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 ------