text:
\section{\large \bf INTRODUCTION AND SURVEY OF RESULTS}

Between the 1940s and the early 1960s, several researchers proposed the
possibility of measuring the retardation of gravitational interaction
using laboratory  experiments
$[1,2,3,4]$. Because of the poor technology at that time and
contradictory theoretical predictions about the retardation,  interest in
the subject declined. No experiments were performed during this  period,
and after 1962, the topic was never discussed again in the literature.
At the 1996  Virgo conference, a new experimental set-up was described
for the purpose of  testing the retardation of gravitational interaction
in the immediate vicinity of  a vibrating mass distribution $[5]$.
Discussions following the talk indicated that there is still ambiguity
about the existence of such a retardation. In this paper, we will discuss
the common arguments which lead to the conclusion that gravitational
forces generated by  oscillating mass distributions are instantaneous in
the near-field. All of these arguments have the weakness that they are
not valid at extremely small distances from the oscillating source. We
will analyze the gravitational forces in the immediate vicinity of a
specific oscillating mass distribution, for which the  dominant  part of
the corresponding linearized Einstein equations can be solved.  It shows
that there is a possibly detectable retardation of the gravitational
forces in the immediate vicinity of the source, which converges to zero
with increasing  distance. The dominant length scale for the decay of the
retardation is given by  the {\em oscillation amplitude} of the mass
distribution and can be very small. Experimental verification of this
local retardation effect would provide the first direct observation of
propagating gravitational fields. We propose a laboratory experiment
which requires a highly accurate phase measurement to test our  result.
Given the state of modern  technology, this measurement may now be
possible.

\section{\large \bf DEFINITION, DISCUSSION AND ANALYSIS OF THE  \\
 MATHEMATICAL MODEL}

We consider an idealized experiment in a laboratory environment,
consisting of a mass-balanced, mechanical two-body oscillator, which
generates disturbances in the space-time metric. The oscillator consists
of a point mass $m$ which  is connected by way of a spring with
negligible mass to a second point mass $M
\gg m$. The resulting mass-spring system oscillates with eigenfrequency
$\omega$ about its center of gravity, and does not interact dynamically
with additional, external masses. The distance between the masses
$m$ and $M$ is assumed to be much larger than the oscillation amplitude
$d$ of the smaller mass $m$. The oscillation amplitude $D=\frac{m}{M}d$
of $M$, which is calculated with classical mechanics, is much smaller
than $d$ and leads to negligible time-dependent gravitational effects in
the immediate vicinity of
$m$, as will be shown in section II.1. We will mainly consider the
time-dependent gravitational forces generated by
$m$, and will thus refer to $m$ as the "source", or the "source mass".
Another mechanical oscillator,  tuned to resonance to detect these
gravitational forces, is placed on the oscillator axis at a distance of
order
$O(d)$ from $m$. The purpose of this paper is to show that the
gravitational forces generated in this extreme near-field  laboratory
experiment are retarded, which may be verifiable with modern technology.
Due to many objections against experiments of this kind in the past, we
will first discuss the common counterarguments.

The occurrence of a measurable retardation in the proposed system may
seem  problematic  for several reasons. One may suspect that the theorem
about the  non-existence of  gravitational dipole radiation is violated
by the mass-balanced, mechanical two-body oscillator described above. It
states that isolated mechanical systems  cannot generate any dipolar
gravitational radiation, due to momentum and angular  momentum
conservation within the system
$[6]$. However, this argument does not contradict the existence of
retarded gravitational forces which are strongly  localized around the
source. We will refer to the {\em immediate vicinity} of $m$ as a region
around $m$ with a diameter of order $O(d)$. In section II.1, we will
prove that  the {\em time-dependent} gravitational forces due to the
larger mass $M$ can be neglected in the immediate vicinity of the source
mass $m$, although the static field due to $M$ may dominate over the
static field generated by $m$. The mass $m$, which is by itself not an
isolated system,  appears locally to be an isolated oscillator.  Because
the momentum of $m$ is by itself not conserved, $m$ is allowed to radiate
gravitationally in its immediate vicinity without contradicting the
overall conservation of momentum. At larger distances from the
oscillator, the time-dependent gravitational forces due to $M$ and $m$
have equal strength, and we will show  in section II.2.1 that their
radiative contributions cancel. Hence, there is no contradiction to
overall momentum  conservation.

Near-field set-ups similar to the proposed one are usually analyzed with
the "near  zone" limit used in radiation theory,  typically defined as a
distance range comparable to the wavelength of the radiated signals,
which is usually very large. At these large distances  from the source,
the vibrating mass distribution can be very accurately modelled as a
series of multipole coefficients, which neglect all retardation effects
within the source. But in the immediate vicinity of the source, i.e. at
distances comparable to its vibration amplitude, it is not possible to
make this simplification. Instead, one must take local retardation
effects into account, even if they disappear at large distances.

Another common objection against  the existence of observable
retardations in the proposed set-up arises from an electrodynamic
analogy. Retarded electromagnetic  potentials may result in almost
instantaneous electromagnetic fields, due to certain  cancellation
effects $[7]$. This phenomenon occurs in the "near zone" introduced
above, and is consistent with our results. We will show in section II.2.2
that the retardation of the gravitational forces decreases {\em
continuously} to zero with increasing distance from the source, and that
in the immediate vicinity of $m$, the retardation has possibly measurable
values.
\\

We will first show that our proposed system can be analyzed with the
linearized Einstein equations.  Let $c \approx 3 \cdot
10^{8}[\frac{m}{sec}]$ denote the  vacuum speed of light. We choose a
local Minkowskian coordinate frame $\lbrace ct,x,y,z \rbrace$, in which
$m$ oscillates about the origin with amplitude $d$, angular frequency
$\omega$,  and parallel to the $z$ axis
\begin{equation}
\vec{z}(t) = \; \hat{z} \; d \: \sin \omega t
\end{equation}
$\hat{z}$ denotes the unit vector in the $z$ direction, and $\vec{z}(t)$
is the location of $m$ at time $t$. We assume mass $m \approx
O(10^{-1}[kg])$,  oscillation amplitude $d\approx O(10^{-2}[m])$, and
angular frequency $\omega \approx O(10^{3}[\frac{rad}{sec}])$  as a set of
reasonable parameters.

To keep track of order-of-magnitude estimates, we  introduce dimensionless
variables. We define the dimensionless four-vector
$(\tau,\vec{\xi})\,:=\,\frac{1}{d}\,(ct,\vec{x})$ and use the oscillation
amplitude $d$ to represent the length scale. The energy momentum tensor
${\bf T}_{\mu\nu}$ is related  to the dimensionless $T_{\mu \nu}$ by
${\bf T}_{\mu \nu} =: \frac{m c^{2}}{d^{3}}T_{\mu \nu}$, and the Einstein
tensor ${\bf G}_{\mu \nu}$ which has the dimensions $[m^{-2}]$ introduces
${\bf G}_{\mu\nu} =: \frac{1}{d^{2}} G_{\mu \nu}$. The Einstein  equations,
written in terms of dimensionless variables, yield
\begin{equation}
G_{\mu \nu} = \; \frac{8 \pi m G}{c^{2}\; d}\;\; T_{\mu
\nu}\;\;\;,
\label{dimlEe}
\end{equation}
in which $G \approx 6.67 \cdot 10^{-11}[\frac{m^{3}}{sec^{2}kg}]$ is the
universal gravitational constant. The number
$\frac{8 \pi G m}{c^{2} d} \approx 10^{-25}$ estimates the strength of
gravitational signals due to $m$. We bound the mass of $M$ by
$\frac{M}{m}<O(10^{2})$, such that all considerations about $m$ also
apply to $M$. The RHS of Eq. (~\ref{dimlEe}) is very  small if
$\parallel T_{\mu \nu} \parallel\ll 10^{25}$, and the linearized Einstein
equations can be used in this case. Consequently, one expands the
space-time metric $g_{\mu\nu} = \eta_{\mu\nu} + h_{\mu\nu}$ around the
flat Minkowski metric $\eta_{\mu\nu}$, and introducing
$\gamma_{\mu\nu}:=h_{\mu\nu}-\frac{1}{2}\eta_{\mu\nu}h^{\lambda}_{\lambda}$,
Eq. (~\ref{dimlEe}) reduces to
\begin{equation}
\left(\partial^{2}_{\tau} - \Delta_{\vec{\xi}}\right)\;
\gamma_{\mu\nu}(\tau,\vec{\xi}) = \; - \;
\frac{16 \pi m G}{c^{2} d} \; \; T_{\mu\nu}(\tau,\vec{\xi}) \;\;\; ,
\label{linEinstEq}
\end{equation} by use of the Hilbert gauge condition
$\gamma^{\nu}_{\mu,\nu}=0$ $[8]$. $\Delta_{\vec{\xi}}$ is the Laplace
operator in the dimensionless spatial coordinates
$\vec{\xi}$. Eq. (~\ref{linEinstEq}) is solved by the superposition of a
particular solution with a homogenous solution. The full particular
solution includes the influences of both $M$ and $m$. We impose the
boundary condition
$\gamma_{\mu\nu}\rightarrow 0$ in the limit $|\vec{\xi}|\rightarrow
\infty$. Since the full particular solution is asymptotically zero, as
will be shown in section II.2, this requires the homogenous solution,
given by a superposition of plane waves with constant amplitudes, to be
zero. Therefore,
$\gamma_{\mu\nu}$ is the particular solution of Eq. (~\ref{linEinstEq}).
Due to linearity,  the contributions from $M$ and $m$ to $\gamma_{\mu\nu}$
and $T_{\mu\nu}$ are additive and can be discussed separately, thus
$\gamma_{\mu\nu}=\gamma^{(m)}_{\mu\nu}+\gamma^{(M)}_{\mu\nu}$ and
$T_{\mu\nu}=T^{(m)}_{\mu\nu}+T^{(M)}_{\mu\nu}$. We will first analyze the
influences due to $m$, determined by $\gamma^{(m)}_{\mu\nu}$ and
$T^{(m)}_{\mu\nu}$. We obtain
\begin{equation}
\gamma^{(m)}_{\mu\nu}(\tau,\vec{\xi}) = \; - \; \frac{4 m G}{c^{2}d}
\int d \tau' d^{3}\vec{\xi}' \; \frac{T^{(m)}_{\mu\nu} (\tau',\vec{\xi}')}
{|\vec{\xi} -
\vec{\xi}'|}\; \delta(\tau' - \tau + |\vec{\xi} - \vec{\xi}'|) \;
\Theta(\tau - \tau')\;,
\end{equation}
in which $\delta$ is the Dirac-delta distribution and $\Theta$ is the
Heaviside function. The perturbation parameter of our analysis is the
ratio $\beta = \frac{\omega d}{c} \approx O(10^{-8})$ between the maximal
velocity
$\omega d$ of the oscillating mass $m$ and the speed of light $c$. Our
analysis will show that the retardation is an effect of the order
$O(\beta)$. Therefore, a relative accuracy of the order $O(\beta^{2})$ is
sufficient for our calculations. $T^{(m)}_{00}$ can be decomposed into
\begin{eqnarray*}
T^{(m)}_{00}(\tau',\vec{\xi}')\,=\,T_{00}^{(m,0)}(\tau',\vec{\xi}')\,+\,
T_{00}^{(m,2)}(\tau',\vec{\xi}')\;,
\end{eqnarray*}
where $T_{00}^{(m,i)}$ is of order $O(\beta^{i})$. Note
that this decomposition does not correspond to the full Taylor expansion
with respect to $\beta$. $T_{00}^{(m,0)}$ is the  only contribution of
order $O(1\,=\,\beta^{0})$ to $T_{\mu\nu}$, and is determined by the
dimensionless rest energy density $\rho(\tau',\vec{\xi}')$ of $m$, which
satisfies $\int d\vec{\xi}'\rho(\tau',\vec{\xi}')=1$. In all physical
systems,
$\rho(\tau',\vec{\xi}')$ can be assumed to be a sharply-peaked, smooth
function with $\sup_{\vec{\xi}'}\,\rho(\tau',\vec{\xi}')\ll O(10^{25})$,
such that Eq. (~\ref{linEinstEq}) can be used. For mathematical
convenience, we replace
$\rho(\tau',\vec{\xi}')$ by a Dirac delta distribution
$\delta^{(3)}$, and consequently obtain
\begin{equation}
T_{00}^{(m,0)}(\tau',\vec{\xi}') =
\delta^{(3)}(\vec{\xi}' - \hat{z} \sin \beta \tau') \;.
\end{equation}
Note that the space and time dependent terms on the RHS of Eq. (5) cannot
be separated, as opposed to the expression $\rho(\vec{\xi'})\,\exp[i\omega
\tau']$ commonly found in the literature which is suitable for multipole
decomposition.
$T_{00}^{(m,2)}$ is determined by the sum of the kinetic energy of $m$
and the potential energy  of the spring, and is of order $O(\beta^{2})$.
The components $T^{(m)}_{0i}$, $i=1,2,3$, are given by
\begin{eqnarray*}
T^{(m)}_{0i}(\tau',\vec{\xi}') = \beta\;\hat{z}_{i}
\;\cos\beta\tau'\;\delta^{(3)}(\vec{\xi}' - \hat{z} \sin \beta \tau')\;,
\end{eqnarray*}
and are of order $O(\beta)$. The components $T^{(m)}_{ij}$,
$i,j=1,2,3$, given by
\begin{eqnarray*}
T^{(m)}_{ij}(\tau',\vec{\xi}') =
\beta^{2}\;\hat{z}_{i}\;\hat{z}_{j}
\;\cos^{2} \beta
\tau'\;
\delta^{(3)}(\vec{\xi}' - \hat{z} \sin \beta \tau') \;,
\end{eqnarray*}
will only contribute to error terms of the order $O(\beta^{2})$.

We evaluate $\gamma^{(m)}_{\mu\nu}(\tau,\vec{\xi})$ at the point
$\vec{\xi}\,=\,\frac{r}{d}\hat{z}$ on the  positive $z$ axis, such that
$\xi_{3} = \frac{r}{d}\,>\,1$. Inserting Eq. (5) into Eq. (4), we first
calculate $\gamma_{0 0}^{(m,0)}(\tau,\xi_{3}\hat{z})$, defined by
$\gamma^{(m)}_{00}=\gamma_{0 0}^{(m,0)}+\gamma_{0 0}^{(m,2)}$. The
$\delta$-integration in $\xi_{1}$ and $\xi_{2}$ can be readily carried
out, yielding
\begin{eqnarray}
\gamma_{0 0}^{(m,0)}(\tau,\xi_{3}\hat{z}) &=&\; - \;
\frac{4 m G}{c^{2} d}
\int d\xi_{3}' d\tau' \; \frac{\delta(\xi_{3}' - \sin \beta \tau')}
{\xi_{3}-\xi_{3}'} \;
\delta(\tau' + \xi_{3} - \xi_{3}' - \tau) \;
\Theta(\tau - \tau')
\nonumber
\\ &=&  - \; \frac{4 m G}{c^{2} d}
\int d\tau' \; \frac{\delta(\tau' + \xi_{3} - \sin \beta \tau' - \tau)}
{\xi_{3} - \sin \beta \tau'} \;
\Theta(\tau - \tau')\;.
\end{eqnarray}
Further reduction is possible using the formula
\begin{eqnarray*}
\int d\tau' \; \delta\left(f(\tau')\right) \;g(\tau') = \sum_{\theta \in
\lbrace {\theta|f(\theta) = 0} \rbrace} \;
\frac{1}{f'(\theta)}\; \; g(\theta) \; \;,
\end{eqnarray*}
in which  we identify the zeros of the argument in the
delta distribution as the roots of $\theta$ in the equation
\begin{equation}
\theta(\tau,\xi_{3}) = \sin \beta \theta(\tau,\xi_{3}) + \tau - \xi_{3}
\;\;.
\label{theta}
\end{equation}
Note that $\theta(\tau,\xi_{3})$ is a function of the
combination $\tau -
\xi_{3}$. The derivative of the argument of the delta in Eq. (6) yields
$1 -\beta\cos\beta \theta(\tau,\xi_{3})$ at $\theta(\tau,\xi_{3})$.  We
obtain for $\gamma_{00}^{(m,0)} (\tau,\xi_{3}\hat{z})$
\begin{equation}
\gamma_{0 0}^{(m,0)}(\tau,\xi_{3}\hat{z}) = \; - \;
\frac{4 mG}{c^{2} d}\;\;
\frac{1}{1 - \beta \cos \beta \theta(\tau,\xi_{3})} \;\;
\frac{1}{\xi_{3} - \sin \beta\theta(\tau,\xi_{3})} \;.
\label{sol1}
\end{equation}
In Eq. (~\ref{sol1}),
$\beta$ is not only a small perturbation parameter, but  also a
"dimensionless angular frequency". In contrast to $\beta$, the arguments
$\beta\theta(\tau,\xi_{3})$ of the trigonometric functions need not be
small for arbitrary $\tau$ or $\xi_{3}$, and cannot be used as
perturbation parameters. Since $T_{00}^{(m,2)}$ is of order
$O(\beta^{2})$, it follows that $\gamma_{00}^{(m,2)}= O(\beta^{2})$ is an
error term, and that
$\gamma^{(m)}_{00}(\tau,\vec{\xi}\hat{z})=\gamma_{00}^{(m,0)}(\tau,\vec{\xi}
\hat{z})
+O(\beta^{2})$. Hence it is sufficient to analyze $\gamma_{0 0}^{(m,0)}$
to the order of $O(1=\beta^{0})$ and $O(\beta)$, to determine
$\gamma^{(m)}_{0 0}$ with a relative error of order $O(\beta^{2})$. The
solutions for
$\gamma^{(m)}_{0i}(\tau,\xi_{3}\hat{z})$, $i=1,2,3$, can be derived in a
similar manner, yielding
\begin{eqnarray*}
\gamma^{(m)}_{0i}(\tau,\xi_{3}\hat{z}) = \; - \;\frac{4 m G}{c^{2} d}
\;\;
\frac{\hat{z}_{i}\;\beta \cos \beta \theta(\tau,\xi_{3})}{1 - \beta \cos
\beta
\theta(\tau,\xi_{3})} \;\;
\frac{1}{\xi_{3} - \sin \beta\theta(\tau,\xi_{3})} \;.
\end{eqnarray*}
The solutions for
$\gamma^{(m)}_{ij}(\tau,\xi_{3}\hat{z})$, $i,j=1,2,3$, which are given by
\begin{eqnarray*}
\gamma^{(m)}_{ij}(\tau,\xi_{3}\hat{z}) = \; - \;\frac{4 m G}{c^{2} d}
\;\;
\frac{\hat{z}_{i}\hat{z}_{j}\;\beta^{2} \cos^{2} \beta
\theta(\tau,\xi_{3})} {1 -\beta
\cos \beta
\theta(\tau,\xi_{3})} \;\;
\frac{1}{\xi_{3} - \sin \beta\theta(\tau,\xi_{3})} \;,
\end{eqnarray*}
contribute to error terms of order $O(\beta^{2})$. The contributions
$\gamma^{(M)}_{\mu\nu}(\tau,\xi_{3}\hat{z})$ of the mass $M$ can be
obtained by substituting $d\rightarrow D$,
$r\rightarrow R$, $m\rightarrow M$,
$\beta\rightarrow -\frac{D}{d}\beta$, $\theta\rightarrow
\frac{d}{D}\theta$,
$(\tau,\vec{\xi})\rightarrow \frac{d}{D}(\tau,\vec{\xi})$,
$\xi_{3}=\frac{r}{d}\rightarrow \frac{R}{D}$ in
$\gamma^{(m)}_{\mu\nu}(\tau,\xi_{3}\hat{z})$, where $D=\frac{m}{M}d$ is
the oscillation amplitude of $M$, and $R$ is its average distance to the
point of measurement. This is because both masses oscillate sinusoidally
with the same frequency $\omega$ and opposite phases along the $z$ axis.

It follows that $\partial_{\tau}\gamma^{(m,M)}_{0i}(\tau,\xi_{3}\hat{z})$
is of  order $O(\beta^{2})$ for both $M$ and $m$. We will show below that
the only Levi-Civita connection coefficients needed for our analysis are
\begin{eqnarray}
\Gamma^{\mu}_{00}(\tau,\xi_{3}\hat{z})&=&
-\frac{1}{2}(2h_{0\mu,0}(\tau,\xi_{3}\hat{z})
-h_{00,\mu}(\tau,\xi_{3}\hat{z}))
\nonumber
\\ &=&
\frac{1}{4}\,\gamma_{00,\mu}(\tau,\xi_{3}\hat{z})
-\gamma_{0\mu,0}(\tau,\xi_{3}\hat{z})
+\frac{1}{4}\,\gamma^{k}_{k,\mu}(\tau,\xi_{3}\hat{z})\;.
\label{LeviCivita}
\end{eqnarray}
Thus, $\Gamma^{i}_{00}=\frac{1}{4}\,\gamma_{00,i}^{(0)}+O(\beta^{2})$ for
$i=1,2,3$. Here, we have used that
$h_{\mu\nu}=\gamma_{\mu\nu}-\frac{1}{2}\eta_{\mu\nu}
\gamma^{\lambda}_{\lambda}$ and
$\Gamma^{\mu}_{\rho\sigma}=\frac{1}{2}\eta^{\mu\nu}(h_{\rho\nu,\sigma}+
h_{\sigma\nu,\rho}-h_{\sigma\rho,\nu})$, which include the influences of
both $M$ and $m$.

Given the metric $g_{\mu\nu}=\eta_{\mu\nu} + h_{\mu\nu}$, we intend to
study the motion of a test mass point
$\tilde{m}\ll m$ in the immediate vicinity of $m$, that is part of
another  mechanical two-body oscillator on the
$z$ axis. The dimensionless space-time coordinates of $\tilde{m}$ are
scaled with $d$, yielding
$(\xi^{0}(\tau),\vec{\xi}(\tau))$. We are only interested in oscillatory
solutions with small amplitudes of order
$\approx d\cdot O(\beta)$, which are induced by the oscillations of the
space-time metric.  Therefore, we require that the dimensionless velocity
components $\xi_{,0}^{i}$,
$i=1,2,3$, of $\tilde{m}$, are of order
$O(\beta^{2})$. The subscript "{\scriptsize ,0}" denotes the derivative
with respect to $\tau$. The proper time of the test mass satisfies
$\xi^{0}(\tau)\approx\tau$ and $\xi_{,0}^{0}=O(1)$, since the deviations
from flat Minkowskian space-time induced by $M$ and $m$ are very small.
The action which  determines the dynamics of the mass
$\tilde{m}$ in our coordinate system is given by
\begin{eqnarray*}
S= \tilde{m}c d \int_{\tau_{0}}^{\tau_{1}} d\tau
\left\lbrace-\sqrt{g_{\mu\nu}\xi_{,0}^{\mu}\xi_{,0}^{\nu}}- U(\xi^{i})
\right\rbrace\;,
\end{eqnarray*}
where $U(\xi^{i})$ is the dimensionless potential energy
due to the spring. For the moment, we assume that the second mass of the
pick-up system is "infinitely" larger than
$\tilde{m}$, and static.  The space-time trajectory of the test mass
$\tilde{m}$ is determined by the Euler-Lagrange equation
\begin{eqnarray*}
-\frac{\xi_{,00}^{\mu}+
\Gamma^{\mu}_{\rho\sigma}\xi_{,0}^{\rho}\xi_{,0}^{\sigma}}
{\sqrt{g_{\mu\nu}\xi_{,0}^{\mu}\xi_{,0}^{\nu}}} + U_{,\mu} =0\;,
\end{eqnarray*}
where $\Gamma^{\mu}_{\rho\sigma}$ are linearized Levi-Civita connection
coefficients. The dominant terms in the sum
$\Gamma^{\mu}_{\rho\sigma}\xi_{,0}^{\rho}\xi_{,0}^{\sigma}$ arise from
$\Gamma^{\mu}_{00}\xi_{,0}^{0}\xi_{,0}^{0}$ . All terms
$\Gamma^{i}_{\rho\sigma}\xi_{,0}^{\rho}\xi_{,0}^{\sigma}$ which involve
$\xi_{,0}^{j}$, $j=1,2,3$, are at least a factor of order
$O(\beta^{2})$ smaller, and can be neglected. From the equation of motion
for
$\xi^{0}$ follows that $\frac{\xi_{,00}^{0}}{(\xi_{,0}^{0})^{2}} +
\Gamma^{0}_{00} =0$ with a relative error of order $O(\beta^{2})$. Using
the fact that
$\Gamma^{0}_{00}$ is a total derivative with respect to $\tau$, and that
$\parallel\gamma_{\mu\nu}\parallel\ll O(\beta^{2})$, one  obtains
$\xi_{,0}^{0} = 1 + O(\beta^{2})$ and
$\sqrt{g_{\mu\nu}\xi_{,0}^{\mu}\xi_{,0}^{\nu}} = 1 + O(\beta^{2})$.
Consequently, the motion of $\tilde{m}$ is determined by
\begin{eqnarray}
\xi_{i,00} + U_{,i} +
\frac{1}{4}\,\gamma_{00,i}^{(0)}=0\;,
\label{EuLa}
\end{eqnarray}
with a relative error of the order $O(\beta^{2})$.  The
contributions of $M$ and $m$ to the "gravitational force"
$\frac{1}{4}\,\gamma_{00,i}^{(0)}$ are additive, and have the same
functional form. This weak-curvature limit is usually referred to as the
post-Newtonian approximation, or the Newtonian limit. The pick-up
oscillator is typically driven at resonance, but has a finite $Q$ factor.
In all realistic systems, the condition that the velocity is of order
$\approx O(\beta^{2})$ is satisfied, because the gravitational excitation
of the pick-up system is very weak, and  Eq. (~\ref{EuLa}) can be used.

The Levi-Civita connection coefficients Eq. (~\ref{LeviCivita}) depend on
our specific choice of coordinates, or gauge. It is not a priori clear
that these coefficients are the correct expression for the physical
gravitational force, since they could be influenced by meaningless
coordinate effects. The physically measurable force is determined by the
change of these coefficients in the absence of the source, i.e. for
$T_{\mu\nu}=0$, calculated in the same gauge, and using the same boundary
conditions. In the Hilbert gauge,
$T_{\mu\nu}=0$ results in the vacuum field equations
$\left(\partial^{2}_{\tau}-\Delta_{\vec{\xi}}\right)\,
\gamma_{\mu\nu}(\tau,\vec{\xi}) = \,0$. The solution is a superposition of
plane waves with constant amplitudes, and must be zero due to the boundary
condition $\gamma_{\mu\nu}\rightarrow 0$ for
$|\vec{\xi}|\rightarrow \infty$. Consequently, the corresponding
Levi-Civita connection coefficients are zero, which shows that the terms
$\Gamma^{i}_{00}$ in Eq. (~\ref{LeviCivita}), $i=1,2,3$, correctly
describe the physical force.

In the Newtonian limit, $\frac{c^{2}}{4}$ times (8) is interpreted as the
classical gravitational potential
\begin{equation}
V(\tau,\xi_{3}\hat{z}) = \; - \;\frac{m G}{d} \;\;
\frac{1}{1 - \beta \cos \beta \theta(\tau,\xi_{3})} \;\;
\frac{1}{\xi_{3} - \sin \beta\theta(\tau,\xi_{3})} \;\;
\label{gravpot}
\end{equation}
generated by $m$, which acts on the external mass point
$\tilde{m}$ by a gravitational force that is proportional to the
gradient  of
$V$, according to Eq. (~\ref{EuLa}). The physical meaning of the solution
Eq. (~\ref{gravpot}) becomes more  apparent if one expands the first
fraction in a geometric series, and the second fraction in a Fourier
series
\begin{eqnarray}
\lefteqn{V(t,r \hat{z}) = \; \;
 - \; \frac{m G}{r} \;\;
\left\lbrace 1 + \beta \cos \beta \theta(\frac{c}{d}\;t\;,\;\frac{r}{d})
+O(\beta^{2})\right\rbrace \,\cdot\;}\;
\nonumber
\\ & &\left\lbrace \;\frac{1}{\sqrt{1-\left(\frac{d}{r}\right)^{2}}} \, +
\,
\left(\frac{r}{d}\right)\left[\,
\frac{2}{\sqrt{1-\left(\frac{d}{r}\right)^{2}}}\,-\,2 \,\right] \,
\sin \,\beta \,\theta(\frac{c}{d}\,t\,,\,\frac{r}{d}) \,+ \right.
\nonumber
\\ & &
\sum_{n>2,\,n\,odd}\;
\left(\frac{d}{r}\right)^{n}\;\;2^{1-n}\;\;\left[\;\;1 + c_{n}
\;\;\right]
\; \sin n \;\beta\; \theta(\frac{c}{d}\;t\;,\;\frac{r}{d}) \,+
\;\;\;\;
\nonumber
\\ & & \left. \sum_{n>1,\,n\,even}
\left(\frac{d}{r}\right)^{n}\;\;2^{1-n}\;\;\left[\;\;1 + d_{n}
\;\;\right]
\; \cos n \;\beta\; \theta(\frac{c}{d}\;t\;,\;\frac{r}{d})
\;\;\;\;
\right\rbrace \;\;\; ,
\label{potFour}
\end{eqnarray}
in which all coefficients $c_{n}$ and $d_{n}$ are of order
$O((\frac{d}{r})^{2})$. The leading terms of order
$O(1=\beta^{0})$ can be  obtained by setting $\beta$ equal to zero in the
first bracket. The time-independent contribution
$\frac{ m G}{r}\lbrace1-\left(\frac{d}{r}\right)^{2}\rbrace^{\,-1/2}$  in
the Fourier expansion is the static potential of a resting mass
distribution centered at the origin,  and converges to the classical
Newtonian potential
$\frac{m G}{r}$ for large  $r$. The next, first harmonic  term has the
asymptotic form
$\frac{m G d}{r^{2}}(1+O((\frac{d}{r})^{2}))\sin\beta\theta(\frac{c}{d}t,
\frac{r}{d})$. For large $r$, it describes a propagating, sinusoidal
oscillation  proportional to $\frac{1}{r^{2}}$, which decays more rapidly
than the usual radiative $\frac{1}{r}$ solutions. All following terms are
higher harmonics  that decay even faster with increasing distance. The
contributions of
$O(\beta)$ exhibit the same asymptotic behaviour with respect to
$\frac{d}{r}$.

\subsection{\normalsize \bf GRAVITATIONAL EFFECTS OF THE MASS $M$}

In this section, we will discuss the gravitational effects of the mass
$M$ in the immediate vicinity of
$m$. The average distance $R$ between $M$ and the point of measurement,
lying in the immediate vicinity of $m$, is much larger than $d$, and also
much larger than $r$. Due to $M\gg m$, the oscillation amplitude
$D =\frac{m}{M}d$ of $M$, which is calculated from classical mechanics,
is much smaller than
$d$. Both masses oscillate at frequency $\omega$ along the $z$ axis, and
the gravitational potential due to $M$  at
$\xi =\frac{r}{d}\hat{z}$ can be obtained by inserting $d\rightarrow D$,
$r\rightarrow R$, $m\rightarrow M$,
$\beta\rightarrow -\frac{D}{d}\beta$, $\theta\rightarrow
\frac{d}{D}\theta$,
$(\tau,\vec{\xi})\rightarrow \frac{d}{D}(\tau,\vec{\xi})$,
$\xi_{3}=\frac{r}{d}\rightarrow \frac{R}{D}$ in Eq. (~\ref{potFour}). The
static term is approximately
$-\,\frac{MG}{R}$ and can dominate over the static field stemming from
$m$. However, one obtains approximately $\frac{MG}{R}\frac{D}{R}\,=\,
\frac{mGd}{r^{2}}(\frac{r}{R})^{2}$ for the amplitude of the first
time-dependent term in Eq. (~\ref{potFour}), which is a factor of
$(\frac{r}{R})^{2}$ {\em smaller} than the corresponding term due to $m$.
The amplitude of the first harmonic  term due to $M$ has the {\em
opposite sign} as  compared to corresponding term due to $m$, because $M$
and $m$ oscillate with opposite phases.

In addition, the amplitudes of the higher harmonic terms, approximately
given by
$\frac{MG}{R}(\frac{D}{R})^{n}\,=\,\frac{mG}{r}(\frac{d}{r})^{n}
(\frac{r}{R})^{n+1}(\frac{m}{M})^{n-1}$, are a factor of
$(\frac{r}{R})^{n+1}(\frac{m}{M})^{n-1}$ smaller than the corresponding
terms due to $m$. One can therefore neglect the  {\em time-dependent}
gravitational influences due to $M$ if $\frac{r}{R}$ is small, which is
the case in the immediate  vicinity of
$m$. At larger distances from $m$, the  number $\frac{r}{R}$ approaches
$1$, and all radiative effects cancel,  which is required by momentum
conservation.

\subsection{\normalsize \bf RETARDATION OF GRAVITATIONAL FORCES}

It will first be shown that the forces derived from the gravitational
potential Eq. (~\ref{gravpot}) are not retarded in the region known as the
"near zone" in the literature, which is in accordance to
$[7]$.  Then, it will be proved that these gravitational forces are
retarded in the immediate vicinity of $m$. As discussed in the derivation
of Eq. (~\ref{EuLa}), we place a small test mass
$\tilde{m}$ which is part of a resonant mechanical oscillator at position
$\vec{\xi}\,=\,r\,\hat{z}$ on the $z$ axis to detect the gravitational
forces generated by the source $m$. From
$F(\tau,\frac{r}{d}\hat{z})=-\,\tilde{m}\,\partial_{r}\,V(\tau,\frac{r}{d}
\hat{z})$ it follows that the gravitational force acting on $\tilde{m}$ is
\begin{equation}
F(\tau,\frac{r}{d}\hat{z}) = \; - \;\frac{\tilde{m} m
G}{d^{2}}\;
\left\lbrace\left(\frac{1}{1 - \beta \cos \beta \theta(\tau,\frac{r}{d})}
\;
\frac{1}{\frac{r}{d} - \sin \beta\theta(\tau,\frac{r}{d})}\right)^{2}
\;+\;O(\beta^{2})\right\rbrace\;.
\label{force1}
\end{equation}
$F(\tau,\frac{r}{d}\hat{z})$ points along the $z$ axis, whereas the other
force components vanish due to symmetry reasons. Eq. (~\ref{force1}) is
accurate to  orders
$O(1=\beta^{0})$ and $O(\beta)$, but not to the order $O(\beta^{2})$,
since
$T_{00}^{(m,2)}$  has not been considered in
$\gamma_{00}^{(m,0)}$. For our analysis it suffices that the results
derived from  Eq. (~\ref{force1}) are conclusive to $O(1=\beta^{0})$ and
$O(\beta)$. To obtain Eq. (~\ref{force1}),  we have used the fact that
the  derivative of
$\theta(\tau,\frac{r}{d})$ with respect to $r$ is given by
\begin{equation}
\partial_{r}\;\theta(\tau,\frac{r}{d})\;=\;-\;\frac{1}{d}\;\;
\frac{1}{1\;-\;\beta\,\cos\;\beta\;\theta(\tau,\frac{r}{d})}
\label{dertheta}
\end{equation}
which follows from
\begin{eqnarray}
\partial_{r}\,\theta(\tau,\frac{r}{d})\;&=&\;\partial_{r}\;\sin\;\beta\;
\theta(\tau,\frac{r}{d})\;-\;\frac{1}{d}
\nonumber
\\ &=&\;\beta\;\cos\;\beta\;\theta(\tau,\frac{r}{d})\;\;
\partial_{r}\,\theta(\tau,\frac{r}{d})
\,-\,\frac{1}{d}\;\;.
\end{eqnarray}
Note that the leading term in $F(\tau,\frac{r}{d})$ is proportional to
$V(\tau,\frac{r}{d}\hat{z})^{\,2}$. The expression for the gravitational
force generated by
$M$ is similar to Eq. (~\ref{force1}). It has a static component  which is
much stronger than the static term due to $m$. However, the time-dependent
gravitational forces generated by $M$  are negligible in the immediate
vicinity of $m$, because
$\frac{d}{r}\,\approx\,1$ and therefore $\frac{r}{R}\,\ll\,1$. At large
distances from
$m$, $M$ and $m$ produce time-dependent gravitational forces of the same
strength, since $\frac{d}{r}\,\rightarrow\,0$ and
$\frac{r}{R}\,\rightarrow\,1$.

\subsubsection{GRAVITATIONAL FORCES IN THE "NEAR ZONE"}

The spherical region $\lbrace r=|\vec{x}|;\beta \ll\frac{d}{r} \ll
1\rbrace$ is commonly defined as the "near zone"  in the literature. For
this region, the approximation
$\theta(\tau,\frac{r}{d})\,\approx\,\tau\,-\,\frac{r}{d}$ can be used,
which is familiar from radiation theory. In addition, we have used the
identity
$\frac{1}{1+y}= 1-y +O(|y|^{2})$, with $|y| < 1$, to simplify the
fractions in
$V(\tau,\frac{r}{d}\hat{z})$, and to  reduce  the potential to
\begin{equation}
V(\tau,\frac{r}{d}\hat{z}) \,= \, - \,\frac{m G}{d} \,
\left\lbrace 1 + \beta \cos \beta (\tau\,-\,\frac{r}{d})\right\rbrace \,
\left\lbrace\frac{d}{r} + \left(\frac{d}{r}\right)^{2}
\sin \beta(\tau\,-\,\frac{r}{d})\right\rbrace \,+\,O(\beta^{2})\;.
\label{gravpot1}
\end{equation}
The trigonometric functions can be approximated by their Taylor
expansions to first order in the variable
$\beta\,\frac{r}{d}\;\ll\,1$. Keeping terms only to the orders $O(\beta)$
and
$O(\frac{d}{r})$, one obtains
\begin{eqnarray}
F(\tau,\frac{r}{d}\hat{z}) &=& \, - \,\frac{\tilde{m} m
G}{r^{2}} \,
\left\lbrace 1 + 2\beta \cos \beta\tau\right\rbrace \,
\left\lbrace 1 + 2\frac{d}{r}\sin \beta\tau - 2\beta\,\cos
\beta\tau\right\rbrace
\,+\,O(\beta^{2})
\nonumber
\\ &=&\, - \,\frac{\tilde{m} m G}{r^{2}} \,
\left\lbrace 1 + 2\frac{d}{r}\sin \beta\tau
 + 4\beta\, \frac{d}{r}\,\cos \beta\tau \,\sin
\beta\tau\right\rbrace\,+\,O(\beta^{2})
\label{gravpot2}
\end{eqnarray}
for the gravitational force acting on the test mass $\tilde{m}$. The
term of order $O(\beta\, \frac{d}{r})\ll O(\beta)$ is a negligible
contribution to the second  harmonics. Hence the contributions of order
$O(\beta)$  {\em cancel}. The time-dependent term of order
$O(1=\beta^{0})$ in the force acts  instantaneously, thus there  is no
measurable retardation in the "near zone" where
$\frac{d}{r}\,\ll\,1$. The electromagnetic version of this result can be
found in $[7]$. Historically, this result has convinced the physics
community that there exists no region at all where any retardation can be
observed.

The additional  constraint $\frac{r}{R}\,\ll\,1$ allows the influence of
the second mass $M$ to be neglected. As $r$ increases, this condition can
not be satisfied, and $\frac{r}{R}\,\rightarrow\,1$. The complete
gravitational potential in the "near zone" limit, which includes the
contributions of both
$m$ and $M$ is given by
\begin{eqnarray*}
V_{tot}(\tau,\frac{r}{d}\hat{z})\;
\approx\;-\frac{mG}{r}\left\lbrace 1 +
\frac{M}{m}\;\frac{r}{R}\right\rbrace\;
-\;\frac{mGd}{r^{2}}\left\lbrace\sin\,\beta\,\tau\;-\;\left(\frac{r}{R}
\right)^{2}
\sin\,\beta\,\tau\right\rbrace\;\;,
\end{eqnarray*}
which follows from the discussion in section II.1. The
time-dependent part of this solution vanishes in the limit
$\frac{r}{R}\,\rightarrow\,1$, and there remains a static solution which
is dominated  by the larger mass $M$. Note that $\frac{(m+M)G}{r}$ is  the
rotation symmetric limit solution for $r\rightarrow \infty$, which
corresponds to the asymptotically vanishing particular solution of Eq.
(~\ref{linEinstEq}). We conclude that our result is consistent with
$[7]$, and that it is in accordance with the conservation of momentum.

\subsubsection{GRAVITATIONAL FORCES IN THE IMMEDIATE VICINITY OF THE
SOURCE}

The immediate vicinity of the source is characterized by
$\frac{d}{r}\,\approx\,1$,  in contrast to $\frac{d}{r}\,\ll\,1$ which is
a  necessary condition for radiation theory. Consequently, radiation
theory breaks down. At this distance  range,
$\frac{r}{R}\,\ll\,1$ holds, and time-dependent influences of $M$ are
negligible, as shown in section II.1. As opposed to the situation in the
"near zone", it is not possible to approximate functions of $\frac{d}{r}$
by the leading terms in their Taylor series. For this reason,  we will
have to explicitly calculate the dominant Fourier components of the
lowest harmonics  in Eq. (~\ref{force1}). To order $O(\beta)$, we find
\begin{eqnarray}
F(\tau,\frac{r}{d} \hat{z})  &=&
 - \; \frac{\tilde{m} m G}{d^{2}} \;\;
\left( 1 + 2\beta \cos \beta \theta(\tau\,,\,\frac{r}{d})\right)
\left(\frac{1}{\frac{r}{d} - \sin
\beta\theta(\tau,\frac{r}{d})}\right)^{2}
\; +\;O(\beta^{2})\;.
\label{potFourlead}
\end{eqnarray}
The condition $\beta\,\ll\,\frac{d}{r}$ which has defined
the "near zone"  is also valid for the immediate neighborhood of the
oscillating mass point. Therefore, it is still possible to expand the
trigonometric functions with respect to $\beta\,\frac{r}{d}\approx
O(\beta)$. From the defining  equation Eq. (~\ref{theta}) for
$\theta(\tau,\frac{r}{d})$, it can be seen that
$\beta\,\theta(\tau,\frac{r}{d})$ is a function of the variable
$\beta\,\frac{r}{d}$. From  Eq. (~\ref{dertheta}), one finds
\begin{equation}
\beta\;\theta(\tau,\;\frac{r}{d})\;=\;\beta\;\theta(\tau,0)\;-\;
\beta\;\frac{r}{d}
\;+\;O\left(\beta^{2}\right)
\label{thetaTaylor}
\end{equation}
for the leading terms of the Taylor series in
$\beta\,\frac{r}{d}$. We expand the trigonometric functions in Eq.
(~\ref{potFourlead}) with respect to
$\beta\;\theta(\tau,\frac{r}{d})\,\approx\,\beta\,\theta(\tau,0)\,-\,
\beta\,\frac{r}{d}$, and perform the Taylor series to first order in
$\beta$ in the second bracket. Consequently, the RHS of Eq.
(~\ref{potFourlead}) yields
\begin{eqnarray}
 - \, \frac{\tilde{m} m G}{r^{2}} \,
\left( 1 + 2\beta \cos \beta \theta(\tau\,,\,0)\right)\,
\left(\frac{1}{1 - \frac{d}{r}\sin \beta\theta(\tau,0)}
\,-\,\frac{\beta\,\cos\beta\theta(\tau,0)} {\left(1 - \frac{d}{r}\sin
\beta\theta(\tau,0)\right)^{2}}\right)^{2}
\; +\;O(\beta^{2})\;.
\nonumber
\end{eqnarray}
The expansion of this product to order $O(\beta)$ gives
\begin{eqnarray}
 - \, \frac{\tilde{m} m G}{r^{2}} \,
\left(\frac{1}{\left(1 - \frac{d}{r}\sin \beta\theta(\tau,0)\right)^{2}}
\,-\,\frac{\frac{d}{r}\beta\,\sin 2\beta\theta(\tau,0)} {\left(1 -
\frac{d}{r}\sin \beta\theta(\tau,0)\right)^{3}}\right)\,+
\,O(\beta^{2})\;\;.
\nonumber
\end{eqnarray}
Calculation of the Fourier components of the first harmonics to order
$O(\beta)$ results in
\begin{eqnarray} - \, \frac{\tilde{m} m G}{r^{2}} \,
\frac{1}
{\left(1\,-\,\left(\frac{d}{r}\right)^{2}\right)^{\frac{3}{2}}}\left\lbrace
1\,+\,  2\,\frac{d}{r}
\sin \beta\theta(\tau,0)\,-\,2\beta\Phi(\frac{d}{r})\cos\beta
\theta(\tau,0)\right\rbrace
 +\,h.h.\,+\,O(\beta^{2})\,,
\label{retpot}
\end{eqnarray} where the abbreviation $h.h.$ stands for "higher
harmonics". The function
$\Phi\left( x\right)$ is defined by
\begin{equation}
\Phi\left( x \right)\;=\;\frac{2}{x^{2}}\,
\left(\left(1-x^{2}\right)^{\frac{3}{2}}\;-\;1\;+\;\frac{3}{2}\,x^{2}\right)
\end{equation} for $x\,=\,\frac{d}{r}\,\in\,[0,1]$. $\Phi\left( x\right)$
is a monotonically  increasing function on the unit interval with values
$\Phi(0)\,=\,0$ and
$\Phi(1)\,=\,1$ at the boundaries of its domain, see Fig. 1.
 We have only calculated the first harmonic terms of maximal order
$O(\beta)$ in Eq. (~\ref{retpot}), because we assume that the measurement
in our proposed  experiment is only sensitive to the first harmonics.
Using the relationship
\begin{equation}
\beta \theta(\tau,\Phi(\frac{d}{r})\frac{r}{d})\,=\,\beta\theta(\tau,0)\,
-\,\beta\Phi(\frac{d}{r})\frac{r}{d}\,+\,O(\beta^{2})\;,
\end{equation} which is a generalization of Eq. (~\ref{thetaTaylor}), we
finally obtain
\begin{eqnarray} F(\tau,\frac{r}{d} \hat{z}) \, =\,
 - \, \frac{\tilde{m} m G}{r^{2}} \,
\frac{1}
{\left(1\,-\,\left(\frac{d}{r}\right)^{2}\right)^{\frac{3}{2}}}\left\lbrace
1\,+\,  2\,\frac{d}{r}
\sin \beta\theta(\tau,
\Phi(\frac{d}{r})\frac{r}{d})\right\rbrace \,+
\, h.h.\,+\,O(\beta^{2}) \;.
\label{sol}
\end{eqnarray}
This result shows that the first harmonic  term in the gravitational
force of order $O(\beta)$ can be absorbed into the contribution of order
$O(1\,=\,\beta^{0})$. Moreover, it is obvious from  Eq. (~\ref{theta})
that
$\theta(\tau,\Phi(\frac{d}{r})\frac{r}{d})$ is  a function of the
combination
$\tau-\Phi(\frac{d}{r})\frac{r}{d}$, which shows that the gravitational
force is retarded. For two points
$r_{1}\hat{z}$ and
$r_{2}\hat{z}$ on the oscillator axis, the  relative phase difference
$\Delta\phi$ of the gravitational force is given by
\begin{eqnarray}
\Delta\phi\,&=&\,\beta\,(\Phi(\frac{d}{r_{1}})\frac{r_{1}}{d}
\,-\,\Phi(\frac{d}{r_{2}})\frac{r_{2}}{d})
\nonumber
\\ &=&\,\frac{\omega}{c}\,(\Phi(\frac{d}{r_{1}})\,r_{1}
\,-\,\Phi(\frac{d}{r_{2}})\,r_{2})\;\;,
\label{phsh}
\end{eqnarray}
and is of order $O(\beta)$. At very small distances $r$ from the source,
where
$\frac{d}{r}\,\rightarrow\,1$ and $\Phi(\frac{d}{r})\,\rightarrow\,1$, the
value of the phase shift approximates the result which would occur for a
wave  that travels at speed of light. At larger distances in the "near
zone", we have
$\frac{d}{r}\,\rightarrow\,0$ and
$\frac{r}{d}\Phi(\frac{d}{r})\,\rightarrow\,0$.  Hence there is no
measurable phase shift, and the gravitational forces seem to act
instantaneously, as was shown above. In the intermediate region where
$\frac{d}{r}\,\approx\,1$, the phase shift can be calculated from Eq.
(~\ref{phsh}). Note that in the limit $\frac{d}{r}\rightarrow 0$,
(~\ref{sol}) converges to (~\ref{gravpot2}), as it should be. The absolute
phase shift
$\phi(r):=\frac{\omega}{c}\Phi(\frac{d}{r})r$ converges rapidly to zero
for
$r\rightarrow \infty$, see Fig. 2.

We conclude that there is a possibly measurable retardation of the
gravitational forces in the immediate vicinity of the oscillating source
in our proposed system. A discussion of extended gravitating sources with
the linearized Einstein equations would be a straightforward
generalization of the presented analysis. Due to the superposition
principle, expressions similar to Eq. (~\ref{sol}) would then have to be
integrated over the  spatial spread of the oscillating continuum.
However, we have assumed cylindrical symmetry in our mathematical model,
and thus could find a solution for the dominating gravitational force
term. For systems without cylindrical  symmetry, the analysis will be
much more difficult.  From the results in this section, we will now
discuss how they could be experimentally verified.

\section{\large\bf  EXPERIMENTAL POSSIBILITIES}

Eq. (~\ref{sol}) suggests that it may be possible to experimentally verify
the retardation of gravitational forces in the  immediate vicinity of an
oscillating mass distribution. This would  require both the amplitude and
phase detection of gravitationally transmitted  vibrations. With the
previous mathematical  model in mind, we propose the following experiment:

A mass $m$ within a mass-balanced apparatus is oscillated with a very
stable phase and frequency
$\omega$,  as described in the mathematical model. If a mechanical
resonator with eigenfrequency $\omega$, mass
$\tilde{m}$, and quality factor $Q$ is placed at position $r \hat{z}$,  it
will be driven into resonance by the first harmonic term in the
gravitational  force. Given suitably chosen parameters, the amplitude of
the sinusoidally  vibrating resonator, typically of the order
$O(10^{-9}[m])$, can be detected with modern technology $[5]$.

We propose to measure the retardation of the gravitational force in the
following way. Place the mechanical resonator at the location
$r_{1}\hat{z}$ on the oscillator axis, such that
$\frac{d}{r_{1}}\,\approx\,1$. From the observed gravitationally induced
sinusoidal vibration, the phase difference
$\Delta
\phi_{1}$ between the phase of the resonator  and the phase of the
vibrating source mass can be measured. If the mechanical  resonator is
placed at another location
$r_{2} \hat{z}$ on the oscillator axis, a different result $\Delta
\phi_{2}$ will be observed. By subtracting
$\Delta \phi_{1}$ from $\Delta \phi_{2}$, all internal influences from
the  experimental measuring instruments can be eliminated, resulting in
the relative  phase shift $\Delta \phi_{1}\,-\,\Delta \phi_{2}$. The
value of $c$ in Eq. (~\ref{phsh}) can then be calculated from the
measured relative phase shift
$\Delta \phi_{2} - \Delta \phi_{1}$, which would be the  speed of light
according to General Relativity. The expected values for the relative
phase shift are shown in Fig. 3. Since linearized General Relativity is
formally a special relativistic field theory, measurement of
$c$ with the proposed system would provide a new test of its Lorentz
covariance. Moreover, our proposed laboratory experiment would provide the
first direct observation of propagating gravitational fields. In
addition,  the scalar component of order $O(1=\beta^{0})$ in
Eq. (~\ref{linEinstEq}) also determines the Coulomb potential of an
oscillating point charge after a substitution of parameters. Therefore,
our solution Eq. (~\ref{sol}) also applies to the retarded Coulomb force
generated by an oscillating point charge. Measurement of the retardation in
the immediate vicinity of the charge would thus be another interesting
experimental possibility.

Since the 1960s, several researchers have detected the amplitudes of
gravitationally  induced vibrations in laboratory experiments
$[5,9,10,11]$. It may be possible that these experiments can be analyzed
in a similar way as the model in this paper, which would provide
information about  the magnitude of the retardation, if present. The
detection of the retardation of  gravitational interaction in laboratory
experiments has not been discussed  much recently because the usual "near
zone" calculations predict instantaneous  interactions, as was shown in
section II. However, this result does not  apply in the immediate
vicinity of the  oscillating source, as was also shown in section II.
Note that our experiment is not related to the gravitational waves of
helicity two, which are far more  difficult to detect, since they are of
order
$O(\beta^{2})$.  Unfortunately, several technical problems must be solved
before measurements to test these retardations can be realized. In 1958,
Q. Kerns demonstrated  an analog electronic circuit capable of  measuring
$10^{-6}$ degree phase shifts $[4]$. We have made several modifications to
Kerns' original design, and we are currently able to measure
$10^{-7}$ degree relative phase shifts over a $30$ second measurement
period $[13]$. Currently, the technology is thermally limited, but thermal
control of the system and application of noise reduction techniques may
soon enable us tho increase the phase sensitivity to the
$10^{-9}$ degree phase accuracy required, to measure the retardation to
$1\%$
$[5]$. It is not yet known if the phase stability of the mechanical
systems used for the experiments can be maintained to this accuracy over
the measurement time.

\section{\large \bf CONCLUSIONS}

Using the linearized Einstein  equations, we have proved that the
gravitational force generated by a specific oscillating mass distribution
is retarded in its immediate vicinity.  We have proposed an experiment to
measure this retardation which may enable the first direct experimental
observation of propagating gravitational fields.  The amplitudes of
gravitationally induced vibrations in systems similar to  ours have been
successfully  detected since the 1960s. The detection of the retardation
requires a very sensitive phase measurement, which may now be possible
given the state of modern technology.
\\
\\ {\bf REFERENCES}

\newcounter{ct}
\begin{list}{[\arabic{ct}]}{\usecounter{ct}}

\item J. Cook, "An analysis of methods for measuring the velocity of
gravitational  disturbances", thesis on file at Pennsylvania State
University (1947).

\item J. Cook, "On measuring the phase velocity of an oscillating
gravitational field", J. of the Franklin Inst., Vol. 273, No. 6, June
(1962).

\item I. Bershtein and M. Gertsenshtein, "Possibility of  measuring the
velocity  of propagation of gravitation in the laboratory", J. Expt.
Theort. Phys. U.S.S.R.,  37, pp. 1832-1833 (1959).

\item Q. Kerns, "Proposed laboratory measurement of the  propagation
velocity of  gravitational interaction", UCRL - 8438, Berkeley, CA (1958).

\item W. D. Walker and J. Dual, "Experiment to measure the propagation
speed of  gravitational interaction", Talk presented at Virgo
International Conference on  Gravitational Waves: Sources and  Detectors,
March (1996). To be published in Virgo conference proceedings.

\item W. Misner, K. Thorne, J. Wheeler, "Gravitation", W. H. Freeman and
Company New York, Ch. 36.1 - 36.3,  (1973).

\item R. P. Feynman, "Feynman Lectures in Physics", Vol. 2, Addison
Wesley,   Ch. 21, (1989)

\item N. Straumann, "General Relativity and Relativistic Astrophysics",
texts  and monographs in physics, Springer Verlag Berlin Heidelberg, pp.
218-219 (1991).

\item J. Sinsky and J. Weber, "New source for dynamical gravitational
fields",  Physical Review Letters, Vol. 18, No. 19 (1967).

\item Y. Ogawa, K. Tsubono, H. Hirakawa, "Experimental test of the law of
gravitation", Phys. Rev. D, Vol. 26, No.4, August (1982).

\item  P. Astone et al., "Evaluation and preliminary measurement of the
interaction  of a dynamical gravitational near field with a cryogenic
gravitational wave antenna",  Z. Phys. C 50, pp. 21-29 (1991).

\item Y. T. Chen, A. Cook, "Gravitational Experiments in the Laboratory",
Cambridge University Press, pp. 187-195 (1993).

\item W. D. Walker and J. Dual, "Sub-Microdegree Phase Measurement
Technique", submitted for publication in Review of Scientific Instruments,
American Institute of Physics.
\end{list}

\section{\large \bf Figure captions} Fig. 1: The function $\Phi(x)$
versus $x$, where $x=\frac{d}{r}$.
\\
\\ Fig. 2: The absolute phase shift $\phi(r)$ for $r$ between $d$ and
$1[m]$, at fixed parameter values  $d=0.01[m]$,
$\omega=251.3[rad/sec]$, and  $c=3\cdot10^{8}[m/sec]$.
\\
\\ Fig. 3: The change in phase shift $\Delta\phi$ for $r_{2}$ between
$r_{1}$ and $0.1[m]$, and for fixed parameter values $r_{1}=0.03[m]$,
$d=0.01[m]$,
$\omega=251.3[rad/sec]$, $c=3\cdot10^{8}[m/sec]$. Note that the value
$r_{1}=0.03[m]$ corresponds to the smallest possible separation between
the centers of the source mass and the detector mass in our experiment,
due to the finite size of the physical systems being used.

\end{document}

redpajama_set_name: RedPajamaArXiv


text:
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For the very beginner to intermediate, we offer lessons in a group format. We offer lessons for advanced students and our beginner lessons. Lessons are 25 minutes in length and include an hour practice session directly following lessons. The cost is $95.00 per child for the five weeks of lessons and skate rental is included.
Hockey lessons will be 50 minutes and are for children with an interest in learning the game with prior skating experience. Each student will need his/her own equipment. Lessons are $105.00 for five weeks.
Adults will be able to enjoy lessons on Sunday mornings in a quiet and calm environment. Lessons will include a 50 minute lesson and 50 minute practice session with instructors on hand to assist. Lessons are $105.00 for the five weeks of lessons.


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Home / News & publications / Latest news / Media releases / Million dollar grant offers dignity and hope for homeless
Million dollar grant offers dignity and hope for homeless
A million dollar grant from the City of Sydney will help transform an inner-city crisis accommodation centre with upgraded rooms and facilities, providing access to critical services for people experiencing homelessness.
Wesley Mission Superintendent and CEO, the Rev Keith V Garner AM, said the major refurbishment of the Wesley Edward Eagar Centre will offer those in need comfort, dignity and an extensive support network.
"This grant from the City will help us dramatically improve the service we provide and allow us to give compassionate and holistic care that reaches into every part of people's lives," Mr Garner said.
"The refurbished centre will offer clients the security of a single room with an ensuite. We will also provide access to a diverse service network, including mental health, financial counselling and employment support.
"For decades the Wesley Edward Eagar Centre has provided crisis accommodation for men and women, but the landscape has dramatically changed over that time and we need to look to the future.
"We're no longer just providing a bed, we're offering a whole range of services and support. I'm delighted that we're once again working with the City of Sydney, who have always been good partners of Wesley Mission.
Together we are giving our very best to those who need it most."
The City has also awarded $150,000 to St George Community Housing for a research project focusing on improving affordable housing opportunities for Aboriginal and Torres Strait Islander peoples.
Both grants were awarded from the City's Affordable and Diverse Housing Fund, which was established with $10.35 million from the sale of land at Harold Park in 2015. In total four grants have been approved from the fund totalling $5.65 million, as well as an additional $350,000 for the City's Alternative Housing Ideas Challenge.
Lord Mayor Clover Moore said Council was proud to support these crucial services dedicated to helping the most vulnerable in the community.
"Providing affordable housing and supporting those experiencing homelessness is one of our top priorities at the City," the Lord Mayor said.
"It's unacceptable that in a city as prosperous as Sydney, people are living rough on the streets or experiencing extreme rental stress. That's why we use every lever we can to increase the supply of social and affordable housing in our city, and are delighted to partner with Wesley Mission on this important upgrade.
"By ensuring that everyone has a home, and access to the help they need, we can create and maintain a city that is truly diverse, and welcoming to all."
For interviews with the Rev Keith V Garner AM, contact Amanda Bailey
Phone 0429 484 632 or email amanda.bailey@wesleymission.org.au
For media inquiries or images, contact Belinda Wallis
Phone 0467 810 160 or email bwallis@cityofsydney.nsw.gov.au
For interviews with Lord Mayor Clover Moore, contact Anusha Muller
Phone 0408 494 545 or email amuller@cityofsydney.nsw.gov.au
Reproduced with permission of City of Sydney.


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Wednesday | July 2nd, 2014
Controversial Currency Being Converted To Cash
Jatrice Martel Gaiter
The University of Puget Sound in Tacoma, Wash., often receives donations from alumni so it wasn't a surprise to Sherry Mondou, the university's vice president of finance and administration, when 2007 graduate Nicolas Cary expressed interest in donating to the school.
The revelation was the form in which he wanted to give. Cary's $10,000 donation was to be made in Bitcoins, specifically 14.5 Bitcoins.
Bitcoins are a virtual currency launched in 2009 that is quickly gaining popularity and controversy. Cary is chief executive officer of the Bitcoin firm Blockchain, which is one of the many so-called "wallets" that act as banks where users can store their Bitcoins.
The school's leaders were already hesitant to accept foreign donations, let alone virtual ones. Mondou had some reservations. "We were proud and grateful that this young, successful alumnus wanted to give back to Puget Sound and we were intrigued by Bitcoin as a new paradigm," said Mondou. "At the same time, we needed a better understanding and risk assessment of Bitcoin and needed to determine how such a gift transaction could take place."
Part of the concern had to do with the negative press the currency has been getting in recent months. Mt. Gox, a Bitcoin exchange that was based in Tokyo, Japan, announced in February that 850,000 Bitcoins valued at $450 million at the time had gone missing and trading was suspended. Although 200,000 of those Bitcoins have since been found, the remaining 650,000 were still missing at presstime and there has yet to be a concrete explanation of how they disappeared.
At the time trading was suspended, the currency was valued at $565 per Bitcoin, less than half its value in November.
"Unfortunately there were some bad business practices there," said Stephanie Wargo, vice president of marketing at BitPay, a payment processor for Bitcoins. "With an emerging technology not everyone is going to be successful." Wargo also made a point that the price of Bitcoins has "rebounded nicely" since the Mt. Gox crash. Mondou, too, said that the value of their donation increased since it was originally made.
The Mt. Gox incident was soon followed by the death of a 28-year-old American woman living in Singapore who ran the First Meta Bitcoin exchange. Police ruled that the death was "unnatural" and was thought to be a suicide, though the reason for that remains unclear. More negative press followed when an article in Newsweek purported to identify the creator of Bitcoin. The problem is that person — Dorian Nakamoto — strongly denies the claim. He told media outlets he had never heard of the currency and claimed he was subject to harassment because of the article.
Despite this volatility, Mondou said the school felt comfortable dealing with Bitcoins, mostly because they would not have to keep the currency on hand. Instead, they could immediately convert it into cash. There was one problem, however. Having never accepted a donation of virtual currency, they had to find an exchange agent. Cary recommended the school use BitPay, a Bitcoin payment processor.
"Using [BitPay] made the gift transaction simple to process and eliminated the exchange rate risk," Mondou said. "The Bitcoin gift was immediately exchanged for U.S. dollars and funds were transferred to our bank account the next business day."
The university has received three more Bitcoin donations, though Mondou declined to identify the donors. Combined with the initial gift, the school has received $12,570 in Bitcoins. Mondou said she anticipates receiving more Bitcoin donations and that the university will continue to examine other forms of digital currency.
"Because digital currency is in its infancy and is evolving, our assessment will be ongoing," she said.
Cary said that he decided to make the donation as a "thank you" to the university. "I always wanted to give back to them [University of Puget Sound] when I was in a position to do it," he said. "I was the grateful recipient of a lot of student aid."
Cary added that due to Bitcoins, he has been able to pay off 100 percent of his student loans nearly a decade earlier than he would have been otherwise able. This is partly because, in his words, he is "dedicating [his] life to Bitcoins." He first learned of the digital currency in 2011 from a friend and after doing research, he quickly learned of what he considers its benefits. One of the perceived benefits is the small transaction fee when compared to credit cards. Some Bitcoin processors, such as BitPay, will charge no transaction fee so long as the nonprofit provides the proper documentation.
BitPay Vice President of Marketing Stephanie Wargo said that they chose to have no transaction fees for nonprofits as a way to encourage organizations to get involved. "That's one of the things we like to do to support nonprofits and to allow the Bitcoin community to work with their favorite nonprofit," she said.
"The Bitcoin community is also incredibly giving," added Cary. "With Bitcoin, anyone can instantly share their address and take donations from anyone, anywhere on planet Earth."
The process for accepting Bitcoin donations with BitPay — or any other Bitcoin processor — is similar to any other payment processing company. Set up a donation widget on your website to add Bitcoins as a donation method. After you receive the donation, you can either choose to keep the Bitcoins or have BitPay process them into cash, which typically takes one business day.
"We act like any other payment processor. In this case, we only facilitate Bitcoin payments," Wargo said.
For Bitcoin processors that don't waive transaction fees, the price is still low when compared to credit card or PayPal transactions. For example, BitDazzle, which creates online stores for organizations to sell products for purchase with Bitcoins, charges a 1 percent transaction fee. PayPal charges 2.2 percent plus 30 cents per domestic transaction for nonprofits. The average fee for credit card transactions is between 1.95 and 2 percent.
"This is a worldwide payment method," said Hieu Bui, CEO of BitDazzle. "You're opening yourself to a world you didn't have access to before."
Mondou said that the university's experience with BitPay was very good, and she said that the fact the transaction fee was waived helped make easier the acceptance and selection decisions. "Using a payment processor like BitPay simplifies the process for the nonprofit and donor alike," she said.
Although dollars are the only accepted form of legal tender in the United States, Bitcoins are able to be legally traded and exchanged. Adam Levine, editor-in-chief of LetstalkBitcoins.com explained: "Legal tender laws require you to accept dollars, they do not restrict you from accepting anything else. If I want to pay you in seashells, and you like the idea nothing stops us although it must be reported as a barter trade."
Jason Shim, digital media manager at Pathways to Education in Canada, which accepts Bitcoin donations, likened it to gold. "You could post on an online forum and look for people who are buying/selling or you could find an online exchange, in which you can buy and sell for fiat currency and have it deposited it directly into your bank account," he said. "If you are a merchant, you could use something in which they would accept the Bitcoin, sell it, and convert it into cash, which is then deposited into your bank account."
When a donor makes a gift to an organization, they count on a receipt that they can use for tax purposes. One of the concerns some organizations have is how they can guarantee this for a virtual currency. That's why Pathways to Education took it upon themselves to become the first national organization in Canada to issue tax receipts for Bitcoin donations.
Shim said they started looking into Bitcoins as a donation method in March 2013 and fully launched their initiative in November. "Our main concern was how to handle tax receipting but the rest of it was pretty straightforward," he explained. What Shim found out was that as long as they can establish fair market value they can issue a receipt for the donation.
In a release from April 2013, the Canadian Revenue Agency (CRA) announced its own position on Bitcoins, stating that any transactions involving the currency would be treated as barter transactions and that Bitcoin-related gains could be treated as income or capital depending on the circumstances.
Receipts are also given to donors through BitPay, said Wargo, and other Bitcoin accepting organizations are starting to follow the same path. This is all in an effort to bring more legitimacy to a currency that, while not officially recognized as legal tender by the Internal Revenue Service (IRS), is still subject to taxation, according to a recent notice published by the agency. Bitcoins are treated as "property" under U.S. tax laws and thus would be subject to capital gains taxes.
"A payment made using virtual currency is subject to information reporting to the same extent as any other payment made in property," the IRS stated.
Bitcoins held for more than a year would be taxed at a maximum of 23.8 percent under capital gains and, according to Levine; normal capital gains rates are applied based on your tax bracket. This might not be a worry for nonprofits, however, as they are under no obligation to hold the Bitcoins and many choose not to, because of their perceived volatility.
Pathways to Education in Toronto, Ontario, Canada has received $2,200 in Bitcoin donations, with the majority of that activity happening during the online day of giving called #GivingTuesday.
The Lois Merrill Foundation (LMF) in Encinitas, Calif., is another organization that is beginning to accept Bitcoin donations and, like Pathways to Education, immediately sell off their Bitcoins.
The organization partnered with BitDazzle to create an online store where they sell their products for Bitcoins. According to Bui, it took only "a matter of days" to get their store up and running. "The idea that we could get something up and running on their behalf, it was a really attractive thing for us to do," he said.
As they only just recently had the site set up, LMF Founder Angela Merrill said the group has not received any "significant" contributions as of yet, but they are very optimistic about the future.
"We feel that there's a lot of potential with Bitcoins, and we wanted to be an early adopter of it," she said.
LMF, like many organizations investigating Bitcoins, paid close attention to the Mt. Gox incident and did have some concerns about the currency's volatility. They were ultimately swayed by the fact that they would never have to hold on to the Bitcoins.
"Once they learn they don't have to ever touch a Bitcoin if they don't want to, that gets them over the hurdle pretty quickly," said BitPay's Wargo. She added that the current cash value of Bitcoins is locked in for 15 minutes on their site.
"We felt we could convert [to cash] fast enough where it wouldn't be an issue for us," said Merrill, explaining how they got over the volatility issue.
"Bitcoin can be volatile but we mitigate that by not holding any Bitcoins. We immediately sell them off," said Shim. The volatility is only an issue if you are speculating or investing in them, he said. "Look beyond the news and do research into it. There's a rich story behind it beyond all the sensationalism," said Shim.
Mondou of the University of Puget Sound echoed that point, saying that she thinks the popularity of Bitcoins is just starting to grow. "I can imagine that donors holding and transacting in Bitcoin will want to make their donations in that form due to the convenience and low transaction cost," she said.
Bui said that there really is no downside for a nonprofit to accept Bitcoin donations since they will never have to handle a Bitcoin. And, if the price continues to grow, an organization can choose to hold onto them and sell them for the increased value. "It's like a mini investment," he explained.
If you do plan to hold onto Bitcoins instead of selling them immediately, Cary recommended following security best practices and to keep an eye on the value of the currency to figure out the best time to sell.
"It's true that Bitcoin is prone to fast value changes. I would never advise anyone to invest more money into something than they are comfortable losing," he said. "That being said, in the entire history, over the long run, there has only been about an 11-week period [the Mt. Gox incident] where you would have lost value." E
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Road Safety World Series 2022, Where To Watch: Live Streaming & TV Details For RSWS Season 2
The 2022 Road Safety World Series is the second edition of the T20 league that features a number of retired stalwarts from around the world — here is where you can watch the RSWS Season 2, including live streaming and telecast details.
Former cricketers will take part in the second edition of the RSWS, beginning on September 10. There will be global stars from eight countries taking part, with New Zealand being the latest entrant in the tournament. India, England, Sri Lanka, West Indies, South Africa, Bangladesh and Australia will field teams in the competition that is played to create road safety awareness in the world.
There will be a total of 23 matches in the edition, with each team playing five league games. The first round will be held till September 27, before the playoffs begin. The first semifinal will be played on September 28, with the second semifinal following a day later. The final will be staged on October 1.
The games will be played in four venues: Green Park in Kanpur, Holkar Cricket Stadium in Indore, the Rajiv Gandhi International Stadium in Dehradun and the Shaheed Veer Narayan Singh International Stadium in Raipur. The first seven games will be played in Kanpur before the action shifts to Indore for the next five games. The remaining league matches will be played in Dehradun, and Raipur will host the three playoff matches.
Read the full schedule of the 2022 Road Safety World Series here.
A number of legends will also be in action. India Legends will be led by Sachin Tendulkar, with the side also featuring Suresh Raina, Yuvraj Singh and Irfan Pathan. Jonty Rhodes, Brian Lara, Shane Watson, Brett Lee, Chaminda Vaas, Sanath Jayasuriya, Ian Bell and Shane Bond will be the other overseas players in action.
Road Safety World Series: Where to watch RSWS 2022
In India, various platforms will telecast the tournament, with Viacom18 bagging streaming rights.
Colors Cineplex, Colors Cineplex Superhits and Sports18.
Voot and Jio TV apps.
England women all-rounder Nat Sciver pulls out of white-ball series against India to focus on mental health


"The tragic events in Orlando should concern all of us. A crime as heinous and cruel as the homophobic attack committed in the Pulse Nightclub this weekend is distressing to anyone with any compassion for the welfare and lives of the innocent people affected by this mass murder.
"Such a terrible event rightly gives us cause to stop, think and examine our own environment. I, like many of my colleagues in Sussex Police, in common with the people living in Brighton and Hove are proud and value greatly, the large, vibrant and diverse LGBT community, who play a huge part in making the city the wonderful place that it is to live, visit and enjoy. We will be flying the rainbow flag from John Street police station at half-mast.
"When reflecting on the terrible events in America, it is natural and healthy to consider what it means for us here. We know that whilst it is not impossible to get hold of a firearm in the UK, it is far more difficult to do so than in the US and far more difficult still, to get hold of the kind of deadly assault weapon that was used in the Pulse Nightclub attack.
"We have well developed and rehearsed counter terrorism plans but also work relentlessly on prevention, part of which involves continuously developing intelligence and acting on it.
"We know, too, that we will not tolerate hate crime, even if it seems relatively minor and we will continue to work closely with our partners in the City Council and LGBT Community Safety Forum, event organisers and licensed premises to try to prevent it, but to encourage reporting and tackle it when does occur.
"The threat level in the UK from international terrorism remains unchanged at 'severe' and we will be meeting with the organisers of Pride to consider what if any impact the events in Orlando might have on this event, because we are not complacent and our priority and that of our partners working on the event is and will remain the safety of the public.
- Hundreds turned out at New Steine Gardens yesterday evening (Monday, June 13), to stand in solidarity with Orlando, Florida, after the attack on a gay nightclub.
The vigil was organised in Kemptown after a gathering at the Marlborough Pub and Theatre.


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England / Greater Manchester / Manchester / Reference Library
Confusion, controversy and quiet chaos erupts on the streets of Levenshulme
It's just a couple of hours after the Prime Minister has addressed the nation on Monday evening, and there's a quiet chaos emerging within the streets of Levenshulme. This isn't in response to the newly-announced national lockdown but, in fact, due to new 'modal filters' being installed in the streets – an attempt by Manchester Council to ease road traffic in the area. The 14 plant filters were installed across Levenshulme on Monday (January 4) as part of a six month trial for an Active Neighbourhood project that's been a long time in the works.
The plans for the project include improved road crossings, traffic calming measures to improve air quality and 'strategically placed' planters to be used as road filters. The planters mark the starting point for the trials but, just hours after their installation, they've caused confusion and controversy among some residents. It may seem trivial to be talking about plant boxes while the country is placed under a third national lockdown but it's something that residents in the area, on either side of opinion, are incredibly passionate about.
The project has been in development since 2018 and getting to this point has featured more twists and turns than a M.
Night Shyamalan production. It is hoped that the trials could finally be the start of something positive to improve the area's traffic woes but residents say that, to become a success, there's a lot still needed to be done. "It's a well-intended scheme," one resident, who asked to remain anonymous, told the Manchester Evening News.
"I appreciate there's a few bits that need to be ironed out but in order to prove that it will have a positive effect, it needs to be well executed – this feels like half a job."
Filters for the Levenshulme Active Neighbourhood were installed on Monday (January 4) as part of a six month trial.
One of the main concerns among residents is that the planters have been installed without much instruction. While an announcement was made last month to indicate when they would be installed, residents say there are no signs or notices indicating they are now in use or how drivers should make adjustments to their journeys. "It's good to see something finally happening," resident Jeremy Hoad adds.
"I think a lot of people presumed that the project wasn't going to happen because it's been in the works for so long so I think they have been caught off guard. "After waiting so long for these planters to go up as filters, they've been put in and haven't been done properly. Not only that but they could be potentially dangerous."
Cars could also be seen attempting to bypass the filters
There are also safety fears as the planters do not have any high visibility on them, which makes it difficult to see them in the evening.
Manchester Council said it was taking residents' feedback on board to ensure the trials helped to benefit the 'health and well-being of the community', and would now be looking at installing reflective signage and additional planters. But Jeremy says he believes the ever-changing nature of the project over the last few years has now 'caused friction' within the community. "It's quite frustrating really after waiting all this time," he says.
"We shouldn't be at a point where people are asking what is going on. To me, it only highlights the missed opportunities to engage with people. "There's been two years where it could have been explained to people and it feels like the huge potential of the project has been blown by alienating and causing division within the community."
What do you think of the scheme? Have your say below Just several hours after the installation of planters on Delamere Road, soil has already started pouring out onto the street.
As many might have predicted, some of the planters have been moved and knocked over. The same has happened on the nearby Manor Road. No one's saying whether they were deliberate attempts from someone opposing the plans, but there are murmurs of a forklift truck being spotted in the area late at night.
Marc Geoffrey was one of a group of residents who were out until 1am in the morning tidying up the filters and moving them back. "There is clearly frustration from both people who are for and against the trial but there are some condoning acts of vandalism that I don't think are very productive," Marc says.
The filters on Delamere Road were knocked down within hours of being installed (Image: submitted)
"The filters were definitely moved by some kind of machinery. You cannot manually move them as we had to empty all of the soil out just to lift them back onto their feet."
Marc says he remains optimistic about the trial but echoed that there is still a lot of confusion surrounding it. "As soon as they were installed, people were wondering what they were – there are no signs or labels around," he says. "We really need for there to be high-visibility signs put on them to avoid the risks of accidents."
Resident Nick Purcell says he too remains in favour of the scheme but adds he has been left 'in shock' at the first stage of the trials. He says he has already seen multiple cars driving around the filters and illegally onto pavements to bypass the diversions – which Manchester Council has since condemned as 'unacceptable'. They have promised to look at installing additional planters.
An oven has appeared next to one of the filters in an apparent attempt to stop drivers from using the pavement to cut through
"Whilst it's a relief to see the delayed scheme finally implemented it is with disbelief that this project has been so poorly handled," Nick explains.
"The diagonal filter at Gordon Avenue and Delamere Road arrived yesterday and with just three minutes of observation there were five cars mounting the pavement to cross it. "With no road signage, no pavement bollards and not even any reflectivity, it beggars belief that Manchester City Council and our local Councillors could be so belligerent in their poor delivery of this scheme. "They have now poured fuel on the fire of an already controversial project and made it more likely to fail from day one due to their mismanagement.
"They have made it a greater risk for pedestrians and cyclists while also confusing and angering motorists and local residents." Streets for People, a group in favour of the scheme, says the trial is a welcome answer to 'overwhelming local support' for measures to make it easier for people to get around on foot and by bike. While the group says it is glad to finally have 'something on the ground after two years', they acknowledge there are some issues that need to be addressed as soon as possible.
"We hope that the installation of the trial modal filters marks the beginning of a series of improvements over the next few months," Tom Haines-Doran, Chair of Streets for People Levenshulme and Burnage, said. "However, it is apparent that the council is making some big mistakes. They have placed the filters in such a way that car drivers can go around them on the pavement, which is very dangerous."
Tom says that, as the scheme is still in a trial phase, the problems can be addressed and believes the project can still be beneficial to the area. "Thankfully, all of these issues can be fixed during the trial, and the council have both the money and public backing to do so," he adds. "We ask that the council act quickly to fix these problems, and create a trial which works for the majority of residents."
The filters are designed to divert traffic, making the roads safer for people to travel on foot and bike.
Executive Member for the Environment, Planning and Transport, Councillor Angeliki Stogia, said: "We've installed new traffic filters at locations across Levenshulme, on a six-month trial basis, where consultation told us that the majority of local people who responded were in favour of this going ahead.
"Where people have reservations about the trial, we urge them to continue to raise these with us in a positive way. "It's disappointing that a small number of planters were moved overnight and it's really heartening to know that members of the community acted to clear up after the act of vandalism. "We're also aware that in some locations, vehicles have illegally driven on the pavement to go around the filters.
This is unacceptable and dangerous. We'll be looking at positioning additional planters where possible to deter this behaviour, while protecting essential access for people on bikes, pedestrians and people with disabilities. "In line with feedback from residents, we'll also be adding reflective signage, to improve the filters' visibility at night.
"This investment into Levenshulme has the potential to benefit the health and well-being of the community in the wake of the pandemic, by making streets safer for people as they go about their journeys.
"The point of the current trial is to find out what difference the measures make on the ground and to carry on listening to local residents and businesses, so that we can work together and make changes where necessary to get it right, before any permanent decisions are made."
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Q: Anchor Ids arent accuarate on mobile with react router hash link Having problems with react router hash link on mobile.
On desktop its working great but on mobile its giving me an offset that it sometimes over 100vh away from my anchor tag.
This is where the links get set
 <AnchorLink
  to={`audio-demos/#${anchorTitle}`}
  className={`item ${classItem}`}
  style={{ backgroundImage: `url(${src})` }}

  >
</AnchorLink>

This is where the id is set
return (
<>

{title}

The site im developing is
https://ingrid-voice.netlify.app/
you can recreate the issue by opening devtools in chrome and going on iphone 5 or 7 for example. go to home page and click a link in the portfolio section. This takes you to audio page and an anchor link. On desktop works but on mobile anchor is not at top of screen.
Any ideas?
Thanks

A: I've managed to do a workaround by removing the animated hero image on mobile. Seems to have fixed the problem on my android but still seeing the problem on iphone 7.

redpajama_set_name: RedPajamaStackExchange


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Sending Love Letters to Animals and Other Totally Normal Human Behaviors by Chase Connors
I got behind on my ARC reading this week because of the celebration in the Facebook group, and I think I saved the best for last... it's not a typical MM Romance Reviewed read, but even though it's a YA read, it is definitely a slow burn M/M romance! Let me introduce you to Sending Love Letters to Animals and Other Totally Normal Human Behaviors by Chase Connors:
Ryan Offsteader had one major problem, but now that he's out of the closet and no one in his family or school actually cares, his problems are few. Life is a cycle of family, school, homework, Journalism Club, his friends, hanging out, and waiting for life to begin. It's a simple, boring life at times, but his problems are few.
When Ms. Tabatabai, his English teacher and Journalism Club mentor, announces to the class that there will be a project where students pair up, Ryan and his best friend, Jules, assume they will work together. Ms. Tabatabai has other plans. Students will be paired off randomly. Ryan is left without a partner since his English class has an odd number of students. However, Ms. Tabatabai assures him that he will have a partner since a new student is enrolling. It's not an ideal situation for Ryan since he is used to working with Jules on every project, but it's not the worst.
Until the new student shows up and Ryan realizes this isn't their first time meeting.
Ms. Tabatabai announces to the students that they are to get to know each other and write a paper about their partner. An oral report in front of the class will be expected once the project deadline arrives. There's just one caveat—the pairs must get to know each other without speaking. How they do this is up to them. Points will be given for creativity.
Ryan's partner does everything he can to make the project impossible, Ms. Tabatabai assigns Ryan to a new project in Journalism Club, his friends want to occupy all of his time, and, if all that wasn't enough, he's tasked with helping the Drama teacher, Mr. Melvin, organize the spring singing recital, A Night on Broadway.
Unless Ryan can confront his history and right a wrong, his whole world could fall apart. Will he choose to confront his past, or will history repeat itself?
Even though I figured out the plot twist fairly early on, Sending Love Letters to Animals and Other Totally Normal Human Behaviors was an amazing read! It blends just enough life philosophy with teen angst and obliviousness. Employing sweet, endearing and even somewhat mysterious characters, and told from Ryan's POV, you see him struggle to learn both life and love lessons and survive his final year of highschool.
Slow build and completely g rated, Sending Love Letters to Animals and Other Totally Normal Human Behaviors is a great book for teens and young adults to see themselves mirrored in a sweet story that blends friendship and more to bring things to a satisfying HFN.
5 Stars Contemporary sweet Teen Young Adult


This refers to a technique for calculating an appropriate transfer price for internal goods or services.
Market based, or arms length, transfer pricing assumes goods and services used internally are 'sold' in a similar way to external sales. There are no internal concessions or cost offsets; the approach assumes that, if the supplying unit is operating efficiently it should be able to make a profit at this price; equally, if the receiving unit is operating efficiently, it should be able to make a profit since it would have to purchase the item at this price if it was not available internally.


其實是 Hypermedia as the Engine of Application State 縮寫啦.
那這個在 Spring Data 裡面你只要是用 @RepositoryrestResource 他回傳的就是這個格式, 這邊還有個好處是, 你只要使用 SpringData 操作的不管是 MongoDB ElasticSearch 還是 傳統資料庫, 他提供的 Rest API 就是這個相同的結構, 你們前端也不用 呼天喊地 辛苦的接不同格式資料.
前端只需要從 _links 抽出 class 這個資訊位置, 再去呼叫就可以取得相關資料了.


All of us at CPGS would like to congratulate Vlad Kramar on signing with the Snow Barys of the MHL. The MHL is the top feeder league to the KHL (Top Pro League in Russia). Vlad has participated in the CPGS Goalies Only Prospects Camp for both years it has been in existence and also was mentored by Steve Briere at the Northern Educate Academy last season.


Along with its needed effects, porfimer may cause some unwanted effects. Although not all of these side effects may occur, if they do occur they may need medical attention.
1. "Product Information. Photofrin (porfimer)." Sanofi Winthrop Pharmaceuticals, New York, NY.


Over the years, there have been many times that out elf Josie has been caught in the kitchen. So, even though I have made her an apron skirt, I thought she also needed an Elf on the Shelf Cooking Apron. We have caught her baking a pie and some brownies, hanging out in the pantry and refrigerator, and hanging out by the oven. She has even brought Mia freshly baked teeny tiny gingerbread cookies. So I thought it was appropriate to make her a cooking apron for all her kitchen related antics.
First, here is a video of some of my ideas. Enjoy!
The first thing I did was eyeball the size I needed. I cut the main shape of the apron out of felt. The size will differ, depending on your elf.
I used some ribbon for straps, a tie, and some trim. I used hot glue to put it all together.
I also cut a little rectangle of felt and made a pocket.
In a few simple steps, I had a little cooking apron. No sewing required!
Here is Josie in the kitchen again. Apparently she was decorating cupcakes with red and green sprinkles.
Check out all of my Elf on the Shelf posts. There are a lot of fun and unique ideas. I also made a video that includes over 75 ideas! Enjoy!


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News Forums General Gaming PC/Mac Independent games that are actually worth your time
Independent games that are actually worth your time
Talk about PC and Mac games, etc. here.
BrianC
Dreamcast Swirl
Post#1 » Tue Jul 03, 2012 2:55 pm
Hi guys, I'm a big PC gamer and Its been a truly hellish few years for the industry. A lot of us don't like the direction new games are taking and because of that we are staying with the Dreamcast (and because the Dreamcast kicks ass and all). I built a PC a few years back to play Crysis at nearly the highest settings only to find out that no game since has surpassed it graphically and all we see are inferior ports of games I wouldn't even like to play in the first place. So I've shifted my focus to the independent gaming scene and have found a lot of happiness in some of the titles I'm about to list off. First of all, there is a mainstream indie scene (much like seen in music, when indie, somehow, became a genre when it actually refers to the developmental process and label) where we see games like Bastion (fucking abysmal in my opinion) heralded as great indie (made by Warner Brothers, not exactly a small company) treasures. I want to focus on the dev's that are really taking hits and taking chances, the people that do things differently and because of that aren't making a whole lot of money off their projects despite how great they've turned out. Here we go!
(title-dev-description)
1. Super Laser Racer - New Star Games - Graphically it looks like geometry wars but in reality its a kart racer without any of the bullshit. Short tracks that require tight handling and really test your racing skills. And then there's the weapons! All while speeding through beautifully complex tracks that feature speed boosts and laser traps. Techno music isn't my thing but it works great here and there's plenty of it to last through the large number of tracks. There is an online mode but no one else plays the game (fucking sucks), fortunately the single player features great AI and even allows you to make and race your own tracks.
2. Swarm Arena - Dedication Games - Another geometry wars looking game, in fact when I bought the game I was expecting a geometry wars clone. What I got was about a million times cooler. Basically you play as an organism that has a core and a sphere of influence around it. Drones circle the playing field and if they enter your sphere of influence they buzz around your core and can be used either defensively or offensively. There are two weapon types that can be upgraded by power up pickups, shoot and circle. Shoot propels the drones in the direction you are moving and is insanely complicated to figure out but so rewarding once you master it. If you press fire while standing still the drones shoot out from all sides since the fire button causes them to propel in the direction they were originally traveling (in this case floating around your ship at random causes them to propel in what seems like a random pattern). Circle causes the drones to circle around your core in a clockwise motion allowing you to use them as a bludgeon or as a defensive barrier against shoot. Using your fire is dangerous however since the drones tend to leave your sphere of influence causing them to turn from green to white. When drones are white they can either be collected by your opponent or destroyed by your opponents drones (otherwise the drones trade, i.e. a drone hits a drone and both are owned by players then both drones disappear, in the case of a white drone only the white drone is destroyed and the controlled drone survives). The game is basically an arena style game where it is you versus an opponent core. What a long fucking description but this game truly deserves it. I didn't even get in to the A.I. that learns off of your play style and then can be used to battle other A.I.'s or opponents online or the online opponents own learned A.I.
3. Mount and Blade - TaleWorlds - This game actually developed a pretty huge cult following and a couple sequels/expansion packs. It is a medieval combat game where you can ride around on a horse and fuck people up. Or you can stand on foot with a big pole-arm and stab a horse in the face while it rides at you and then proceed to beat the rider to death as he attempts to recover from the fall. Or you can hide by a tree towards the back of the battle and shoot people with a bow and arrow or do it from a horse if you want. Basically, you can do anything and its all awesome. The sequel, Warband, features online play which is a lot of fun but the games main strength lies in its single player where there are lots of RPG elements such as leveling up and training and equipping your army as you see fit and story moments such as storming a castle (a hundred archers line the walls and your hundred man army has to set up a ladder and fit through a tiny hole full of people waiting to fucking murder you hoping your shield is big enough to keep you from getting shot in the crotch).
4. AI War - Arcen Games - I'm not a big RTS fan, in my opinion no RTS game could ever best Total Annihilation, UNTIL NOW! This game has so much depth, so many options and is so ungodly complicated that I haven't seen a tenth of what it has to offer. Really. The average game takes about 14 hours to play. Really. You are not fighting a standard opponent, you are fighting an AI which follows its own unique rule set and will not play like you. Really. There is no hard cap to your units and if you play correctly you can have 50k v 50k battles. Really. Well, that whole really bit was getting annoying but this game just blows my fucking mind. You chose the number of planets you want to play on which are all seeded randomly into a map with different connections between different planets. There are tons of AI personalities you can choose from which will dictate which units and strategies they favor or play a well rounded one. Some planets have special structures that you can capture from the AI and each planet you take allows you to mine knowledge allowing you to upgrade your units and increase their cap. Each planet you take also causes the AI progress to go up which makes the AI stronger and more aggressive. Basically, if you take every planet you will get buttfucked so you have to use an incredible amount of strategy to determine where you will place your troops and defensive structures, what you will take, and how to best get to the enemy's home and later murder the prick.
Well that's enough for now, these are my favorites and hopefully you guys check them out. I'm gonna grab a twelve pack and play AI wars, see everyone in 20 hours.
Dreamcast Games you play Online: I haven't played any dreamcast games online yet.
But I'm planning to do so soon.
Re: Independent games that are actually worth your time
Post#2 » Thu Oct 07, 2021 12:19 am
Check out Tormented Souls. I haven't played it yet, but that horror game is really good. It's like Resident Evil 1, Silent Hill, and Alone in the Dark combined together, with a slight bit of anime waifu horror goodness thrown into it. And believe it or not, it was made in Chile.
Motoracer5
How do you find these posts beanboy?!?! It's over 9 years old!
jabajava01
Dreamcast Games you play Online: Sonic Adventure
Post#4 » Fri Oct 22, 2021 4:51 pm
As far as I'm concerned. Aquanox Deep Descent is also worth a look. I recently tried to play a game. I got it at a discount this shop. The game is set on a submerged Earth. The locals call their home Aqua, they inhabit underwater stations and large submarines. The only available form of personal transportation - armed bathyscaphes. This is the one the player will use. In the course of the campaign six bathyscaphes are available. They differ mainly in speed and strength. They can be armed with any of the weapons the player has. Each bathyscaphe can be upgraded for money and resources. The former are issued for completed missions, the latter are picked up from the bottom of the ocean. In addition, both money and resources are sometimes dropped from killed enemies.
ParkerLemke
Joined: Mon Nov 14, 2022 9:06 pm
Investigate Tormented Souls. Although I haven't played it yet, that horror game is excellent. It resembles a combination of Resident Evil 1, Silent Hill, and Alone in the Dark, with a dash of anime waifu horror goodness. Incredibly, it was manufactured in Chile. basketball stars
Ryo_Hazuki
dirty sailor
Post#6 » Tue Nov 15, 2022 11:36 am
This Mount and Blade game looks like it's open source! Could the Dreamcast handle a Port?
Tetress
I would say that there are a lot of them actually. And some of them actually have been done in retro style, like maybe Undertale and Deltarune. There are also a lot of games that are based on blockchain technology, and their author can get These awards and prizes for their job. I'm also interested in playing those games actually, who knows maybe there hidden gems among them
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