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OtherRealms Issue 26 Part 02
Electronic OtherRealms #26
Winter, 1990
Part 2 of 8
Copyright 1990 by Chuq Von Rospach
All Rights Reserved.
OtherRealms may be distributed electronically only in the original
form and with copyrights, credits and return addresses intact.
OtherRealms may be reproduced in printed form only for your personal use.
No part of OtherRealms may be reprinted or used in any other
publication without permission of the author.
All rights to material published in OtherRealms hereby revert to the author.
Behind the Scenes: Redshift Rendezvous
John E. Stith
Copyright 1990 by John E. Stith
Suppose you saw a jogger run past you fast enough that her body was
contracted in her direction of travel.
All right. You're imagining a significant change to our environment, so
we can encounter relativistic effects at low speeds.
A jogger in this altered environment would find that as she runs fast,
stationary observers she passes appear contracted in her direction of
travel. Stationary clocks would be speeded up. Of course, those clocks
wouldn't actually be fast; her internal clock would be slowed. Just like
the traveling twin in the so-called twin paradox, she is moving through
time more slowly than her sister who sits in a chair by the pool taking
in the chlorine. If she runs fast enough, she can slow her internal
clock to the point that she experiences only one second for every minute
that her motionless sister ages. Looking at it another way, by running
she slows her own aging process, so jogging really is good for her
health.
The idea of relativistic effects happening at low speeds is the initial
idea that led to the novel Redshift Rendezvous, due from Ace in June 1990.
One of the things the novel does is make relativity a personal
experience rather than an abstract astronomical idea. This article talks
about the evolution of the idea, the ripples it generated, the dead ends
it led to, the expedient assumptions required, and the weak areas I
haven't yet come to terms with.
My first totally arbitrary decision was to pick ten meters per second
as the speed of light. To justify the speed of light being lowered, I
presumed the existence of multiple layers of space, hyperspace, in
which the speed of light decreases as one moves farther from layer
zero, our familiar region of space-time. Table One shows the dimensions
of the Redshift.
So that it would be useful to go into these other layers, I also assumed
that distances between corresponding points in these higher layers would
shrink by an even greater factor, so the light-speed distance between
two corresponding points drops by a factor of two for each level farther
from level zero. Hence, light-speed travel in layer ten is equivalent to
1024 times as fast as light-speed travel in our layer zero, even though
ships move at not quite ten meters per second. Table Two shows the
relative dimensions and speeds in each layer of hyperspace.
These assumptions about quantum layers of the universe are unjustified
fabrication on my part, but at the same time they are probably going to
be hard to unequivocally disprove for a few years (at least for someone
with my education and inclination). Slow light in alternate hyperspace
layers is the foundation for all the resulting ideas. Where I was
unhampered by worrying about contradicting known facts or values, I've
picked values that make the relativistic effects pronounced, in the same
way that authors sometimes exaggerate trends or traits to look at a
society skewed in one direction or another.
The hyperspace craft, the Redshift, resides in layer ten so it can cut
travel time between widely spaced points. In layer ten, I've attempted
to keep the rules of physics as we currently know them unchanged. The
only alteration is to make the speed of light ten meters per second
instead of 3x10^^8 meters per second.
I hope you'll agree this is a lot more exciting than, for instance,
3x10^^7.
As long as I assumed people in this future know enough to warp space so
they can translate between hyperspace layers, I assumed they also know
enough to warp space to simulate a mass large enough to create a
comfortable gravitational field. As long as curved space causes gravity,
why not eliminate the mass? For the Redshift itself, I picked a
spherical shape like a miniature planet, with spherical levels for
floors. That way, gravity pulls the inhabitants toward the center of the
ship, unlike one conventional approach that uses spin to create
centrifugal force in the opposite direction, (which wouldn't work for a
sphere anyway). Figure One shows the configuration of the Redshift.
Immediately, the ten-meters-per-second velocity of light leads to an
environment in which a runner sees the surroundings undergo relativistic
contraction. Also, the clocks in the motionless frame of reference
appear to run fast. By the way, for those readers who think the
motionless clocks should be going slowly when observed by the runner,
bear in mind that this environment is not the special relativity
environment in which two unaccelerated observers pass one another. Since
a gravitational field is present, and the runner is accelerated while
running around the circumference of the ship, we are dealing with
general relativity.
Okay. We're at the point where contraction and time dilation are
justified. So is Doppler shift of light. The runner sees objects ahead
of him shifted higher into the spectrum. He always measures light as
having the same velocity, so the fact that the distance between him and
approaching objects is decreasing shows up as increased energy in the
light, hence higher frequency. Objects in his wake are similarly red
shifted down the spectrum.
As I was growing more comfortable with the effects that stem from the
original assumption, I remembered that light is deflected by warped
space (large masses). In this environment, with light moving so slowly,
that effect is enormously magnified.
On the Earth's surface, as in any gravitational field, light falls at
the same rate as mass does. We don't think much about it because light
speed is so high that the fall rate is negligible. Take two vertical
face-to face mirrors and shine a light perpendicular to one of the
surfaces. At the same time, throw a ball directly perpendicular to one
of two face-to-face walls. The ball will bounce back and forth, falling
under the accelerating force of the Earth's gravity. So will the light.
The ball and the light, although traveling at much different horizontal
speeds, will reach bottom at the same time.
Aboard the Redshift, the same is true. The only real difference is that
since the light is traveling slowly, it falls in about the same arc that
a fast-moving object would move.
Hence, light from a flashlight takes about the same path that water from
a pressure hose would take.
Bending light is certain to cause more optical illusions than I have
even thought of yet. At exactly the right distance from the central
warped space, the speed of light matches orbital velocity, so the curved
path that light takes when traveling around the circumference of the
Redshift tricks the eye into thinking the light moves in a straight path
on a level corridor.
Downstairs, inside that same radius, gravity makes light fall fast
enough to cause different optical illusions. On level two, if you aim a
flashlight at wall ten meters away, the light falls about half that
distance on the way there. You have to point the flashlight higher than
the spot you want to illuminate. Since light moves slower than orbital
velocity, it falls to the floor. Light from the floor out of direct
(straight) line of sight curves around the body of the ship, so the
observer can see much more of the floor than would otherwise be visible.
This means that the light reaching one's eyes horizontally comes-from
the floor, and in turn this means that there is generated the illusion
that the inner levels are bowls rather than the spheres they actually
are.
I was busily drawing paths that light would take on the seven levels of
the ship when I realized that with light dropping so fast, gravitational
redshift would probably be easily observable. In fact, it's a major
factor, especially on the lower levels. As light rises through a
gravitational field, it loses energy, and hence lowers its frequency.
The converse is true also.
So we've got bending light and gravitational red shift. The next ripple
is -- why is the light bending? Because of gravity, of course. But that's
not the precise answer. Warped space, which gives us gravitation, makes
light bend because time slows down in gravitational fields.
In our part of the universe, the speed of light in vacuum is constant.
But, as verified during eclipses, light from distant stars does indeed
bend around the sun on its way to Earth. It curves either because one
side of the wavefront is going slower than the other -- not acceptable
because the speed of light is constant -- or because time is slowed on
one side of the wavefront. If time is slowed, light is still moving at
the constant speed of light; it's only an observer outside the field who
thinks the speed has apparently decreased.
So gravitational fields slow down time. It's true here, and it's true on
the Redshift. But when you plug c = 10 into the gravitational
time-dilation equation, there's a huge influence generated by the
pseudo-mass at the core of the Redshift. Therefore, the closer one gets
to the center of the ship, the more slowly time progresses. Each level
is its own time zone, as though, for instance, time progresses more
slowly in Denver than in New York. But I'm getting into another theory
entirely. Back to time zones. Not only does the rate of time passage
depend on what level you're on, no matter where you are on the Redshift,
time progresses more slowly at your feet than at your head (assuming
you're standing). One side benefit of this is that you don't have to cut
your toenails as often as your fingernails.
Let's look at some of the fringe areas this environment requires. For
instance, if the speed of light is ten meters per second, what's the
speed of sound? In fact, since at room temperature on Earth, air
molecules move at several hundred meters per second, why doesn't the air
on the Redshift freeze out?
As we start dealing with molecules and atoms, we start to enter the land
between rigidly worked out implications and handwaving. I think that
even if the idea development stopped here, the Redshift environment
still makes an interesting thought experiment, and I liked the idea
enough that I would have been willing to do even more handwaving if
required, but there's an obvious attraction to having everything
rationalized.
Let's look at molecules in air for a moment. Oh, humor me; pretend you
can see them. On Earth, not only do they move faster than they are
allowed to in the Redshift environment, but we've got problems with
atoms as well. Atomic orbital electrons move around their nuclei at a
big fraction of our normal speed of light. I've assumed (handwaved) that
in the Redshift environment atomic particles are moving at almost the
new speed of light, and hence are heavily mass shifted. This means
electrons move more slowly in their orbits, (at larger radii) and it
means chemical reactions will slow down. For convenience, I've assumed
that however physical constants change from one layer to another, they
will allow the weak and strong nuclear forces, and electromagnetic
force, to maintain values appropriate to keep matter intact and inert.
This also means that most molecules move at almost the speed of light
and are heavier than normal. This extra mass-shift-caused mass coupled
with the slower motion results in the same total kinetic energy as the
molecule would have here. And since the combined molecular kinetic
energy determines temperature, the air doesn't turn into a freeze-dried
mist.
The speed of sound depends on the average molecular speed in air, since
sound is transmitted by those same molecules bumping into one another.
On Earth, for oxygen, the speed of sound is about two-thirds of the
average molecular speed. On the Redshift, if we assume the average
molecule speed is nearly ten meters per second, that makes the speed of
sound about six and two-thirds meters per second. Therefore, a person
can run faster than the speed of sound and create sonic booms for people
along the way. Here, anyone annoyed by joggers will be even more
provoked. Plug this new speed of sound into normal Doppler equations for
pitch changes, and you find that walking away from someone as you listen
lowers the voice pitch you hear.
Lifebelts are one of the weakest elements in the environment, but vital,
since a human being whose synapses are slowed to ten meters per second
won't live (at least it certainly wouldn't be a comfortable and
productive life). If the environment were unavoidably deadly to people,
it would be deadly dull to the reader.
Lifebelts generate a field within which the speed of light is the
familiar rate in this universe. To eliminate some of the magical quality
of the lifebelts, I assume the speed of light in our universe is still
an absolute maximum, so lifebelts are not capable of making light go
even faster than we currently believe, but rather compensating for a
characteristic in hyperspace layers other than layer zero.
Reflected light is another weak area. I assume that any person or
equipment protected by a lifebelt field will reflect light normally.
However, any unprotected surface consists of molecules whose electrons
move so slowly in their orbits that they don't resonate at the
frequencies required to absorb and then reradiate selected bands of
reflected energy. Here I've taken the unjustified approach that,
depending on the surface, light either bounces off those surfaces
diffused but unaltered, or it is totally absorbed. Hence, unprotected
surfaces can be seen in shades of gray.
Table One shows the dimensions of the Redshift, with the actual values
used in and generated by the equations. I arbitrarily chose the central
pseudo-mass and the dimensions of the levels to maximize the phenomena
inherent in the idea. If I had made the ship much larger, then the
gravity changes from level to level would be small, and hence so would
the other changes, like time zone differences. Table Three shows the
equations used.
The research for the Redshift was not without dead ends. One reader who
saw an early draft raised the possibility that with the gravity
differential of over four gees downstairs to less than one-fifth gee
upstairs, all the air might fall to the bottom level. I worried at
first, considering the possibility that level one might not be
habitable, or that the levels would require pressure doors and
independent ventilation systems.
Finally after some time spent looking at air pressure as a function of
height, I realized that common sense could have saved me some trouble.
(This is another universal law.) Air pressure in an open system such as
the Earth's atmosphere merely amounts to the weight of the air above
that point. In the Redshift, even if the four-gee gravity extended
twenty meters from the floor of level one, that would still result in a
column of air the equivalent of only eighty meters high in one gee. You
will feel a pressure difference by rising eighty meters from the Earth's
surface, but it's not an effect large enough to worry about.
I had an enjoyable time inventing the Redshift. It turned out to be more
work that I had expected, but it also turned into an even more
interesting environment than I thought it might. I've exposed some of
the weaknesses of the environmental construction partly to say that I at
least thought about them, and to provide a few starting points for those
readers who enjoy either discovering loopholes or inventing patches for
them.
I attempted to include most of the prominent relativistic effects, but
the novel doesn't feature every possible effect. There are bound to be
implications that haven't yet occurred to me. Discovering all the
ramifications immediately would be a little like having someone involved
in the early days of television anticipating an actor becoming
president, or The Gong Show. If, for instance, the environment were
expanded to encompass black-hole theory, one possibility to think about
is the idea of black-hole wastebaskets. I imagine something that looks
and acts a little like a black version of an electrostatic
insect-zapper. If we can warp space to provide gravity for the ship, we
can make tiny warps strong enough to trap any free material that comes
within, say, a centimeter. One obstacle to overcome is to make sure the
warp doesn't trap all the free air molecules. A way around that is to
turn on the warp only when it's approached by something that passes the
required tests to identify it as garbage.
Strange things happen aboard the Redshift. Although this base of
hypotheses is large enough that I've had to pick convenient assumptions
when offered a choice, I have made every effort to play fair with the
established rules. I hope the result, Redshift Rendezvous, puts a little
science back in science fiction, tickles the sense of wonder in a few
minds, and makes at least some readers care about the characters as much
as I do.
Table One
Master Plan of the Redshift
(Downstairs) (Upstairs)
Level: 1 2 3 4 5 6 7 Outside
Radius, floor (m) 5 7 9.8 13 16 19 23.5 27
Radius, ceiling (m) 6.8 9.5 12.3 15.5 18.5 23 26 Inf
Height of ceiling(m) 1.8 2.5 2.5 2.5 2.5 4 2.5 Inf
Gravity, floor (g) 4.62 2.36 1.2 .68 .45 .32 .21 .16
Gravity 1.5m up (g) 2.74 1.6 .91 .55 .38 .28 .18 .14
Gravity, ceiling(g) 2.5 1.28 .76 .48 .34 .22 .17 .00
Circumference (m) 1.4 44 61.6 81.7 100.5 119.4 147.6 169.6
Floor Area (m2) 314 616 1207 2124 3217 4536 6940 9161
Orbital velocity,
1.5m up, m/s 13.2 11.5 10 8.8 8.1 7.4 6.7 6.3
Escape velocity,
1.5m up, m/s 18.7 16.3 14.2 12.5 11.4 10.5 9.5 8.9
Rate of time, floor .31 .38 .46 .53 .59 .63 .67 .7
Rate of time, ceiling .37 .46 .52 .58 .62 .67 .7 1
Rate of time/level 4 .57 .71 .87 1 1.1 1.17 1.26
Red shift %,
floor to ceiling -18.4 -16.3 -10.9 -7.5 -5.6 -6.5 -3.1 -29.6
Elevators leading up 4 6 6 6 6 6 0
Stairwells leading up 0 8 8 16 16 16 0
Appearance bowl bowl flat sphere sphere sphere sphere
Uses high-value-cargo cargo cargo guest/galley/bridge guest/recreation bulky cargo cargo
Table Two
Relative Speeds and Distances in Hyperspace Layers
Hyperspace Speed SOL Dimension equivalents Use for
layer of light Improvement compared to this layer
(m/s) factor layer zero
0 3x10^^8 1 1.00 Normal Space
1 5.36x10^^7 2 0.08938
2 9.59x10^^6 4 .007989
3 1.71x10^^6 8 7.141x10^^-4
4 3.06x10^^5 16 6.383X10^^-5
5 5.48x10^^4 32 5.705x10^^-6
6 9790 64 5.100x10^^-7
7 1750 128 4.558x10^^-8
8 313 256 4.074x10^^-9
9 55.9 512 3.64x10^^-10
10 10.0 1024 3.26x10^^-11 Ship Travel
11 1.79 2048 2.91x10^^-12
12 0.32 4096 2.60x10^^-13
13 0.06 8192 2.32x10^^-14
14 1.0x10^^-2 16384 2.08x10^^-15
15 1.8x10^^-3 32768 1.86x10^^-16 High-speed comm net
By going one layer higher, the speed of light drops to .1787 (about
1/5.6) of current, and relative distances drop to .08938 (about 1/11.2)
of current, so speed-of-light travel is twice as effective.
Table Three
Fundamental Assumptions, Equations, and Constants
c = velocity of light on the Redshift = 10 meters per second
Pseudo-Mass at center of ship = 1.7x10^^13 Kg
Gravitational Constant (G) = 6.67x10^^-11 nt-m^^2/kg^^2
Gravity (in gees) = (G x Mass / Radius^^2) / 9.81 (Newtonian)
Circumference = 2 x Pi x Radius
Area = 4 x Pi x Radius^^2
Orbital Velocity = (G x Mass / Radius)^^5 (Newtonian)
Escape Velocity = (2 x G x Mass / Radius)^^5 (Newtonian)
Rate of time = 1 / (1 + (G x Mass / c^^2 x Radius))
Red shift % change = rate of time difference: floor to ceiling
Notes:
Dimensions are in meters. Masses are in Kilograms.
Most of the above equations are easily available in many physics texts.
The rate-of-time equation is derived from one in Gravitation and
Spacetime by Hans C. Ohanian (W.W. Norton and Co., 1976):
dt(sub)2/dt(sub)1 = 1 + Gm/r(sub)1c(sub)2 - Gm/r(sub)2c(sub)2
by assuming r(sub)2 is infinite -- meaning a point infinitely far from the
gravitational field, at which time progresses unslowed by gravitational
fields.
------ End ------
