[OS X TeX] Date on top of graphic

Richard J Benish rjbenish at teleport.com
Sat Feb 2 21:04:43 EST 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.

















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 



>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:
>Where is the stray 3?
>Alan Litchfield GradDipBus, MBus(Hons), CTT, MNZCS
>PO Box 1941, Auckland, NZ. 1140
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