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.] 

Summary:

0. INTRODUCTION

1. SUBLIGHT FUTURE, in which the problems and frustration of living in universe without faster than light travel are outlined. These problems are expected to be magnified by the adoption of nanotechnology. 
2. FAILED FTL, examines other proposals for breaking the light barrier and rejects them all. 
3. TRAVERSABLE WORMHOLES, introduces the latest candidate for FTL 
4. TIME TRAVEL, examines whether or not traversable wormholes imply time travel. The latest work indicates they do not. 
5. EXPLORING THE UNIVERSE, examines how,long it might take to reach various places in the universe with a 1-gee drive. 
6. EMPIRE-TIME vs CO-MOVING TIME, explores the differences between the local time frame an expanding civilisation imposes on its surrounding and the more conventional conception of time. 
7. ALIENS, considers some of the problems of contacting aliens. In particular it examines how local empire time zones fuse together, forming... 
8. UNIVERSAL TIME, the return of a universal simultaneity, which has some of the characteristics of Newtonian time. 
9. BEYOND THE OBSERVABLE UNIVERSE, looks at the implications of exploring beyond the edge of the observable universe. 
10. OTHER USES, looks at other uses of wormholes, eg in superior computer architectures and basement universes. 
11. LIMITS, contrasts the pros and cons of euclidean space with some of the alternatives 
12. CONCLUSION 
13. ACKNOWLEDGEMENTS 
14. REFERENCES 

1. SUBLIGHT FUTURE

Nanotechnology[12] 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. 

2. FAILED FTL

Since the advent of relativity there have been a number of approaches to travelling faster than light: 

3. TRAVERSABLE WORMHOLES

Later, in 1989, Matt Visser published an article [1] 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 [16] and others [14] 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 [15]. 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 [12]. 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 [15]. 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. 

4. TIME TRAVEL

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 [7] 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 [2], 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. 

5. EXPLORING THE UNIVERSE

[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. 

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. 

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. 

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. 

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. 

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. 

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. 

References:

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

[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) 

SOURCE: http://www.aleph.se/Trans/Tech/Space-Time/wormholes.html