4,225 research outputs found

### 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

### 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

### Change of the plane of oscillation of a Foucault pendulum from simple pictures

The change of the plane of oscillation of a Foucault pendulum is calculated
without using equations of motion, the Gauss-Bonnet theorem, parallel
transport, or assumptions that are difficult to explain.Comment: 5 pages, 4 figure

### 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

### Cosmology calculations almost without general relativity

The Friedmann equation is derived for a Newtonian universe. Changing mass
density to energy density gives exactly the Friedmann equation of general
relativity. Accounting for work done by pressure then yields the two Einstein
equations that govern the expansion of the universe. Descriptions and
explanations of radiation pressure and vacuum pressure are added to complete a
basic kit of cosmology tools. It provides a basis for teaching cosmology to
undergraduates in a way that quickly equips them to do basic calculations. This
is demonstrated with calculations involving: characteristics of the expansion
for densities dominated by radiation, matter, or vacuum; the closeness of the
density to the critical density; how much vacuum energy compared to matter
energy is needed to make the expansion accelerate; and how little is needed to
make it stop. Travel time and luninosity distance are calculated in terms of
the redshift and the densities of matter and vacuum energy, using a scaled
Friedmann equation with the constant in the curvature term determined by
matching with the present values of the Hubble parameter and energy density.
General relativity is needed only for the luminosity distance, to describe how
the curvature of space, determined by the energy density, can change the
intensity of light by changing the area of the sphere to which the light has
spread. Thirty-one problems are included.Comment: 21 pages, 31 problems, 1 figure, submitted to American Journal of
Physics, refereed, revised, recommended for publication by refere

### 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

### 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

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