Interpretation Of Wave Function Research Articles

A revised double-slit experiment to explore the mechanism of photon wavefunction collapse by numerical design

The double-slit experiment has long been pivotal in understanding matter’s wave–particle duality. A central question revolves around Born’s interpretation of wavefunction whether a single photon demonstrates a 50% probability of passing through each slit individually as particles or simultaneously traverses both as waves. Experimentally, once the photon’s path is detected, the observer effect causes its wavefunction to collapse, rendering the results inconclusive. Designing an experiment to minimize instrumental involvement during the wavefunction collapse of photons, while aiming to gain insight into its collapse mechanism, becomes necessary. We propose a revised experiment that replaces the traditional setup with two Au nanoparticles acting as observers, triggering photon collapse before spectrum collection. In single-photon scenarios, we consider two assumptions: first, the photon wavefunctions collapse into a particle and transfer energy to one of the nanoparticles exclusively, and second, the photon acts as a wave, splitting and transferring its energy to two nanoparticles simultaneously, which does not align well with Born’s interpretation of wavefunction as spatial probabilities. These two assumptions would generate distinctly different spectra. Conversely, in high-intensity experiments, both nanoparticles collectively undergo excitation, regardless of the collapse mechanism. A comparative analysis of scattering spectra under the two conditions reveals crucial insights into the genuine nature of photon collapse. We also proposed using two molecules attached to a metal nanoparticle as an alternative design. Whether affirming or refuting the observer effect, this research holds promise for resolving the theoretical debate surrounding the collapse of wavefunctions and advancing quantum computing and communication fields.

A New Finding Relating Subatomic Particles' Mass to the Square of the Magnetic Flux Quantum Provides a Novel Interpretation of the Mass and a Novel Wave Function Interpretation

A New Finding Relating Subatomic Particles' Mass to the Square of the Magnetic Flux Quantum Provides a Novel Interpretation of the Mass and a Novel Wave Function Interpretation

Possibility of Geometrical Interpretation of Quantum Mechanics and Geometrical Meaning of “Hidden Variables”

Interpretation of wave function for free particle is suggested as a description of microscopic distortion of the space-time geometry, namely, as some closed topological 4-manifold. Such geometrical object looks in three-dimensional Euclidean space as its topological defect having stochastic and wave-corpuscular properties of quantum particle. All possible deformations (homeomorphisms) of closed topological manifold play the role of “hidden variables”, responsible for statistical character of the theory.

Quantum-Information Conservation. The Problem About ‘Hidden Variables’, or the ‘Conservation of Energy Conservation’ in Quantum Mechanics: A Historical Lesson for Future Discoveries

The explicit history of the “hidden variables” problem is well-known and established. The main events of its chronology are traced. An implicit context of that history is suggested. It links the problem with the “conservation of energy conservation” in quantum mechanics. Bohr, Kramers, and Slaters (1924) admitted its violation being due to the “fourth Heisenberg uncertainty”, that of energy in relation to time. Wolfgang Pauli rejected the conjecture and even forecast the existence of a new and unknown then elementary particle, neutrino, on the ground of energy conservation in quantum mechanics, afterwards confirmed experimentally. Bohr recognized his defeat and Pauli’s truth: the paradigm of elementary particles (furthermore underlying the Standard model) dominates nowadays. However, the reason of energy conservation in quantum mechanics is quite different from that in classical mechanics (the Lie group of all translations in time). Even more, if the reason was the latter, Bohr, Cramers, and Slatters’s argument would be valid. The link between the “conservation of energy conservation” and the problem of hidden variables is the following: the former is equivalent to their absence. The same can be verified historically by the unification of Heisenberg’s matrix mechanics and Schrodinger’s wave mechanics in the contemporary quantum mechanics by means of the separable complex Hilbert space. The Heisenberg version relies on the vector interpretation of Hilbert space, and the Schrodinger one, on the wave-function interpretation. However the both are equivalent to each other only under the additional condition that a certain well-ordering is equivalent to the corresponding ordinal number (as in Neumann’s definition of “ordinal number”). The same condition interpreted in the proper terms of quantum mechanics means its “unitarity”, therefore the “conservation of energy conservation”. In other words, the “conservation of energy conservation” is postulated in the foundations of quantum mechanics by means of the concept of the separable complex Hilbert space, which furthermore is equivalent to postulating the absence of hidden variables in quantum mechanics (directly deducible from the properties of that Hilbert space). Further, the lesson of that unification (of Heisenberg’s approach and Schrodinger’s version) can be directly interpreted in terms of the unification of general relativity and quantum mechanics in the cherished “quantum gravity” as well as a “manual” of how one can do this considering them as isomorphic to each other in a new mathematical structure corresponding to quantum information. Even more, the condition of the unification is analogical to that in the historical precedent of the unifying mathematical structure (namely the separable complex Hilbert space of quantum mechanics) and consists in the class of equivalence of any smooth deformations of the pseudo-Riemannian space of general relativity: each element of that class is a wave function and vice versa as well. Thus, quantum mechanics can be considered as a “thermodynamic version” of general relativity, after which the universe is observed as if “outside” (similarly to a phenomenological thermodynamic system observable only “outside” as a whole). The statistical approach to that “phenomenological thermodynamics” of quantum mechanics implies Gibbs classes of equivalence of all states of the universe, furthermore re-presentable in Boltzmann’s manner implying general relativity properly … The meta-lesson is that the historical lesson can serve for future discoveries.

Microscopic Manifestations of the Wave Nature and the Fifth Fundamental Field

In Quantum Mechanics, one knows that the wave function interpretation is probabilistic. We previously established that any particle scalar field is the cause of its existence. Here, one examined the plane solution regarding a moving particle in vacuum, through the relativistic formalism. It appeared the following. (i) The solution presents four alternatives, like in Dirac unified formalism; when searching stationary solutions of the system vacuum-particle or the system vacuum-antiparticle. (ii) Considering the former, each spinner component shows the interaction of one particle charge with three vacuum fermions of spin-½; each oriented along one space direction. Furthermore, this allows deducting the triple nature of any gauge fermion. (iii) Each solution case is definable with a same wave front width. This determination became possible from the vector companion of that wave function one introduced before. Here, this points out the existence of transverse time. (iv) Both functions let emphasizing the existence of a third fundamental field of long range, which is identifiable to the fundamental spin field. (v) This unites the particle spin and orbital momenta and bears in addition a magnetic-like field, which is yet unknown. (vi) According to the charge, a particle field is observable in wave phenomena, from the manifestations of its gauge fermions or gauge bosons; when ejected from their stationary states by a perturbation… At last, the results highlight the quantum composition of wave functions, the spin-field patency, and the wave nature manifestation from five differentiable fields.

Law of Creation and Grand Unification Theory

The understanding about the creation of our universe is explored in many philosophies, natural sciences, religions, ideologies, traditions and many other disciplines. Currently, natural science cannot answer this question at the most fundamental level. In this work, based on the ancient Chinese Tao wisdom about creation, we propose the Law of Tao Yin–Yang Creation. This law states that everything is created from emptiness through yin–yang interaction. Yin and yang are the two basic elements that make up everything. Yin and yang are opposite, relative, co-created, inseparable and co-dependent. The Law of Tao Yin–Yang Creation gives us a deeper insight about space and time. We propose that space and time are two basic measurements we conduct. Time relates to the measurement of movement and change. Space relates to the measurement of stillness and solidity. Space and time are a yin–yang pair. Interaction of two fundamental yin–yang pairs, the space and time yin–yang pair and the inclusion and exclusion duality pair, create our universe. We demonstrate that from this insight, one can derive string theory, superstring or M-theory and the universal wave function interpretation of string theory. We suggest that the Law of Tao Yin–Yang Creation presents the exact process how “it from bit” and it could be the fundamental principle leading to the grand unification theory and the theory of everything.

New aspects of quantum electrodynamics on electronic structure and dynamics.

Application of Alpha-oscillator theory to quantum electrodynamics (QED) solves the mystery (Feynman) of the double-slit phenomenon involved in the foundation of quantum mechanics (QM). Even if with the same initial condition given, different spots on the screen can be predicted deterministically with no introduction of hidden variables. The interference pattern is similar to, but cannot be reproduced quantitatively by, that of the QM wave function, contrary to many-years-anticipation: a new prediction, awaiting experimental test over and above the Bohr-Einstein gedanken experiment. The general proof has already been published in Ref. [3a] and the concrete numerical algorithm of the extended normal mode technique for concrete trajectory of one electron in Ref. [3b]. In this article, (1) the new "interpretation" of the QED wave function is given in section "Interpretation of Wave Function in QED": the QED wave function used in the extended normal mode technique gives probability density distribution function of the initial values of trajectories. Moreover, (2) for the sake of demonstration of this new interpretation, the time-independent stationary state QM wave function is substituted to the QED wave function in section "Internal Self-Stress of Energetic Particles": the QED wave function is realized by internal self-stress revealed as energy density at the initial conditions. The renewed energy density is applied to study a unified scheme for generalized chemical reactivity. This is a new kind of chemical force acting in between electrons not in between nuclei. This paves a way for more advanced time-dependent simulation of electronic structure and dynamics in chemical reaction dynamics by tracing trajectories of many electrons. © 2018 Wiley Periodicals, Inc.

String Theory Explanation of Large-Scale Anisotropy and Anomalous Alignment

The discovery of anomalies in the cosmic microwave background (CMB) indicates large-scale anisotropies, non-Gaussian distributions, and anomalous alignments of the quadrupole and octupole modes of the anisotropy with each other and with both the ecliptic and equinoxes. Further analysis indicates that the statistical anisotropy and non-Gaussian temperature fluctuations are mainly due to long-range correlations. However, the source of the large-scale correlation and the cause of the anomalous alignment in CMB remains unknown. In this work, we show a new development in string theory, the universal wave function interpretation of string theory (UWFIST) indicates the existence of large-scale quantum vibrations. These large-scale quantum vibrations can cause the large-scale correlation and anomalous alignment observed in the background field. They can explain the observed large-scale anisotropies, non-Gaussian distributions, and anomalous alignments of the quadrupole and octupole modes in the microwave background.

Indeterminación y potencialidad en la física cuántica

Abstract: One of the main philosophical problems of quantum mechanics is understanding in what manner Schodinger’s wave function can said to be real. In this paper I explore the ways in which the Aristotelian notion of potentiality could be used to understand the reality of the wave function, as suggested by Heisenberg in some of his writings. For this reason I sketch some of the potential complications in the interpretation of wave function while trying to develop Aristotle’s philosophy of potentiality in relation to quantum mechanics. I will also attempt to demonstrate the connections of Popper’s account of propensities with the notion of potentiality

Derivation of Multiverse from Universal Wave Function Interpretation of String Theory

Derivation of Multiverse from Universal Wave Function Interpretation of String Theory

Inflation Scheme Derived from Universal Wave Function Interpretation of String Theory

Inflation Scheme Derived from Universal Wave Function Interpretation of String Theory

Inflation Scheme Derived from Universal Wave Function Interpretation of String Theory

Inflation is the most commonly accepted theory in cosmology to explain why the universe appears flat, homogeneous, and isotropic, as well as the origin of the large-scale structure of the cosmos and why no magnetic monopoles have been detected. However, so far, the origin of the inflation epoch and what is the hypothetical field, the inflaton, giving rise to inflation, remains unknown. String theory is one of the promising candidates for the grand unification theory. Grand unification theory is to use one mathematic formula to describe everything. In this work, we study the inflation scheme in a new development in string theory, universal function interpretation of string theory (UWFIST). We show that from UWFIST we can derive from the fundamental theory that the long-range vibration is the possible candidate of inflaton. We estimate the vacuum energy created by the long-range vibration and show that it can indeed drives the inflation.

Operators and meaning of wave function

The interpretation problems of quantum theory are considered. In the formalism of quantum theory the possible states of a system are described by a state vector. The state vector, which will be represented as |ψ> in Dirac notation, is the most general form of the quantum mechanical description. The central problem of the interpretation of quantum theory is to explain the physical significance of the |ψ>. In this paper we have shown that one of the best way to make of interpretation of wave function is to take the wave function as an operator.

The universal wave function interpretation of string theory

In this work, we will show that a deeper understanding of space-time provided by both quantum physics and general relativity can lead to a new way to understand string theory. This new way of understanding and applying string theory, the universal wave function interpretation of string theory (UWFIST), may yield to a more powerful string theory and testable prediction. We will show how to derive UWFIST and what new result we can obtain from UWFIST. We will demonstrate that UWFIST indicates that the observed space-time and all phenomena are the projections from the world-sheet hologram. UWFIST provides the possible source for dark energy and dark matter and the explanation about why the dark energy and dark matter is beyond the detection of our current detector. We will show that UWFIST may also yield correct prediction of the cosmological constant to be of the order 10-121 in the unit of Planck scale. It may also help us understand and derive the energy source for inflation and the flatness of our observed 4-dimensional universe. UWFIST may also make other testable predictions that may be detected by interferometers.We conclude that UWFIST has the potential to make string theory a more powerful physics theory that can yield testable predictions. It is worth further investigation by more physicists.

Part and whole in wavefunction/DFT embedding

Density functional theory (DFT)-based subsystem and embedding methods have found a widespread use in Quantum Chemistry. The combination of correlated wavefunction (WF) methods and density-based embedding methods is particularly promising for accurate descriptions of complex systems. Here, we address some conceptual issues in such WF/DFT methods concerning (1) the interpretation of wavefunctions and densities in these frameworks, (2) the interpretation of subsystem and supersystem density changes as a polarization of the electronic system, and (3) non-orthogonality effects between wavefunctions of ground and excited states in WF/DFT embedding making use of state-specific embedding potentials. Illustrative examples are provided to analyze the significance of these issues in practical calculations. We find that physically reasonable subsystem densities and subsystem dipole moments can often be obtained from subsystem calculations making use of typical setups in practice, in spite of formal issues that are in principle in conflict with such interpretations. For excited-state WF/DFT calculations, we demonstrate that orthogonality violations due to state-specific embedding potentials are usually small.

De Broglie wave and electromagnetic travelling wave model of electron and other charged particles

The original wave theory proposed by de Broglie necessitates a stationary (localized) monochromatic plane wave of high frequency ν_{o} associated with particle. As particle moves the de Broglie wavelength appears as an observable (a relativistic effect). The nature and interpretation of high frequency oscillations remained unrevealed so far. This paper presents a self trapped circular Electromagnetic (EM) travelling wave model of Electron (specifically) and other charged particles generally. Curling EM wave is localized (stationary) and still a plane monochromatic travelling wave, against the customary wave packet approach, where number of frequencies are made to interfere to build a stationary localized wave-packet. The model reveals facts such as interpretation of wave function ψ (de Broglie wave) as a relativistic effect of a real wave function and removes the discrepancy of very high phase velocity (c²/v) associated with it. The model also incorporates zitterbewegung of electron and 4π rotation needed, for a complete round of wave cycle.

Quantum Dynamics and Kinematics from a Statistical Model Selected by the Principle of Locality

Quantum mechanics predicts correlation between spacelike separated events which is widely argued to violate the principle of local causality. By contrast, here we shall show that the Schrödinger equation with Born’s statistical interpretation of wave function and uncertainty relation can be derived from a statistical model of microscopic stochastic deviation from classical mechanics which is selected uniquely, up to a free parameter, by the principle of Local Causality. Quantization is thus argued to be physical and Planck constant acquires an interpretation as the average stochastic deviation from classical mechanics in a microscopic time scale. Unlike canonical quantization, the resulting quantum system always has a definite configuration all the time as in classical mechanics, fluctuating randomly along a continuous trajectory. The average of the relevant physical quantities over the distribution of the configuration are shown to be equal numerically to the quantum mechanical average of the corresponding Hermitian operators over a quantum state.

Front Cover: On the interpretation of wave function overlaps in quantum dots (Phys. Status Solidi B 4/2011)

Front Cover: On the interpretation of wave function overlaps in quantum dots (Phys. Status Solidi B 4/2011)

On the interpretation of wave function overlaps in quantum dots

AbstractThe spontaneous emission rate of excitons strongly confined in quantum dots (QDs) is proportional to the overlap integral of electron and hole envelope wave functions. A common and intuitive interpretation of this result is that the spontaneous emission rate is proportional to the probability that the electron and the hole are located at the same point or region in space, i.e., they must coincide spatially to recombine. Here, we show that this interpretation is not correct even loosely speaking.By general mathematical considerations we compare the envelope wave function overlap, the exchange overlap integral, and the probability of electrons and holes coinciding, and find that the frequency dependence of the envelope wave function overlap integral is very different from that expected from the common interpretation. We show that these theoretical considerations lead to predictions for measurements. We compare our qualitative predictions with recent measurements of the wave function overlap and find good agreement.

Measuring orbital interaction using quantum information theory

Quantum information theory gives rise to a straightforward definition of the interaction of electrons I p,q in two orbitals p,q for a given many-body wave function. A convenient way to calculate the von Neumann entropies needed is presented in this work, and the orbital interaction I p,q is successfully tested for different types of chemical bonds. As an example of an application of I p,q beyond the interpretation of wave functions, I p,q is then used to investigate the ordering problem in the density-matrix renormalization group.