Search Results (50)

This paper identifies theoretical vulnerabilities in quantum integrity verification by demonstrating that Bell inequality (BI) violations, central to the detection of quantum entanglement, can align with predictions from hidden variable theories (HVTs) under specific measurement configurations. By invoking a Heisenberg-inspired measurement resolution constraint and finite-resolution positive operator-valued measures (POVMs), we identify “convergence vicinities” where the statistical outputs of quantum and classical models become operationally indistinguishable. These results do not challenge Bell’s theorem itself; rather, they expose a vulnerability in quantum integrity frameworks that treat observed Bell violations as definitive, experiment-level evidence of nonclassical entanglement correlations. We support our theoretical analysis with simulations and experimental results from IBM quantum hardware. Our findings call for more robust quantum-verification frameworks, with direct implications for the security of quantum computing, quantum-network architectures, and device-independent cryptographic protocols (e.g., device-independent quantum key distribution (DIQKD)). Full article

Starting from the realization that the theory of quantum gravity (QG) cannot be deterministic due to its intrinsic quantum nature, the requirement is posed that QG should fulfill a suitable Heisenberg Generalized Uncertainty Principle (GUP) to be expressed as a local relationship determined from first principles and expressed in covariant 4-tensor form. We prove that such a principle places also a physical realizability condition denoted as “quantum covariance criterion”, which provides a possible selection rule for physically-admissible spacetimes. Such a requirement is not met by most of current QG theories (e.g., string theory, Geometrodynamics, loop quantum gravity, GUP and minimum-length-theories), which are based on the so-called multiverse representation of space-time in which the variational tensor field coincides with the spacetime metric tensor. However, an alternative is provided by theories characterized by a universe representation, namely in which the variational tensor field differs from the unique “background” metric tensor. It is shown that the latter theories satisfy the said Heisenberg GUP and also fulfill the aforementioned physical realizability condition. Full article

A refinement of the Heisenberg uncertainty principle has been proved by Luo using Wigner–Yanase information. Generalizations of this result have been proved by Yanagi and by other scholars for regular Quantum Fisher Information in the matrix case. In this paper, we prove these results in the von Neumann algebra setting. Full article

The Schrödinger equation, Heisenberg’s uncertainty principles, and the Boltzmann constant represent transformative scientific achievements, the impacts of which extend far beyond their original domain of physics. As we celebrate the centenary of these fundamental quantum mechanical formulations, this review examines their evolution from abstract mathematical concepts to essential tools in contemporary drug discovery and development. While these principles describe the behavior of subatomic particles and molecules at the quantum level, they have profound implications for understanding biological processes such as enzyme catalysis, receptor–ligand interactions, and drug–target binding. Quantum tunneling, a direct consequence of these principles, explains how some reactions occur despite classical energy barriers, enabling novel therapeutic approaches for previously untreatable diseases. This understanding of quantum mechanics from 100 years ago is now creating innovative approaches to drug discovery with diverse prospects, as explored in this review. However, the fact that the quantum phenomenon can be described but never understood places us in a conundrum with both philosophical and ethical implications; a prospective and inconclusive discussion of these aspects is added to ensure the incompleteness of the paradigm remains unshifted. Full article

The linear canonical Fourier transform is one of the most celebrated time-frequency tools for analyzing non-transient signals. In this paper, we will introduce and study the deformed Gabor transform associated with the linear canonical Dunkl transform (LCDT). Then, we will formulate several weighted uncertainty principles for the resulting integral transform, called the linear canonical Dunkl-Gabor transform (LCDGT). More precisely, we will prove some variations in Heisenberg’s uncertainty inequality. Then, we will show an analog of Pitt’s inequality for the LCDGT and formulate a Beckner-type uncertainty inequality via two approaches. Finally, we will derive a Benedicks-type uncertainty principle for the LCDGT, which shows the impossibility of a non-trivial function and its LCDGT to both be supported on sets of finite measure. As a side result, we will prove local uncertainty principles for the LCDGT. Full article

This paper presents a generalized fractional Stockwell transform (GFST), extending the classical Stockwell transform and fractional Stockwell transform, which are widely used tools in time–frequency analysis. The GFST on $L^2(\mathbb{R},\mathbb{C})$ is defined as a convolution consistent with the classical Stockwell transform, and the fundamental properties of GFST such as linearity, translation, scaling, etc., are discussed. We focus on establishing an orthogonality relation and derive an inversion formula as a direct application of this relation. Additionally, we characterize the range of the GFST on $L^2(\mathbb{R},\mathbb{C})$. Finally, we prove an uncertainty principle of the Heisenberg type for the proposed GFST. Full article

Most physicists are dissatisfied with the current explanation of quantum mechanics, and want to find a method to solve this problem. However, this problem has not been solved perfectly up to now. In this paper, annihilation-generation movement (AGM) is developed according to the electron motion in hydrogen atoms. To verify the AGM, a curved surface that fits the dark fringe of the single-slit diffraction is proposed. Based on the AGM, the wave function of a free electron is rewritten and the double-slit experiment can be understood. Here, we show that the AGM is an alternative physical image that can be used to solve the puzzles of quantum mechanics, such as Heisenberg’s uncertainty principle and steady-state transition. We anticipate that we can find a new way to explain quantum mechanics based on AGM. Full article

In 1974, Stephen Hawking made the groundbreaking discovery that black holes emit thermal radiation, characterized by a specific temperature now known as the Hawking temperature. While his original derivation is intricate, retrieving the exact expressions for black hole temperature and entropy in a simpler, more intuitive way without losing the core physical principles behind Hawking’s assumptions is possible. This is obtained by employing the Heisenberg Uncertainty Principle, which is known to be connected to thenvacuum fluctuation. This exercise allows us to easily perform more complex calculations involving the effects of quantum gravity. This work aims to answer the following question: Is it possible to reconcile Prigogine’s second law of thermodynamics for open systems and the second law of black hole dynamics with Hawking radiation? Due to quantum gravity effects, the Heisenberg Uncertainty Principle has been extended to the Generalized Uncertainty Principle (GUP) and successively to the Extended Uncertainty Principle (EUP). The expression for the EUP parameter is obtained by conjecturing that Prigogine’s second law of thermodynamics and the second law of black holes are not violated by the Hawking thermal radiation mechanism. The modified expression for the entropy of a Schwarzschild black hole is also derived. Full article

The meaning of the quantum minimum effective length that should distinguish the quantum nature of a gravitational field is investigated in the context of manifestly covariant quantum gravity theory (CQG-theory). In such a framework, the possible occurrence of a non-vanishing minimum length requires one to identify it necessarily with a 4-scalar proper length s.It is shown that the latter must be treated in a statistical way and associated with a lower bound in the error measurement of distance, namely to be identified with a standard deviation. In this reference, the existence of a minimum length is proven based on a canonical form of Heisenberg inequality that is peculiar to CQG-theory in predicting massive quantum gravitons with finite path-length trajectories. As a notable outcome, it is found that, apart from a numerical factor of $O\left(1\right)$, the invariant minimum length is realized by the Planck length, which, therefore, arises as a constitutive element of quantum gravity phenomenology. This theoretical result permits one to establish the intrinsic minimum-length character of CQG-theory, which emerges consistently with manifest covariance as one of its foundational properties and is rooted both on the mathematical structure of canonical Hamiltonian quantization, as well as on the logic underlying the Heisenberg uncertainty principle. Full article

The classically defined minimum uncertainty of the optical phase is known as the standard quantum limit or shot-noise limit (SNL), originating in the uncertainty principle of quantum mechanics. Based on the SNL, the phase sensitivity is inversely proportional to $\sqrt{K}$, where K is the number of interfering photons or statistically measured events. Thus, using a high-power laser is advantageous to enhance sensitivity due to the $\sqrt{K}$ gain in the signal-to-noise ratio. In a typical interferometer, however, the resolution remains in the diffraction limit of the K = 1 case unless the interfering photons are resolved as in quantum sensing. Here, a projection measurement method in quantum sensing is adapted for classical sensing to achieve an additional $\sqrt{K}$ gain in the resolution. To understand the projection measurements, several types of conventional interferometers based on N-wave interference are coherently analyzed as a classical reference and numerically compared with the proposed method. As a result, the Kth-order intensity product applied to the N-wave spectrometer exceeds the diffraction limit in classical sensing and the Heisenberg limit in quantum sensing, where the classical N-slit system inherently satisfies the Heisenberg limit of $\mathsf{\pi }/\mathrm{N}$ in resolution. Full article

I consider the electro-weak (EW) masses and interactions generated by photons using vacuum expectation values of Stueckelberg and Higgs fields. I provide a prescription to relate their parametric values to a cosmological range derived from the fundamental Heisenberg uncertainty principle and the Einstein–de Sitter cosmological constant and horizon. This yields qualitative connections between microscopic ranges acquired by $W^{\pm }$ or $Z^0$ gauge Bosons and the cosmological scale and minimal mass acquired by g-photons. I apply this procedure to an established Stueckelberg–Higgs mechanism, while I consider a similar procedure for a pair of Higgs fields that may spontaneously break all U(1) × SU(2) gauge invariances. My estimates of photon masses and their additional parity-breaking interactions with leptons and neutrinos may be detectable in suitable accelerator experiments. Their effects may also be observable astronomically through massive g-photon condensates that may contribute to dark matter and dark energy. Full article

The relation between de Broglie’s double-solution approach to quantum dynamics and the hydrodynamic pilot-wave system has motivated a number of recent revisitations and extensions of de Broglie’s theory. Building upon these recent developments, we here introduce a rich family of pilot-wave systems, with a view to reformulating and studying de Broglie’s double-solution program in the modern language of classical field theory. Notably, the entire family is local and Lorentz-invariant, follows from a variational principle, and exhibits time-invariant, two-way coupling between particle and pilot-wave field. We first introduce a variational framework for generic pilot-wave systems, including a derivation of particle-wave exchange of Noether currents. We then focus on a particular limit of our system, in which the particle is propelled by the local gradient of its pilot wave. In this case, we see that the Compton-scale oscillations proposed by de Broglie emerge naturally in the form of particle vibrations, and that the vibration modes dynamically adjust to match the Compton frequency in the rest frame of the particle. The underlying field dynamically changes its radiation patterns in order to satisfy the de Broglie relation $p=\hslash k$ at the particle’s position, even as the particle momentum p changes. The wave form and frequency thus evolve so as to conform to de Broglie’s harmony of phases, even for unsteady particle motion. We show that the particle is always dressed with a Compton-scale Yukawa wavepacket, independent of its trajectory, and that the associated energy imparts a constant increase to the particle’s inertial mass. Finally, we see that the particle’s wave-induced Compton-scale oscillation gives rise to a classical version of the Heisenberg uncertainty principle. Full article

In this contribution, motivated by the quest to understand cosmic acceleration, based on the theory of Hořava–Lifshitz and on the branch-cut gravitation, we investigate the effects of non-commutativity of a mini-superspace of variables obeying the Poisson algebra on the structure of the branch-cut scale factor and on the acceleration of the Universe. We follow the guiding lines of a previous approach, which we complement to allow a symmetrical treatment of the Poisson algebraic variables and eliminate ambiguities in the ordering of quantum operators. On this line of investigation, we propose a phase-space transformation that generates a super-Hamiltonian, expressed in terms of new variables, which describes the behavior of a Wheeler–DeWitt wave function of the Universe within a non-commutative algebraic quantum gravity formulation. The formal structure of the super-Hamiltonian allows us to identify one of the new variables with a modified branch-cut quantum scale factor, which incorporates, as a result of the imposed variable transformations, in an underlying way, elements of the non-commutative algebra. Due to its structural character, this algebraic structure allows the identification of the other variable as the dual quantum counterpart of the modified branch-cut scale factor, with both quantities scanning reciprocal spaces. Using the iterative Range–Kutta–Fehlberg numerical analysis for solving differential equations, without resorting to computational approximations, we obtained numerical solutions, with the boundary conditions of the wave function of the Universe based on the Bekenstein criterion, which provides an upper limit for entropy. Our results indicate the acceleration of the early Universe in the context of the non-commutative branch-cut gravity formulation. These results have implications when confronted with information theory; so to accommodate gravitational effects close to the Planck scale, a formulation à la Heisenberg’s Generalized Uncertainty Principle in Quantum Mechanics involving the energy and entropy of the primordial Universe is proposed. Full article

A fundamental tool in mathematical physics is the logarithmic Sobolev inequality. A quantitative version proven by Carlen with a remainder involving the Fourier–Wiener transform is equivalent to an entropic uncertainty principle more general than the Heisenberg uncertainty principle. In the stability inequality, the remainder is in terms of the entropy, not a metric. Recently, a stability result for $H^1$ was obtained by Dolbeault, Esteban, Figalli, Frank, and Loss in terms of an $L^p$ norm. Afterward, Brigati, Dolbeault, and Simonov discussed the stability problem involving a stronger norm. A full characterization with a necessary and sufficient condition to have $H^1$ convergence is identified in this paper. Moreover, an explicit $H^1$ bound via a moment assumption is shown. Additionally, the $L^p$ stability of Dolbeault, Esteban, Figalli, Frank, and Loss is proven to be sharp. Full article