First draft, later published in Extropy.
[This paper has been published in Extropy #11, where there is an error in one of the diagrams which implies that a wormhole in flight could travel FTL, which is not true.]
Since 1985 there has been much theoretical progress on traversable wormholes. At first they were thought to enable time travel, so not taken seriously. More recent work rules out time travel and associated paradoxes, but still permits faster-than-light travel. This article explores some of the implications traversable wormholes have on the expansion of civilisations through the universe. In particular it is found each civilisation would impose a local region of simultaneity, or empire-time, which differs from the more natural, co-moving timeframe which astrophysicists usually use. Distant regions of the universe and alien civilisations can be reached in short periods of empire-time, whereupon their respective empire-time zones fuse together. Shortly after first contact is made all expanding civilisations connect together to form a universal time. Finally some limitations of euclidean space are contrasted with wormhole connected non-euclidean space.
To establish an interstellar trading civilisation we need a mechanism for travel or communication at faster-than-light (FTL) velocities. This article considers how we may achieve this and consists of this introduction followed by the following sections:
Without FTL travel we can still colonise the universe at sub-light velocities, but the resulting colonies are separated from each other by the vastness of interstellar space. In the past trading empires have coped with time delays on commerce routes of the order of a few years at most. This suggests that economic zones would find it difficult to encompass more than one star system. Travelling beyond this would require significant re-orientation upon return, catching up with cultural changes etc. It's unlikely people would routinely travel much beyond this and return.
Nanotechnology  only exacerbates the situation. We expect full- nanotech, uploading, AIs etc to arrive before interstellar travel becomes practical. Assume we keep the same dimensions for our bodies and brains as at the moment. Once we are uploaded onto a decent nanotech platform our mental speeds can be expected to exceed our present rates by the same factor as electrical impulses exceed the speed of our neurochemical impulses - about a million. Subjective time would speed up by this factor. Taking a couple of subjective-years as the limit beyond which people would be reluctant to routinely travel this defines the size of a typical trade zone / culture as not exceeding a couple of light minutes. Even single stellar systems would be unable to form a single culture/trade zone. The closest planet then would seem further away than the nearest star today.
With full nanotech there will be little need to transfer matter. Trade in the distant future is likely to consist of mostly information. Design plans for new products, assembled on receipt. Patterns of uploaded consciousness of intrepid travellers. Gossip and news. But with communication delays to Alpha Centauri of the order of millions of subjective years two-way exchanges are difficult to imagine - even when we are enjoying unlimited life spans.
Communication and exploration would be, essentially, a one-way process. If you had a yen to travel to the Alpha Centauri you could. Squirt your encoded engrams down an interstellar modem and arrive decode at Alpha. Assuming the receiving station hasn't shut in the intervening millions of years of subjective cultural change. You could leave a copy behind as redundancy or if you wanted to explore both regions, but I suspect many of us will not find this completely satisfactory. The speed of light barrier would limit us and cramp our style us much more than it does at present.
What stops faster than light travel? According to relativity as an objects accelerates towards the light-speed barrier its mass increases asymptotically, slowing its acceleration with constant thrust. Ship time slows down, which also reduces thrust (eg for a photon driven ship the frequency of the beam red-shifts). Both make effects make light speed an insurmountable barrier.
Since the advent of relativity there have been a number of approaches to travelling faster than light:
For all the above reasons the conventional wisdom is that faster than light travel is the 20th century's analog of the alchemist's dream of transmuting lead into gold or flying to the moon. Or living for ever. They seemed impossible dreams at the time....
The prospects for FTL travel looked bleak in the mid 1980s. Then Carl Sagan asked some theoretical physicists for plausible methods for FTL to include in his forthcoming book, Contact. Amongst the team that worked on this problem was Kip Thorne and his graduate students at Caltech. They turned the problem around and asked what forms of matter are required to hold a wormhole open permanently, so no pinch off occurs? The answer is 'exotic' matter, a highly stressed matter, with enormous tensile strengths. The tension or pressure of exotic matter exceeds the energy density. We have no familiarity with such matter today, but it existed under conditions of extraordinary pressure in the early universe. Carl Sagan published Contact in 1985 , incorporating the early results from Thorne's team in the novel. Thorne et al published their conclusions in 1988 , and included a recommendation for students to read Contact as a light introduction to traversable wormholes and exotic matter!.
Later, in 1989, Matt Visser published an article  showing how more general traversable wormholes could be constructed. A wormhole could be constructed, according to Visser, by confining exotic matter to narrow regions to form the edges of three-dimensional volume, for example the edges of a cube. The faces of the cube would resemble mirrors, except that the image is of the view from the other end of the wormhole. Although there is only one cube of material, it appears at two locations to the external observer. The cube links two 'ends' of a wormhole together. A traveller, avoiding the edges and crossing through a face of one of the cubes, experiences no stresses and emerges from the corresponding face of the other cube. The cube has no interior but merely facilitates passage from 'one' cube to the 'other'.
The exotic nature of the edge material requires negative energy density and tension/pressure. But the laws of physics do not forbid such materials. The energy density of the vacuum may be negative, as is the Casimir field between two narrow conductors. Negative pressure fields, according to standard astrophysics, drove the expansion of the universe during its 'inflationary' phase. Cosmic string (another astrophysical speculation) has negative tension. The mass of negative energy the wormhole needs is just the amount to form a black hole if it were positive, normal energy. A traversable wormhole can be thought of as the negative energy counterpart to a black hole, and so justifies the appellation 'white' hole. The amount of negative energy required for a traversable wormhole scales with the linear dimensions of the wormhole mouth. A one meter cube entrance requires a negative mass of roughly 10^27 kg.
Wormholes can be regarded as communication channels with enormous bandwidth. The wormhole will collapse when the amount of mass passing through it approaches the same order as the amount of negative mass confined to its edges. According to Shannon  and others  information has a minimum energy of kTlog2 associated with it. For 1- meter radius cube this implies a potential bandwidth of over 10^60 bits/sec . Even very small nano-scale wormholes have bandwidths of the order > 10^50 bits/sec. This suggests it will usually be more economic to squirt the design of an object down a channel rather than the object itself.
Construction of such cubes is, of course, far, far beyond our present day abilities. With AIs and nanotech combined we expect the limits on intelligences to be governed by physics, not biology . Our brains' processing capacity lies somewhere between 10^15 - 10^18 bit/sec. A comparably sized nanoelectronic brain would have power of 10^32 - 10^36 bit/sec . Assuming a factor of million is lost for the speedup still leaves 8 - 12 orders of magnitude expansion in the complexity, or depth of thought, of our brains as we switch from biology to nanotechnology. So we should not assume construction and manipulation of the materials required will long remain beyond the grasp of future civilisations, populated by such super-intelligences. The remainder of the article will assume the mass production of wormholes is economically achievable.
Wormholes enable travel from one mouth to the other. To travel to distant parts of the universe one wormhole end stays at home and the other is carted away, at sublight velocities, to the destination. Before we examine this first we consider some other properties of wormholes.
Wormholes are constrained by relativity to travel at sublight speeds and are time-dilated as per normal. Clocks placed at the mouths of a wormhole always remain in synchronisation with each other. If I look through one end of a wormhole and compare the near clock with the far clock they always agree. Even if one end of the wormhole is travelling at relativistic speeds many light years away. Einstein says moving clocks run slow. There would appear to be a paradox here. We observe the two clocks keeping time with each other, yet relativity says the 'distant', travelling clock is running slowly. How do we reconcile this? Only by concluding that the distant clock has been displaced in space and time. If a wormhole enables someone travel from Alpha Centauri 2000 to Sol 1993 and vice versa, then no paradox because they can't travel back to Alpha Centauri (through conventional space) and arrive before they left (to cause a paradox).
Problems begin when the distant wormhole end turns about and returns home. According to the twin paradox the traveller returns aged less than the stay-at-home twin (their clocks are no longer in step). Travelling through the wormhole from the stay-at-home end to the go- away-and-come-back end transports you forward in time. Travelling in the reverse direction transports you back in time. Wormholes allow time travel. This conclusion was realised soon after the first articles on traversable wormholes were published. Depending on your view of the plausibility of time travel this is either, if you believe time travel possible, very exciting or, if you scoff at time travel, proof that traversable wormhole can't exist. No general consensus emerged in the pages of various physics journals as the subject was batted back and forth. Elaborate and very interesting papers (by Thorne's group  and others) reconciled time travel with quantum theory, whilst others (like Hawking ) proposed a Chronological Protection Conjecture, CPC, which says the Universe Shalt Not Allow Time Travel.
One of the time travel sceptics was Matt Visser. Early in 1993 he showed that wormholes do not enable time travel , by proposing physical mechanisms that enforce CPC. Visser showed, in a peer reviewed article, the mouths of a wormhole with an induced clock difference could not be brought close enough together to enable a traveller to attempt violation of causality. Quantum field and gravitational effects build up as the two ends of a wormhole approach the critical point and either collapse the wormhole or induce a mutual repulsion. Visser's work is not complete but it seems swarms of virtual particles disrupt the region around a time machine just before it would otherwise become operational.
The virtual particles around a nearly chronologically violating region are able form closed spacelike (superluminal) loops and, via Heisenberg, to borrow energy off themselves, becoming more virulent than usual. Traversable wormholes are closed, or pinched off, by the energy of the virtual particles that flow through them as they approach being time machines which prevents the more dangerous closed timelike loops (which may cause paradoxes). For the purposes of this article I'll adopt Visser's conclusion that the CPC mechanism is generic and blocks all forms of time travel via wormholes, but permits the operation of wormholes for the purpose of FTL travel.
Time dilation has the effect of reducing trip times for relativistic travellers. A traveller accelerating at one-gee reaches close to the speed of light within a few years. As it speeds up ship time dilates more and more. Ship or journey time to various locations, at one gee, are, not allowing for slow-down:
|Destination (light years)||Ship time (years)|
|Centre of Milky Way||11|
|Edge of observable universe||24|
|Edge of inflationary bubble||probably
[trips times are not subjectively much altered if we allow higher accelerations for nanomachines, that can take millions of gees in their stride . 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 . 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 , 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,  may link our post-inflationary, bubble with others, forming an infinitely large chaotic, fractal structure . 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 , .
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.
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