Quantum Wave Mechanics Ch 51 Coupled Oscillators

2007

The present paper presents a new general conception of interaction between physical systems, differing significantly from that of both classical physics and quantum physics as generally understood. We believe this conception could provide the basis for a coherent understanding of several classes of natural phenomena that until now have been studied only in a piece-meal fashion. For example: 1) the universal tendency for physical systems to associate together into stable dynamic formations; 2) the seemingly unlimited capacity for generation of physical objects in Nature, including the emergence of coherent, quantized states in physical systems of the most varied nature; 3) the existence of close couplings between processes whose characteristic lengthscales, frequency-and energy-ranges differ by many orders of magnitude. The proposed conception first emerged in connection with experimental studies of the nonlinear behavior of coupled electromagnetic oscillators, and the discovery of two fundamental phenomena that had been overlooked in the classical theory of oscillations: the quantization of amplitudes as a result of so-called argumental interactions, and the spontaneous aggregative behavior of multiply-coupled resonators placed in a highfrequency field. The essential features of these phenomena are summarized in the first two sections of the paper, after which we demonstrate how the underlying physical principles can be combined under a single notion of interaction, providing a mechanism by which a practically unlimited wealth of physical objects could be generated by the interaction of just a few. The final section puts forward some preliminary ideas about the electromagneto-mechanical dual nature of physical objects as oscillatory processes, suggesting a universal scope for the proposed conceptions.

Quantum Theory: A Two-Time Success Story, 2014

A thought experiment is proposed to demonstrate the existence of a gravitational, vector Aharonov-Bohm effect. We begin the analysis starting from four Maxwell-like equations for weak gravitational fields interacting with slowly moving matter. A connection is made between the gravitational, vector Aharonov-Bohm effect and the principle of local gauge invariance for nonrelativistic quantum matter interacting with weak gravitational fields. The compensating vector fields that are necessitated by this local gauge principle are shown to be incorporated by the DeWitt minimal coupling rule. The nonrelativistic Hamiltonian for weak, time-independent fields interacting with quantum matter is then extended to time-dependent fields, and applied to problem of the interaction of radiation with macroscopically coherent quantum systems, including the problem of gravitational radiation interacting with superconductors. But first we examine the interaction of EM radiation with superconductors in a parametric oscillator consisting of a superconducting wire placed at the center of a high Q superconducting cavity driven by pump microwaves. Some room-temperature data will be presented demonstrating the splitting of a single microwave cavity resonance into a spectral doublet due to the insertion of a central wire. This would represent an unseparated kind of parametric oscillator, in which the signal and idler waves would occupy the same volume of space. We then propose a separated parametric oscillator experiment, in which the signal and idler waves are generated in two disjoint regions of space, which are separated from each other by means of an impermeable superconducting membrane. We find that the threshold for parametric oscillation for EM microwave generation is much lower for the separated configuration than the unseparated one, which then leads to an observable dynamical Casimir effect. We speculate that a separated parametric oscillator for generating coherent GR microwaves could also be built.

Quantum Wave Mechanics 4th ed., 2022

For mass in motion, the gravitational field undergoes a Lorentz contraction in the direction of motion. Mass motion constitutes a mass current analogous to an electric current. As a result, there is a circumferential gravitomagnetic field similar to the magnetic field of an electric current albeit much weaker to the large gravitomagnetic permeability. Relative motion generates a cogravitation field K in the Jefimenko model exerting a force F (= m(v x K) on a moving mass with velocity v in the direction of motion. A gravikinetic field is analogous to an electrokinetic field opposing motion. The cogravitation force associated with Lagrange orbital positions is illustrated.

Quantum Wave Mechanics 4th ed., 2022

Calculation of the gravitation force between electrons according to the Macken model is described in terms of strain amplitude relating the nonlinear vacuum energy resonance at the Compton and Planck scales. Diagrams of the vacuum nonlinearity and electron vacuum resonance are illustrated. Electric charge results from a slight spin precession of the electron with whirl no. equal to the inverse fine structure constant. Electrostatic and gravitation force between electrons are compared. Gravitation force arises as a result of a gradient in the EM spectral energy density gradient. Both light and matter are subject to gravitational scalar and vector potential effects. The generalized Newtonian force equation advanced by Jefimenko includes scalar and vector potential components. The gravitational vector potential is proportional to the velocity of the gravitational scalar potential. The gravikinetic field opposes changes in mass motion. Photon wave function interference produces an effective mass due to change in momentum in regions of increased EM energy density. Similarly, matter wave interference is responsible for relativistic mass increase of a moving standing wave due to change of momentum in regions of increased EM energy density.

2022

Recent spectacular results of gravitational waves obtained by the LIGO system, with frequencies in the 100 Hz regime, make corresponding laboratory experiments with full control over cause and effect of great importance. Dynamic measurements of gravitation in the laboratory have to date been scarce, due to difficulties in assessing non-gravitational crosstalk and the intrinsically weak nature of gravitational forces. In fact, fully controlled quantitative experiments have so far been limited to frequencies in the mHz regime. New experiments in gravity might also yield new physics, thereby opening avenues towards a theory that explains all of physics within one coherent framework. Here we introduce a new, fully-characterized experiment at three orders of magnitude higher frequencies. It allows experimenters to quantitatively determine the dynamic gravitational interaction between two parallel beams vibrating at 42 Hz in bending motion. The large amplitude vibration of the transmitter...

2008

The work reported here originates in the discovery, four decades ago, of a previouslyunknown type of self-organizing interaction among oscillating systems --so-called argumental interactions --and of "quantized" modes of behavior in macroscopic argumentally-coupled oscillators, having no equivalent in the classical theory of oscillations . Argumental interaction is characterized by the property, that the exchange of energy is regulated by phase-frequency-amplitude fluctuations in the participating oscillating systems, while each of them operates at very nearly its own proper frequency and retains (in the mean) its characteristic dynamic parameters. Argumental interactions can be demonstrated in a variety of electromechanical devices, the simplest of which belongs in every physics classroom: A pendulum (1 Hz) interacting with an alternating-current electromagnet (30-1000 Hz), and possessing a discrete series of stable amplitudes. The argumental mechanism lies at the basis of a second remarkable phenomenon, discovered around the same time: when placed in a high-frequency EM field, electrical resonators (such as LCR circuits), coupled to each other by inductive, capacitative and resistive couplings and free to move in space under the influence of the corresponding ponderomotive forces, show the tendency to group themselves into stable spatial configurations .

Reviews of Modern Physics, 1980

The monitoring of a quantum-mechanical harmonic oscillator on which a classical force acts is important in a variety of high-precision experiments, such as the attempt to detect gravitational radiation. This paper reviews the standard techniques for monitoring the oscillator, and introduces a new technique which, in principle, cd determine the details of the force with arbitrary accuracy, despite the quantum properties of the oscillator. The standard method for monitoring the oscillator is the "amplitude-andphase" method (position or momentum transducer with output fed through a narrow-band amplifier). The accuracy obtainable by this method is limited by the uncertainty principle ("standard quantum limit" ). To do better requires a measurement of the type which Braginsky has called "quantum nondemolition. " A well known quantum nondemolition technique is *'quantum counting, " which can detect an arbitrarily weak classical force, but which cannot provide good accuracy in determining its precise time dependence. This paper considers extensively a new type of quantum nondemolition measurementa "back-action-evading" measurement of the real part X, {or the imaginary part X2) of the oscillator's complex amplitude. In principle X, can be measured "arbitrarily quickly and arbitrarily accurately, " and a sequence of such measurements can lead to an arbitrarily accurate monitoring of the classical force. The authors describe explicit Gedanken experiments which demonstrate that X, can be measured arbitrarily quickly and arbitrarily accurately. In these experiments the measuring apparatus must be coupled to both the position {position transducer} and the momentum (momentum transducer) of the oscillator, and both couplings must be modulated sinusoidally. For a given measurement time the strength of the coupling determines the accuracy of the measurement; for arbitrarily strong coupling the measurement can be arbitrarily accurate. The momentum transducer" is constructed by combining a "velocity transducer" with a "negative capacitor'" or "negative spring. " The modulated couplings are provided by an external, -classical generator, which can be realized as a harmonic oscillator excited in an arbitrarily energetic, coherent state. One can avoid the use of two transducers by making "stroboscopic measurements" of X" in which one measures position (or momentum) at half-cycle intervals.

The European Physical Journal D, 2020

Phenomenological models aiming to join gravity and quantum mechanics often predict effects that are potentially measurable in refined low-energy experiments. For instance, modified commutation relations between position and momentum, that account for a minimal scale length, yield a dynamics that can be codified in additional Hamiltonian terms. When applied to the paradigmatic case of a mechanical oscillator, such terms, at the lowest order in the deformation parameter, introduce a weak intrinsic nonlinearity and, consequently, deviations from the classical trajectory. This point of view has stimulated several experimental proposals and realizations, leading to meaningful upper limits to the deformation parameter. All such experiments are based on classical mechanical oscillators, i.e., excited from a thermal state. We remark indeed that decoherence, that plays a major role in distinguishing the classical from the quantum behavior of (macroscopic) systems, is not usually included in ...

2014

Understanding the role of higher derivatives is probably one of the most relevant questions in quantum gravity theory. Already at the semiclassical level, when gravity is a classical background for quantum matter fields, the action of gravity should include fourth derivative terms to provide renormalizability in the vacuum sector. The same situation holds in the quantum theory of metric. At the same time, including the fourth derivative terms means the presence of massive ghosts, which are gauge-independent massive states with negative kinetic energy. At both classical and quantum level such ghosts violate stability and hence the theory becomes inconsistent. Several approaches to solve this contradiction were invented and we are proposing one more, which looks simpler than those what were considered before. We explore the dynamics of the gravitational waves on the background of classical solutions and give certain arguments that massive ghosts produce instability only when they are present as physical particles. At least on the cosmological background one can observe that if the initial frequency of the metric perturbations is much smaller than the mass of the ghost, no instabilities are present.

2012

In this experimental study, the synchronized motion observed in pairs of nonlinear oscillators coupled through a suspended rigid bar, is analyzed. In particular, the dynamics of two mass-spring-damper oscillators and the dynamics of two van der Pol oscillators are considered. It is shown that in both cases, the oscillators may exhibit in-phase and anti-phase synchronization. The experiments are executed in an experimental setup, consisting of two mass-spring-damperoscillators coupled through a suspended rigid bar. A relation between the obtained results and Huygens’ experiment of pendulum clocks is emphasized.