New Mr. Tompkins, Space and Optics

Well, I guess not many people have the New Mr. Tompkins in their shirt pockets, so I'll
add a little more meat to what I describe below. Here's a passage from the book I refer to:

(Recall from below they are standing on a spherical rock in a closed spherical universe
watching a notebook fly away from them. Here the Prof. talks about a person walking away
into the distance.)

"Now, if you think about the globe, you will see that the straightest line on its surface,
the meridians, first diverge from one pole, but, after passing the equator, begin to
converge towards the opposite pole. If the rays of light travelled along the meridians,
you, located for example at one pole, would see the person going away from you growing
smaller and smaller only until she crossed the equator. After this point you would see her
growing larger; it would seem to you that she was returning, albeit going backwards. Once
she reached the opposite pole, you would see her as large as if she were standing right by
your side. You would not be able to touch her, of course, just as you cannot touch the
image formed by a spherical mirror."

I would think the opposite would happen. She grows larger until getting to the equator,
then smaller. The book has not introduced spacetime diagrams, but I would think the sphere
referred to is one. A meridian would be a spatial axis and another 90 degrees from it a
time axis. I would think, perhaps wrongly, that a person traveling through space would
like like an arc between two meridians.


Wayne Watson wrote:
The book Mr. Tompkins by G. Gamow was updated by R. Stannard a few years
ago. Aside from a
lack of index and some small topical index, it's quite good. I
particularly liked the new
chapters on particle accelerators and the one on properties of
particles. The chapter Mr.
Tompkins Visits a Closed Universe left me with a few questions. One on
space and the other
on the optical effect described on the small universe (a few miles
across) the Prof. and
Mr. Tompkins strike up a conversation on.

Regarding space, is it the custom to speak of it as THE universe or that
the universe is
embedded in space and hence shares some of the properties of the larger
space? A lot of
time is spent here (the book) and elsewhere about a universe expanding.
Is it that the
universe is expanding into (a bigger) space or that as the universe
expands and its the
same thing as space expanding, that is they are identical? Another way
of asking this is
is the universe the physical entity, governed by laws of physics,
occupying a portion of
the bigger entity called space, or are they one in the same? Perhaps
there's a good
reference on this.

Regarding the optical effect mentioned on page 63, I don't follow why as
the object heads
across the equator, its image grows larger. The scene is set in a closed
universe that's
five miles in diameter, expanding, there is no sun, there is light,
littered with bits of
small debris, and they stand on a spherical rock about 100 feet in
diameter. A book was
torn out of the hands of the Prof., and is heading way from them. Mr.
Tompkins has spied
the book in binoculars and notices it is growing larger and he concludes
it is coming
back. The Prof. states, "The fact it appears as it is growing in size --
as if it were
coming back -- that's due to a particular focusing effect on the rays
due to the closed,
spherical nature of space." In the next paragraph, the Prof. explains
why with meridians
convering and diverging and an assumption that light hugs the horizon.
Is there another
description someone can give? Maybe there's a non-euclidian text
somewhere that goes over
this material. It certainly an interesting item. I would guess other
such surprises as well.



--
Wayne T. Watson (121.015 Deg. W, 39.262 Deg. N, 2,701 feet, Nevada City, CA)
-- GMT-8 hr std. time, RJ Rcvr 39° 8' 0" N, 121° 1' 0" W

"If I'm given six hours to cut down a tree, then I spend four hours
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