Keywords: wormholes, time dilation, interstellar
travel, starships, general relativity
Published in the May-1990 issue of Analog Science Fiction & Fact Magazine;
This column was written and submitted 10/13/89 and is copyrighted ©1989, John G. Cramer. All rights reserved.
No part may be reproduced in any form without the explicit permission of the author.
This column is a followup to a previous Alternate View column [Analog, June-'89] about "wormholes", faster-than-light travel, and time machines, which was based on a spectacular theoretical breakthrough in general relativity. It described how a sufficiently advanced civilization might construct a stable wormhole (a curved-space shortcut between one region of space and another) and use it both for faster-than-light travel and for time travel, with no laws of physics violated in the process except causality (the principle that a cause must precede its effects).
Kip Thorne and his Caltech colleagues Morris and Yurtsever showed that according to orthodox general relativity (presently the standard theory of gravitation), it should be possible for a civilization with a sufficiently advanced technology to extract a wormhole from the "quantum foam" that exists at ultra-small distance scales, to expand the wormhole to macroscopic dimensions by supplying energy, and to stabilize it by placing very large electrical charges at both wormhole mouths. The wormhole mouths (or portals) could then be transported to widely separated regions of space to provide superluminal communication and even faster-than-light travel. Moreover, if one of the wormhole portal was accelerated to a velocity near that of light, kept at that speed for a year, and then decelerated and returned to its stay-at-home twin, the pair of portals would constitute a time machine that could be used for two-way communication and transport one year into the future or the past. Clearly this is the gimmick that SF based on hard science has needed for many years: a plausible method for faster-than-light transport. To use it, however, we must improve our understanding of wormhole physics and its implications.
Consider for example the law of conservation of energy as it applies to wormholes. If the two wormhole portals are at rest with respect to each other, then there should be no energy cost in moving a massive object through the wormhole from one portal to the other. But suppose that one wormhole portal is at rest on Earth while it's twin is aboard a space ship moving away from Earth at the "special" velocity of 86.6% of the speed of light (c), a velocity such that an object's total mass-energy is composed exactly half of rest mass-energy and half of kinetic energy. One marvelous advantage of placing a wormhole portal aboard a ship is that it can to refuel the ship in flight. The burden of carrying all fuel aboard the vessel as initial payload is eliminated: fuel can be simply piped aboard through the wormhole portal. Suppose we push a 1 kilogram (kg) mass of fuel through the Earth portal so that it emerges at the ship portal. It has been moving quite slowly on Earth and in the local space of the wormhole, so it emerges in the ship travelling at the same speed as the ship or 0.866 c. But the mass of the fuel, as far as earth-based observers are concerned, has just speeded up to 86.6% c and its 1 kg mass has just increased to 2 kg. How did it acquire this extra mass? Isn't the law of conservation of energy violated by this speed increase and mass gain?
The answer is no, energy conservation is not violated in this process. The fuel interacts with the wormhole as it passes through the throat connecting the two portals. If the ends of the wormhole have relative motion, the fuel will steal some mass-energy from the wormhole, the fuel gaining a kilogram of mass while the wormhole loses a kilogram. Since the diameter of the wormhole depends on its mass, the throat will constrict slightly from this process unless the energy is replaced by some power source. Because of this, refueling a moving ship via a wormhole portal will not be cheap. If the wormhole is to be maintained at a given size, pushing one kilogram of mass through will require adding make-up energy equal to moc2, the kinetic energy given to the moving fuel. For 1 kg of mass, this amount of energy is 9 × 1016 joules or 2.5 × 1010 kilowatt-hours. Now 100 kilowatt-hours of electrical energy costs about a dollar at the lowest industrial rates, so it would cost about $250 million to supply the ship with 1 kilogram of fuel, a non-trivial sum even by the standards of the space program. Presumably, however, an advanced civilization would have lower power rates and a better-funded space program.
But the main expense would not be on-the-fly refueling of a ship but the cost of producing the wormhole, constructing the ship to carry it, and boosting the ship to near-light speeds. And even if this were done, it would still require years, even decades or centuries of earth-time for such a ship to reach a destination in another star system. It all seems very inefficient and expensive. Surely, given a technology advanced enough to produce and stabilize wormholes in the first place, there is a better way.
And perhaps there is. Consider the following question (first posed by a young woman at a talk I gave on wormholes at the recent Boston Worldcon): if a very fast starship sets out to carry a wormhole portal to, say, Tau Ceti 11.9 light years away, and the ship has a speed of, say, 99.995 % of c giving a Lorentz time-dilation factor g of 100, how long will Earth-based observers have to wait before they can begin to use the wormhole portal to travel to Tau Ceti?
One would think that the Earth-based observers would have to wait at least 12 years for the ship and wormhole portal to arrive at their new location. But that is not correct. The wormhole connects a region of space-time on one side of the portal to a correlated region of space time on the other. Not only the spatial locations but also the time locations, as measured by the passage of time on each side, are connected. The wormhole portal aboard the ship experiences that same time dilation factor as would a passenger aboard the ship. Because of this time dilation (the clock-slowing phenomenon of special relativity) the trip takes only 0.12 years or 44 days as far as the passengers and the wormhole are concerned. An earth-based observer, watching the trip through the wormhole, would view the ship arriving in just 44 days.
Therefore, since the shipboard wormhole portal arrives at its destination in 44 ship-days, the earth-dwellers can begin to use the wormhole link for communication and travel to the Tau Ceti system just 44 days after the ship leaves Earth! With no violation of known physical laws (except causality), a direct link to a star 11.9 light years away would be established in just 44 days or 1% of the time it would take a photon to travel to that star. To those of us who have been bumping our noses against the lightspeed barrier for many years this is an amazing result. With wormholes we could get there in a time much shorter than the transit time for a photon.
But wait! There's more! If you think about it, it's pretty inefficient to use a spaceship to transport the wormhole. The ship adds extra mass which must be accelerated at great energy cost and then decelerated again. This raises an interesting question: why not just send the wormhole portal without the ship?
There are several serious problems with this proposal. Without a ship, how could you accelerate the portal to the necessary near-light velocity? How could you guide it and make mid-course corrections so that it would arrive at the desired destination? How could you decelerate it when it reached that destination? How could you use it after arrival, with no equipment or crew on the other end?
Even if stable wormholes are possible, these problems may be insoluble. But there is a plausible scenario for solving them. To provide the needed acceleration, consider a conventional particle accelerator like the proposed Superconducting Supercollider (SSC) to be constructed in Waxahachie, Texas in the 1990s. The SSC is designed to accelerate protons to near-light velocities that give a time-dilation factor of g=20,000. This is to be done with "conventional" technology, accelerating the particles repeatedly through a series of superconducting magnets and accelerating cavities.
Now consider a wormhole which is deliberately arranged to have a very small mass, a few micrograms or less, by giving it a relatively small amount of energy. Such a wormhole, according to MTY, is stabilized by placing large electric charges in both of its portal openings. If, once the charges are in place, they remain there without the assistance of external machinery, then the wormhole portal is in effect a stable massive particle with a large mass and a large electric charge. A properly designed SSC-like structure could accelerate this wormhole portal, just as the SSC accelerates protons. In fact, if the wormhole portal has approximately the same charge-to-mass ratio as a proton, the same accelerating structure will serve for accelerating both. In that case the SSC could also accelerate wormhole portals to a time-dilation factor g of 20,000, a nice value, as we shall see, for exploring the nearest hundred thousand light years of our galaxy.
So, given small stable wormholes as a starting point, we should be able to accelerate wormhole portals to g=20,000 and send them out in the general direction of promising nearby star systems. Such an accelerated portal, if it was on a straight-line trajectory, would reach Tau Ceti in just 5.2 hours of portal-time. A wormhole portal would not, however, travel on a straight-line path. All charged particles travelling in the magnetic field of the galaxy will move on curving paths that cannot be calculated because the magnetic fields are not known. Thus, it would be necessary to observe their paths in detail and make mid-course corrections.
Since photons can travel through the wormhole portal, the location of the portal as it travels could be monitored by observing the light that passes through it as it moves. After corrections for the Doppler shifts and the relativistic forward folding of arriving light, it should be possible to deduce the location and direction of the portal from the images of nearby bright stars. Particle beams sent through the earth-portal in appropriate directions should serve as steering jets to make mid-course corrections and to provide deceleration of the portal once it reaches the distant star system which is its destination. When that destination is reached, energy can be added to the portal to expand it to a size that allows the delivery of manned and robot space vehicles to explore the new star system.
Thus, if stable wormholes are possible at all, they may represent a path to the stars that will sweep away many of our previous concepts and prejudices. And this brings us to a variation of the Fermi paradox: if this wormhole transport is possible, shouldn't the technologically advanced civilizations of our galaxy already be sending tiny accelerated wormhole portals in our direction? Where are they?
Perhaps they are already here. In "Children of the Swan", a previous AV column [Analog, 3/86] I described how a number of underground experiments had been detecting muons deep underground, produced by mysterious particles emanating from the Cygnus X-3 , an X-ray object in the constellation Cygnus. Cosmic ray physicists are generally agreed that no known particle can produce these events. Another class of super-energetic cosmic rays, the Centauro events, appear to be particles accelerated somehow to incredibly high energies and which produce too many gamma rays and too few mu mesons. They produce giant large-area showers of energetic particles when they strike our atmosphere. Like the particles from Cygnus X-3, the Centauro events lack any explanation based on known physics.
Cosmic ray experts conventionally assume that, whatever the origin and acceleration mechanism of these unexplained cosmic particles, they are a natural phenomenon, not an artifact of some advanced civilization. But that assumption could be wrong. It is interesting to contemplate the possibility that some advanced civilization may be mapping the galaxy with accelerated wormhole portals, sending little time-dilated observation points out into the cosmos as peep-holes for viewing the wonders of the universe. And perhaps, when a particularly promising or interesting scene comes into view, the peep hole is halted and expanded into a portal through which a Visitor can pass.
Clearly we need to gain much more understanding of wormholes. They may be our path to the stars.
Wormholes, FTL, & Time Machines:
Michael S. Morris, Kip S. Thorne, and Ulvi Yurtsever, Physical Review Letters 61, 1446 (1988).
Cramer's new book: a non-fiction work describing his Transactional
Interpretation of quantum mechanics, The Quantum Handshake - Entanglement,
Nonlocality, and Transactions, (Springer, January-2016)
is available for purchase online as a printed or eBook at: http://www.springer.com/gp/book/9783319246406 .
SF Novels by John Cramer: my two hard SF novels, Twistor and Einstein's Bridge, are newly released as eBooks by Book View Cafe and are available at : http://bookviewcafe.com/bookstore/?s=Cramer .
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