Coordinate Analysis for Interpreting the Decoherence in the Coherent NO with Ar Collision: A Physico-mathematical Picture Using the Stereographic Projection and the Cusp Catastrophe
We present here a physico-mathematical picture for explaining the unexpectedly large decoherence cross-section (almost 10 times larger than its gas-kinematic cross-section) recently observed by Ureña and coworkers in their scattering experiment involving a coherent NO beam with Ar gas. The present topological picture consists of a stereographic projection and the cusp catastrophe theory of Thom, and we find that this model enables us to clarify the origin of the collisional decoherence. From the view of the stereographic projection, we can naturally introduce the wave property originating from the singular point at the “North pole” on the circumference S1 coordinate corresponding to a critical point for the collisional decoherence (condition 1). This picture also predicts the sudden changes of wave-phase collapse due to network interaction in the many-body system (condition 2). Thus it is hoped that the model proposed by Ureña et al. based on the dipole-induced dipole interaction in the NO + Ar system could be modified through this picture by including interactions with many Ar atoms in the environment. One way to fill the gap between the single-pair interaction picture and the multiple interaction one would be to employ theoretical calculations by use of the density matrix theory with and without adding the second Ar atom to the NO–Ar system. The cusp catastrophe theory reinforces the necessity of some cooperative network interaction between the coherent NO molecule and many neighboring Ar atoms and provides a qualitative scenario in which the whole system leads to a sudden change of the collisional decoherence of NO as a function of the control parameters (a, b). At this stage, the present physico-mathematical picture cannot give any specific values of the decoherence distance by the theory itself, but it clearly provides us a new topological concept for clarifying the origin of collisional decoherence which is strongly connected with the complexity of the system. Thus it gives us a global guide map toward further clarification of the collisional decoherence phenomenon with the aid of more sophisticated quantum mechanical calculations in the future.
We present here a physico-mathematical picture for explaining the unexpectedly large decoherence cross-section (almost 10 times larger than its gas-kinematic cross-section) recently observed by Ureña and coworkers in their scattering experiment involving a coherent NO beam with Ar gas. The present topological picture consists of a stereographic projection and the cusp catastrophe theory of Thom, and we find that this model enables us to clarify the origin of the collisional decoherence. From the view of the stereographic projection, we can naturally introduce the wave property originating from the singular point at the “North pole” on the circumference S1 coordinate corresponding to a critical point for the collisional decoherence (condition 1). This picture also predicts the sudden changes of wave-phase collapse due to network interaction in the many-body system (condition 2). Thus it is hoped that the model proposed by Ureña et al. based on the dipole-induced dipole interaction in the NO + Ar system could be modified through this picture by including interactions with many Ar atoms in the environment. One way to fill the gap between the single-pair interaction picture and the multiple interaction one would be to employ theoretical calculations by use of the density matrix theory with and without adding the second Ar atom to the NO–Ar system. The cusp catastrophe theory reinforces the necessity of some cooperative network interaction between the coherent NO molecule and many neighboring Ar atoms and provides a qualitative scenario in which the whole system leads to a sudden change of the collisional decoherence of NO as a function of the control parameters (a, b). At this stage, the present physico-mathematical picture cannot give any specific values of the decoherence distance by the theory itself, but it clearly provides us a new topological concept for clarifying the origin of collisional decoherence which is strongly connected with the complexity of the system. Thus it gives us a global guide map toward further clarification of the collisional decoherence phenomenon with the aid of more sophisticated quantum mechanical calculations in the future.
Quantum decoherence can be viewed as the mechanism responsible for the quantum-to-classical transition as the initially prepared quantum state interacts with its environment in an irreversible manner. One of the most common mechanisms responsible for the macroscopically observed decoherence involves collisions of an atom or molecule, initially prepared in a coherent superposition of states, with gas particles. In this work, a coherent superposition of quantum internal states of NO molecules is prepared by the interaction between the molecule with both a static and a radiofrequency electric field. Subsequently, NO + Ar collision decoherence experiments are investigated by measuring the loss of coherence as a function of the number of collisions. Data analysis using a model based on the interaction potential of the collisional partners allowed to unravel the molecular mechanism responsible for the loss of coherence in the prepared NO quantum superposition of internal states. The relevance of the present work relies on several aspects. On the one hand, the use of radio-waves introduces a new way for the production of coherent beams. On the other hand, the employed methodology could be useful in investigating the Stereodynamics of chemical reactions with coherent reagents.
In modern physics, quantum decoherence, a subject still under debate, is viewed as the mechanism responsible for the quantum -to-classical transition as the initially prepared quantum state interacts with its environment in an irreversible manner. As expected, one of the most common mechanisms responsible of the macroscopically observed decoherence involves collisions of an atom or molecule, initially prepared in a coherent superposition of states, with gas particles. In this work, a coherent superposition of quantum internal states of NO molecules is prepared by the interaction between the molecule with both a static and a radiofrequency electric field. Subsequently, NO+Ar collision decoherence experiments, are investigated by measuring the loss of coherence as a function of the number of collisions. Data analysis in the light of the interaction potential of the collisional partners allowed us to unravel the molecular mechanisms responsible for the loss of coherence in the prepared NO quantum superposition of internal states. The relevance of the present work relies on several aspects. On the one hand, the use of radio-waves introduces a new way for the production of coherent beams. On the other hand, the employed methodology, when satisfactorily applied to more collision systems, could be useful in designing experiments to reduce the environmental decoherence rate to levels necessary for quantum information processes.
The framework of classical physics encompasses the well-established and complete Helmholtz wave equation. Capable of accurately describing the propagation, interference and diffraction of steady-state harmonic waves such as acoustic and electromagnetic waves at the macroscopic scale, this equation has been validated by centuries of experiments and is widely recognized as a definitive formula in fundamental physics. Nevertheless, conventional physics has long imposed a rigid scope of application. The academic community has always adopted one-dimensional real scalar coordinates for the Helmholtz equation, limiting its use to macroscopic material wave fields, while never attempting to apply it to the microscopic quantum realm or the underlying ontological structure of the universe. Meanwhile, starting from the microscopic mathematical characteristics, Heisenberg’s matrix mechanics derives the uncertainty principle based on the non-commutation relation of matrices. It directly proves that microscopic mechanical quantities cannot be fully represented by real scalars, and that the microscopic universe is inherently governed by matrix-dimensional structures. This is the fundamental reason why numerous paradoxes persist within quantum mechanics under the framework of real coordinates. Addressing the dual limitations of existing physical theories, this paper presents original research. While fully retaining the differential operators, wave constraints and steady-state solution rules of the classical Helmholtz equation, and introducing no new physical constants or artificial auxiliary hypotheses, this work merely replaces the real spatial coordinates X and Y in the equation with second-order two-dimensional linear matrix coordinates. On this basis, a novel theoretical system of two-dimensional linear waves tailored for the microscopic ontology of the universe is independently established. To clarify: classical physics only adopts the Helmholtz wave with real coordinates to interpret macroscopic wave motions. By contrast, the Helmholtz wave model built upon two-dimensional linear matrix coordinates is an exclusive original theory proposed in this paper. It forms a brand-new independent classical system for depicting the true microscopic essence of the universe. Employing rigorously verified classical mathematical and physical tools, including the classical Helmholtz wave principle, Heisenberg’s matrix mechanics, the uncertainty principle, the linear projection theorem and the wave field superposition principle, this paper systematically elaborates the mathematical structure, dimensional properties and evolutionary laws of two-dimensional linear waves. It further reveals the ultimate physical nature of quantum measurement collapse. All substances in the microscopic world exist inherently as two-dimensional linear Helmholtz waves. Human macroscopic perception and detection devices can only process one-dimensional real-valued information. Essentially, the act of observation is not the random collapse of the wave function as defined in standard quantum mechanics. Instead, the observing system actively extracts one degree of freedom from the two-dimensional matrix wave. The remaining single dimension undergoes dimensionality reduction and projection onto the one-dimensional real physical space, giving rise to the apparent phenomenon of localized particles. This original theory explains two core experimental puzzles that have perplexed quantum physics for a century, without logical contradictions or ad hoc supplements. First, continuous observation of the interference pattern in the double-slit experiment collects global steady-state information of the superimposed two-dimensional waves, and no dimensional extraction occurs, so no collapse takes place. Second, when a single photon reaches the human retina or a single-point detector conducts fixed-position detection, the observing system imposes localized boundary conditions to forcibly extract dimensions from the wave field. This projects the two-dimensional wave onto the one-dimensional physical space, which manifests macroscopically as wave function collapse. This research breaks down the barrier between macroscopic classical waves and microscopic quantum phenomena. The proposed original classical model provides a unified interpretation of microscopic effects including wave-particle duality and quantum measurement collapse, offering a new fundamental perspective for the research on the grand unification of fundamental physics.
The framework of classical physics includes the well-established Helmholtz wave equation, which accurately describes the propagation, interference, and diffraction behaviors of steady-state time-harmonic waves such as acoustic and electromagnetic waves at the macroscopic level. Verified by centuries of experiments, it is a universally recognized deterministic formula in fundamental physics. However, traditional physics has long operated within fixed boundaries: academia has always matched the Helmholtz equation with one-dimensional real scalar coordinates, applying it only to macroscopic matter wave fields, and never attempting to use it to describe the microscopic quantum world or the underlying ontology of the universe. Meanwhile, Heisenberg’s matrix mechanics, starting from the microscopic mathematical properties, derived the uncertainty principle based on the non-commutation relations of matrices, directly proving that microscopic mechanical quantities cannot be completely represented by real scalars. The microscopic universe is inherently adapted to matrix-dimensional structures, which is the fundamental cause of the proliferation of paradoxes in quantum mechanics under the real-coordinate framework.Addressing these dual shortcomings of the existing physical system, this paper presents original research: it fully retains the differential operators, wave constraints, and steady-state solution rules of the classical Helmholtz equation, introduces no new physical constants or artificial ad-hoc assumptions, and only replaces the real-space coordinates X and Y within the equation with second-order two-dimensional linear matrix coordinates, independently constructing a theoretical system of two-dimensional linear two-dimensional waves adapted to the microscopic ontology of the universe. It must be clearly defined: classical physics only has real-coordinate Helmholtz waves, used to explain macroscopic waves; the Helmholtz wave model based on two-dimensional linear matrix coordinates is an exclusive original theory of this paper, forming a dedicated new classical system to describe the true microscopic ontology of the universe.Drawing on rigorously verified traditional mathematical and physical tools such as the classical Helmholtz wave principle, Heisenberg’s matrix mechanics, the uncertainty principle, the linear projection theorem, and the principle of wave field superposition, this paper systematically elaborates the mathematical structure, dimensional characteristics, and evolutionary laws of two-dimensional linear two-dimensional waves, and reveals the ultimate physical nature of quantum observation collapse: all material entities in the microscopic world are two-dimensional linear two-dimensional Helmholtz waves, while the human macroscopic perceptual world and detection devices can only carry one-dimensional real information. The essence of the observation process is not the random collapse of the wavefunction as defined by quantum mechanics, but rather the observation system actively extracting one degree of freedom from the two-dimensional matrix wave, with the remaining single dimension completing dimensionality-reduction projection and mapping into the one-dimensional real physical space, ultimately forming the observational illusion of localized particles.This original theory can explain the two core experimental puzzles that have plagued quantum physics for a century without contradictions or ad-hoc patches: First, when observing the interference pattern throughout the double-slit experiment, this observation mode collects the steady-state information of the global superposition of two-dimensional waves without performing dimensional extraction, and thus does not trigger collapse; Second, when a single photon enters the human eye’s retina or a single-point detector completes fixed-point detection, the observation system imposes localized boundary conditions to force the extraction of the wave field dimension, realizing the "screen projection" imaging of two-dimensional waves onto one-dimensional reality, which macroscopically manifests as wavefunction collapse. This study breaks down the barriers between macroscopic classical waves and microscopic quantum phenomena, providing a unified explanation for microscopic phenomena such as wave-particle duality and quantum observation collapse with an original classical model, and offering a new underlying perspective for the grand unification research in fundamental physics.
We study the loss of spatial coherence in the extended wave function of fullerenes due to collisions with background gases. From the gradual suppression of quantum interference with increasing gas pressure we are able to support quantitatively both the predictions of decoherence theory and our picture of the interaction process. We thus explore the practical limits of matter wave interferometry at finite gas pressures and estimate the required experimental vacuum conditions for interferometry with even larger objects.
The act of measurement on a quantum state is supposed to "dephase" (dephasing refers to the phenomenon that the states lose phase coherence; then the phases get randomized in interaction with a bath of other oscillators, which is referred to as "decoherence"), then "decohere" and "collapse" (or more precisely "register" and "reduce") the state into one of several eigenstates of the operator corresponding to the observable being measured. This measurement process is sometimes described as outside standard quantum-mechanical evolution and not calculable from Schrödinger's equation. Progress has, however, been made in studying this problem with two main calculation tools-one uses a time-independent Hamiltonian, while a rather more general approach proving that decoherence occurs under some generic conditions. The two general approaches to the study of wave-function collapse are as follows. The first approach, called the "consistent" or "decoherent"' histories approach, studies microscopic histories that diverge probabilistically and explains collapse as an event in our particular history. The other, referred to as the "environmental decoherence" approach studies the effect of the environment upon the quantum system, to explain wave-function decoherence which is produced by irreversible effects of various sorts. However, as we know, wave-function collapse is not related to thermal connection with the environment, rather, it is inherent to how measurements are performed by macroscopic apparata. In the "environmental decoherence" approach, one studies decoherence using a Markovian-approximated Master equation to study the time-evolution of the reduced density matrix (post dephasing) and obtains the long-time dependence of the off-diagonal elements of this matrix. The calculation in this paper studies the evolution of a quantum system starting with "dephasing" followed by the effects of the environment with some differences from prior analyses. We start from the Schrödinger equation for the state of the system, with a time-dependent Hamiltonian that reflects the actual microscopic interactions that are occurring. Then we systematically solve (exactly) for the time-evolved state, without invoking a Markovian approximation when writing out the effective time-evolution equation, i.e., keeping the evolution unitary until the end. This approach is useful, and it shows that the system wave-function will explicitly "un-collapse" if the measurement apparatus is sufficiently small. However, in the limit of a macroscopic system, this "dephasing" quickly leads to "decoherence"-collapse is a temporary state that will simply take extremely long (of the order of multiple universe lifetimes) to reverse. This has been attempted previously and our calculation is particularly simple and calculable. We make some connections to the work by Linden et al. while doing so. The calculation in this paper has interesting implications for the interpretation of the Wigner's friend experiment, as well as the Mott experiment, which is explored in "Connection to some general theoretical results" and "Recurrence times" (especially the enumerated points in "Recurrence times"). The upshot is that as long as Wigner's friend is macroscopically large (or uses a macroscopically large measuring instrument), no one needs to worry that Wigner would see something different from his friend. Indeed, Wigner's friend does not even need to be conscious during the measurement that she conducts. It also allows one to reasonably interpret some of the more recent thought experiments proposed. In particular, as a result of the mathematical analysis, the short-time behavior of a collapsing system, at least the one considered in this paper, is not exponential. Instead, it is the usual Fermi-golden rule result. The long-term behavior is, of course, still exponential. This is a second novel feature of the paper-we connect the short-term Fermi-golden rule (quadratic-in-time behavior) transition probability to the exponential long-time behavior of a collapsing wave-function in one continuous mathematical formulation.