[OS X TeX] Date on top of graphic
Richard J Benish
rjbenish at teleport.com
Sun Feb 3 03:04:43 CET 2008
Hi Alan,
Hoooray! The date is gone.
The three is not on the graphic, but at the lower left of the text
block on page 2. It's indented about as far as the first lines of the
paragraphs are indented.
I suppose I'll just send you all of it, because it's only a half a
page or so. My only hesitation is that it's in a rough stage and,
sheesh, you could actually read it. Oh well, not worth the trouble of
replacing it with dummy text. I really appreciate your help.
Thanks much.
Richard
\documentclass{book}
\date{}
\usepackage{geometry}
\usepackage{epstopdf}
\usepackage{mathptmx}
\usepackage{multicol}
\usepackage{pdfpages}
\geometry{landscape}
\geometry{legalpaper,lmargin=.75in,rmargin=.75in,tmargin=.95in,bmargin=.95in}
\usepackage{eso-pic,graphicx}
\begin{document}
\AddToShipoutPicture*
{\AtPageLowerLeft
{\includegraphics
[height=\paperheight,width=1.0\paperwidth]{SGM-Radial-Fall-Feb-2-08-1.pdf}}}
\maketitle
\setlength{\columnsep}{25pt}
\begin{multicols}{3}
The objective is to show that both the acceleration and the velocity
due to gravity derive from motion ``into or outfrom'' the fourth
dimension of space, where this motion is conceived as being generated
by the perpetual creation of new space by matter. This objective
might be reached along three possible routes: 1) Accepting as given
the slowing effect on clocks (velocity) and showing how this ``leads
to,'' without further assumption, the observed effect on
accelerometers; 2) accepting as given the positive accelerometer
readings (acceleration) and showing how this ``leads to,'' without
further assumption, the observed effect on clocks (velocity; or 3) to
show that these effects necessarily go with each other, which would
imply that these approaches are ultimately equivalent.
The graphic model is obviously very abstract. Due to the addition of
one more space dimension it is more abstract than Epstein's tubular
spacetime graph, which serves well as a basis for comparison, since
his model is clearly related to the equations of General Relativity.
Let's see how far we get by adopting option (1). By virtue of the
ticking of one's clock, in the context of relativity we have movement
up the time line. If the spacepropertime graph is rolled into a tube
and a massive body is nearby, the body's gravity causes the tube to
flare (or the body's gravity can be represented by the flaring of the
tube). This ``induces'' motion in a particular direction through
space (toward the body). What makes the tube flare? How does matter
cause this to happen? Nobody knows.
By definition, increasing the number of space dimensions means
introducing a new perpendicular direction along which motion can
occur. To represent this new direction, we conceive that the tube
rotates. Although there may (or may not) be other rotation schemes
that better reflect the physical situation, I propose that we think
of the whole length of the tube, from 0 < r < infin as having a
uniform angular speed. The velocity at a given radial distance from
the massive source then corresponds to the height of the outer
envelope in the above figure. A key difference between Epstein's
approach and our is as follows. Epstein's tube represents the path
and the clock rate of a falling object. Whereas in the present scheme
the tube, having a constant rotational velocity, represents the rates
of clocks attached to the gravitating body. We would find clocks with
rates corresponding to the indicated velocity, for example, if they
were attached to a very tall (``rigid,'' yet negligibly massed) pole
that projects radially from the source body. The rate of a falling
clock has not yet been specified. ``Dropping'' an object alongside
the pole would correspond to ``disconnecting'' it from the outer
envelope
\end{multicols}{3}
\end{document}
>Hi Richard,
>
>
>On 3/02/2008, at 2:13 PM, Richard J Benish wrote:
>
>>Hi Alan,
>>
>>Many thanks for the suggestions.
>>
>>\nodate in the preamble brings up an error.
>
>Sorry my mistake. Use \date{} instead.
>
>>
>>
>>Here's a link to the graphic:
>>
>>http://www.gravitationlab.com/Grav%20Lab%20Links/SGM-Radial-Fall-Feb-2-08-1.pdf
>
>Where is the stray 3?
>
>Cheers
>Alan
>
>--
>Alan Litchfield GradDipBus, MBus(Hons), CTT, MNZCS
>AlphaByte
>PO Box 1941, Auckland, NZ. 1140
>
>
>
>
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