Uncertainty Principle Research Articles

Recommending Probabilistic Approaches for Hypothesis Evaluation: A Gainful Extension of the Certainty Uncertainty Principle for the Social Sciences

Recommending Probabilistic Approaches for Hypothesis Evaluation: A Gainful Extension of the Certainty Uncertainty Principle for the Social Sciences

Introducing wave-particle duality with low-cost quantitative experiments on light diffraction

We present a quantitative optical low-cost experiment aimed at introducing students to wave-particle duality from a phenomenological point of view. The experiment, focused on light diffraction, clearly shows the intermediate crossover regime which characterize the transition from geometric optics (in which light behaves like a stream of particles) to the Fraunhofer diffraction regime (where the wave aspects are most evident). It can also be considered for introducing students to the uncertainty relations through diffraction of light waves. The experiments do not require expensive materials or specific laboratory instruments and employ the sensors and camera of common mobile devices. The experiments were tested with master students in mathematics and physics, who aim at becoming high school teachers.

Measuring the roles of variation and phonological density into the development of branching CCV onsets in Brazilian Portuguese

This study focuses on the acquisition of CCV syllables (Consonant1+Consonant2+Vowel) in Brazilian Portuguese. Our aim is to cast light on the roles of linguistic variation and phonological density into the phonotactic development. We used adult and child directed speech corpora to quantify the optional process of CCV→CV reduction in unstressed contexts in the input, as well as the frequency, segmental pattern, and phonological density of CCV syllables. Based in their distributional properties, we argue that CCV acquisition in BP goes through a moment of incorrect structural and segmental contrast neutralization, modelled by the Tolerance Principle (Yang 2006). The neutralization is caused by an overgeneralization of CCV variation, combined with CCV-CV low density; and an overgeneralization of the C/ɾ/V frequent segmental pattern, combined with the low density of C/ɾ/V-C/l/V but high density and equal frequency of /ɾ/V-/l/V.Data from a mispronunciation detection task confirms that the phonological density influences the development: children who do not articulate CCV syllables detect more CCV→CV stimuli when there are phonological neighbors (/pɾato/→[ˈpa.tʊ], but not /pɾeto/→*[ˈpe.tʊ]) and high phonological density ([l]V↔[ɾ]V are detected, but not C[l]V↔C[ɾ]V, with the lowest rates of detection in the C/l/V→C[ɾ]V direction).

Quantum and AI-based uncertainties for impact-relation map of multidimensional NFT investment decisions

The purpose of this study is to identify the most essential determinants of NFT investments with a novel artificial intelligence based fuzzy decision-making model. First, the expert choices are prioritized with artificial intelligence methodology. Secondly, the criteria for multidimensional NFT investment decisions are weighted with Quantum picture fuzzy rough sets based DEMATEL. The findings denote that market trends and expected quality have the greatest weight. It is understood that customer satisfaction plays the most crucial role to increase the effectiveness of NFT investments.

Thermodynamic cost for precision of general counting observables.

We analytically derive universal bounds that describe the tradeoff between thermodynamic cost and precision in a sequence of events related to some internal changes of an otherwise hidden physical system. The precision is quantified by the fluctuations in either the number of events counted over time or the waiting times between successive events. Our results are valid for the same broad class of nonequilibrium driven systems considered by the thermodynamic uncertainty relation, but they extend to both time-symmetric and asymmetric observables. We show how optimal precision saturating the bounds can be achieved. For waiting-time fluctuations of asymmetric observables, a phase transition in the optimal configuration arises, where higher precision can be achieved by combining several signals.

Duality in spontaneous broken time translation symmetry: Sisyphus dynamics and the Liénard equation

In this paper, we establish a connection between Sisyphus dynamics and the Liénard-II equation through branched Hamiltonians. Sisyphus dynamics stem from a higher-order Lagrangian. Surprisingly, when expressed in terms of velocity, the Sisyphus dynamical equations align closely with the Liénard-II equation. Sisyphus dynamics introduces velocity-dependent “mass functions”, a departure from conventional position-dependent mass, potentially linked to cosmological time crystals. Additionally, we demonstrate that spontaneously broken time translational symmetry results in a deformed symplectic structure, resembling the classical counterpart of the Generalized Uncertainty Principle (GUP).

Two applications of stochastic thermodynamics to hydrodynamics

Recently, the theoretical framework of stochastic thermodynamics has been revealed to be useful for macroscopic systems. However, despite its conceptual and practical importance, the connection to hydrodynamics has yet to be explored. In this Letter, we reformulate the thermodynamics of compressible and incompressible Newtonian fluids so that it becomes comparable to stochastic thermodynamics and unveil their connections; we obtain the housekeeping–excess decomposition of the entropy production rate (EPR) for hydrodynamic systems and find a lower bound on EPR given by relative fluctuation similar to the thermodynamic uncertainty relation. These results not only prove the universality of stochastic thermodynamics but also suggest the potential extensibility of the thermodynamic theory of hydrodynamic systems. Published by the American Physical Society 2024

Quantum gravity effects on the tachyon inflation from thermodynamic perspective

By considering the Friedmann equations emerging from the entropy-area law of black hole thermodynamics in the context of the generalized uncertainty principle, we study tachyon inflation in the early universe. The presence of a minimal length modifies the Friedmann equations and hence the slow-roll and perturbation parameters in the tachyon model. These modifications, though small, affect the viability of the tachyon inflation in confrontation with observational data. We compare the numerical results of the model with Planck2018 TT, TE, EE +lowE+lensing+BAO+BK14(18) data and Planck2018 TT, TE,EE +lowE+lensing+BK14(18) +BAO+LIGO & Virgo2016 data at 68% and 95% CL. We show that while the tachyon inflation with power-law, inverse power-law and inverse exponential potentials is not observationally viable in comparison with the 1σ and 2σ confidence levels of the new joint data, in the presence of the minimal length the model becomes observationally viable.

Finite-Time Dynamics of an Entanglement Engine: Current, Fluctuations and Kinetic Uncertainty Relations.

Entanglement engines are autonomous quantum thermal machines designed to generate entanglement from the presence of a particle current flowing through the device. In this work, we investigate the functioning of a two-qubit entanglement engine beyond the steady-state regime. Within a master equation approach, we derive the time-dependent state, the particle current, as well as the associated current correlation functions. Our findings establish a direct connection between coherence and internal current, elucidating the existence of a critical current that serves as an indicator for entanglement in the steady state. We then apply our results to investigate kinetic uncertainty relations (KURs) at finite times. We demonstrate that there is more than one possible definition for KURs at finite times. Although the two definitions agree in the steady-state regime, they lead to different parameter ranges for violating KUR at finite times.

The entropic uncertainty preservation in non-Markovian environment via classical driving fields

Uncertainty relations in terms of entropies were initially proposed to deal with conceptual shortcomings in the original formulation of the uncertainty principle and, hence, play an important role in quantum foundations. In quantum information theory, the preferred mathematical quantity to express the entropic uncertainty relation is the Shannon’s entropy. In this work, we investigate the effect of a classical driving field on entropic uncertainty lower bound (EULB). In this regard, we consider a particle as the quantum memory correlated with a measured particle, where during the interaction with the environment, the quantum memory is driven by the external classical field. Our result reveals that in the presence of the classical driving fields, the EULB is reduced and consequently, the measurement accuracy is increased.

Hybrid quantum-classical systems: Quasi-free Markovian dynamics

In the case of a quantum-classical hybrid system with a finite number of degrees of freedom, the problem of characterizing the most general dynamical semigroup is solved, under the restriction of being quasi-free. This is a generalization of a Gaussian dynamics, and it is defined by the property of sending (hybrid) Weyl operators into Weyl operators in the Heisenberg description. The result is a quantum generalization of the Lévy–Khintchine formula; Gaussian and jump contributions are included. As a byproduct, the most general quasi-free quantum-dynamical semigroup is obtained; on the classical side the Liouville equation and the Kolmogorov–Fokker–Planck equation are included. As a classical subsystem can be observed, in principle, without perturbing it, information can be extracted from the quantum system, even in continuous time; indeed, the whole construction is related to the theory of quantum measurements in continuous time. While the dynamics is formulated to give the hybrid state at a generic time [Formula: see text], we show how to extract multi-time probabilities and how to connect them to the quantum notions of positive operator-valued measure and instrument. The structure of the generator of the dynamical semigroup is analyzed, in order to understand how to go on to non-quasi-free cases and to understand the possible classical-quantum interactions; in particular, all the interaction terms which allow to extract information from the quantum system necessarily vanish if no dissipation is present in the dynamics of the quantum component. A concrete example is given, showing how a classical component can input noise into a quantum one and how the classical system can extract information on the behavior of the quantum one.

Signal-to-noise and spatial resolution in in-line imaging. 1. Basic theory, numerical simulations and planar experimental images.

Signal-to-noise ratio and spatial resolution are quantitatively analysed in the context of in-line (propagation based) X-ray phase-contrast imaging. It is known that free-space propagation of a coherent X-ray beam from the imaged object to the detector plane, followed by phase retrieval in accordance with Paganin's method, can increase the signal-to-noise in the resultant images without deteriorating the spatial resolution. This results in violation of the noise-resolution uncertainty principle and demonstrates `unreasonable' effectiveness of the method. On the other hand, when the process of free-space propagation is performed in software, using the detected intensity distribution in the object plane, it cannot reproduce the same effectiveness, due to the amplification of photon shot noise. Here, it is shown that the performance of Paganin's method is determined by just two dimensionless parameters: the Fresnel number and the ratio of the real decrement to the imaginary part of the refractive index of the imaged object. The relevant theoretical analysis is performed first, followed by computer simulations and then by a brief test using experimental images collected at a synchrotron beamline. More extensive experimental tests will be presented in the second part of this paper.

Quantum coherence from Kirkwood–Dirac nonclassicality, some bounds, and operational interpretation

Just a few years after the inception of quantum mechanics, there has been a research program using the nonclassical values of some quasiprobability distributions to delineate the nonclassical aspects of quantum phenomena. In particular, in Kirkwood–Dirac (KD) quasiprobability distribution, the distinctive quantum mechanical feature of noncommutativity which underlies many nonclassical phenomena, manifests in the nonreal values and/or the negative values of the real part. Here, we develop a faithful quantifier of quantum coherence based on the KD nonclassicality which captures simultaneously the nonreality and the negativity of the KD quasiprobability. The KD-nonclassicality coherence thus defined, is upper bounded by the uncertainty of the outcomes of measurement described by a rank-1 orthogonal projection-valued measure (PVM) corresponding to the incoherent orthonormal basis which is quantified by the Tsallis 12 -entropy. Moreover, they are identical for pure states so that the KD-nonclassicality coherence for pure state admits a simple closed expression in terms of measurement probabilities. We then use the Maassen–Uffink uncertainty relation for min-entropy and max-entropy to obtain a lower bound for the KD-nonclassicality coherence of a pure state in terms of optimal guessing probability in measurement described by a PVM noncommuting with the incoherent orthonormal basis. We also derive a trade-off relation for the KD-nonclassicality coherences of a pure state relative to a pair of noncommuting orthonormal bases with a state-independent lower bound. Finally, we sketch a variational scheme for a direct estimation of the KD-nonclassicality coherence based on weak value measurement and thereby discuss its relation with quantum contextuality.

‘The ‘Vector-Model’ wavefunction: spatial description and wavepacket formation of quantum-mechanical angular momenta’

We introduce the concept of an asymptotic spatial angular-momentum wavefunction, Xmjφ,θ,χ=eimφδθ−θm eij+12χ, which treats j in the jm state as a three-dimensional entity; φ, θ, χ are the Euler angles, and θm is the Vector-Model polar angle, given by cosθm=m/j. A wealth of geometric information about j can be deduced from the eigenvalues and spatial transformation properties of the Xmjφ,θ,χ. Specifically, the Xmjφ,θ,χ wavefunction gives a computationally simple description of the sizes of the particle and orbital-angular-momentum wavepackets (constructed from Gaussian distributions in j and m ), given by effective wavepacket angular uncertainty relations for ΔmΔφ, ΔjΔχ, and ΔφΔθ. The Xmjφ,θ,χ also predicts the position of the particle-wavepacket angular motion in the orbital plane, so that the particle-wavepacket rotation can be experimentally probed through continuous and non-destructive j -rotation measurements. Finally, we use the Xmj(φ,θ,χ) to determine geometrically well-known asymptotic expressions for Clebsch–Gordan coefficients, Wigner d-functions, the gyromagnetic ratio of elementary particles, g=2, and the m -state-correlation matrix elements. Interestingly, for low j, even down to j=1/2, these expressions are either exact (the last two) or excellent approximations (the first two), showing that the Xmj(φ,θ,χ) give a useful spatial description of quantum-mechanical angular momentum, and provide a smooth connection with classical angular momentum.

Understanding quantum mechanics

Quantum mechanics presently has many unanswered questions, paradoxes, and even outright logical contradictions. To make progress in understanding quantum mechanics, we begin by proposing that relativity be set aside in favor of an absolute aetherial theory. Once that step is taken, we can understand quantum collapse as a description of real wave-packets collapsing in a faster-than-light way. By assuming that a partially observable reality exists, we can then extend our analysis of wave-packets into the subquantum, and the Heisenberg uncertainty principle then follows from the Fourier uncertainty principle coupled with the de Broglie relation. Further progress in understanding quantum mechanics is possible by modifying the de Broglie and Planck relations. Those modifications lead to matter-waves moving at the speed of light rather than superluminally as presently theorized, and they allow the results of matter-wave two-slit experiments to be understood from any reference frame. A modified time-dependent Schrödinger Equation results from our modifications, but the spatial time-independent Schrödinger equation is retained.

Evaluating extractable work of quantum batteries via entropic uncertainty relations.

In this study, we investigate the effectiveness of entropic uncertainty relations (EURs) in discerning the energy variation in quantum batteries (QBs) modelled by battery-charger field in the presence of bosonic and fermionic reservoirs. Our results suggest that the extractable works (exergy and ergotropy) have versatile characteristics in different scenarios, resulting in a complex relationship between tightness and extractable work. It is worth noting that the tightness of the lower bound of entropic uncertainty can be a good indicator for energy conversion efficiency in charging QBs. Furthermore, we disclose how the EUR including uncertainty and lower bound contributes to energy conversion efficiency in the QB system. It is believed that these findings will be beneficial for better understanding the role of quantum uncertainty in evaluating quantum battery performance.

Autoethnography, Storytelling and Lego® Serious Play®: Embracing the Subjectivity of Practice to Engage Students Within Academic Librarianship

AbstractIn this article Alan Wheeler advocates for academic librarians to employ the principles of autoethnography and storytelling within their practice, as a tactic for student engagement. As a librarian and researcher operating within Higher Education (HE), Alan has always illustrated his practice with personal accounts of how to operate effectively as a student. Here, he proposes that librarians in academia embrace the autoethnographic principles of vulnerability, uncertainty and subjectivity to explore their position within HE, but also as a teaching tool.

New models of d-dimensional black holes without inner horizon and with an integrable singularity

Theoretically, it has been proposed that objects traveling radially along regular black holes (RBHs) would not be destroyed because of finite tidal forces and the absence of a singularity. However, the matter source allows the creation of an inner horizon linked to an unstable de Sitter core due to mass inflation instability. This inner horizon also gives rise to the appearance of a remnant, inhibiting complete evaporation. We introduce here a d-dimensional black hole model with Localized Sources of Matter (LSM), characterized by the absence of an inner horizon and featuring a central integrable singularity instead of an unstable de Sitter core. In our model, any object tracing a radial and timelike world-line would not be crushed by the singularity. This is attributed to finite tidal forces, the extendability of radial geodesics, and the weak nature of the singularity. Our LSM model enables the potential complete evaporation down to r h = 0 without forming a remnant. In higher dimensions, complete evaporation occurs through a phase transition, which could occur at Planck scales and be speculatively driven by the Generalized Uncertainty Principle (GUP). Unlike RBHs, our model satisfies the energy conditions. We demonstrate a linear correction to the conventional area law of entropy, distinct from the RBH's correction. Additionally, we investigate the stability of the solutions through the speed of sound.

Spin-charged point particle in a non-Abelian external field with the generalized uncertainty relation

The dynamics of a particle carrying a non-Abelian charge is studied in the presence of a minimal length. By choosing an appropriate non-Abelian gauge field, the system identifies with the Hamiltonian of the Jaynes-Cummings model whose solutions can be determined algebraically. The model has an underlying graded Lie algebra symmetry reminiscent of supersymmetric quantum mechanics. We calculate the energy levels and associated eigenstates using conservation of the number of excitations of the system. Then, we present the effect of the minimal length on the dynamics of the system and we are particularly interested in two particular cases, that of Rabi oscillations and that of the collapse-revival of the wave function. The results show that the higher the deformation parameter, the faster the oscillatory behavior of the atomic inversion.

On the uniqueness of variable coefficient Schrödinger equations

In this paper, we prove unique continuation properties for linear variable coefficient Schrödinger equations with bounded real potentials. Under certain smallness conditions on the leading coefficients, we prove that solutions decaying faster than any cubic exponential rate at two different times must be identically zero. Assuming a transversally anisotropic type condition, we recover the sharp Gaussian (quadratic exponential) rate in the series of works by Escauriaza–Kenig–Ponce–Vega [On uniqueness properties of solutions of Schrödinger equations, Comm. Partial Differential Equations 31(10–12) (2006) 1811–1823; Hardy’s uncertainty principle, convexity and Schrödinger evolutions, J. Eur. Math. Soc. (JEMS) 10(4) (2008) 883–907; The sharp Hardy uncertainty principle for Schrödinger evolutions, Duke Math. J. 155(1) (2010) 163–187].