TRAVERSABLE WORMHOLES: SOME IMPLICATIONS

by

Michael Clive Price

price@price.demon.co.uk

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:

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.

0. INTRODUCTION

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:

1. SUBLIGHT FUTURE

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 [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

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:

Tachyons: Faster than light particles compatible with relativity. They never have to cross the lightspeed barrier because they are posited to be created already travelling at over the speed of light. No general consensus on whether they would permit the transmission of information. However none have been detected, so things look bleak either way. Superluminal quantum effects: EPR, quantum teleportation and all that. Relies on transmitting information via the posited collapse of the wavefunction. Often relies on an accompanying classical sublight signal as well. People argue passionately above the reality of the wavefunction and whether it collapses. Until this is settled we can't expect too much here. No quantum superluminal laboratory effect been demonstrated either. Spinning black holes: Things looked hopeful for a while that spinning or charged black holes might permit travel into other regions of somewhere. More recently people have become doubtful. It seems the passage of anything through a black hole sets off a feedback process that crushes the traveller to death. Also infalling radiation blueshifts to infinity [10] and fries the traveller, if tidal forces don't shred her first. Non-traversable Wormholes: First developed in the form of Einstein-Rosen bridges. An Einstein-Rosen bridge connects two otherwise widely separated regions of space. Unfortunately they are very short-lived and pinch off so quickly that only tachyons (if they existed) could travel through them and get out the other end without getting caught in the singularity needed to create them. But if you could travel faster than light you wouldn't need a wormhole- Catch-22!

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....

3. TRAVERSABLE WORMHOLES

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 [13], incorporating the early results from Thorne's team in the novel. Thorne et al published their conclusions in 1988 [3], 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 [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

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 [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

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: