the previous generation
These are the voyages of the Starhip Boobyprize,
her continuing mission:
to deplore strange new worlds,
to shriek at strange new life and new civilizations,
to cautiously come from where
no thing, object, or entity of any kind
whatsoever(8) will come from again.
Captain’s log: stardate the day after yesterday. We have finally reversed the time-reversal field that has reversed time for the last five episodes. The year is hmmm, 2366. H.G.Wells’s Time Traveller has heard about Federation heavy engineering. Very heavy: they build black holes. The Federation can make a matter-transmitter by connecting a black hole to a white hole to form a wormhole which can be used as a time machine. Rotating wormholes are recommended, in order to leave time for anything to get through. Unfortunately there are no rotating black holes within reach: the union is on strike. We have escaped from the Lazarus star by means of a cunning trick, which has left us drifting hopelessly with no power. Situation would be normal, except that the bar on holodeck two is dispensing only Kaliber. Situation desperate.
No rotating black holes? The Time Traveller looked extremely disappointed. Outa-Data was disappointed too. Wait, what had he been watching on the virtual reality hypermedia system the other night? The Comic Thing? No, but something like that. Got it! "I have an idea, sir. If you do not wish to try to control a Kerr black hole, you can settle for a much simpler kind of singularity: a cosmic string."
"Sounds good," said the Cat. "Now all we need is a beach."
"No, Cat, a cosmic string is a static spacetime, so that spacelike sections remain unchanged as time passes. The best way to visualise cosmic string is to use two dimensions of space. Cut out a wedge-shaped sector and paste the edges together (Fig.13a). If you do this with paper you end up with a pointed cone (Fig.13b); but mathematically you can just identify the corresponding edges without doing any bending. The time coordinate works just as it does in Minkowski spacetime (and to get the right shape for light cones you should identify the edges without making actual cones)."
If you throw in a third space coordinate and repeat the same construction on every perpendicular cross-section, you get a line mass. This is the fully-fledged cosmic string. To make a model of one, thread lots of identical cones on a length of well, string (Fig.13c). Remember, each cone is a constant-time section of the actual spacetime.
Fig.13 (a) Spatial structure of cosmic string (flattened). (b) Identifying the edges of the missing sector to get a cone. (c) Adding an extra dimension of space.
"I am not sure I fully understand the physical interpretation of a cosmic string as a spacetime," said the Time Traveller.
"The cosmic string has a mass, proportional to the angle of the sector that gets cut out. But it does not behave like an ordinary mass. Everywhere except the cone point, spacetime is locally flat just like Minkowski spacetime."
"Flat along what?"
"The apparent curvature of a real cone is ‘harmless’. But the cosmic string creates global changes in the spacetime topology, affecting the large-scale structure of geodesics particle paths. For instance, matter or light that goes past a cosmic string is ‘gravitationally lensed’."
"Pardon?"
"Bent, like light through a conventional lens. I will explain that in a moment. A cosmic string is much like a wormhole, because the mathematical glue allows one to ‘jump across’ the sector of Minkowski spacetime that is cut out. Back in 1991 J.R.Gott exploited this analogy to construct a time machine: more precisely, he showed that the spacetime formed by two cosmic strings that whizz past each other at nearly lightspeed contains CTCs. The starting-point is two static strings, symmetrically placed, as in Fig.14, which as usual is a constant-time spacelike section." The time coordinate is suppressed; but if it were added, it would run perpendicular to the page.
Figure 14 Two cosmic strings, opened flat for clarity.
"Because of the ‘gluing’, points P and P’ are identical, and so are Q and Q’. The figure shows three geodesics joining two points A and B: the horizontal line AB, the line APP’B, and the symmetrically placed line AQQ’B. This demonstrates gravitational lensing by the cosmic strings: an observer at B would see three copies of A, one along each of these three directions.
"Gott calculated that if the two cosmic strings are close enough together, then it takes light longer to traverse the path AB than to traverse the other two. This has an important consequence. If a particle starts from position A but at time T in the past, it can get to B at time T into the future. Call these events A(past) and B(future). If the strings R and S are now made to move, so that S moves rapidly to the right and R rapidly to the left, then A(past) and B(future) become simultaneous in the frame of a stationary observer (thanks to time-dilation).
"So, to construct the required CTC, we make the particle move from A(past) to B(future) passing via PP’; then by symmetry we make it return from B(future) to A(past) via QQ’. Gott’s calculations show that provided the cosmic strings travel at close to lightspeed, this CTC really does exist mathematically."
"I’m glad I can empath all that," said Counsellor Coi. "I’d hate to have to follow it any other way."
The Time Traveller scratched his head and grimaced. "By now I have learned to ask: can such a scenario be realised physically?"
"Well... in 1992 Sean Carroll, Edward Farhi, and Alan Guth proved that there is not enough available energy in the universe to build a Gott time machine. More precisely, the universe never contains enough matter to provide such energy from the decay products of stationary particles."
"Then let’s give it some matter," yelled Kert. "Right where it hurts!"
"It seems yet again that I am trapped forever in my own future," muttered the Time Traveller.
"Let me check you out physically," said Cleverly Blusher. "You may be suffering from future shock. Pass me the tofflometer, will you, Pox?" She hurled the Time Traveller to the floor and began to loosen his clothing.
"Trapped in his own furture. Unless... we could develop a sufficiently powerful new energy source," said Captain Pickup. "But I’m afraid that’s not in the works yet."
"Captain!"
"Yes, Mr Outa-Data?"
"I recall that Federation surveys of the distribution of galaxies in our universe has revealed that they clump on vast scales, forming structures hundreds of millions of light years long."
"That’s fascinating, Mr Outa-Data."
"This clumpiness is too great to have been caused by gravitational attraction among the known matter. Space-time should be nearly flat, but it’s not."
"Flat along what?" yelled the Cat, whose frustration had come to the boil.
"One theory is that the clumps were ‘seeded’ by naturally occurring cosmic strings. Provided Federation data-banks contain the coordinates of a naturally occurring cosmic string remnant, we may yet be able to send the Time Traveller home." And make us all a fortune...
"If so, mother Nature has outdone all of the engineering skills of the Federation," said Pickup.
"You are in luck," Outa-Data said. There is a suitable cosmic string in the Dunroamin system."
"We’ll need to get there fast," said Pickup. "Warp factor sev "
"What is ‘warp factor’, Captain Pickup?"
"A faster-than-light drive."
"Faster? Than light? But I thought Mr Outa-Data said..."
There was an embarrassed silence. Eventually Pickup said "Outa-Data, warp drives do work, don’t they? How else could we be here?"
The android was desperately sorting through his memory banks. The Time Traveller was trying to do up his shirt. Counsellor Coi looked terribly concerned for everybody except herself. Kert was looking for something to shoot and someone to shoot with it. Cleverly Blusher was wondering if she ought to shoot Kert. Schr dinger was superposing quantumly and making a right nuisance of itself in the process. Pox was practicing his Vulgarian death-grip on Schr dinger in an effort to collapse its wave-function...
"Ah," said Outa-Data. "Yes, the records are in the history section. The point is that although there is a limit to the speed with which matter can move through space, there is no upper limit to the speed with which space can move through space. And moving space can carry matter passively along with it."
"Sounds like a cop-out to me," said the Cat.
"No, it was shown by Miguel Alcubierre in 1994. Admittedly his method does violate the ‘weak energy condition’ that requires all energies to be positive. But that is a purely technical difficulty that can be overcome using the Casimir effect, which creates negative energies between two parallel plates in a vacuum."
"Then I’m home!" yelled the Time Traveller. "I’d do anything to get home again!"
Gotcha, thought Outa-Data. "Of course, a warp drive will be rather expensive in energy use, will it not, Captain?"
"Um, yes," said Pickup, puzzled by Outa-Data’s tone of voice. The Time Traveller looked worried.
"However, there is a way you can repay us," said Outa-Data, giving the history section of the computer new instructions.
"How?" asked the Time Traveller. "I’d do anything to get back to the end of the nineteenth century."
The printout whirred into motion. Outa-Data handed him a sheaf of papers. "Captain, here is is a complete listing of the stockmarket prices for major stocks over the entire period 1895-2366." Outa-Data waited.
Pickup as his name suggested was quick on the uptake. "I want you to start a trust fund in my name. Invest one pound I believe that was the currency in an account with "
"With the Bank of England, sir. It is still in existence today and it was in the Traveller’s time too."
"Good. Use that printout to make sure that my investment grows very fast. Understand?"
"Of course. If you can predict the future of the market, your fortune is guaranteed."
"A cosmic sting!" cried the Cat.
"Exactly," said Captain Renault Pickup.
"Provided we do not get switched to a parallel world," Outa-Data pointed out.
"But then," replied Pox, "in the past parallel world whose future will become this one, parallel versions of us are probably doing the same thing. There’s a lot of convergence to history."
"I’ll risk it," said Kert.
"Set up a board of trustees to make sure the system keeps working," said Pickup. "Take 50% of the profits as an operating fee. Set the trust fund to mature on 16 October 2366 tomorrow on presentation of my signature. Here’s a specimen signature to put on record."
"But what if I cheat and keep all the money?" the Time Traveller asked.
"We may just have to come back to the nineteenth century and convince you not to," said Kert. "Me and my Rats."
"Oh. Right. Don’t worry, I’ll do anything you ask. No, really, anything. Fine, don’t mention it."
Lieutenant Woof led the Time Traveller to an acceleration chair. Pickup looked at Outa-Data, and smiled. He raised a finger.
"Engage."
Andreas Albrecht, Robert Brandenberger, and Neil Turok, Cosmic strings and cosmic structure, New Scientist 16 April 1987, 40-44.
J. Richard Gott, III, Closed timelike curves produced by pairs of moving cosmic strings: exact solutions, Physical Review Letters 66 (1991) 1126-1129.
John Gribbin, In Search of the Edge of Time, Bantam Press, New York 1992.
Ian Stewart, The real physics of time travel, Analog 114 (January 1994) 106-130.
(8)It has been pointed out to us that this is existentialist. We'll get it right next time.