Time Quantization Research Articles

Micro-cosmos model of a nucleon

This study explores the age-old quest to construct a geometric model of a quantum particle. While static classical particle models have largely been dismissed, the focus has now shifted to intricate dynamic models that hold the promise of reconciling general relativity with quantum mechanics. We propose that matter particles can be described as radiation confined within dynamically curved spacetime regions, without the need for quantization of space and time, and using standard field equations and natural Planck units. Specifically, we investigate a cyclic or oscillating radiation-dominated micro-cosmos undergoing repeated bouncing. Our methodology employs integration, with carefully defined initial conditions. The results include several observable properties characteristic of quantum particles. We calculate the total mass, revealing a compelling inverse proportionality between mass and radius identical with the de Broglie relationship. Applying this model to protons, we discover a profound and surprisingly simple relationship between the proton’s radius and mass expressed in Planck units. This enables a definition of the proton radius that aligns remarkably well with the 2018 CODATA value. Furthermore, our analysis demonstrates that the radial density profile of the proton (or nucleon), averaged over a cycle time, increases toward the center. The problem of embedding the micro-cosmos within a background spacetime is also described. These results underscore the relevance of general relativity in the domain of nuclear physics. Moreover, the model offers a fresh perspective that can stimulate new ideas in the ongoing quest to unify general relativity with quantum physics.

Multi-laser source interference suppression using the time-coding method for SPAD-based flash DToF systems

Flash-type direct time-of-flight (DToF) image sensors use an in-pixel successive approximation register time-to-digital converter (SAR TDC) for time quantization. However, in a scene where multiple DToF systems exist simultaneously, different laser signals from multiple sources will produce mutual signal interference between DToF systems, causing the DToF system’s incorrect measurement. In this paper, we present a method called time coding, which inserts delay time bins between different working periods to suppress the interference laser together with the SAR TDC. The time-coding method is designed using a 110 nm complementary metal oxide semiconductor (CMOS) technology and verified by behavioral model and circuit simulation. Regardless of traditional systems or systems equipped with time coding, DToF systems with certain patterns of time coding can reduce interference noise by at least 95%, maintaining a measurement accuracy of 99% or higher at long distances.

An 8-bit 5-GS/s Single-Channel Hybrid ADC With a $\lambda$/4 Transmission Line Based Time Quantizer

An 8-bit 5-GS/s Single-Channel Hybrid ADC With a $\lambda$/4 Transmission Line Based Time Quantizer

Ідентифікація параметрів математичних моделей та визначення діагностичних ознак

In this article, the object of research is two main units of the AR20N aggregate – electrohydraulic amplifier (EHA) and power cylinder (PC). Detection of the occurrence and development of faults in them will be considered on the basis of the identification of parameters of the developed mathematical models. The main objectives of the research were to identify the parameters of mathematical models of EHA and PC using different steps of time quantization, determination of the optimal step of time quantization for numerical integration of differential equations; determination of diagnostic features that have the most probable influence on the operation of aggregate units at the occurrence of various faults. For achievement of the set objectives the following tasks were solved: mathematical models of EHA, PC, and simulation model of the aggregate research on the test bench were developed; identification of parameters of mathematical models of EHA and PC by the method of least squares (MLS) was carried out; the permissible step of time quantization was determined; upper and lower permissible limits of the identifiable parameters for a serviceable aggregate were determined; a methodology for determining the diagnostic features that are most probable to determine the emerging faults of the aggregate has been developed. Methods are used for this purpose: analytical, numerical, statistical, hydraulic systems theory, and system identification theory. The following results were obtained: differential equations describing the displacements of the distributive spool (DS) of the EHA and the output link (OL) of the PC; algorithms for identifying the parameters of mathematical models by MLS; the permissible step of time quantization was determined; and a technique for determining the diagnostic features using the Shewhart diagnostic chart for the parameters of mathematical models was developed. The scientific and practical novelty of the obtained results consists of the following: mathematical models of EHA and PC of the aggregate have been developed; simulation model of the aggregate on the test bench has been developed; simulation of various faults of the aggregate units has been carried out and identification of parameters of mathematical models of these units has been carried out; changes of estimations of parameters of mathematical models of EHA and PC depending on changes of each influencing factor have been obtained; upper and lower permissible limits of parameters and average values of these parameters have been determined; diagnostic features that are most probable to influence aggregate performance have been determined. It is shown that time quantization step D t = 0.01 (c) provides the determination of DS and OL displacements with errors of 1.914×10-6mm and 2.157×10-5 mm.

현대물리학의 시간에 대한 존재론적 고찰

This paper examines the change of the concept of time and its ontological meaning in physics, focusing on modern physics. The concept of absolute time was presented in Newton's classical physics, and since then, the concepts of relativistic time and quantized time have been introduced in Einstein's theory of relativity and quantum gravity theory, respectively. This change raises question about the true concept of time in the universe. In this paper, in order to find an answer to this question, the ontological meaning of the concept of time presented by each theory is compared. First, the concept of absolute time is regarded as a concept of time that we usually accept, and it is revealed that the meanings of uniqueness, independent reality, separability, directionality, continuity, uniformity, transcendence, and objectivity are included in it. And, in the concepts of relativistic time and quantized time, these characteristics are dismantled one by one. Nevertheless, whether the concept of time in the world we experience is compatible with the concept of quantized time is investigated through the thermal time hypothesis. Finally, we examine the implications of time quantization in philosophy of science, even though (loop) quantum gravity theory is a theoretical imagination that has not yet been empirically verified.

Quantum corrections to the Weyl quantization of the classical time of arrival

A time of arrival (TOA) operator that is conjugate with the system Hamiltonian was constructed by Galapon without canonical quantization in Galapon (J. Math. Phys. 45:3180–3215, 2004). The constructed operator was expressed as an infinite series but only the leading term was investigated which was shown to be equal to the Weyl-quantized TOA-operator for entire analytic potentials. In this paper, we give a full account of the said operator by explicitly solving all the terms in the expansion. We interpret the terms beyond the leading term as the quantum corrections to the Weyl quantization of the classical arrival time. These quantum corrections are expressed as some integrals of the interaction potential and their properties are investigated in detail. In particular, the quantum corrections always vanish for linear systems but nonvanishing for nonlinear systems. Finally, we consider the case of an anharmonic oscillator potential as an example.

Comparison of quantized transfers of a given volume of gas through a pipe under its temporal and velocity probability distributions

The paper considers the quantization of gas volume transfers along a hypothetical pipe. The volume of gas is represented by two probability distributions in temporal and velocity form. The known model of optimal in the sense of filling information quantization is applied to quantization of material objects. There is a constant size gap between quanta. Technological aspects of formation of quanta are not considered. On the basis of the carried out minimum cost study the advantage of velocity quantization over time quantization for a number of selected quanta is determined. A normal probability distribution is taken as the initial distribution of the gas volume. The results of the article can be applied to any material and information processes. The main purpose in future research is recommended for any complex network processes, analysis and synthesis of their quality.

Bandlimited Signal Reconstruction From Leaky Integrate-and-Fire Encoding Using POCS

Leaky integrate-and-fire (LIF) encoding is a model of neuron transfer function in biology that has recently attracted the attention of the signal processing and neuromorphic computing communities as a technique of event-based sampling for data acquisition. While LIF enables the implementation of analog-circuit signal samplers of lower complexity and higher accuracy simultaneously, the core difficulty of this technique is the retrieval of an input from its LIF-encoded output. In this article, we study this problem in the context of bandlimited inputs, by extracting the most abstract features of an LIF encoder as a generalized nonuniform sampler. In this view, the LIF output is seen as the transformation of the input by a known linear operator. We show that the signal reconstruction method of projection onto convex sets (POCS) converges to a weighted pseudo-inverse of this operator. This allows perfect recovery under uniqueness of reconstruction, minimum-norm reconstruction under incomplete sampling, as well as a noise shaping of time quantization that outperforms standard pseudo-inversion. On the practical side, a single iteration of the POCS method can be used to improve <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">any</i> estimate whose LIF samples are not consistent with those of the input, and a rigorous discrete-time implementation of this iteration is proposed that does not require a Nyquist-rate representation of the signals.

A 10-GS/s 8-bit 2850-μm2 Two-Step Time-Domain ADC With Speed and Efficiency Enhanced by the Delay-Tracking Pipelined-SAR TDC

This article presents an 8-bit time-domain analog-to-digital converter (ADC) achieving ten-GS/s conversion speed with only two time-interleaved (TI) channels. A successive approximation register (SAR) time-to-digital converter (TDC) is implemented for the subpicosecond resolution time quantization with high power/area efficiency and low jitter. The throughput of the SAR TDC is enhanced by a unique delay-tracking pipelining technique to enable a 5-GS/s single-channel conversion. On the circuit level, the reference time generation for the SAR TDC is realized by the proposed selective delay tuning (SDT) cell for high efficiency and small reference time variation. Fabricated in the 14-nm FinFet CMOS technology, this ADC achieves a 37.2-dB signal-to-noise and distortion ratio (SNDR) and a 50.6-dB spurious-free dynamic range (SFDR) at the Nyquist input frequency, leading to a 24.8-fJ/conv-step Walden figure of merit with an active area of only 2850 <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$\mu \text{m}^{2}$ </tex-math></inline-formula> .

The Uncertainty Principle and the Minimal Space–Time Length Element

Quantum gravity theories rely on a minimal measurable length for their formulations, which clashes with the classical formulation of the uncertainty principle and with Lorentz invariance from general relativity. These incompatibilities led to the development of the generalized uncertainty principle (GUP) from string theories and its various modifications. GUP and covariant formulations of the uncertainty principle are discussed, together with implications for space–time quantization.

Fuzzy Schwarzschild (2 + 1)-spacetime

We present a toy model of a fuzzy Schwarzschild space slice (as a noncommutative manifold), in which quantum mean values and quantum quasi-coherent states (states minimizing the quantum uncertainties) have properties close to the classical slice of (r, θ) Schwarzschild coordinates (the so-called Flamm’s paraboloid). This fuzzy Schwarzschild slice is built as a deformation of the noncommutative plane. Quantum time observables are introduced to add a time quantization in the model. We study the structure of the quasi-coherent state of the fuzzy Schwarzschild slice with respect to the quasi-coherent state and the deformation states of the noncommutative plane. The quantum dynamics of a fermion interacting with a fuzzy black hole described by the present model is studied. In particular, we study the decoherence effects appearing in the neighborhood of the fuzzy event horizon. An extension of the model to describe a quantum wormhole is also proposed, where we show that fermions cross the wormhole not by traveling by its internal space but by quantum tunneling, in accordance with the non-traversable character of classical Einstein–Rosen bridges.

Proper time quantization of a thin shell

“Time” has different meanings in classical general relativity and in quantum theory. While all choices of a time function yield the same local classical geometries, quantum theories built on different time functions are not unitarily equivalent. This incompatibility is most vivid in model systems for which exact quantum descriptions in different time variables are available. One such system is a spherically symmetric, thin dust shell. In this paper, we will compare the quantum theories of the shell built on proper time and on a particular coordinate time. We find wholly incompatible descriptions: whereas the shell quantum mechanics in coordinate time admits no solutions when the mass is greater than the Planck mass, its proper time quantum mechanics only admits solutions when the mass is greater than the Planck mass. The latter is in better agreement with what is expected from observation. We argue that proper time quantization provides a superior approach to the problem of time in canonical quantization.

The Truth on Gravity and Terrestrial Global Warming. Part II: The Regenerative Mass

The parabolic gravitized space {Rs, Re} = e3/2 Ker-1(3/4)•(1010-1012)m, back-scattering of radiant energy at the onset of light, or the depth of gravity field, engenders a thermodynamic field upon caustic developable surfaces characterized by certain caustic developable polar (twisted ) curves, where the surrounding of their tangent lines (or rulings) envelop embodied matter or gravitized mass. In contrast to the gravity polarization (Ker = ¾) of photon nature (e, e2, e3), occurring reversible cyclical processes with excess energy, the thermal polarization (Ker = 2/3) can produce cross exchanges of heat, matter and work with the surrounding area in the inverse order, i.e. in a reversed cycle, only in the case of microscopic atomic-molecular structures of statistical nature (principle of the microscopic reversibility). At the macroscale, such a reciprocating mass process, together with its conservation, is possible only for self-regenerating matter processes. The relative mass concept and invariance of regenerative mass process along with its frozen metastable equilibrium are considered, including the time quantization (clock’s law) as the half-life of mass (gravitized matter).

Photon Characteristics and Behavior under Refractive Index

The effective mass, energy and momentum of photon in medium is described. The photon has both kinetic and potential energy and displays an effective mass when travelling through a medium. The photon is a type of elementary particle that serves as the quantum of the electromagnetic field and is explained through equations to have an elastic constant, volume, momentum, force, power and zero rest mass. The theory that photons a massless only applies to rest mass. A photon undergoes different dynamics such as strain and changes in effective mass under the influence of the refractive index that gives rise to a refractive force. This study synthesizes some properties of energy such as elastic constant, weight, and volume in order to explain the nature of photons and photon dynamics under refractive index. In this study, a helical spring model has been used to describe the behavior of a photon in the medium. The model connects together the exhibited properties such as energy, effective mass, spin, elastic constant and volume. Further explanation is given to the effect of gravitational force on wavelength and refractive index of air, and how gravitational force causes red and blue shifts in photon propagation. The quantization of energy has been extended to the quantization of space, time and matter. This study is consistent and consolidates the existing classical and quantum theories. There are further potential applications in optical communication, quantum cryptography, quantum optics, and medicine, especially in the use of two-photon excitation microscopy and photodynamic therapy.

Measurement-induced quantum walks.

We investigate a tight-binding quantum walk on a graph. Repeated stroboscopic measurements of the position of the particle yield a measured "trajectory," and a combination of classical and quantum mechanical properties for the walk are observed. We explore the effects of the measurements on the spreading of the packet on a one-dimensional line, showing that except for the Zeno limit, the system converges to Gaussian statistics similarly to a classical random walk. A large deviation analysis and an Edgeworth expansion yield quantum corrections to this normal behavior. We then explore the first passage time to a target state using a generating function method, yielding properties like the quantization of the mean first return time. In particular, we study the effects of certain sampling rates that cause remarkable changes in the behavior in the system, such as divergence of the mean detection time in finite systems and decomposition of the phase space into mutually exclusive regions, an effect that mimics ergodicity breaking, whose origin here is the destructive interference in quantum mechanics. For a quantum walk on a line, we show that in our system the first detection probability decays classically like (time)^{-3/2}. This is dramatically different compared to local measurements, which yield a decay rate of (time)^{-3}, indicating that the exponents of the first passage time depend on the type of measurements used.

The Mathematical Models of Lattice Functions in Modelling of Control System

The paper proposes an approach to constructing a mathematical model of lattice functions, which are mainly used in the study of discrete control systems in the time and domain of the Laplace transform. The proposed approach is based on the assumption of the physical absence of an impulse element. An alternative to the classical approach to the description of discrete data acquisition - the process of quantization in time, is considered. As a result, models of the lattice function in the time domain and the domain of the discrete Laplace transform are obtained. Based on the obtained mathematical models of lattice functions, a mathematical model of the time quantization element of the system is obtained. This will allow in the future to proceed to the construction of mathematical models of various discrete control systems, incl. expanding the proposed approaches to the construction of mathematical models of multi-cycle continuous-discrete automatic control systems

Randomly repeated measurements on quantum systems: correlations and topological invariants of the quantum evolution

Randomly repeated measurements during the evolution of a closed quantum system create a sequence of probabilities for the first detection of a certain quantum state. The related discrete monitored evolution for the return of the quantum system to its initial state is investigated. We found that the mean number of measurements (MNM) until the first detection is an integer, namely the dimensionality of the accessible Hilbert space. Moreover, the mean first detected return (FDR) time is equal to the average time step between successive measurements times the MNM. Thus, the mean FDR time scales linearly with the dimensionality of the accessible Hilbert space. The main goal of this work is to explain the quantization of the mean return time in terms of a quantized Berry phase.

Loss of ergodicity in a quantum hopping model of a dense many body system with repulsive interactions

In this work we report on a loss of ergodicity in a simple hopping model, motivated by the Hubbard Hamiltonian, of a many body quantum system at zero temperature, quantized in Euclidean time. We show that this quantum system may lose ergodicity at high densities on a large lattice, as a result of both Pauli exclusion and strong Coulomb repulsion. In particular we study particle hopping susceptibilities and the tendency towards particle localization. It is found that the appearance and existence of quantum phase transitions in this model, in the case of high density and strong Coulomb repulsion, depends on the starting configuration of particle trajectories in the numerical simulation. We argue that this breakdown may be the Euclidean time version of a breakdown of the eigenstate thermalization hypothesis in real time quantization.

Beta and Theta Oscillations Correlate With Subjective Time During Musical Improvisation in Ecological and Controlled Settings: A Single Subject Study.

In this paper, we describe the results of a single subject study attempting at a better understanding of the subjective mental state during musical improvisation. In a first experiment, we setup an ecological paradigm measuring EEG on a musician in free improvised concerts with an audience, followed by retrospective rating of the mental state of the improviser. We introduce Subjective Temporal Resolution (STR), a retrospective rating assessing the instantaneous quantization of subjective timing of the improviser. We identified high and low STR states using Hidden Markov Models in two performances, and were able to decode those states using supervised learning on instantaneous EEG power spectrum, showing increases in theta and alpha power with high STR values. In a second experiment, we found an increase of theta and beta power when experimentally manipulating STR in a musical improvisation imagery experiment. These results are interpreted with respect to previous research on flow state in creativity, as well as with the temporal processing literature. We suggest that a component of the subjective state of musical improvisation may be reflected in an underlying mechanism related to the subjective quantization of time. We also demonstrate the feasibility of single case studies of musical improvisation using brain activity measurements and retrospective reports, by obtaining consistent results across multiple sessions.

Super-relaxation of space–time-quantized ensemble of energy loads to curtail their synchronization after demand response perturbation

Ensembles of thermostatically controlled loads (TCL) provide a significant demand response reserve for the system operator to balance power grids. However, this also results in the parasitic synchronization of individual devices within the ensemble leading to long post-demand-response oscillations in the integrated energy consumption of the ensemble. The synchronization is eventually destructed by fluctuations, thus leading to the (pre-demand response) steady state; however, this natural desynchronization, or relaxation to a statistically steady state, is too long. A resolution of this problem consists in measuring the ensemble’s instantaneous consumption and using it as a feedback to stochastic switching of the ensemble’s devices between on- and off-states. A simplified continuous-time model showed that carefully tuned nonlinear feedback results in a fast (super-) relaxation of the ensemble energy consumption. Since both state information and control signals are discrete, the actual TCL devices operation is space–time quantized, and this must be considered for realistic TCL ensemble modeling. Here, assuming that states are characterized by indoor temperature (quantifying comfort) and air conditioner regime (on, off), we construct a discrete model based on the probabilistic description of state transitions. We demonstrate that super-relaxation holds in such a more realistic setting, and that while it is stable against randomness in the stochastic matrix of the quantized model, it remains sensitive to the time discretization scheme. Aiming to achieve a balance between super-relaxation and customer’s comfort, we analyze the dependence of super-relaxation on details of the space–time quantization, and provide a simple analytical criterion to avoid undesirable oscillations in consumption.