Pathspace: The Space of Paths (56 page)

A man stepped forward, holding his hat
in his hands. He cleared his throat. “Sorry to hold you up, sir.
It's the spring. It's on my neighbor's land, and he won't let my
livestock cross over to use it. The boundary between our farms is
this road, so I'm afraid sometimes it holds up traffic.”

“
Don't listen to him!”
Another man lurched forward. Why should I have to chase his animals
off and mend my fences every time he wants to use our water? Look
for yourself,” he said, gesturing to the snow all around them.
There's plenty of water everywhere. He doesn't need to come on my
land for water.”

Isaac shook his head. “It
is not for me to say who is right and who is wrong. But blocking
the road,
that
is
wrong.”

He turned to the man holding his hat.
“How far is it to your house? My wife and son are waiting for
me.”

“
Not far, Righteous One.
Just over the hill to the left. See, there is the road up
ahead.”

Isaac looked ahead and nodded. “Very
well. This is what will happen. You and your family and your
animals will lead the way back to your house, and we will follow.
When we get back to your house I will see what can be
done.”

He then looked to the second man who
had spoken. “Your land will not be trespassed. Please take your
family home and clear the road. I'm probably not the only one who
wants to get home before it snows again.”

Both men bowed and backed away, and
Isaac returned to the coach. “Why didn't you stay in the coach?” he
asked Nathan.

Nathan hurried back inside
the vehicle. “I wanted to see what was going on. What does it
mean,
Tzaddik
? I
heard someone say that.”

“
We'll talk about it
later,” said Isaac, climbing in beside him. He rapped on the roof,
and the driver picked up his reins.

The coach lurched ahead. Isaac looked
at his wife. “What could I do? It's my job.”

Rebekah laid a hand on his arm,
melting a few snowflakes that hand landed on his sleeve. “You don't
have to solve every squabble, you know.”

“
No,” he agreed. “Only the
ones I know about.”

The coach jolted as the driver pulled
off the road onto the farm path. Rebekah shook her head, but Nathan
could see she was smiling.

Soon enough, the driver pulled up in
the driveway of an old farmhouse. The man with the hat was standing
there among a flock of sheep, gesturing to his right. “You see? The
pond is frozen over. My neighbor has a pond with a spring, and it
keeps the ice melted over where the water comes up. But I don't
have a spring.”

Isaac got out of the coach again. “I
see,” he said. He turned to the farmer with the hat. “Do you have
faith, sir?”

The man swallowed. “As much as any
man.”

“
That will have to do. If
God allows you water, will you agree never to lead your livestock
to trespass on your neighbor's farm again?”

The farmer nodded, never taking his
eyes off Isaac.

“
Very well,” said Isaac.
“Lead your animals down to the edge of the pond.”

Looking baffled but hopeful, the man
picked up a shepherd's crook and began to lead the sheep down
toward where the frozen pond lay nestled in the cupped hands of the
earth.

Nathan looked at his father in that
white robe. “But it's still frozen.”

“
Watch.”

The man and his sheep were almost to
the edge of the pond. Suddenly, as if on cue, a semicircle of ice
at the edge simply melted away.

He heard the farmer's joyful cry as
the sheep began to cluster around the melted part, drinking the
water.

Nathan looked at his father again.
“What happened?”

Isaac shrugged and smiled. “A
miracle,” he said, and climbed back into the coach. “Let's continue
on,” he told the driver. “If we linger we'll be here half the
night.”

Nathan climbed back in too. He looked
at his father again, as if seeing him for the first time. It
occurred to him suddenly that he had never asked his father's
occupation.

End of preview

It is easy to imagine that
the concept of
pathspace
as presented in this novel is simply an invention
for narrative convenience.

However, I feel it is my
duty to point out that some aspects of it are definitely
not
fictitious.

Ever since Einstein
released his General Theory of Relativity, we have been able to
visualize gravity not as a mysterious force that somehow “pulls” us
toward massive objects, but, instead, as simply a
pattern
in space that
dictates the sort of paths objects will take when moving through
that region of space.

Unfortunately, the geometry that
Einstein used to map gravity onto space has more than three
dimensions, which makes it rather difficult to visualize. To make
it easier, people who lecture on this subject usually subtract one
dimension and say something like this. “Imagine a bowling ball
lying in the middle of a waterbed. The weight of the ball distorts
the flat surface of the waterbed. If you roll a tennis ball on the
waterbed it will travel in a curved line (usually ending on the
bowling ball unless you roll the tennis ball really fast) because
of the presence of the bowling ball. This is similar to the way
that the Sun's 'weight' distorts space around it and makes the
Earth travel in a path that keeps curving around the
Sun.”

There are couple of problems with this
explanation.

In the case of the bowling ball, it is
weight (the force of gravity on the ball) that makes it press down
on the waterbed. Weight is what you experience when you try to keep
something from going where it wants to go in a gravity field. If
you were falling off a building with the bowling ball next to you
it would not appear to weigh anything.

But the Sun has no weight! Nothing is
keeping it from orbiting the center of the galaxy. It is like a
skydiver in free fall.

The Sun's effect on space
is due to its
mass
, not its “weight.”

Another problem with the
bowling ball + waterbed analogy is that it fails in the
3
^rd
dimension. If you
toss the tennis ball above the bed, it feels a need to curve down
toward the floor, but it is not the surface of the waterbed that is
causing this.

A better way to imagine the Sun's
gravity field might be to imagine a hole in space into which space
is falling from all directions in an inward radial waterfall If you
throw a tennis ball past such a hole the radial inward movement of
the space it is traveling through will cause the ball's path to
curve toward the hole. If it is moving too slowly, it will be
pulled into the hole. If it is moving faster enough it will be
caught in an orbit around the hole. If it is moving even faster, it
will fly past the hole and curve only slightly toward it as it
passes.

This is how objects behave
near the sun It is almost as if
the space
itself
were getting pulled into the sun,
and dragging anything embedded in the space along with
it

The idea of space “moving” is pretty
incomprehensible, so physicists speak instead of the “curvature” of
spacetime. The equations describe it well enough, even if it is
hard to visualize.

Fine. But my point is this:
it is just as easy to say that there is a distortion in the
pathspace
around the
sun. Every object that travels is traveling on a path – we call
them trajectories. If the space the path passes through is
distorted, the path will be curved by an amount that is less
noticeable at higher speeds because the distortion has less time to
affect the momentum of the object.

Simply put, Einsteinian
“space curvature” is a simple kind of
pathspace
, a kind caused not by human
telekinesis but by the presence of matter. When it is oriented
radially in a gravity “field”, an elevator shaft is definitely a
kind of swizzle! While fast-moving objects like hot air molecules
or motorcycles can hop across the elevator shaft opening and ignore
it, slower-moving objects like cold air – or a walking person –
will definitely be sucked into the shaft if they get to close and
accelerate toward the other end.

Now if we remove the gravity field –
say by moving the elevator shaft far from any sun or planet out in
flat” space – then we have “turned the swizzle off” – now if we
step into the open end we will just float there instead of falling
in.

Now turn the analogy around. A swizzle
is simply a portable spacetime distortion, like a piece of a
gravitational field that you can carry around and point in any
direction you want. If it is strong enough, you can make water flow
uphill or even fire tennis balls straight up.

The only difference between the
elevator shaft and the pipe swizzle is that in my novel, the
distortion is imposed by a sentient mind rather than a big hunk of
matter. Just as the gravity field of the Earth's pathspace is
anchored by the actual matter of the Earth (so that it follows the
Earth around and keeps affecting us and the moon), so the pathspace
of a swizzle is anchored by the matter of the pipe it is defined
upon – so that it follows the pipe around if you are walking around
while holding it.

If you activate a swizzle and drop it
into a fluid – such as seawater or the thin gas of interstellar
space – it will accelerate until the drag equals its
thrust.

The only real difference
between a pathspace weave and a piece of Earth's gravity well is
that the mass particles of the Earth do not have to “concentrate”
to create their pathspace distortion. It is part of them. If a
photon decays into an electron and a positron, each of the
particles is
born
with mass and a charge and a gravitational field – their
pathspace distortions appear when they do.

Einstein's space-curvature tensor is
simply a compact and elegant way of specifying the local pathspace
– the space of paths.

--- MRK

Other books by Matthew R.
Kennedy

The
Gamers and Gods
trilogy

Gamers and Gods:
AES

Gamers and Gods II:
MACHAON

Gamers and gods III:
ALEXANOR