"The Alternate View" columns of John G. Cramer

**Alternate View Column AV-32**
Keywords: shadow matter, gravitation, hollow Earth, Pellucidar

Published in the April-1989 issue of

This column was written and submitted 9/19/88 and is copyrighted ©1988, John G. Cramer. All rights reserved.

No part may be reproduced in any form without the explicit permission of the author.

In 1914, two years after the great success of * Tarzan of the Apes*, Edgar
Rice Burroughs initiated a brand new series with a magazine serial called

There are a number of geophysical and astrophysical problems with Burroughs' s
setting. Perhaps it is pointless to complain, 75 years too late, about the
"hardness" of such science fantasies, for the strong suit of Burroughs'
writings always lay in their imaginative sweep, never their scientific
accuracy. In the case of Pellucidar, however, Burroughs committed a blunder
that sets the teeth of every physicist on edge: *he assumed that gravity
would pull toward the inner surface of a hollow sphere. *

Consider the following question: Inside a massive hollow sphere, just how much
gravitational force would there be at the center, near an inner wall, etc.?
The answer is: *zero*. It's easy to convince yourself that the force at
the center would be zero, because, if you think of the sphere as two
hemispheres, the gravitational pull from one hemisphere is just cancelled by
the equal and opposite pull of the other hemisphere. What perhaps isn't so
obvious is that away from the center the same cancellation holds. It occurs
because at any point in the hollow region the amount of mass in a section of
wall falling within a given angular cone **increases** with distance as
**r ^{2}**

It has some fascinating consequences. For example, suppose we use David Innes'
mole machine to bore a Manhattan-to-Sydney subway tunnel straight through the
center of the Earth. What would be the pull of gravity inside such a tunnel?
For example, take a point ten miles below the surface. Here there will still
be a strong but diminished gravitational pull toward the center. You can think
of the Earth's mass as being divided into a ten mile thick hollow spherical
shell (which exerts no pull), plus a sphere exactly filling the cavity, which
exerts a diminished pull because it has less mass than the whole Earth. If you
work out this force in detail you will discover that, if the Earth had uniform
density all the way through, the force depends directly on the distance
**r** from the center of the Earth. The pull of gravity behaves precisely
like the pull of a spring: **F=kr** where **k** is a force constant. In
physics this is called a Hooke's law force after Sir James Hooke, a
contemporary of Newton who demonstrated that springs have this property.

If a subway car is put into the Manhattan-to-Sydney subway tunnel, the car behaves like the bob of a pendulum. It bobs back and fourth between the two extreme points of its travel at a rate which is independent of the mass of the subway car and depends only on the mass and diameter of the Earth. Assuming that the Earth has a uniform mass density, that there is no friction or air resistance in the tunnel, and that the subway car is moving solely under the influence of gravity with no other forces, the time required for a one-way Manhattan-to-Sydney trip in the subway car is an amazing 43 minutes. (Flying non-stop from JFK Airport to Sydney by 747 at 500 mph would require about 25 hours.)

Sydney and New York City lie almost along a diameter through the center of the Earth. What about other locations, say Seattle to Moscow, Chicago to Houston, or Tokyo to London. It turns out that under the above assumptions the result is always the same. The transit time from anywhere to anywhere is 43 minutes. Such a subway system would, with no net expenditure of fuel or energy, would provide 43 minute transport between any two point on the Earth's surface.

Actually, the real situation isn't quite this simple because the Earth is not a sphere of uniform density. If one uses a more realistic model that puts more of the planet's mass near its center because of the greater compressional forces and the higher density there, the Manhattan-to-Sydney transit time is reduced to 38 minutes, while trips that only cut through a small chord of a circle through the Earth's center would require somewhat more than 43 minutes.

For other bodies of the solar system, planets, satellites, and even the Sun itself, a one way fall-through time along a diameter remains within a factor of two of the same 43 minutes. This is because that time is inversely proportional to the square root of the density (mass per unit volume) of the body involved, and is otherwise independent of both the mass and radius of the body. A fall-through subway on the Moon, which has an average density that is 61% of the Earth's , would have a transit time of 55 minutes. The Sun, with an average density that is only 26% of Earth's, would have a fall-through time of 85 minutes. And so on.

Because of the obvious technical impossibility of actually putting a subway
tunnel through the center of the Earth (not to mention the Sun), doesn't this
discussion take almost as many liberties with the geophysics of our planet and
the strengths of available construction materials as did the science fantasies
of Burroughs himself? The answer to this question would certainly be
*yes* , except that contemporary physics suggests that certain
hypothetical particles, the so-called "dark matter candidates", may be riding
on just such a "subway", crossing the Earth's diameter every 38 minutes or so
as they orbit back and forth past the center of the Earth, trapped in Earth's
gravity well but unable to interact non-gravitationally with the matter that
produced that well.

Broadly speaking, these hypothetical invisible particles fall into three
classes: axions, WIMPs, and shadow matter. In two previous Alternate View
columns dealing with aspects of the dark matter problem I've written about the
hypothetical axion remnants of the Big Bang ["The Dark Side of the Force of
Gravity", ** Analog**, Feb-85] and about the similarly hypothetical

Let me then turn to shadow matter, which is more hypothetical than the other
two classes of invisible particles, but which is also of more potential
interest to readers and writers of science fiction. Shadow matter is predicted
by some variants of superstring theories. In the past few years an army of
theoretical physicists led by Ed Whitten of Princeton's Institute of Advanced
Studies has attached increasing significance to the fact that, when the
mathematical points in space itself are considered to be extra-dimensional
*strings*, ultra-microscopic loops that close back on themselves in six or
more extra dimensions, an array of forces and particles is generated that bear
a striking resemblance to those of our universe. The extra dimensions invoked
by these theories would have thus far escaped our notice because, unlike
ordinary space-time, they are exceedingly small [See my AV column "The Other
40 Dimensions", * Analog*, Apr-85]. They are rolled up on themselves (or
"compactified") snail-like, into loops so small as to make an atomic nucleus
seem inconceivably vast in comparison.

One of the variants of superstring theory goes by the name
E_{6} × E_{8}
(pronounced E-six-cross-E-eight). A consequence of this theory
is that it describes two sets of particles and forces: the normal forces
(strong, electromagnetic, weak) and particles (photons, electrons, neutrinos,
quarks, ...) and a set of shadow-forces and shadow-particles that share only
gravity in common with the normal world. Thus, our universe could, without our
knowledge, be superimposed on another "shadow" universe which has its own light
and matter and even stars and planets and animal life which do not interact
with ours except through their common gravitational attraction.

If one could indeed convert a quantity of normal matter, say a subway-car-size vehicle full of passengers, into shadow matter (and if the vicinity of the Earth was empty of shadow matter otherwise) we would have our through-the-Earth subway without need of David Innes' mole machine. The vehicle would fall through the Earth's gravity well, emerging at a diametrically opposite point on the planet 38 minutes later. There it might, as it entered the subway station, be converted back to normal matter.

Getting into space would be much easier and cheaper with this technology also. No elaborate launch facilities would be needed. A space vehicle could be converted to shadow matter inside a building, and it would then plunge directly toward the center of the Earth. There it could use its rocket fuel far more efficiently because fuel burned deep in a gravity well yields much more net thrust than the same fuel burned in gravity-free space. Moreover, the Earth itself could be made to serve as a fuel source, for the ultra-compressed matter of the Earth's inner core, if it suddenly found itself in the vacuum of empty space, would explode with the volcanic force of a miniature Mt. Saint Helens.

There is not space here to develop the implications of the existence of shadow
matter and the possibility of its conversion to normal matter as fully as they
have been developed in my first SF novel,
** Twistor**, which is being
published in hardcover by the William Morrow & Co. (March, 1989).

Is there really such a thing as shadow matter? I have no way of knowing at the
moment, and neither does anyone else. *Something* gives galactic
clusters many times more mass than can be explained with present-day physics.
The extra mass or "dark matter" may come from shadow matter, or from WIMPs, or
from axions, or from something else that no one has yet even thought of. Let
me simply say that, from my point of view, one of the most remote and esoteric
areas of theoretical physics has predicted something that is the science
fiction writer's dream, a doorway to parallel "shadow" worlds, a method of
nearly free worldwide transportation, and a cheap route into space.

It's actually more fun than Pellucidar!

John G. Cramer's 2016 nonfiction book (Amazon gives it 5 stars) describing his *transactional
interpretation of quantum mechanics*, ** The Quantum Handshake -
Entanglement, Nonlocality, and Transactions**, (Springer, January-2016) is
available online as a hardcover or eBook at: http://www.springer.com/gp/book/9783319246406
or https://www.amazon.com/dp/3319246402.

**SF Novels by John Cramer: **Printed editions of John's hard SF novels ** Twistor**
and

**Alternate View Columns Online:** Electronic reprints of 212 or more
"The Alternate View" columns by John G. Cramer published in ** Analog**
between 1984 and the present are currently available online at: http://www.npl.washington.edu/av
.

*This page was created by John G. Cramer
on 7/12/96.*