Re: Setterfield c-decay: question about objections

On Thu, 6 Apr 2006 01:41:40 -0400, shepherdmoon@xxxxxxxxx wrote
(in article <1144302100.439218.254070@xxxxxxxxxxxxxxxxxxxxxxxxxxxx>):


2. Whether or not the claim that c has been dropping implies observable
contradictions.

================================================================
I'm not even sure I can verbalize this topic properly, since I have
trouble visualizing the way time and c values shift according to
Setterfield's claim. But I will try to mention one specific item that
an opponent of mine once used.

My opponent claimed that Setterfield's claim does not imply observable
contradictions because:
A. Only the frequency, not the wavelength, of light has been changing,
thus avoiding the problem of having the Garden of Eden fried by
high-energy light.
B. The speed of light changes everywhere in the universe
instantaneously, thus avoiding the problem of having light arrive in
detectably different time frames (making the universe move in slow
motion, I think).

Try this graphic here:
http://homepage.mac.com/cygnusx1/cdecay/presentation.html

This is scheduled for the 2nd edition of my c-decay analysis which I
hope to release by early June at the latest.

Here's some of the text from the paper. Apologize since equations are
in LaTeX.

Consider a simple space-time diagram like
Figure~\ref{fig:graphicaltimedilation}. We can choose our coordinate
system so we only need to examine motion in one spatial dimension, $x$,
and time, $\tau$. If we consider two different `observers' at rest in
this system, the Emitter and Receiver, their space-time trajectory will
be straight lines at some fixed position on the x-axis and running
parallel to the $\tau$-axis.

In this diagram, we represent the trajectories of photons as the curved
red lines. If the photons traveled at a constant speed, these lines
would be straight. However, we want to consider the case where the
speed of light decreases with time over all space so these lines are
curved. In the case of the speed of light decreasing with time, the
photon trajectories will start with a higher speed (a large amount of
distance in $x$ is covered for a fixed amount of time on the left side
of the figure so the slope of the blue curve is small) and decrease to
a slower speed (a smaller amount of distance in $x$ is covered for the
same amount of time on the right side of the figure so the slope is
steep). The speed of the photons is represented by the slope of their
trajectory in this diagram, with a {\it steeper} slope representing a
{\it slower} speed.
Consider a photon traveling from the Emitter to the Receiver. The
first wave crest of the photon is emitted at point $\tau_{e0}$ on the
emitter's worldline with some velocity, $c \zeta (\tau_{e0})$. The
wave travels out from the emitter at a decreasing speed, represented by
the red curve. The next wave crest leaves the emitter at time,
$\tau_{e1} + P_e$. At this point, we know the distance between the
wavecrests, by definition, is the wavelength, $\lambda_{e0}$. Now a
key point: because in this model, we have the speed of light changing
to the same value over the {\it entire} universe, the velocity of the
{\it entire} segment of the wave is $c \zeta(\tau_{e0} + P_e)$ at that
instant. {\it And because the speed varies over the entire universe by
the same amount, the speed of these adjacent wavecrests will not change
relative to each other after emission, their separation will remain a
constant, so the wavelength, $\lambda_{e0}$, will not change as the
wave travels across the universe.}

The first wavecrest arrives at the Receiver (located at a distance of
20 units in this diagram) at the time, $\tau_{r0}$ and the second at
time $tau_{r1} = \tau_{r0} + P_{r01}$.
Now note the projections of the events $\tau_{e0}$, $\tau_{e1}$,
$\tau_{r0}$, and $\tau_{r0}$ on the $\tau$-axis. These tell use the
time between the events. We immediately notice that the arrival time
between events $\tau_{r0}$, and $\tau_{r1}$, $P_{r01}$, is larger than
the time between emission events $\tau_{e0}$, and $\tau_{e1}$, $P_e$
(which we choose to be constant).
We've exaggerated the change in the signal speed in
Figure~\ref{fig:graphicaltimedilation} to better illustrate the
concepts, but in the practical application, the wavelength, $\lambda$,
will be much smaller than the light travel distance and the travel
intervals between the wavecrests, $P_e$ and $P_r$, are much smaller
than the light travel time. Under these conditions, the light-travel
speed will not change significantly during these intervals. Therefore,
we can write
\begin{equation}
\lambda \ =\ P({\tau }_{e})\ \bar{c}\ \zeta (\tau_{e})\ =\ P({\tau
}_{r})\ \bar{c}\ \zeta (\tau_{r})
\end{equation}
which can also be manipulated to
\begin{equation}
P({\tau }_{r})\ =\ P({\tau }_{e})\ {\zeta \left({{\tau
}_{e}}\right) \over \zeta \left({{\tau }_{r}}\right)}
\label{eq:periodchange2.2}
\end{equation}
as expected.

Note that as time progresses, the distance between wavecrests/pulses
decreases, so $\lambda_{e0} > \lambda_{e1} > \lambda_{e2}$. This
decrease causes the time between successive pulse arrivals to decrease
so $P_{r01} > P_{r12} > P_{r23}$ so phenomena which have a fixed period
in the dynamical system will appear to have a decreasing period (speed
up) to a distant observer. This is consistent with
Equation~\ref{eq:decreasingperiod}.

Note that from the first edition, equation 25 is correct but I plotted
it with the sign flipped in Figure 2.

The function chosen for the graph is dx/dtau = zeta(tau)=
1+3*exp(-0.3*tau). Easily integrable(sp?) to x(tau) by anyone
competent in calculus. Need a root-finder to determine arrival times.

Tom
--
Dealing with Creationism in Astronomy
http://homepage.mac.com/cygnusx1
cygnusx1@xxxxxxx
"They're trained to believe, not to know. Belief can be manipulated.
Only knowledge is dangerous." --Frank Herbert, "Dune Messiah"

.

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