality. This selection process is not well understood. It is necessarily nonlocal and, acco…
We propose the quantum mechanical description of complex systems should be performed using two types of causality relation: the ordering relation ($x\prec y$) and the subset relation ($A\subseteq B$). The structures with two ordering operations, called the causal sites, have been already proposed in context of quantum gravity (Christensen and Crane, 2005). We suggest they are also common to biological physics and may describe how the brain works. In the spirit of the Penrose ideas we identify the geometry of the space-time with universal field of consciousness. The latter has its evident count…
Several philosophical problems arising from the physics of consciousness, including identity, duplication, teleportation, simulation, self-location, and the Boltzmann Brain problem, hinge on one of the most deeply held but unnecessary convictions of physicalism: the assumption that brain states and their corresponding conscious states can in principle be copied. In this paper I will argue against this assumption by attempting to prove the Unique History Theorem, which states, essentially, that conscious correlations to underlying quantum mechanical measurement events must increase with time an…
The effect of rule (4) on a series or parallel sequence of quantum mechanical steps is to insure that a conscious observer does not skip a step. This rule effectively places the observer in continuous contact with the system. Key Words: brain states, continuous observation, conscious observer, measurement, probability current, state reduction, wave collapse.
In the present work, quantum theory is founded on the framework of consciousness, in contrast to earlier suggestions that consciousness might be understood starting from quantum theory. The notion of streams of consciousness, usually restricted to conscious beings, is extended to the notion of a Universal/Global stream of conscious flow of ordered events. The streams of conscious events which we experience constitute sub-streams of the Universal stream. Our postulated ontological character of consciousness also consists of an operator which acts on a state of potential consciousness to create …
In a previous paper we examined the role of a conscious observer in a typical quantum mechanical measurement. Four rules were given that were found to govern the stochastic choice and state reduction in several cases of continuous and intermittent observation. It was shown that consciousness always accompanies a state reduction leading to observation, but its presence is not sufficient to 'cause' a reduction. The distinction is clarified and codified by the rules that are repeated below. In this paper, these rules are successfully applied to two different versions of the Schrodinger cat experi…
Post-inflationary boundary conditions are essential to the existence of our highly structured universe, and these can only come about through quantum mechanical state reductions - i.e., through measurements. The choice is between: An 'objective' measurement that allows reduction to occur independent of conscious observers, and an 'observer' based measurement that ties reduction to the existence of a conscious observer. It is shown in this paper that that choice cannot be determined empirically; so how we finally understand state reduction will be decided by the way that reduction is used in a …
We address the relation between two apparently distinct problems: The quest for a deeper understanding of the nature of consciousness and the search for time and space as emergent structures in the quantum mechanical world. We also advance a toy-model proposal of emergence of time from a timeless unus mundus quantum-like space by using Aharonov's two state formalism of quantum mechanics. We further speculate on these issues within a quantum cognitive perspective with particular interest in two recent papers on this emerging field of science. One (Aerts et al) entails (as we argue) a panpsychis…
I contemplate the idea that the subjective world and quantum state reductions are one and the same. If true, this resolves with one stroke both the quantum mechanical measurement problem and the hard problem of consciousness.
I start from the fundamental principles of non-relativistic quantum mechanics, without probability, and interpret them using the notion of coexistence: a quantum state can be read, not uniquely, as a coexistence of other quantum states, which are pairwise orthogonal. In this formalism, I prove that a conscious observer is necessarily a physical object that can memorize local events by setting one of its parts in an exactly specified constant quantum state (hypotheses H1, H2 and H3). Then I define the probability of a future event as the proportion of initial observers, all identical, who will …
We present a description of finite dimensional quantum entanglement, based on a study of the space of all convex decompositions of a given density matrix. On this space we construct a system of real polynomial equations describing separable states. We further study this system using statistical mechanical methods. Finally, we apply our techniques to Werner states of two qubits and obtain a sufficient criterion for separability.
If the statement by Einstein, Podolsky and Rosen on incompleteness of Quantum-Mechanical description of nature is correct, then we can regard Quantum Mechanics as a Method of Indirect Computation. The problem is, whether the theory is incomplete or the nature itself does not allow complete description? And if the first option is correct, how is it possible to complete the Quantum-Mechanical description? Here we try to complement de-Broglie's idea on wave-pilot the stochastic gravitation gives origin to. We assume that de-Broglie's wave-pilots are gravitational stochastic ones, and we shall reg…
The motion of neutral particles with magnetic moments in an inhomogeneous magnetic field is described in a quantum mechanical framework. The validity of the semi-classical approximations which are generally used to describe these phenomena is discussed. Approximate expressions for the evolution operator are derived and compared to the exact calculations. Focusing and spin-flip phenomena are predicted. The reliability of Stern-Gerlach experiments to measure spin projections is assessed in this framework.
The biological hierarchy and the differences between living and non-living systems are considered from the standpoint of quantum mechanics. The hierarchical organization of biological systems requires hierarchical organization of quantum states. The construction of the hierarchical space of state vectors is presented. The application of similar structures to quantum information processing is considered.
When a conscious observer is part of a quantum mechanical system, rule (4) cuts off solutions to the Schrodinger equation. It is important to show that this interruption of the Hamiltonian dynamics does not effect the statistical predictions of the theory. The initial case considered is that of a two atom radioactive source. It is found that when the predictions of standard (Born rule) quantum theory are verified by using a particular experimental procedure, the result is the same as that predicted by quantum theory qualified by rule (4). This example is generalized, and the result is found to…
Quantum mechanics of photons is derived from the theory of representations of the Poincaré group developed by Wigner. This theory places helicity as the most fundamental property; angular momentum and polarization are secondary characteristics. The properties of the beams of light are shown to be fully determined by the quantum states of the photons. Polarization of light beams is explained as the freedom to chose an arbitrary combination of the helicity states. Quantum mechanics of photons enables one to give a precise meaning to the concept of wave-particle duality.
Complete Relational Description of Spin in a Quantum Background
Institute for Quantum Optics and Quantum Information (IQOQI) Vienna, Austrian Academy of Sciences（奥地利科学院维也纳量子光学与量子信息研究所）；University of Vienna, Faculty of Physics, Vienna Center for Quantum Science and Technology (VCQ)（维也纳大学物理学院维也纳量子科学与技术中心）
In this work an example of a cyclic engine based on a quantum-mechanical properties of the strongly non linear quantum oscillator described by the Poschl-Teller [PT] model is examined. Using the [PT] model as shown in our earlier works [1-4], a quantum-mechanical analog of Carnot cycle (i.e quantum heat engine) has been constructed through the changes of both, the width L of the well and its quantum state. This quantum heat engine has a cycle consisting of adiabatic and isothermal quantum processes. The efficiency of the quantum engine based on the Poschl-Teller-like potential is derived and i…
What Niels Bohr called the `epistemological lesson' of `complementarity' was the result of reasoning analogically from the classical conception of a mechanical state to a new quantum mechanical conception of an `object' in a mechanical state. Bohr proposed to redefine the `objectivity' essential for scientific description in terms of the epistemological demand for unambiguously communicable descriptions of observational results, a move which has profound consequences for how we can understand the concept of the quantum mechanical state and the nature of the `system' which is `in' this state. H…
In this paper, without any priori assumption about the post-measurement state of system, we will examine how this state is restricted by assuming each of these following assumptions. First, by using this reasonable assumption that two successive measurements should be describable as one measurement. Second, by assuming the impossibility of faster than light signaling, "No-signaling condition". However, only by using these assumptions it is not possible to obtain the usual projection postulate. Instead, by means of a simple lemma, we will show that the density operator of system after a measure…
Witnessing quantumness in mesoscopic objects is an important milestone for both quantum technologies and foundational reasons. Cavity optomechanics offers the ideal system to achieve this by combing high precision optical measurements with mechanical oscillators. However, mechanical quantumness can only be established if the behaviour is incompatible with any classical description of an oscillator. After explicitly considering classical and hybrid quantum-classical descriptions of an optomechanical system, we rule out squeezing of the optical field as such a witness by showing it is also predi…
The semiclassical theory of light-matter interactions describes the interaction between a classical electromagnetic field with a quantum mechanical two-level system.We show that the quantum mechanical two-level system can be modeled by a system of two coupled classical harmonic oscillators whose eigenstates are split in frequency according to the coupling strength and play the roles of the two levels of the quantum mechanical two-level system. The effect of the light field on the mechanical system is modeled as a modulation of the spring constants of the individual oscillators. Using this full…
It has been accepted that the polarization of the photon in vector beams is entangled with its momentum. Here a quantum description is advanced for the polarization that shows entanglement with the momentum. This is done by showing that the Jones vector at each value of the momentum plays the role of the polarization wavefunction in the sense that the Pauli matrices represent the Cartesian components of the polarization in the local reference system with respect to which the Jones vector is defined. The unit vector that the constraint of transversality condition requires to specify the local r…
Quantum measurements of physical quantities are usually described as ideal measurements. However, only a few measurements fulfil the conditions of ideal measurements. The aim of the present work is to describe real position measurements with detectors that are able to detect single particles. For this purpose, a detector model has been developed that can describe the time dependence of interactions between nonrelativistic particles and a detector. At the beginning of a position measurement, the detector behaves as a target consisting of a large number of quantum mechanical systems. The inciden…
The analysis of twisted (vortex) paraxial photons and electrons is fulfilled in the framework of relativistic quantum mechanics. The use of the Foldy-Wouthuysen representation radically simplifies a description of relativistic electrons and clarifies fundamental properties of twisted particles. It is demonstrated that the twisted photon defined by the Laguerre-Gauss wave function is luminal. Its apparent subluminality takes place because the photon energy is contributed by the hidden transversal motion while the average transversal momentum vanishes. Nevertheless, the Laguerre-Gauss photon can…
Time-dependent nonequilibrium Green's functions (TDNEGF) are shown to provide a flexible, effective tool for the description of quantum mechanical single particle scattering on a spatially localized, time-dependent potential. Focusing on numerical methods, arbitrary space and time dependence of the potential can be treated, provided it is zero before an initial time instant. In this case, appropriate version of the Dyson and Keldysh equations lead to a transparent description with clear physical interpretation. The interaction of a short laser pulse and an electron propagating initially in fre…
In loving memory of Asher Peres, we discuss a most important and influential paper written in 1935 by his thesis supervisor and mentor Nathan Rosen, together with Albert Einstein and Boris Podolsky. In that paper, the trio known as EPR questioned the completeness of quantum mechanics. The authors argued that the then-new theory should not be considered final because they believed it incapable of describing physical reality. The epic battle between Einstein and Bohr intensified following the latter's response later the same year. Three decades elapsed before John S. Bell gave a devastating proo…
Trapped ions are among the leading candidates for quantum computing technologies. Interfacing ion qubits in separate traps and interfacing ion qubits with superconducting qubits are two of the many challenges to scale up quantum computers. One approach to overcome both problems is to use a conducting wire to mediate the Coulomb interaction between ions in different traps, or between ions and superconducting qubits. To this end, a trapped charged particle inducing charge on a conductor has long been modeled as a system of equivalent lumped element electronic components. Careful consideration re…
In this paper we present a solution of the Einstein's boxes paradox by modern Quantum Mechanics in which a notion of density matrix is equivalent to a notion of a quantum state of a system. We use a secondary quantization formalism in the attempt to make a description particularly clear. The aim of this paper is to provide pedagogical help to the students of quantum mechanics.
Quantum dynamics can be regarded as a generalization of classical finite-state dynamics. This is a familiar viewpoint for workers in quantum computation, which encompasses classical computation as a special case. Here this viewpoint is extended to mechanics, where classical dynamics has traditionally been viewed as a macroscopic approximation of quantum behavior, not as a special case. When a classical dynamics is recast as a special case of quantum dynamics, the quantum description can be interpreted classically. For example, sometimes extra information is added to the classical state in orde…
In this article we present a detailed description of an electron in a uniform magnetic field evolving under the Schrödinger equation using ladder operators. Based on this analysis, we describe the same physical system using the Dirac equation, known from relativistic quantum mechanics. The main differences between these two quantum mechanical approaches are discussed and we observe specifically how the relativistic phenomena modify the description of this particular quantum system.
We investigate the thermodynamic consistency of the master equation description of heat transport through an optomechanical system attached to two heat baths, one optical and one mechanical. We employ three different master equations to describe this scenario: (i) The standard master equation used in optomechanics, where each bath acts only on the resonator that it is physically connected to; (ii) the so-called dressed-state master equation, where the mechanical bath acts on the global system; and (iii) what we call the global master equation, where both baths are treated non-locally and affec…
Phase space dynamics in classical mechanics is described by transport along trajectories. Anharmonic quantum mechanical systems do not allow for a trajectory-based description of their phase space dynamics. This invalidates some approaches to quantum phase space studies. We first demonstrate the absenceof trajectories in general terms. We then give an explicit proof for all quantum phase space distributions with negative values: we show that the generation of coherences in anharmonic quantum mechanical systems is responsible for the occurrence of singularities in their phase space velocity fie…
Recent advances in the development of modern quantum technologies have opened the possibility of studying the interplay between spontaneous parametric down-conversion and optomechanics, two of the most fundamental nonlinear optical processes. Apart from practical reasons, such scenario is very interesting from a fundamental point of view, because it allows exploring the optomechanical interaction in the presence of a strongly quantum-correlated field, the spontaneously down-converted mode. In this work we analyze such problem from two approximate but valuable perspectives: the classical limit …
The elements of the quantum mechanical diffusion matrix, leading to a Gibbs equilibrium state for a set of $N$ coupled quantum harmonic oscillators are derived within Lindblad's axiomatic approach. Consequences of the fundamental constraints on the quantum friction coefficients are discussed. We derive the equations of motion for the expectation values and variances, and we solve them analytically. We apply our results to the description of the charge and mass asymmetry coordinates in heavy-ion collisions, and we investigate the effect of dissipation on tunneling in sub-barrier processes.
In this paper, we study the distributions and the affine distributions of the quantum mechanical system. Also, we discuss the controllability of the quantum mechanical system with the related question concerning the minimum time needed to steer a quantum system from a unitary evolution $U(0)=I$ of the unitary propagator to a desired unitary propagator $U_f$. Furthermore, the paper introduces a description of a $\mathfrak{k} \oplus \mathfrak{p}$ sub-Finsler manifold with its geodesics, which equivalents to the problem of driving the quantum mechanical system from an arbitrary initial state $U(0…
For a particle in a box, the operator $- i \partial_x$ is not Hermitean. We provide an alternative construction of a momentum operator $p = p_R + i p_I$, which has a Hermitean component $p_R$ that can be extended to a self-adjoint operator, as well as an anti-Hermitean component $i p_I$. This leads to a description of momentum measurements performed on a particle that is strictly limited to the interior of a box.
