Wormholes in Wonderland

THE NORTH POLE, A DECEMBER SOMEWHERE NEAR YOU: “My customer base has gone up fivefold in less than a century,” Father Christmas explained to his assembled subordinates. “If it wasn’t for the new X/MAS ultra-paragigaprocessor, I’d never be able to maintain my extremely tight delivery schedule. But now, at last, all my problems have been solved.”

A loud explosion echoed around the underground ice caves. A dishevelled Vice-Gnome for Computing rushed in. “Major hardware failure in the X/MAS ultrawhatsit, Santa,” he said, panting.

“What happened?”

“Algorithmic gridlock. We were running the travelling salesman program to optimise the delivery route, and the flash memory flashed. The computing requirements are growing exponentially with the number of PASCUs we have to visit.”

“PASCUs?” asked Santa.

“Personal Activity System Consumer Units,” the Vice-Gnome for Marketing answered. “Previously known as, um, let me see, children.”

Santa shook his head sadly. “I should never have sent you gnomes to business school. Why do we need to optimise deliveries, anyway?”

“The sleigh is running perilously close to the speed of light as it is. Unless we choose the shortest route, we’ll never be able to visit every PASCU on Christmas Eve.” Computing flopped into a chair.

“That’s not the only problem,” the Vice-Gnome for Distribution added. “The sleigh is travelling so fast that the reindeers’ energy requirements are skyrocketing, and Rudolph’s nose has turned blue with cold because his metabolism can’t keep up. I really do urge you to consider my memo proposing that we stagger deliveries over several weeks. Our business is ridiculously seasonal.”

“I agree that something must be done,” said Santa. “But I refuse to abandon my traditional role.”

“Well, there’s always Finance’s plan to change our corporate structure to a chain of subsidiaries owned by Claus Holdings plc, based in the Cayman Islands. That way the group as a whole can avoid taking responsibility for late deliveries.”

“No,” said Santa, with a nasty glint in his eye.

Marketing backtracked rapidly. “Right, I can go with that. Preservation of corporate image, yes, yes, very important, yes, of course.”

“Desperate times,” said Santa, “demand desperate measures. “We must leapfrog to an entirely new level of technology, one with the capacity to solve all of our problems for the indefinite future.”

The Vice-Gnomes for Production, Marketing, and Finance nodded. “I like the idea,” said Marketing. “But what exactly do you have in mind?”

“I’m dreaming of a relativistic Christmas,” said Santa. “I’ve been keeping an eye on the physics journals, and over the past few years a lot of potentially useful new concepts have appeared.”

“We’re a product-oriented corporation,” said Finance, worriedly. “We’re geared up for manufacture of Personal Activity Systems, not for R&D.”

“On this occasion, as an exceptional measure,” said Santa, “I am willing to bring in outside consultants. I shall secure the services of Hawkthorne Wheelstein, Chartered Relativists.” Santa dismissed his Vice-Gnomes and pulled a cellphone from his beard.

THE NORTH POLE, SOME DAYS LATER: Amanda Banda-Gander, Hawkthorne Wheelstein’s salesperson, stabbed at the brochure with a beautifully manicured fingernail. “l recommend a boundary across which no matter or energy can return. It’s called a black hole.”

“Because it’s black and things fall into it?” Marketing hazarded.

“More or less. Things do fall into it, and can’t then escape, but it actually gives off radiation, and looks red to someone on the outside.”

“And a white hole?”

“Like a black hole but reversed. Matter comes out, but it can’t get back in.”

“Ah, I see. And when you join the two together, you get a one-way tube?”

“Known as a wormhole, yes. What’s more, it is a tube that goes outside the normal Universe altogether – a cosmic short cut, connecting two regions of space like the handle on a briefcase. So Mr Claus can carry the black end, as we call it, on his vehicle, and arrange for the white end to materialise inside each dwelling that he visits. No more sooty chimneys, and no trouble at all getting stuck inside central heating systems.”

“Fantastic,” said Santa. “But how do I get out again?”

Amanda smiled. “By using a second wormhole, of course. And if you buy the black and white holes separately, together with a special linking module, then you can make a substantial efficiency gain. Just as black holes constantly suck matter in, so white holes constantly spew matter out. We can customise your white holes so that they emit an endless stream of toys.”

“Personal Activity Systems,” said Advertising.

“Sorry. And wrapping paper and ribbons, thereby solving all your manufacturing problems at a stroke.”

“I like the sound of that,” said Finance. Production was less sure – it looked like she might be out of a job.

“Conversely, black holes can solve forever the problem of disposing of unwanted wrapping paper and ribbons.”

“And unwanted Personal Activity Systems,” said Marketing sagely. “They all end up in the dustbin eventually.”

“True. You could recycle almost everything if you wanted to.”

“This is all very well,” said Santa, “but our most urgent problem is one of time. The faster-than-light sleigh has not yet been invented.”

“No, but the warp-drive sleigh has. Our Enterprise model has proved to be especially popular.”

“Warp drive?”

“According to relativity theory, matter can’t move through space faster than the speed of light. But, and this is the neat bit, there’s no limit on the speed with which space itself can move. So here’s what I suggest – the sleigh can sit at rest in a small bubble of space, and we will arrange for the bubble to flow at superluminal velocities through normal space. I know it sounds like science fiction, but Miguel Alcubierre at the University of Wales College of Cardiff has recently shown that it is entirely consistent with modern physics. Admittedly, it does violate the ‘weak energy condition’ that requires all energies to be positive. But that’s a purely technical difficulty that can be overcome using the Casimir effect, which creates negative energies between two parallel plates in a vacuum.” She waved her hands dismissively.

“Supersonic flight produces sonic booms,” said a gnome from the Legal Department, wary of possible third-party lawsuits. “Does a warp drive produce gravitic booms?”

“No, it’s guaranteed free of gravity-shock-wave emissions,” said Amanda, rather too glibly.

“I don’t like it,” muttered Legal’s gnome to Santa worriedly. “Even if Hawkthorne Wheelstein indemnified us, we could be held responsible if they go out of business.”

“That’s a good point,” said Santa. “Do you have any alternative solutions to our scheduling difficulties?”

Amanda pursed her lips. “Well … there’s our latest range of products. Time machines.” She waited as the idea soaked in. “That way, you can stagger deliveries throughout the year, while making sure that every single item is delivered on Christmas Eve.”

“How does this time machine work?”

“We have several models. The simplest is the moving wormhole, invented by Michael Morris, Kip Thorne and Ulvi Yurtsever in 1988, and based on the twin paradox of relativity theory. If an object travels very close to the speed of light, then time, as experienced by an observer moving with the object, slows to a crawl relative to that experienced elsewhere. Imagine two identical reindeer, Donner and Blitzen. Donner remains on Earth, and Blitzen heads off into space at nearly lightspeed, returning forty years later as measured by an Earthbound observer. Donner has aged forty years, but because of this time dilation Blitzen has aged only five, say.

“Morris, Thorne and Yurtsever realised that by combining a wormhole with the twin paradox, they could get a time machine. The idea is to leave the white end of the wormhole fixed, and to zigzag the black end to and fro at just below the speed of light. Seen from inside the wormhole, both ends age at the same rate. But from outside, the black end ages more slowly because of its speed. This time differential means that the passage of time is different if you go from one end to the other through the normal Universe, or through the wormhole itself. In fact, if you travel through normal space to the black end and then dive through the wormhole, you end up in your own past. You can read all about it in New Scientist, 28 April 1990, if you don’t believe me.

“There’s another approach that we’re working on at the moment, which should be operational very soon. It was invented by Richard Gott in 1991, and it involves using two cosmic strings – thin massive objects whose existence was first predicted by some grand unified theories – that pass very close to each other at near lightspeed,” said Amanda. “And we’ve got some new methods coming along that don’t need any singularities at all.”

“Brilliant,” said Santa. “We’ll take ten of everything.”

THE NORTH POLE, DECEMBER 2994: Santa sat at his computer monitor, studying the time travel schedules, frowning. A thousand years had passed, and still deliveries for 1994 had not been completed. There had been teething troubles. The wormholes were always being coned off for repairs, and the contraflows were a nightmare. The sleigh was getting totally clapped out and spent most of its time in the garage; sleigh rides were constantly being cancelled because reindeer were getting time-travel sick. Leaves kept blowing into the wormholes – the wrong kind of leaves, apparently.

But what the heck. Santa relaxed and cracked a smile. There was literally all the time in the world to get the system working. He sipped at a glass of sherry and nibbled a biscuit. Suddenly his peace was shattered.

“Emergency! Santa, quick, do something!”

“What’s happened?”

“I know we’ve only a few time machines here and now, but because all of our deliveries happen on the same Christmas Eve there are billions of white holes, accumulating all the time, on Earth in 1994. The topology of spacetime is becoming so entangled that baby universes keep budding off, and I’m worried that one of them may take the Earth with it.”

Santa suddenly realised that he had never seen this particular gnome before.

“Where’s your superior?”

“Um, gone on a course about intellectual property rights.”

“Don’t lie to me. Bad little gnomes don’t get their Christmas presents, remember?”

“Oh, all right. Er, he’s gone to see the birth of Christ.”

“WHAT?”

“It’s become a very popular tourist attraction since the invention of the time machine, Santa. All the major historical events have. The Sacking of Rome, the Battle of Hastings, the signing of the Declaration of Independence.”

“You’re telling me that my gnomes are using my time machines to bunk off work and go see the historical sights?” yelled Santa.

“Um, yes.” The gnome looked embarrassed. “They do take Him presents.”

“Idiots! The inn at Bethlehem will start to resemble a football match with all those gawping gnomes piling up! Do you recall any reports in the Bible about thousands of gnomes paying their respects to the infant Jesus? Bringing gifts of gold, frankincense, and My Little Pony?”

The gnome hung her head in shame as Santa raged. “You mindless incompetents have created a cumulative audience paradox!”

He paused, reflected, simmered down. “Except that in the real Universe, you don’t get paradoxes. Hmmm.” Santa chewed on the problem for a while. “Of course! The many worlds interpretation of quantum mechanics must be valid. Each time shift carries us into a new version of the Universe, coexisting with the original but separated from it along some totally new kind of dimension.”

“Oh. So that’s alright, then.”

“Well, I don’t see why it should cause us any serious difficulties. But until science has fully mastered the intricacies of parallel universes, well, jaunts to see the Nativity are out. Do you understand?”

The gnome hurried off, relieved. Santa returned to his schedules with a vague feeling that he was missing something.

A BILLION PARALLEL NORTH POLES, A BILLION PARALLEL DECEMBERS: “My customer base has gone up fivefold in less than a century,” a billion parallel Father Christmases explained to their assembled subordinates. “If it wasn’t for the new X/MAS ultraparagiga processor, I’d never be able to maintain my extremely tight delivery schedule. But now, at last, all my problems have been solved …”