TRAVERSABLE WORMHOLES: SOME IMPLICATIONS

[trips times are not subjectively much altered if we allow higher accelerations for nanomachines, that can take millions of gees in their stride [12]. Actual trip times are reduced, but increased mental speeds compensate to make a journey of a day seem like centuries]

A space probe with a wormhole could be powered from base. The fuel is uploaded through the wormhole from base to the in-flight ship. There would an energetically very strong potential hill for the fuel to climb to reach the ship. For a ship moving at relativistic speeds most of the energy of the fuel would be lost in the climb. This suggests that the ship would be stripped to the bare minimum, just modern rockets are.

The probe remains in contact with the home base, throughout the trip. As a drop point approaches another wormhole plus deceleration rig would be loaded through to detach itself from the mother craft. Deceleration would likely be quicker and less expensive than acceleration because the daughter craft could brake itself against interstellar/galactic gas, dust and magnetic fields. For energy cost reasons it is not likely that transfer of colonists would begin until deceleration is complete.

The colonists transfer through this hole, whilst the main probe continues its outward voyage. One of the first activities of colonists would be to secure the connections with home by increasing the wormhole capacity and numbers. Transport of manufacturing plants, more wormholes etc would continue until local nanotech factories become locally more competitive than transport of finished product via wormholes. After this point the wormholes would be increasingly used for communications rather than materials transport.

An analogy with the cloud chamber spring to mind here. Charged particles are tracked through cloud chambers. Each particle is invisible, but its presence is deduced from the trail of growing droplets left behind. Similarly the space probe is all but invisible, lost in the immensity of the dark of space. The burgeoning colonies left behind mark its passage. The colonies send out further wormholes probes. From a distance the whole affair would resemble a growing 3-D snowflake.

Road, sea and air routes let commerce draw on the whole earth's resources and the telecommunications highways keep us in contact with each other. Wormhole connections laid down by space probes enable a space-faring civilisation to remain a single economic entity, with all the social and material benefits that follow. Wormholes connections enable the region colonised to stay interconnected as civilisation expands through the universe.

Wormholes do have one major trick up their sleeves. We have seen that wormholes don't permit time travel. But they do exhibit some very strange effects. Consider a colonist stepping through the home wormhole to transfer to the landing ship. Ship time and home time are running in synchronisation. If I wait 15 years at home after launch before stepping through then I appear at the travelling end at the point when the probe passes Andromeda. In crossing 2,250,000 light years of conventional space I travel 2,250,015 million years into the future as defined relative to the co-moving frame of the universe.

6. EMPIRE-TIME vs CO-MOVING TIME At this stage it worth a digression to explain what this means. Co- moving space-time is the space-time frame in which the average background distribution of matter is stationary. Our galaxy is moving relative to this background distribution. We can measure this drift by noticing the slight shift in frequency in the cosmic microwave background distribution. Backwards along our path it is slightly red- shifted. Forward along our direction of motion it is slightly blue shifted. Relativity tells us all reference frames are relative, but in truth most astronomers think of the co-moving frame as a natural choice, or Schelling point, to adopt, even though we are drifting with respect to it. It makes the dynamics of the expansion of the universe much easier to calculate, for starters. At each point in co-moving time the averaged distribution of matter is even.

The time frame being defined by the expansion of wormholes, which I dub empire-time, is not coincident with the co-moving time. Wormholes sent to the Andromeda at near light speeds arrive in approx year 2,250,000 co-moving time, but in year 15 empire-time (setting year zero at start of expansion). Assuming once wormhole technology is developed we expand at near light speeds then the surface of constant empire-time forms an inverted cone in co-moving space time, with Earth at apex. [I use the language of cones to describe what is really a sphere, but this is conventional in relativity texts, because it lends itself to greater ease of visualisation] At any particular moment in empire-time the entire surface of the time cone is accessible to the wormhole traveller.

Travelling along the wormhole highways away from Earth takes you into the future of co-moving time, but not in empire-time. Later empire-time zones form inverted cones, like inverted dunces's hats stacked on top of each other.

Attempts to redefine the empire-time already laid down by wormhole structure is resisted by CPC. To redefine empire-time you would have to repopulate a region with holes travelling at a vastly different speed than the original colonists. The CPC mechanism says two holes disturb each other as they approach closer than their empire-time difference times speed of light eg two holes with an empire-time difference of a year can't approach closer than a light year. If the holes are of greatly different size then only the smaller hole is destroyed. Otherwise they both are violently disrupted and destroyed.

Once the empire-time frame has been defined it becomes increasingly difficult to change it. As the population and economy of a region grows they increase the wormhole traffic carrying capacity of the locale. Once established to change the relationship between co-moving and empire-time would require the complete upheaval of the local economy and denizens. Economic growth would breed chronological stability.

Questions about the distant co-moving future of our universe are answered directly by travel. How quickly is the Hubble constant decaying? Would the natural universe expand forever or re-collapse? Is the universe spatially closed? Send out a probe at one-gee. From the above table we see that within a century of empire-time it is reporting back on the universe at almost inconceivable distances and futurities, answering questions about the fate of the natural universe. If you wish you can visit the end of the universe, and come back. "Go see the end of the universe" might be a catchy travel company's jingo. (Actually this would only be possible in an open universe. In a closed universe there would be a limit to how far you travel before CPC prevented you.)

7. ALIENS Circumstantial evidence indicates alien civilisations are very few and far flung in the universe. Frank Tipler has pointed out that the easiest way to explore the universe is send out self-replicating space probes [11]. Within a cosmologically short period of co-moving time (ie millions of years) we could colonise the Milky Way and the rest of the Local Group. Tipler argues (and I agree) that the arrival of such a probe at a star system would preclude and supersede local biological evolution. Since life on Earth has evolved over billions of years then we can't expect (statistically speaking) to find civilisations within our local group. Where are the aliens, asked Fermi. Many megaparsecs away, says Tipler.

An elaboration of this argument gives grounds for believing that the nearest aliens are currently over a 100 million light years distant. In the co-moving frame, without wormholes, we won't make contact with them for over 100 million years. Which makes their existence an object of theoretical speculation that can't be resolved for millions of years.

With relativistic probes and on-board wormholes, though, we can reach alien colonised regions within decades of empire-time, no matter (almost) how far away they are. No probe can penetrate into a region of alien colonised space. Each civilisation defines its own empire-time that is in conflict with the empire-time of the other. A probe from Earth flying into a alien zone not only crosses alien space, but also crosses alien empire-time zones. As it approaches the alien home world it passes into the alien empire-time future. CPC forbids such travel by destroying lone wormholes that attempt to interpenetrate each others empires. Only a full scale invasion with masses of wormholes could ever succeed. Such an invading fleet would have to overwhelm the native wormholes (destroy them) and impose their own empire time on the stranded natives. Given the rates of economic growth we expect the advantage would almost always lie with the defenders. As the invading fleet cut deeper and deeper into the alien heartlands it find itself opposed by later and later alien time zones, more advanced technology and greater forces of numbers. Economic might, then as now, ensures protection. Brute force invasion would be suicide for the invaders and their whole empire: once defeated the invader's whole wormhole connected empire would be open to subversion from 'aliens from tomorrow'.

A much more likely scenario would be: Contact is signalled by our leading wormhole probes failing in the overlap of our sphere of influence with the alien empire's sphere. Finding each other's probe colony ships would be non-trivial. It might be easier to find the colonists than the original exploration vessels. To push the analogy with a particle zipping through a cloud chamber, search for the droplets, rather than the elusive particle. The easiest way of doing this is, at the point where the relativistic wormholes are destroyed, is to send out sub-light non-relativistic survey probes to establish diplomatic relations. If both sides explore each other with non- relativistic probes (relative to the co-moving frame) then their empire times will realign themselves, over the locale of the 'neutral zone', permitting diplomatic contact and, assuming no wars, eventual exchanges of wormholes. The spheres of colonisation are then available to each other and the two empire times merge.

Other expansion scenarios are possible. A well coordinated, centrally controlled species might halt expansion at the boundary of their home galaxy (say) for a few subjective million years, building up numbers, armaments etc. When their technology seemed to have plateaued they resume their expansion relying on technology and numbers to overwhelm aliens. Such a strategy is technology dependent. If it turns out that wormholes can be booby-trapped to explode on tampering or hostile attack such a strategy would fail.

8. UNIVERSAL TIME Barring such hostile aliens we can expect to have contacted and be trading with alien civilisations within a few centuries or millennia of starting our wormhole exploration of the universe. This is a symmetrical situation. Not only will be meeting aliens within historically short period, but they will be meeting us shortly after their expansion begins. Consequently all the species of the universe will be linking up at about the same stage in their development. This gives us all shared interests and hence markets in common. We might expect each civilisation to go through two future phase changes. First phase change is when they develop nanotechnology and start redesigning themselves, speeding up etc. Second phase change occurs when they link up with the rest of the universe and get the benefits of the near- infinite economies of scale this brings.

At this point all the local empire-times have merged to form a universal time or simultaneity surface. On a very large scale the sheet of universal time conforms with the co-moving average. On closer inspection (ie scales of billions of years and light years) the universal time surface reveals conical pit-like indentations that mark the place where each civilisation arose and stamped its own chronological footprint on the surrounding space-time topology before merging with their neighbours. By saying the universal time surface is indented I am revealing my co-moving prejudices. From the vantage of point of someone from universal time it would be co-moving time that would appear bumpy. To them civilisation birth points appear as the summits of cones in the co-moving time surface. Universal time would be the preferred time for discussing life, history, politics etc - everything except prehistory before Link-Up. Absolute time, as Newton conceived of it [18], would have finally returned. The notion of relative time frames would be irrelevant.

Half the civilisations we meet are likely to have been around, in co- moving terms, hundreds of millions or even billions of years before us. Gaining access to their time zones would enable our astronomers to observe the expansion of the universe in the distant past (although always further away from here in space than co-moving time). The occurrence of the first civilisation in the universe would be the limit beyond which we could not travel.

9. BEYOND THE OBSERVABLE UNIVERSE The expansion of the universe is defined by a parameter called Hubble's constant, which relates the distance of a far galaxy with its velocity of recession. Beyond a certain distance the recession velocity exceeds the speed of light. Objects beyond this are red-shifted to infinity and are unobservable. This distances defines the edge of our observable universe, an event horizon, and lies approximately (subject to experimental error) 15-30 billion light years away. This is limit of the astronomer's universe. What lies beyond is pure conjecture and is left to cosmologists. Cosmological theories expounded over the last decade (in particular inflationary theories) indicate that the observable universe is just an infinitesimal speck in a greater post- inflationary bubble that extends over distances of 10^30 light years or more, looking pretty much everywhere as it does here. Inflationary theories differ about what lies beyond this, although one suggestion is that naturally occurring wormholes, inflated to astronomical dimensions, [6] may link our post-inflationary, bubble with others, forming an infinitely large chaotic, fractal structure [17]. Unless we link up with aliens then we may never directly observe this since these regions will have changed greatly in the century or two of empire-time (> 10^30 years of co-moving time) it takes to reach them.

A couple of paragraphs back I mentioned the phase change, Link-Up, associated with linking up with the rest of the universe. It's worth while stopping for a moment and considering what this might do to our perception of ourselves and our place in the universe. At the moment we are the only civilisation we know, unique and conceited. Even if civilisations are scattered at distances of 100 million light years, in a universe of radius 10^30 light years this still yields over 10^60 alien cultures. It is unlikely anyone could ever catalogue all the civilisations and cultures, even if they did have a nanoelectronic brain! No single mind could encompass all of history. We would have returned to the medieval world, surrounded by legends of distant lands populated by mythical and fantastic creatures. Construction of a universal map would be impossible. A trans-human traveller, exploring the highways and byways of life, would likely never encounter another trans-human, beyond the 'here be dragons' point. If she lost her personal wormhole and forgot her trans-species designation code (a sixty digit number!) she would never, ever find her way home again. None of her descriptions of where she comes from would relate to anything anyone else knows.

10. OTHER USES Other uses of wormholes may be where the euclidean geometry of space is already confining us. As an example computer architectures are cramped and hindered by speed of light limitations which are causing timing problems, limiting chip clock speeds, I/O delays etc. Nanoscale wormholes, with their fantastic bandwidths could be used to supplement the data buses, conveying data from one section of a chip or computer to another, faster than conventional transfer would allow. Or link up networks of computers for super fast number crunching.

Initially, no doubt, the wormhole connections would supplement existing architectures. The next logical step would be to design things for different topologies other than the natural euclidean one. Instead of having computers in euclidean space, linked together with wormholes, why not place them in the wormhole, out of harms way. The technologies involved in generating artificial inflation to expand the interiors of wormholes into basement or baby universes are of the same orders of magnitude as creating traversable wormholes. Construction of basement or baby universes has already been discussed and computer-simulated in the literature [4], [8].

We have already mentioned that we expect speedup rates of a million or so with the adoption of full nanotech. If just a factor of a thousand translates into GDP growth and population rates then doubling times for the economy may drop from decades to days. I don't know if these growth rates are sustainable, even in empire-time, but they indicate that any limited resource is likely to be at a premium, within a years / subjective millennia of empire-time. Since the amount of natural space per civilisation is finite economics dictates that eventually more and more of the economy will shift over and occupy the artificial space provided by basement universes.

11. LIMITS In a sense exponential growth and euclidean space are natural enemies. The volume enclosed by a euclidean 3-sphere only increases with the cube of the radius. With exponential growth pressures driving expansion all civilisations confined to euclidean space will rapidly hit technological limitations or each other. Wormholes and associated basement universes offer the long term prospect of escaping from this dilemma. An array of basement universes connected by wormholes has the useful property that the volume of space enclosed grows exponentially with distance from origin. A civilisation driven by exponential expansion need only grow radially at a constant rate, unlike in euclidean space where it must expand at ever faster rates.

This might seem some like subtle and obtuse piece of mathematics, but in fact it's just a restating that a tree with continually branching twigs eventually strangles itself (in euclidean space), whereas it could grow for ever through a tangled array of wormholes and basement universes. A related limitation of euclidean space is the amount of information a volume can contain before a black hole forms. This limitation, given by the Bekenstein-Hawking bound [], grows with the radius squared. No such limitation applies to a space of connected basement universes. Each basement universe is shielded from the positive energy contribution of its neighbours by the connecting (negative energy) wormhole

12. CONCLUSION We have seen that whilst the construction of wormholes is technically very difficult the long-term payoffs are very great. A civilisation can expand through the universe, stamping its own chronology on its locality, at a speed only limited by its energy resources. At the very least the problems of construction, theoretical and practical, will exercise the advanced intelligences of the future considerably. In the longer term the capabilities of opened-ended infinite information processing lie before the civilisations who solve the problem.

13. ACKNOWLEDGEMENTS I am very grateful to Robin Hanson for initially directing my attention to the subject of information processing limits and his subsequent help on all aspects. My thanks to all the other recipients of the extropians (tm) mailing list for their feedback. Needless to say none of the above share any responsibility for some of my conclusions or any of my errors.

It has all been enormous fun.

References: [1] Matt Visser. Traversable Wormholes: Some Simple Examples. Physical Review D v39, n10, p3182, 15-May-1989.

[2] Matt Visser. From Wormholes to Time Machines: Remarks on Hawking's Chronology Protection Conjecture. Physical Review D v47, n2, p554. 15-Jan-1993.

[3] Morris and Thorne. Wormholes in Spacetime and Their Use for Interstellar Travel. American Journal of Physics v56, p395 (1988)

[4] M Visser. Wormholes, Baby Universes and Causality. Physical Review D v41, n4, p1116 (1990).

[5] S Hawking. Chronology Protection Conjecture. Physical Review D v46 n2 p603 15-July-1992.

[6] Thomas Roman. Inflating Lorentzian Wormholes. Physical Review D v47, n4, p1370 15-Feb-1993.

[7] Thorne et al. Cauchy Problem in Spacetimes with Closed Timelike Curves. Physical Review D v42 p1915 (1990).

[8] KA Holcomb et al. Formation of a "child" universe in an inflationary cosmological model. Physical Review D v39, n4 15-Feb- 1989.

AD Guth, Blau and Guendelman. Dynamics of False Vacuum Bubbles. Physical Review D v35, n4 p174 (198?).

[9] Mikheeva and Novikov. Inelastic Billiard Ball in a Spacetime with a Time Machine. Physical Review D v47, n4 p1432 15-Feb-1993.

[10] W Israel & AE Sikkema. Nature v349 n6304 p45 (1991).

[11] FJ Tipler. Quarterly Journal of the Royal Astronomical Society v22 p279 (1981)

[12] Eric K Drexler. Engines of Creation (1986) Garden City, New York: Anchor Press. Also Nanosystems 1991 draft

[13] Carl Sagan, Contact, pub New York: Simon & Schuster(1985)

[14] T Schneider. Energy Dissipation from Molecular Machines. Journal of Theoretical Biology, v148, p125 (1991).

[15] T Schneider. Channel Capacity of Molecular Machines. Journal of Theoretical Biology, v148, p83 (1991).

[16] C Shannon. Communication in the Presence of Noise. Proceedings of the IRE (now the IEEE), v37, p10-21 (1949).

[17] Scientific American, April 1993, p10. AD Linde

[18] Isaac Newton. On the Gravity and Equilibrium of Fluids (1668?) Translated in 'Unpublished Papers of Isaac Newton' ed AR and Marie Boas Hall (1962)

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