The problem with Bronnikov-Lemos wormholes is that they should be infinite in length, and that is difficult in a universe that may not itself be of infinite extent. This difficulty can be avoided by “putting the snake's tail in its mouth,” in other words, bending the cosmic string in a circle, so that the wormhole becomes a torus (doughnut shape). Bronnikov and Lemos have investigated this possibility, but the results are inconclusive. It is not at the moment clear whether a toroidal wormhole needs negative mass-energy for stabilization or violates the weak and/or null energy conditions. But there are indications that the desirable properties of the cylindrical geometry may be retained when the infinite string becomes a circle and the infinite cylinder becomes a torus. Therefore, perhaps we should be searching for indications of wormhole leftovers from the Big Bang in the form of doughnut shaped objects.
A second recent advance in our understanding of wormhole physics came from the work of Maeda, Harada, and Carr. Their work was motivated by their investigation of numerical relativity, in which the equations of general relativity are solved in a dynamic situation where conditions are changing (for example, the universe is expanding) using numerical approximations on a large computer. That numerical work pointed to dynamic wormhole solutions that had unusual properties, and caused the authors to look for corresponding algebraic GR solutions. The result is what the authors describe as cosmological wormholes. These are dynamic wormholes that cannot connect within a single universe, but instead must connect one Friedmann universe to another.
Here, a Friedmann universe is the present Standard Model of cosmology. It uses general relativity to describe a simplified version of the universe in which we live. It is a universe that is expanding at a regular rate and that contains matter that is uniformly distributed and that acts as a fluid characterized by pressure and density. The lumpy stars and galaxies of our universe are averaged out in the Friedmann model and characterized by a universal fluid, a good approximation if one takes a very large-scale view of the universe.
The cosmological wormholes of Maeda, Harada, and Carr connect two Friedmann universes (presumably ours and another one). They are dynamic, changing with time. They satisfy all of the energy conditions, and they do not require any negative mass-energy for stability. At least in isolation, they cannot lead to time-like loops and time travel paradoxes because they lead to another universe with its own time structure (and perhaps its own laws of physics). The authors suggest that such wormholes may have formed naturally in the early phases of the Big Bang and may have influenced the behavior of the universe during its initial expansion phase.
The Maeda, Harada, and Carr paper does not address the issue of whether two independent cosmological wormholes might connect the same pair of universes. Their calculations require certain symmetries and probably do not tolerate the consideration of two wormhole connections in the same universes. However, the presence of two wormhole paths connecting arbitrary space-time points in a pair of universes would make possible time-like loops that threaded both wormholes and lead to time paradoxes. I suspect that there is an underlying exclusion principle implicit in the wormhole mathematics that prevents such dual connections.
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The implication of this work is that we now know of two wormhole types that do not require negative mass-energy for stability. These provide an “existence theorem” that negative mass-energy is not always required for stable wormholes (and perhaps also for warp drives as well). Further, the cosmological wormholes of Maeda, Harada, and Carr could have been produced during the Big Bang, perhaps in great numbers. They could still be around and could provide gateways to many other universes. Writers of inter-universe science fiction should take note.
Copyright © 2009 John G. Cramer
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AV Columns Online: Electronic reprints of over 140 “The Alternate View” columns by John G. Cramer, previously published in Analog, are available online at: www.npl.washington.edu/av.
References:
"Cylindrical wormholes,” K. A. Bronnikov and J. P. S. Lemos, arXiv preprint 0902.2360v3 [gr-qc], February 24, 2009.
"Cosmological Wormholes,” H. Maeda, T. Harada, and B. J. Carr, arXiv preprint 0901.1153v3 [gr-qc], March 3, 2009.
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Probability Zero: GLOBAL WARMING by Harry Turtledove
Try as we will, we can no longer deny the truth. The world is getting warmer. Glaciers everywhere are in full retreat. Shamans and wizards of many clans have joined together, and rightly so, in stressing the disastrous environmental impact the withdrawal of the ice will have.
Many large mammal species—the bases of our economy and our very way of life—are certain to face displacement or even extinction as the weather worsens. Clans dependant upon woolly mammoths and woolly rhinoceri for sustenance will either have to migrate into new and unfamiliar hunting grounds or begin feeding upon smaller, less satisfactory prey animals such as caribou and horses. In certain heavily impacted areas, clans may be reduced to eating beavers and marmots. There have even been reports of the regular consumption of crayfish, mussels, and other fare normally contemplated only during famines. All such movements and lifestyle shifts, of course, also entail numerous violations of tabu. The cost of propitiation is certain to be high.
Worse problems may also lie ahead for affected areas. As the tundra retreats northward, invasive foliage from the south encroaches upon it. These “trees,” as they are technically known, cannot support the biodiversity upon which we depend. Not only that, hunting becomes far more difficult: with the severely reduced horizon among trees, visibility and tracking suffer badly.
Furthermore, anecdotal reports trickling up from areas in the south already afflicted with trees indicated that predators peculiar to this degraded environment pose significant risks to hunters and even gatherers. These so-called “bears,” if such sources may be relied upon, are large, wily, and dangerous in the extreme.
It is as yet unclear to those studying issues pertaining to “forests” (as accumulations of trees are termed) whether the beasts called “boars” are predators or prey. Not to be confused with bears, boars are simultaneously alleged to be both extremely tasty and swift and savage. As trees continue to advance onto tundra, cautious experimentation seems indicated.
So far, it will be noted, I have discussed only the incontrovertible fact of global warming, its likely impact upon us in the relatively near future, and short-term coping strategies. Many will say that we should not remain in a reactive mode, but should proactively seek to reverse the deleterious effects of this warming trend. In some ways, though, such a proactive response seems more readily proposed than implemented.
Forward-thinking shamans—including some among the first to recognize the reality of our predicament—have naturally sought sorcerous countermeasures. Considerable appropriations of dried meat have enabled a large-scale research program unmatched since the one that led to the partial taming of fire (about which, in a rather different context, more soon). If only success were commensurate with effort! Even spells essayed in the dead of winter and in the anomalous cold darkness of solar eclipses have failed to halt or even slow the steady, apparently inexorably retreat of the glaciers and degradation of the tundra south of them.
Which brings me back to fire. Wizards have conclusively demonstrated that fire is a spear with a point at both ends, as likely to wound the ones who wield it as to aid
them. Fire gives heat. It cooks food. So much has been known for many generations. Because of this, tundra clans, almost without dissent, reckon it highly valuable. Lately, the truth of that assumption has come under question.
You see, fire, while burning, releases invisible spirits into the atmosphere. Because they spring from fire these spirits trap heat, in much the same way hunters trap mammoths with pitfalls. Once the mammoth tumbles into the pit, it cannot hope to escape. And, once the liberated fire spirits trap the sun's heat, that cannot hope to escape, either.
The more fires our clans burn, then, the more fire spirits commence to prowl the air. And, the more fire spirits prowl the air, the more solar heat they snare near the earth's surface. This obviously is a factor—and an increasingly significant factor as the use of fire grows—in the emerging global-warming crisis.
From this, it follows that reducing the fire spirits’ footprints as they prowl the atmosphere would correspondingly reduce the amount of trapped solar heat contributing to the warming of the earth. We must use fire less. Those habituated to the savor and chewability of cooked meat may well object to that. So may those who have grown accustomed to sleeping soft in their tents even when snow swirls outside.
Their shortsighted, deluded self-interest must—I repeat: must—be rejected, and in the most emphatic way possible. The environment and its continued protection take priority over all the commonplace concerns. If fire causes the glaciers to retreat; if fire causes the tundra to follow the ice north and causes longtime clan hunting grounds to be overrun with useless, obstructive vegetation pushing up from the south in the wake of global warming; if fire causes the very seas to rise, threatening to displace or drown the clans living in low-lying regions—if fire causes these things, I say, we must suppress it. Cause them it does. Our wizards and shamans no longer leave us any room for doubt. Therefore, suppress it we must.
Let this be a warning, then, to all those so enamored of their temporary comfort that they are willing (perhaps even eager) to cling to fire despite the ever more obvious long-term environmental consequences. If they persist in releasing fire spirits into the air, we shall oppose them with all necessary measures, up to and including war.
And once we vanquish them—and vanquish them we shall, for our cause is just—we will make an example of them, so that we discourage and intimidate potential future backsliders. We will catch them and kill them and eat them.
Raw, of course.
Copyright © 2009 Harry Turtledove
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"Many of our most important decisions are made by someone too inexperienced to have much idea what he's doing."—Kelvin Throop
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Special Feature: MUSINGS FROM THE FIRST GENERATION by Michael Carroll
Anniversaries make us wonder about the nature of things, about origins and beginnings, about where we've been and where we're going. On this 40th anniversary of the Apollo 11 Moon landing, I wonder why the Moon holds such power over us. Why do poets rhyme and romantic couples linger under its light? Perhaps we are drawn to it simply because it is so ever-present in the night sky, a force second only to the Sun. Or maybe its proximity in the cosmic scheme of things makes it the obvious next site for humanity to inhabit.
It is fitting that someone like me would be doing this wondering. I am a member of a unique generation. It's a generation with its feet planted in two worlds. The first is the world of dreams, a place inhabited by four-armed green Martians, Tiger Women of the Moon, astronauts wearing gravity belts and aviator caps. The second world is a place every bit as wondrous, a realm of real worlds, planets and moons seething with volcanoes, awash of methane oceans, blanketed by cloud depths of multi-colored poisons.
In 1960 my father took me into the backyard. It was a cool Colorado evening. The stars shimmered in a purple twilight sky, nailed in their places since the ancients gave them names like Antares and Rigel and Betelgeuse. And there, among the points of steady light, one moved. “That's Echo One,” my father pointed. It was brighter than the others, a giant Mylar balloon circling a thousand miles above our heads. “They bounce radio waves off it,” he said. I could feel him smiling in the darkness.
"Why Echo One?” I asked. “Why not just Echo?"
"Because,” my rocket scientist father said into the night, defying the darkness, “because there will be more."
And there were. Our human-crafted stars circled the world like buzzing bees. Some cast off Earth's gravitational chains, and sent back reports from new, far-away worlds.
And nothing would ever be the same again.
We barreled—like a hell-bent locomotive—from a dark and ignorant tunnel into the blazing light of discovery. It was a light that brightened gradually, incrementally. And what a light it is, infused with the glow of planets great and small, the drifting clouds of Eagle and Orion nebulae.
Our fuzzy telescopic maps have blossomed into real territories of mountain and desert, canyon and cloud. Mapmakers, armed with their new, clear views, put names to those canyons and mountains. There is power in a name. It lays ambiguity in concrete, sets down secure borders, brings definition to the unfocused. So the worlds out there went from “Thar Be Dragons” to places you could put your feet on. The cartographers and astronomers gave us the gift of names, some by cultural assent and others by a vote of an international committee of labelers. They bequeathed us Olympus Mons, Syrtis Major, and Valles Marineris, the heights and depths of the red planet. Their charts displayed Ganesa Macula on Saturn's mighty Titan, and Discovery Rupes, simmering beneath the swollen Sun in Mercury's sky. They endowed Saturn's moon Mimas with Arthurian names, like Camelot Chasm and Gwynevere Crater. Jupiter's volcanic satellite Io bristled with the monikers of fire gods: Pele, Prometheus, Amirani.
But before the new names came the explorers. On another night, in another place, my father pointed to the sky again, this time at a star moving from north to south. “And that one may be a spy satellite. It's probably got a hammer and sickle on it."
The evening air scattered goose bumps across my shoulders. There were people on the other side of the world, hiding behind an opaque curtain made of iron, who were sending up spacecraft, too. I was too young to understand the ins and outs of the political world. I was blissfully ignorant of the uneasiness—even fear—that permeated daily life for my parents and their friends. Those people on the other side of Earth were as mysterious as the planets out there. Were they like us? Did they have the same fears and dreams? Did they like ice cream? Hate broccoli?
They were the ones who had sent the first person into space in 1961. Yuri Gagarin circled the world once while we, in the western hemisphere, stayed glued to the dirt, yearning for the skies. Cold War competition was strong motivation in those days. The Soviet Union had taken to the high ground, and we watched in frustration as our televised rockets blew up in shades of gray on our rabbit-eared television sets. As if sending things overhead in circles above the Earth weren't enough, those mysterious communists were first to hit the surface of the Moon with an artificial craft. Two years before the first cosmonaut looped around the world, Luna 2 slammed into the eastern edge of the Moon carrying political pennants, radiation monitors, and micrometeorite detectors. The little metal ball represented a technological and scientific triumph, and had a profound sociological effect on those of us who had not yet escaped Earth orbit.
The Moon stared at us from the cosmos, closer than the stars but still impossibly far away. And up there, on its once pristine face, was a human artifact. Half a world was celebrating. The other half was nervous.
I may have been too young to comprehend political or theological nuances, but I wasn't too young to catch the fever of excitement. A pandemic was sweeping across the world, infecting the generals, the corporate types, and my young contemporaries alike. The fever incubated deep down, stoked by newspapers and television hungry for glimpses into the great unknown. We were a generation of Magellans and Hudsons, wanting desperately to
set sail on a new sea. But there were no tall ships to be had. The only vessels at dock were dinghies.
Some of us younger people didn't need Atlas boosters or Gemini spacecraft. By the time NASA was sending twin astronauts around the Earth in Gemini capsules, my sister and I had been to the Moon dozens of times. We traveled there in our family Volkswagen, parked in the garage while speeding through the starry void. When we wanted power, we pushed on a pedal and watched as brake-light rocket plumes spread across the garage door. It was a time inspired by bedtime stories, space picture books, and most of all, that sorcerer's box in our living room. Mom warned us of its two-edged nature. Sunday nights, The Wonderful World of Disney played, with the likes of Mary Poppins and Chitty Chitty Bang Bang. The tube offered The Patty Duke Show, Hogan's Heroes, and Family Affair. But there was a darker side, too. With The Twilight Zone and The Outer Limits and various thrillers and science fiction movies, a boy turned loose had no chance of self-discipline.
So I watched it. I wasn't sure what the show was. All I knew was that it had astronauts, and they were wandering around on the Moon. What could be better? But things went south fast. As creepy music swelled, several of the hapless explorers sank into the quicksand, meeting a long, agonizing demise. What was left of the party took several glowing balls, newly dug up, back to their base. Hadn't they ever seen a science fiction movie? They should have known better. I can't remember, specifically, how the glowing balls took over, but the result provided plenty of material for my Id when it was busy constructing my bad dreams.
Only later would I find a more capable tour guide in the form of Jules Verne. His From the Earth to the Moon captivated me. Barbicane, Nicholl, and Ardan traveled in their cushioned artillery shell—launched from Florida in a precognitive echo of later Apollo Moon missions—to coast around the far side of the Moon. As luck would have it, it was dark there, of course, so that they could not see what was on the mysterious unseen side of Earth's nearest neighbor. Fortunately for the first lunar visitors, a brief meteor shower illuminated the unlit landscape below them. Did they glimpse forests? Did oceans wash across a verdant landscape of cloud and valley? Were their eyes playing tricks on them? We would have to wait for Neil and Buzz to take us there in person.
Analog SFF, July-August 2009 Page 27