What is tested when experiments test that quantum dynamics is linear

Experiments that look for nonlinear quantum dynamics test the fundamental premise of physics that one of two separate systems can influence the physical behavior of the other only if there is a force between them, an interaction that involves momentum and energy. The premise is tested because it is the assumption of a proof that quantum dynamics must be linear. Here variations of a familiar example are used to show how results of nonlinear dynamics in one system can depend on correlations with the other. Effects of one system on the other, influence without interaction between separate systems, not previously considered possible, would be expected with nonlinear quantum dynamics. Whether it is possible or not is subject to experimental tests together with the linearity of quantum dynamics. Concluding comments and questions consider directions our thinking might take in response to this surprising unprecedented situation.Comment: 14 pages, Title changed, sentences adde

Weak Decoherence and Quantum Trajectory Graphs

Griffiths' ``quantum trajectories'' formalism is extended to describe weak decoherence. The decoherence conditions are shown to severely limit the complexity of histories composed of fine-grained events.Comment: 12 pages, LaTeX, 3 figures (uses psfig), all in a uuencoded compressed tar fil

Assumptions that imply quantum dynamics is linear

A basic linearity of quantum dynamics, that density matrices are mapped linearly to density matrices, is proved very simply for a system that does not interact with anything else. It is assumed that at each time the physical quantities and states are described by the usual linear structures of quantum mechanics. Beyond that, the proof assumes only that the dynamics does not depend on anything outside the system but must allow the system to be described as part of a larger system. The basic linearity is linked with previously established results to complete a simple derivation of the linear Schrodinger equation. For this it is assumed that density matrices are mapped one-to-one onto density matrices. An alternative is to assume that pure states are mapped one-to-one onto pure states and that entropy does not decrease.Comment: 10 pages. Added references. Improved discussion of equations of motion for mean values. Expanded Introductio

One qubit almost completely reveals the dynamics of two

From the time dependence of states of one of them, the dynamics of two interacting qubits is determined to be one of two possibilities that differ only by a change of signs of parameters in the Hamiltonian. The only exception is a simple particular case where several parameters in the Hamiltonian are zero and one of the remaining nonzero parameters has no effect on the time dependence of states of the one qubit. The mean values that describe the initial state of the other qubit and of the correlations between the two qubits also are generally determined to within a change of signs by the time dependence of states of the one qubit, but with many more exceptions. An example demonstrates all the results. Feedback in the equations of motion that allows time dependence in a subsystem to determine the dynamics of the larger system can occur in both classical and quantum mechanics. The role of quantum mechanics here is just to identify qubits as the simplest objects to consider and specify the form that equations of motion for two interacting qubits can take.Comment: 6 pages with new and updated materia

Lorentz transformations that entangle spins and entangle momenta

Simple examples are presented of Lorentz transformations that entangle the spins and momenta of two particles with positive mass and spin 1/2. They apply to indistinguishable particles, produce maximal entanglement from finite Lorentz transformations of states for finite momenta, and describe entanglement of spins produced together with entanglement of momenta. From the entanglements considered, no sum of entanglements is found to be unchanged.Comment: 5 Pages, 2 Figures, One new paragraph and reference adde

Affine maps of density matrices

For quantum systems described by finite matrices, linear and affine maps of matrices are shown to provide equivalent descriptions of evolution of density matrices for a subsystem caused by unitary Hamiltonian evolution in a larger system; an affine map can be replaced by a linear map, and a linear map can be replaced by an affine map. There may be significant advantage in using an affine map. The linear map is generally not completely positive, but the linear part of an equivalent affine map can be chosen to be completely positive and related in the simplest possible way to the unitary Hamiltonian evolution in the larger system.Comment: 4 pages, title changed, sentence added, reference update

Subscale Flight Testing for Aircraft Loss of Control: Accomplishments and Future Directions

Subscale flight-testing provides a means to validate both dynamic models and mitigation technologies in the high-risk flight conditions associated with aircraft loss of control. The Airborne Subscale Transport Aircraft Research (AirSTAR) facility was designed to be a flexible and efficient research facility to address this type of flight-testing. Over the last several years (2009-2011) it has been used to perform 58 research flights with an unmanned, remotely-piloted, dynamically-scaled airplane. This paper will present an overview of the facility and its architecture and summarize the experimental data collected. All flights to date have been conducted within visual range of a safety observer. Current plans for the facility include expanding the test volume to altitudes and distances well beyond visual range. The architecture and instrumentation changes associated with this upgrade will also be presented

Average symptom trajectories following incident radiographic knee osteoarthritis: data from the Osteoarthritis Initiative

Introduction Previous research has identified the existence of a prodromal phase of symptom worsening beginning on average 2–3 years prior to the first appearance of radiographic knee osteoarthritis (OA). The current study extends these observations to investigate the trajectory of self-reported pain, stiffness, function and other symptoms following the incidence of radiographic OA. Methods Data were from the incidence cohort of the Osteoarthritis Initiative public use data sets. Cases were defined as knees without symptoms at enrolment, which developed incident radiographic OA (Kellgren and Lawrence grade ≥2) at any of the first 4 annual follow-up visits. Symptoms investigated were knee-specific Western Ontario & McMaster Universities Osteoarthritis Index and Knee injury and Osteoarthritis Outcome Score subscale scores and individual items, available up to 3 years before and 5 years after the incidence of radiographic OA. Trajectories of having at least one of the symptoms from a subscale, and for each individual symptom over time, were fitted using multilevel logistic regression models. Results The probability of symptoms following the initial prodromal phase generally stabilised, whereas the probability of moderate, severe or extreme symptoms was consistently low. Two exceptions were pain frequency, which increased greatly in the lead up to incidence, then decreased slightly, and audible joint sounds, which had a much higher overall probability, and after increasing prior to incident radiographic OA, stabilised then started to increase again at 5 years. Conclusions Following an increase in the risk of symptoms during the prodromal phase, this risk does not continue to increase in the period up to 5 years after the incidence of radiographic OA