Classical signal model reproducing quantum probabilities for single and coincidence detections

Towards new Grangier type experiments

We present a purely wave model (based on classical random field) which reproduces quantum probabilities (given by the fundamental law of quantum mechanics, Born's rule) including probabilities for joint detection of a pair of quantum observables (e.g., spin or polarization projections). The crucial point of our approach is that the presence of detector's threshold and calibration procedure have to be treated not as simply experimental technicalities, but as the basic counteparts of the theoretical model. The presence of the background field (vacuum fluctuations) is also the key-element of our prequantum model. It is of the classical signal type and the methods of classical signal theory (including statistical radiophysics) are used for its development. We stress that our prequantum model is not objective, i.e., the values of observables (clicks of detectors) cannot be assigned in advance, i.e., before measurement. Hence, the dilemma, nonobjectivity or nonlocality, is resolved in favor of nonobjectivity (our model is local of the classical field type). In particular, we reproduce the probabilities for the EPR-experiment for photon polarization and, hence, violate CHSH inequality for classical random signals (measured by the threshold type and properly calibrated detectors acting in the presence of the background field).

The equivalence between classical epidemic model and non-dissipative and dissipative quantum tight-binding model is derived. Classical epidemic model can reproduce the quantum entanglement emerging in the case of electrostatically coupled qubits described by von-Neumann entropy both in non-dissipative and dissipative case. The obtained results shows that quantum mechanical phenomena might be almost entirely simulated by classical statistical model. It includes the quantum like entanglement and superposition of states. Therefore coupled epidemic models expressed by classical systems in terms of classical physics can be the base for possible incorporation of quantum technologies and in particular for quantum like computation and quantum like communication. The classical density matrix is derived and described by the equation of motion in terms of anticommutator. Existence of Rabi like oscillations is pointed in classical epidemic model. Furthermore the existence of Aharonov-Bohm effect in quantum systems can also be reproduced by the classical epidemic model. Every quantum system made from quantum dots and described by simplistic tight-binding model by use of position-based qubits can be effectively described by classical model with very specific structure of S matrix that has twice bigger size as it is the case of quantum matrix Hamiltonian. Obtained results partly question fundamental and unique character of quantum mechanics and are placing ontology of quantum mechanics much in the framework of classical statistical physics what can bring motivation for emergence of other fundamental theories bringing suggestion that quantum mechanical is only effective and phenomenological but not fundamental picture of reality.KeywordsEpidemic modelTight-binding modelStochastic finite state machinePosition-based qubits

Advantages of new cardiovascular risk-assessment strategies in high-risk patients with hypertension

Based on the prequantum classical statistical field theory (PCSFT), we present the results of numerical simulations of a model with hidden variables of the field-type reproducing probabilistic predictions of quantum mechanics (QM). PCSFT is combined with measurement theory based on detectors of the threshold type. The latter describes discrete events corresponding to the continuous field model. Using numerical modeling, we show that the classical Brownian motion (the Wiener process valued in the complex Hilbert space), producing clicks when approaching the detection threshold, gives the probabilities of detection predicted by the QM formalism (as well as PCSFT). This numerical result is important, since the transition from PCSFT to the threshold detection has a complex mathematical structure (within the framework of classical random processes) and it was modeled only approximately. Also we perform numerical simulation for the PCSFT value of the coefficient of the second-order coherence. Our result matches well with the prediction of quantum theory. Thus, in contrast to a semiclassical theory, PCSFT cannot be rejected as a consequence of measurements of g(2)(0). Finally, we analyze the output of the recent experiment performed in NIST questioning the validity of some predictions of PCSFT.

Wide-sense stationary discrete-time random processes: Analyses in the discrete-Fresnel and discrete-frequency domains

Homologies between decision sciences, economics, and physics have been observed and applied for quite some time. Even von Neumann, who established the foundations of mathematics for quantum mechanics and game theory, noted what he considered obvious relationships between these fields of study. However, it is the physical world that is often used as a source of models for application in behavioral, micro, and macroeconomics rather than the other way around. This research seeks to advance prior work that identified an analogy between the Entropy Decision Risk Model's (EDRM) definition of proximity, which relates objective and subjective probability to explain how subjects perceive uncertainty, and the Born Rule of Quantum Mechanics. So far, there has been no derivation for the Born Rule, as it is based only upon an editor's remark in a footnote of Born's foundational 1926 paper, leaving an unanswered question. The goal of this research is to understand homologies and isomorphologies between quantum mechanics and decision engineering that will benefit both disciplines.

The recent rigorous derivation of the Born rule from the dynamical law of quantum mechanics Allahverdyan et al. (Phys Rep 525:1–166. https://doi.org/10.1016/j.physrep.2012.11.001 , 2013) is taken as incentive to reexamine whether quantum mechanics has to be an inherently probabilistic theory. It is shown, as an existence proof, that an alternative perspective on quantum mechanics is possible where the fundamental ontological element, the ket, is not probabilistic in nature and in which the Born rule can also be derived from the dynamics. The probabilistic phenomenology of quantum mechanics follows from a new definition of statistical state in the form of a probability measure on the Hilbert space of kets that is a replacement for the von Neumann statistical operator to address the lack of uniqueness in recovering the pure states included in mixed states, as was pointed out by Schrodinger. From the statistical state of a quantum system, classical variables are defined as collective variables with negligible dispersion. In this framework, classical variables can be chosen to define a derived classical system that obeys, by Ehrenfest’s theorem, the laws of classical mechanics and that describes the macroscopic behavior of the quantum system. The Born rule is derived from the dynamics of the statistical state of the quantum system composed of the observed system interacting with the measurement system and the role of the derived classical system in the process is exhibited. The approach suggests to formulate physical systems in second quantization in terms of local quantum fields to ensure conceptually equivalent treatment of space and time. A real double-slit experiment, as opposed to a thought experiment, is studied in detail to illustrate the measurement process.

Comparison of 3D classical and quantum mechanical He scattering on Rh(3 1 1)

Quantum structure in cognition

The chapter contains elements of theory of random processes required for time series analysis and for understanding its results. The time series discussed in this book belong to the class of stationary random processes, which means that their statistical properties averaged over an ensemble of realizations of the process do not depend upon the time origin. If averaging over an ensemble of realizations is equivalent to averaging over time of any single realization, the process is ergodic. If a stationary process is Gaussian, it is also ergodic. In our research, we mostly have just one sample realization (one time series) of finite length and by extending the properties estimated from a single time series to the entire process under the study, we assume that the process is ergodic. The most important characteristics of any time series include the covariance function and spectral density, which describe the time series properties in the time and frequency domains, respectively. The two stationary discrete random processes typical for climatology and other disciplines are white noise and Markov chains. Examples of the true and estimated correlation functions and spectral densities including their sampling variability are briefly discussed for simulated time series of length \( N = 100 \).

A new method for representing and generating realizations of a wide-sense stationary non-Gaussian random process is described. The representation allows one to independently specify the power spectral density and the first-order probability density function of the random process. The only proviso is that the probability density function must be symmetric and infinitely divisible. The method proposed models the sinusoidal component frequencies as random variables, a key departure from the usual representation a of wide-sense stationary random process by the spectral theorem. Ergodicity in the mean and autocorrelation is also proven, under certain conditions. An example is given to illustrate its application to the K distribution, which is important in many physical modeling problems in radar and sonar.

Absolute L X-ray intensities in the decays of 230Th, 234U, 238Pu and 244Cm

Quantum mechanics and gravitation are two pillars of modern physics. Despite their success in describing the physical world around us, they seem to be incompatible theories. There are suggestions that one of these theories must be generalized to achieve unification. For example, Born's rule--one of the axioms of quantum mechanics--could be violated. Born's rule predicts that quantum interference, as shown by a double-slit diffraction experiment, occurs from pairs of paths. A generalized version of quantum mechanics might allow multipath (i.e., higher-order) interference, thus leading to a deviation from the theory. We performed a three-slit experiment with photons and bounded the magnitude of three-path interference to less than 10(-2) of the expected two-path interference, thus ruling out third- and higher-order interference and providing a bound on the accuracy of Born's rule. Our experiment is consistent with the postulate both in semiclassical and quantum regimes.

Phosphate groups are essential components of nucleic acids and proteins, whose interactions with solvent, metal ions, and ionic side chains help control folding and binding. Methyl phosphate (MP) represents a simple analog of phosphate moieties that are post-translation modifications in proteins and present at the termini of nucleic acids, among other environments. In the present study, we optimized parameters for use in polarizable molecular dynamics simulations of MP in its mono- and dianionic forms, MP- ≡ CH3HPO4- and MP2- ≡ CH3PO42-, along with P i2- ≡ HPO42-, in the context of the classical Drude oscillator model. Parameter optimization was done in a manner consistent with the remainder of the Drude molecular mechanics force field, choosing atomic charges and polarizabilities to reproduce molecular properties from quantum mechanics as well as experimental hydration free energies. Optimized parameters were similar to existing dimethyl phosphate parameters, with a few significant differences. The developed parameters were then used to compute magnesium binding affinities in aqueous solution, using alchemical molecular dynamics free energy simulations. Good agreement with experiment was obtained, and outer sphere binding was shown to be predominant for MP- and MP2-.