The Journal of the Mega Society
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IN THIS ISSUE
ARTICLE BY MICHAEL PRICE
LETTER AND AD FROM KEVIN SCHWARTZ
LETTER AND ANALOGIES
FROM MARCEL FEENSTRA
TRAVERSABLE WORMHOLES: SOME
CONTACT! A POST-SINGULARITY PHASE CHANGE
Copyright (C) Michael Clive Price, June 1993 email: email@example.com (Internet)
is often the way it is in physics - our mistake is not that we take our theories too seriously, but that we do not take them seriously enough.
Everything will be accomplished that does not violate known
"You must follow
me carefully. I shall
have to controvert one
or two ideas that are almost universally
Opening words of the Time
Traveler, from _The Time Machine_, by HG Wells
Summary: Traversable wormholes permit FTL travel,
within general relativity, but not time travel and associated acausal paradoxes. 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,
or empire, imposes a local, accessible, region of simultaneity, or empire-time,
which differs from the more natural
time frame cosmologists use. Distant regions of the universe, and alien
civilisations if they
exist, can be reached in short periods
of empire-time. Expanding empire- time zones
fuse, on contact
with each other, forming an absolute, but artificial, universal time
frame. Finally some information-processing limitations of Euclidean
space are contrasted with wormhole connected non-Euclidean space.
To establish an interstellar trading civilisation we need faster-than- light (FTL) travel or communication, which the recently
proposed traversable wormholes provide. This article is a what-if, and, in the words
of Weinberg, takes the idea
implications seriously. In the spirit of
Feinberg I assume
are best suggested
by the laws of
The article is structured thus:
0. INTRODUCTION: You're reading it.
1. SLOWER THAN LIGHT: Problems and frustrations of
living in a universe without FTL travel, exacerbated by the adoption of nanotechnology.
2. FASTER THAN LIGHT: Other
proposals for breaking the light
3. TRAVERSABLE WORMHOLES: The latest candidate for FTL, and some of their properties.
4. EXPLORING THE UNIVERSE: How to explore the universe with a modified
Bussard ramscoop and on-board wormhole.
5. TIME TRAVEL: Why traversable wormholes do not permit time
travel, but allow FTL, and remain compatible with relativity
6. EMPIRE-TIME: The differences between the local, or empire, time
frame an expanding
civilisation imposes on its
surroundings and the more conventional conception of time.
7. ALIENS: Contacting
aliens. In particular it examines how
local empire-time zones fuse together, forming...
8. UNIVERSAL TIME: ... a universal simultaneity, creating a
post-Singularity phase change,
9. BEYOND THE OBSERVABLE UNIVERSE: Implications of exploring beyond the edge of
the observable universe.
10. BASEMENT UNIVERSES: Some
pros and cons of Euclidean space against wormhole-linked arrays of basement
14. FURTHER READING
1. SLOWER THAN LIGHT
We can colonize the universe at sub-light
velocities , , but the colonies remain separated from each other by the vastness of
interstellar space. In the past trading
empires have coped with time delays
on trade routes of the order
of a few years, or decades at most. This suggests that
integrated, interstellar economic and cultural zones are limited, at most, to only a few star systems.
Nanotechnology  only
exacerbates the situation. We expect full- nanotech, uploading, AIs
and other self-transformative
arrive (over a period
of some few
years, often dubbed the Singularity) before interstellar travel becomes
practical. Assume, for illustrative purposes, that we keep the same dimensions for our brains as
at the moment. Once we are uploaded
onto, and redesigned on, a decent
nanotech platform our mental speeds can be expected to exceed our present rates by the ratio of the speed of
electrical impulses to neurochemical impulses - about a million-fold
speed-up. Subjective time, in the information world Hans Moravec
has called cyberspace , speeds up by this factor. Perhaps we can't expect an ultimately
materials-based economy (which even cyberspace is, with its need for raw processing power) to speed up by this amount. Economic speed-up of a factor of a thousand,
as the geometric mean
of one and a
million, might be more reasonable and I shall adopt
this factor for illustrative purposes. Even so, the doubling time for the economy is reduced
from decades to weeks. Trade across more
than light weeks
is much less
due to the growth and change
in markets during a doubling. Although
individual stellar systems can form single economic zones, they remain in economic
isolation from even their nearest neighbours, including their surrounding Oort cloud or cometary
nanotech and nuclear
transmutation there is 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 travelers. Gossip and news. But, with communication delays to Alpha Centauri of the order of millions of subjective years, two-way dialogues
are difficult to imagine - even when we are enjoying unlimited life spans. Old
news is no news.
and exploration, without FTL, is 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 decode at Alpha Centauri. Assuming
station hasn't shut down in the intervening millions of years of subjective cultural change and economic
transformation. You could leave a copy of your consciousness 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 and cramp our style much
more than it does at present.
Trade routes, we have seen, are unlikely to spread beyond single star systems,
at least until
after the economy has plateaued (maybe never).
unlikely to spread beyond single planets before time delays cause social
fragmentation. Mars, at its closest to Earth, is 4 light-minutes away. After nanotech speed-up the effective communication distance increases
to several subjective-light-years. Other planets become as distant to nanotech
based societies as the stars are to us.
And stars become as distant as present-day
2. FASTER THAN LIGHT
Life, on the galactic scale, becomes incredibly dull without FTL. In science
fiction a standard
plot device is
to invent some
FTL mechanism, to make stories interesting. As you might expect, there have been a number of efforts to circumvent
the light speed
barrier in science-fact,
as well as science-fiction.
What stops FTL travel? According to
relativity as an object accelerates towards the light-speed barrier its mass increases
asymptotically, slowing its
acceleration with constant thrust. Ship
time also slows down, which also reduces thrust (e.g. for a photon drive the
frequency of the photon beam red-shifts, reducing apparent thrust to a off-ship, stationary observer). Both effects make the speed of light an insurmountable barrier.
Since the advent of relativity there have been a number of approaches to FTL
1) Tachyons: Tachyons are posited FTL particles,
compatible with relativity. They never cross the light speed barrier, which is all
forbids, being superluminal from emission to absorption. Unfortunately there are serious doubts about whether they could be used for transmitting information . However, no tachyons have been detected, so things look bleak either way.
2) Superluminal quantum effects: Einstein-Podolsky-Rosen & quantum
'teleportation' . Relies on an
accompanying classical sublight signal, so no FTL.
Other quantum schemes (e.g. pure EPR signalling) rely on transmitting information via the posited
collapse of the wave function,
on which no general consensus
exists. Until this is settled we can't expect too much here. No quantum superluminal effect has been demonstrated in
the laboratory, either.
3) Spinning black-holes: Things looked hopeful for a while that large spinning or charged
black-holes might permit travel into other regions of somewhere. Recent work shows that the passage of anything through a black-hole sets off a
gravitational feedback process
the traveler to death. Also infalling
radiation blue-shifts to infinity , frying the traveler, if tidal forces,
which are similarly
inflated (no matter how big the black-hole), don't shred her first.
4) Einstein-Rosen bridges: An Einstein-Rosen bridge connects two
otherwise widely separated
regions of space, with a bridge, throat or tunnel of space, whose length is
independent of the conventional separation.
Unfortunately the throat is very short-lived, pinching off so quickly that only tachyons (if they existed) could travel through them and get out the other end, . But if you could travel FTL you wouldn't need a wormhole- Catch-22! Einstein-Rosen bridges are non-traversable
As each attempt
has failed the conventional wisdom has strengthened that FTL travel is the 20th
century's analogue of the alchemist's dream of transmuting lead into gold or flying to the
moon. Or living forever. They
seemed impossible dreams at the time....
3. TRAVERSABLE WORMHOLES
In 1985 Carl Sagan appealed to theoretical physicists for plausible methods of FTL travel to include in his forthcoming book,
_Contact_. Stimulated by this request, amongst others,
were Kip Thorne and his graduate
students at Caltech. Instead of looking
at how different
forms of matter distort space they
turned the problem
around and asked,
what states of matter are required to hold a wormhole open permanently, so no pinch off occurs? The answer
is 'exotic' states, a highly stressed state, with enormous tensile strengths. The tension or pressure of 'exotic' states exceeds the local energy
density. We have no familiarity with
substantial 'exotic' states today, but it existed under conditions of
extraordinary pressure in the early universe and exists in very tenuous forms today. Carl Sagan published _Contact_ in 1985 ,
incorporating the Caltech team's early work on traversable wormholes in the novel. Thorne et al published their conclusions in
1988 , including
a recommendation for students to read _Contact_ as a light introduction to traversable wormholes and
In 1989 Matt Visser showed
how more general traversable wormholes could be constructed  or, more precisely, gave the material requirements for
wormhole stability. A Visser-style wormhole
requires 'exotic' states confined to the edges of a three-dimensional volume,
for example the edges of a cube.
Although there is only
one cube of material, it appears at two
locations to the external observer. The
cube links the two 'ends' of a wormhole together. The cube has no interior, but merely
facilitates passage from 'one'
cube to the 'other'. Each face of the
cube, instead of showing
the interior of the cube, opens onto the view from the corresponding face of
the other cube. A traveler, passing between the edges of 'one' cube, emerges from between the edges of the 'other'
cube, unaware of anything special
about the journey.
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 generated in the empty
space between two
plate conductors or in the particle creating region around a black-hole. Negative pressure fields, according to standard astrophysics, drove the
expansion of the universe during its
'inflationary' phase. Cosmic string has
negative tension. Clearly 'exotic'
states are not barred by physics.
The negative energy of a wormhole has equal magnitude to the energy of a
black-hole, where the wormhole throat radius equals the black-hole
Schwarzschild radius. A traversable
wormhole can be thought
of as the negative energy counterpart to a black-hole. The energy of a traversable wormhole, like a black-hole, scales with its linear dimensions. A one
meter cube entrance requires a negative mass of roughly 10^27 kg. A planck-scale wormhole, throat diameter of
10^-33 m, has a negative mass of 10^-8 kg.
Negative energies, though
they exist in
nature, have so
far only been
seen in association with other positive energies, yielding systems with total
positive mass. The negative Casimir
energies observed are confined between
metal conductors whose mass gives the total system of conductor plus vacuum a positive, overall
energy. Similarly the particle creating
region of an event horizon is energetically dwarfed by the associated
black-hole mass. Being conservative in my induction I'll
assume that the total mass of a
wormhole is positive, of the same
order as the
core's negative energy, which is suggested
by some other
, although only
Construction of 'exotic' cubes is, of course,
far, far beyond our present
day engineering capabilities. I would
seriously doubt the possibility of achieving such capability were it not for the self- transformative technologies mentioned
earlier. With AIs and nanotech combined
we expect the limits on intelligences to be
governed by physics, not biology , .
Our brain's processing
capacity is conventionally assessed
between 10^15 -
10^18 bit/sec. A comparably sized
nanoelectronic brain would have processing
power of 10^32 -
10^36 bit/sec . The 6 orders of
magnitude absorbed by nanotech speed-up, mentioned in the opening paragraphs,
still leaves 8 - 15 orders of magnitude expansion for complexity, or depth of thought, of our brains as we
switch from biology to nanotechnology. So we should not blithely assume construction and
manipulation of the exotic states required will long remain beyond the grasp of
future, post-Singularity, civilisations, populated by such super-intelligences, or
cyberminds , unless prohibited by physical law . The
remainder of the article will assume
the mass production of wormholes is economically achievable by future civilisations.
the problems of
construction, let's look at the properties of wormholes. A wormhole collapses, or throat pinches off,
when the amount
of mass passing through
vicinity approaches the same
order as the amount of negative mass confined
to its edges,
threatening to form a black-hole.
Surprisingly, the maximum rate of mass flow through a wormhole is
independent of size. As the diameter of
the throat expands
so does the
time taken to
pass into and beyond the hole's Schwarzschild radius, giving a maximum rate of mass
the hole of c^3 / 2G, or approximately 2.10^35 kg/s, where G is Newton's
constant, c the speed of light.
Wormholes can be viewed as communication
channels with enormous
potential bandwidth. According to
Shannon  and others , , information
has a minimum energy of kTlog2 per
bit associated with it, where T is the absolute ambient temperature. The gravitational field of the hole will
impose a size-dependent lower bound on the Hawking temperature of the wormhole,
giving a channel
scales with hole size, of 10^52 bits/sec * mass (in kg). This suggests it will usually be more economic to squirt the design of an
object down a wormhole channel rather than the object itself. This bandwidth, or channel capacity, is the
upper limit possible through a hole, but doesn't, in
itself, give any
clues as to how to achieve it.
These two properties of wormholes, fixed matter-throughput versus bandwidth
scaling with mass or radius, suggest
cold wormholes will be used
primarily for communications,
rather than matter transference. Some exceptions might be unless
the object is unusually information-rich or can't be reduced to
(e.g. a quantum correlated EPR state ), without destroying the object. Another other class of objects that will need direct physical
transference, rather than being transmitted as information, are wormholes
themselves. Having laboriously dragged one end of a wormhole somewhere,
later wormholes are transferred via the first, to increase the connections between the two distant regions.
An object swallowed by the mouth of a wormhole leaves its electric charge, momentum and
mass associated with the mouth, in an analogous
manner with the no-hair theorem for black-holes. The no-hair theorem for black-holes says that a black-hole only remembers the total charge,
mass and momentum (linear and angular) of objects swallowed. Correspondingly, when an object is disgorged
from a wormhole the mass and charge of the wormhole end is reduced, by the
disgorged object's mass and charge.
Matter and charge flows through
a wormhole have to be balanced in either direction to prevent gravitational and
electric flux lines being trapped and distorting the hole. To the external observer, who may not know a
wormhole is involved, mass and charge appear locally conserved. Over the long term the wormhole is forced to act as a matter
exchange, rather than a source or sink for matter. I'll return to this point when discussing the Bussard ramscoop idea.
4. EXPLORING THE UNIVERSE
Wormholes enable travel from one
mouth to the other. To travel to distant
parts of the
wormhole end stays at home and the other is carted away, at sublight
velocities, to the destination.
To sustain high
accelerations a space probe with an on-board, small, light, wormhole could be powered from base. The fuel (perhaps antimatter, in the form of
anti-particles) is uploaded through
the base end of
the wormhole to the on-board end of the wormhole, powering a photon drive. A corresponding mass (ballast) has to be
exchanged to maintain
the two-way mass balance, as I mentioned earlier. This matter has to be collected by the probe
from its environment, which naturally leads to the suggestion that the probe should be a Bussard ramscoop
, collecting ballast/fuel from interstellar gas with a magnetic
'trawl'. Half the collected matter is
exchanged for antimatter via the wormhole, which is combined with the remaining
matter to power
the photon drive. A Bussard ramscoop
gains in thrust as it reaches higher
relativistic speeds (the Lorentz-Fitzgerald contraction increases the density
of oncoming interstellar plasma). To
protect against relativistic dust impact damage some of the extra energy and
mass could be used for the construction of a
heat shield (whose mass would partially off-set the gain in thrust with
speed). At different velocities different designs are optimal, so the probe would have to effect in-flight redesign.
At the relativistic speeds time dilation becomes a major factor. Time dilation reduces trip times for
relativistic travelers. A probe
accelerating at one-gee
speed within a year. As it speeds up
probe time dilates more and more. I have
1-gee acceleration, after the original plans , based on a hydrogen fusion motor. I've also included a higher 1000-gee flight time plot, based on the greater accelerations a nanotech
ramscoop construction could
withstand, and an antimatter drive could
deliver. Probe or journey time to
various locations, are, not allowing for slow- down:
in light years Trip time at various gees 1-g 1000-g
Alpha Centauri 4.3 2.3
years 3.3 days
Centre of Milky Way 30,000 11
years 6.5 days
Andromeda Galaxy 2,250,000 15
years 8 days
Nearest Alien Civilisation? 100 M 19
years 9.5 days
Edge of observable universe 10,000
years 11 days
Edge of inflationary bubble? 10^30 70
years 28 days
The probe remains in communication with the home base, throughout the trip. As a drop point approaches another wormhole plus deceleration rig is uploaded
detaching itself from the mother craft.
Deceleration is quicker
expensive than acceleration: the daughter craft brakes itself against
interstellar/galactic gas, dust and magnetic fields, or even reflects the
oncoming gas forwards to double the braking force.
Transfer of colonists begins when deceleration is complete. The colonists transfer through the daughter hole,
whilst the main probe continues its
outward voyage. One of the first tasks is to secure the
connections with home by increasing
the local wormhole presence,
transporting more wormholes from base
via existing wormholes. Initial
supplies, plant and machinery are transported as needed from base. Transport of manufacturing plants continues
until local nanotech factories become more competitive than transport of
finished product and local industries reach critical mass.
After this the wormholes become increasingly used for communications rather than
An analogy with
the cloud chamber springs to mind here.
Charged particles are tracked through
cloud chambers. Each particle is
invisible, but its
presence is revealed by the expanding wake of droplets left behind. Similarly
the space probe is all but invisible, lost
in the immensity of deep space. The
burgeoning colonies left
behind mark its
passage. The colonies send out further wormhole probes. >From a distance the whole affair resembles a growing
3-D snowflake, with Earth at the centre.
The tips of the snowflake indicate the positions of colony-probes.
Road, sea and air routes allow the creation and operation of global
markets. With the growth of
transportation once isolated economic zones are now forming more tightly
integrated global trading blocs. Similarly wormhole connections
enable galactic and intergalactic economic blocs or zones to form.
5. TIME TRAVEL
As we have seen, wormholes are constrained by relativity to travel at sublight
speeds, being time-dilated as normal.
Clocks placed at the two 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'll
even if one end
of the wormhole is traveling at relativistic speeds, many light-years away. We observe the two clocks keeping time with each other, yet
relativity says the 'distant', traveling clock, is running slowly. How do we reconcile this?
clock is being displaced in space _and time_ . A wormhole connects different regions of space and
time. If a wormhole enables someone to
travel from Alpha Centauri 2996 to Sol 2993, and vice versa, then no paradox results because they can't travel back to Alpha
conventional space, a distance of about 4.3 light-years) and arrive before they left (to cause a paradox).
if a wormhole connects, say, Alpha Centauri 3000 to Sol 2993. Now a traveler can travel, through the wormhole, from Alpha
Centauri 3000 to Sol 2993 and then make the return journey, through normal space within 5
years, at sublight speeds, arriving before her own departure. This is a problem because we can always time dilate one end of a wormhole and not the
other, either by placing one
end in a gravitational field or transporting it with great speed. Wormholes, it would seem, can be always transformed into time machines.
Problems begin when the wormhole ends move towards each other, and the
time-shifted traveler is able to return, by traveling through conventional space, to
visit herself before departure. If a
traveler can visit an earlier part
of her worldline then the possibility of acausal paradoxes is opened. 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 wormholes can't exist. No
emerged in the pages of various physics journals as the subject was batted back
and forth. Elaborate and very interesting papers ,  reconciled time travel with
whilst Hawking proposed, and gave
plausibility arguments for, a Chronological Protection Conjecture, CPC, which says the
Universe Shalt Not Allow Time Travel .
One of the time
travel sceptics is Matt Visser. Early in
1993 he showed that wormholes do _not_ enable
time travel , by proposing physical mechanisms that enforce CPC. Visser showed that
the mouths of a wormhole, with an induced clock difference, could not be brought close enough together (one wormhole end inside the light cone of the other end) to
permit causality violation. Quantum
field and gravitational effects
build up as the two ends of a wormhole approach each other and either collapse
the wormhole or induce a mutual repulsion.
is not complete,
but it seems swarms of virtual particles (including gravitons) disrupt the region around a
time machine, just before it would otherwise become operational. The virtual particle fluxes around a nearly
chronologically violating region are able, via the uncertainty principle, to form closed space like (superluminal) loops and
borrow energy off themselves, becoming more virulent than usual. As traversable wormholes approach being time
machines, the energy of the virtual space like particle loops pinch off the throats, preventing formation of
closed time like loops. This mechanism still works even if more than one wormhole is involved. One
end of a wormhole is excluded from the light cone of the other end, even if the light cone is transmitted via
another wormhole. 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.
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
the journey from Earth to Andromeda of a 1- gee exploration probe (with the
obligatory on-board wormhole), from the probe's perspective. At launch from Earth, in say the year 3000,
the probe's view of Earth matches the view of Earth through the on-board wormhole -
both show Earth
3000. After 15 years probe-time travel,
at constant 1-gee acceleration, the ship reaches Andromeda. The view of Earth through the wormhole now shows
Earth 3015. But the probe can calculate
trip duration, using
Minkowskian geometry, relative to the stationary, Earth-bound observer. This time works out to be 2,250,001 years. So
the probe knows that
it is 'really' year 2,253,001. We have
to conclude that
wormholes not only
connect widely separated
regions, but also different
times, as we said earlier. In this
example Earth 3015 is connected with Andromeda 2,253,001.
wormhole a traveler can move
3015 and Andromeda 2,253,001. (Note: CPC
prevents paradoxes. Trying to create an _additional_ return
wormhole connecting Andromeda 2,253,016 with Earth 4,503,002, say, would enable
someone from Earth 4,503,002, to travel to Earth 3030, via Andromeda 2,253,016
to disrupt their own past. But the closed space like loops form, via the CPC
mechanism, and block the arrangement.)
Whilst a wormhole bridgehead is established, CPC prevents any connections to different times, within the
cone, even indirectly via other wormhole connections. Because of this strict chronological
enforcement it makes sense
to define a local time, which I call empire-time, for use within the regions linked
up. In this example Earth time is the standard by which clocks can be
The time frame being defined by the expansion of wormholes, which I've dubbed
empire-time, is not coincident with the cosmological time frame. The cosmological space-time is the space-time
frame in which the average
distribution of matter is stationary. The cosmological frame, or co-moving frame, expands with the Hubble expansion
of the universe. At each point in
cosmological time the averaged distribution of matter, on a large scale, is
even, allowing the easiest
calculation of dynamics
of the expansion of the universe.
Relativity says all reference
frames are relative, but in truth most
of the cosmological frame as a natural
Schelling frame, to adopt,
even though we
are drifting with respect
Wormholes sent to the Andromeda, in our example, at near light speeds arrive in
approximately year 2,253,001 cosmological time, but in year 3,015
empire-time. Assuming once wormhole technology is developed we expand at near light speeds then the surface of
constant empire-time forms an inverted cone in cosmological space-time, with
Earth at the 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 - think
of time forming the vertical
scale and the spatial dimensions contributing to the horizontal co-
ordinates. Later times form surfaces
stacked on top of earlier times.) At any
particular moment in empire-time the entire surface of the empire-time cone is
accessible to the wormhole traveler.
Traveling along the wormhole highways away from Earth takes you into the
far future in cosmological time, but not in empire-time. Later empire-time zones form inverted cones,
uppermost, stacked on top of each other.
Empire-time is the time imposed by the wormholes throughout the region they connect up. This region I'll call an empire, although no
central authority is implied but is allowed.
Clocks within the empire can be synchronised with each other, provided they are close to a wormhole. A traveler within the empire could always set their clock by
empire- time, because the wormholes provide
a common reference frame, or a background, against which to
define position and velocity. Because
frame is common
to all occupants the empire-time defined can be used to catalogue events in a
time-ordered fashion. Attempts
to redefine the empire-time already laid
down by the wormhole infrastructure are firmly resisted by CPC. To redefine empire-time you have to
repopulate a region with holes traveling at a vastly different speed than the original
colony probe. The CPC mechanism says, in
empire-time terminology, two holes disturb each other as they approach closer than their empire-time
difference times the speed of light
e.g. two holes with an empire-time difference of a year can't approach closer than a light-year without being both
violently disrupted and destroyed .
Once the empire-time frame has been defined it becomes increasingly difficult
it. As the population and economy of a
region grow the numbers
of holes increases. Once established, to
change the relationship between cosmological time and
empire-time requires the complete
upheaval of the local economy and denizens.
Economic growth breeds chronological stability.
Questions about the distant cosmological future of our universe are answered directly by travel. How quickly
is the Hubble expansion slowing? Would
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 from almost inconceivable distances and
the 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 is only possible in an open, uninhabited
universe, as below. In a closed or alien-infested universe
there is a limit
to how far you can travel before CPC prevents
Enrico Fermi said "if aliens existed they would be here" , reflecting the
view that circumstantial evidence indicates
alien civilisations are very few and far flung in the universe. The easiest
way to explore and colonise the universe is to send out self-replicating space
probes, as Tipler has cogently
argued , , which almost any civilisation will do so at some stage in its evolution. Within a cosmologically short period (i.e. millions of years)
colonise the Milky Way and the rest of the Local Group. The arrival of a colony probe at a star
system precludes and supersedes local biological evolution. This hasn't happened to us, otherwise we
won't be here. Since life on Earth has
evolved over billions of years then we can't expect (statistically speaking) to find
civilisations within our local group or, perhaps, anywhere in the
universe. This is the Fermi Paradox.
A statistical elaboration of this argument  gives grounds for believing that the nearest aliens are
currently over a 100 million light-years
distant. For illustrative purposes I'll assume the nearest alien
civilisation is 100 million light-years
distant. In the cosmological frame,
without wormholes, we won't make contact
with them for over 100 million years.
Which makes their existence an object of theoretical speculation, which
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,
although no probe can penetrate into an alien empire. Each empire defines its own empire-time, in conflict with the empire-time of
the other. A probe from Earth flying
into an alien zone not only
crosses alien space, but also alien empire-time zones. As it approaches the alien home world it
passes increasingly into the alien empire-time future. CPC forbids such travel by destroying lone
wormholes that attempt to interpenetrate each
This opens up the possibility of different
A well coordinated, centrally controlled species might halt expansion at the
boundary of their home galaxy (say) for a few thousand empire- years, building
armaments etc. When their technology seems to have
plateaued they resume expansion relying on technology and numbers to overwhelm aliens. Such
a strategy is technology dependent. If wormholes can be booby-trapped to explode
on tampering or hostile attack
such a strategy fails. Consider
what happens as they
invade a neighbouring, occupied galaxy.
At the first sign
of attack the
defenders destroy their wormholes in the invasion zone and retreat in a
scorched earth policy. The structure of
their respective empire-times operates to favour the defenders. The attackers
penetrate deeply towards the galactic core and home world within a few years of
their empire-time. 'Meanwhile' the
defenders retreat, abandoning
rim worlds one-by-one, over a period of tens of thousands of
years of _their_ empire-time. Each light-year crossed and the
and economic power
advances by a year (likely to be a large gain with nanotech growth rates),
whilst the invaders' technology
is in relative stasis. Eventually science, technology and weight of numbers tells and the balance of attack shifts in favour of the
defenders. Unless an invader overwhelmed
the defenders in some
surprise, sneak attack the attack fails. Wars have to be fought on a more subtle level. Enough material here to keep military strategists busy for a while.
A more likely scenario is: Contact is signalled by our leading wormhole probes failing
in the overlap of our sphere of influence
with the alien empire's sphere, a kind of neutral zone. Finding each other's probes is
non-trivial. It might be easier to find the colonies than
the original exploration vessels. To
push the analogy
with a particle zipping through
a cloud chamber, search for the tell-tale droplets, rather than the elusive particle. The easiest
way of doing this, at the point where the relativistic wormholes are destroyed,
is to send out sub-light,
mildly-relativistic survey probes (with on-board wormholes), from the nearest
drop points, to establish diplomatic relations.
If both sides explore each other with non- or mildly-relativistic probes
(relative to the cosmological frame) then their empire-times will realign
themselves, meshing together over the locale of the neutral zone, although this
may take years,
permitting diplomatic contact
and, assuming no
wars, eventual exchanges of wormholes.
Empire-times merge as empires merge.
Clocks in one
empire are synchronised with the clocks in the other. Initially to travel from one empire to another involves
wormhole travel to the neutral zone and hopping over to a nearby alien hole,
into the alien's wormhole network. As
wormholes are exchanged direct travel becomes possible.
The wormhole networks merge as more and more direct connections open
up. The spheres of colonisation are now available to each other and the
two empire-times merge to form a double conical structure. If the alien empire began expansion before us, in
cosmological time terms, then traveling to the alien home world would take us back to an era of
cosmological time prior to the present.
expansion rates quoted, once the first aliens are contacted the second, third etc. follow soon after. In addition to directly contacting alien empires we'd
also make contact
indirectly. To begin with we'd make contact with alien empires that had not met very many other
aliens - just starting out, so
to speak, as we were. This would soon change. As our probes reach further and further into the distant
cosmological future we contact
larger and larger alien empires, who, in turn, have met more and more other
aliens. The crucial point is reached
when the average number of civilisations a typical
civilisation is in direct contact
with reaches three, or thereabouts. In
our 1-gee flight scenario this point is reached about 4-5 months after first contact is established, i.e. in
under 20 years exploration, plus
time to establish diplomatic relations.
If we plot
the number of
directly _and indirectly_, against empire-time we get an asymptote, bounded only by the total number of alien species in the
universe, at this point.
8. UNIVERSAL TIME
This is a symmetrical situation. Not only will we be meeting aliens
within an historically short period,
but they will
be meeting us shortly after their expansions begin.
Consequently, all the space-faring
species of the universe will be connecting up at about the same stage in their
development. This gives us all shared interests and markets in common. We might expect each civilisation to go through two future phase changes, the first individually,
the second collectively. The first phase
Singularity, is the adoption of full-blown
nanotechnology and the consequent uploading from a biological to a nanotech
platform. The second phase change, which I'll call Contact, occurs when each
civilisation, more or less
empire-time-simultaneously, links up with the rest of the universe, tapping the
benefits of the
near-infinite economies of scale this brings.
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 cosmological average. On closer
inspection (i.e. scales of billions of years and light-years) the universal time
indentations, marking where each civilisation arose and stamped its own chronological footprint
on the surrounding space-time topology, before merging with their neighbours'
zones. By saying the universal time
surface is indented I reveal
my own cosmological time prejudices. From the vantage of point of a future
it is surfaces of equal, cosmological time that appear bumpy, relative to the planes of
constant universal time. To them
civilisation birth points appear as the _summits_ of cones in the cosmological time surface,
relative to the flat universal time surface.
Universal time would be the preferred time for discussing life, history,
politics etc. - everything except prehistory before Contact.
Universal time has many similarities with absolute time, as Newton conceived of
it . Newton viewed absolute time as
deriving from God's immanence, or presence
throughout the universe. The universal
time frame defined by wormholes is created by the civilisations within the
universe, which is much more satisfactory state of affairs to the modern
Roughly half the civilisations we meet are likely to have been around, in
cosmological terms, hundreds of millions or even billions of years before
us. Gaining access to their empire-time zones
will enable our astronomers to observe the expansion of the universe in the
distant past (although always further
away from here in space than cosmological time). The occurrence
of the first civilisation in the universe is the limit before which we could not travel, in cosmological
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
the speed of light. Objects beyond this are red-shifted to
infinity and are unobservable. This
distance defines the edge of our observable universe, an event horizon, and lies approximately (subject to
15-30 billion light-years
away. This is the limit of the astronomers'
universe. What lies beyond is left to cosmology to ponder on. Cosmological theories expounded over the last decade (in particular
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
differ about what lies
beyond the inflationary bubble. Because
these regions are inflating at huge rates, an event horizon prevents any substantial
exploration outside the 'bubble'. Unless
we make Contact
we will never directly observe this since these regions will have changed greatly in the century or
two of empire-time (> 10^30 years of cosmological time) it takes to reach
them. One possibility is that naturally occurring
wormholes, relics of the inflationary period,
and inflated to astronomical dimensions , may link our post-inflationary,
bubble with others, forming an infinitely large chaotic, fractal structure
A couple of
paragraphs back I mentioned the phase change,
associated with linking up with the rest of the universe and gaining the benefits of near-infinite
economies of scale, access
to huge information
markets, etc. The present scope of internet, the
electronic global communications
network, pales into utter insignificance before the size of the pan-universal
will form, post-Contact. It's worth while stopping for a moment and considering what this might do to
of ourselves and our place in the universe.
At the moment we are the only
civilisation we know, unique
and conceited. If civilisations lie scattered at distances of 100
in a universe of radius 10^30 light-years,
this still yields
over 10^60 alien mother cultures. It is unlikely anyone could ever catalogue all the
civilisations and cultures,
even if they
did have a nanoelectronic brain! No
single historian could
encompass the sweep of history, no biologist catalogue the species. We would have returned to the medieval world,
surrounded by legends of distant lands populated by mythical and fantastic creatures. Construction of a single universal map and
would be impossible. The culture shock of absorbing all
the extra data
would likely keep
us occupied for not far short of eternity.
10. BASEMENT UNIVERSES
Initially, no doubt, wormhole connections would supplement existing
architectures, connecting together points in the existing locally Euclidean
universe. The next logical step would be
to start constructing extensions to the existing topology. The technologies involved in generating artificial
inflation to expand
the interiors of wormholes into basement, or baby, universes are of the same order of magnitude as creating
traversable wormholes. A basement
universe is a traversable wormhole with only one
end and an inflated interior (rather than two ends and no interior). Rather like the Tardis, in concept, bigger on the inside
than the outside. Computer simulated
basement universe formation has already been discussed in the literature , , . The technology to construct traversable wormholes
implies the ability to construct basement universes.
We have already mentioned that
speed-up of subjective
time rates of a million or so
with the adoption of full
nanotech. If just a factor of a thousand
translates into GDP and population growth rates then doubling times drop from
decades to weeks. I don't know if these growth rates
are sustainable, even in empire-time, but they indicate that any limited
likely to be at a premium, within years of empire-time. Since the amount of natural
civilisation is likely to be limited
to roughly 10^24 cubic light-years,
space will ultimately be at a premium.
The need for living space dictates that eventually wormholes will be used to provide links to artificial
basement universes. Or perhaps the
possibility of wormhole wars, mentioned earlier, will tempt societies to move wholesale into basement
universes for security.
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 (in historical terms) hit technological limitations or each other. Wormholes and associated basement universes
offer the long
term prospect of
this dilemma. An array of basement universes connected by
wormholes has the useful property that
the volume of habitable space accessible grows exponentially with distance from
origin. A civilisation driven by volumetric
exponential growth need only
grow radially at a constant rate through
basement universe space, unlike in Euclidean space, where it must expand radially exponentially.
This might seem somewhat like
a subtle and obtuse piece of mathematics, but
it's just restating that
a tree with continually
branching twigs eventually strangles itself, in Euclidean space, whereas it could grow forever through a tangled array of
wormholes and basement universes, without the crowding out effect choking off growth. A related limitation of Euclidean space is
the amount of information a volume can contain. This limitation, the Bekenstein bound ,
, implies that
to achieve unlimited information
storage a system must spread itself increasingly thinly and operate more slowly
, in the limit
to zero, or else collapse into a black-hole.
limitation applies to a space of connected basement universes. Each basement universe is shielded from the
positive energy contribution of its
neighbours, allowing infinitely complex,
networked structures to form.
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, problems
of construction, theoretical and practical, will exercise the advanced intelligences of the
future considerably. In the longer term the possibility of
opened-ended, perhaps even infinite, information
processing lie before the civilisations
which solve the problem
of wormhole construction and transport.
Without wormholes a civilisation faces certain fragmentation as it expands. With wormholes it can remain integrated. Whether
the integration is used
or abused is another question.
From a more detached point of view it is interesting that the universal time frame permits a return to
the Newtonian conception of an absolute time and simultaneity, previously thought to be incompatible with
general relativity. It is especially
the shape of the universal time surface is a function of the birth place-times of civilisations,
rather than divine choice
or blind, insensate cosmological processes.
My thanks to all the Extropians and Cryonauts for their feedback, including Gregory Benford, Andrew
Clifford, Ray Cromwell, Dani Eder, Carl Feynman and Timothy Freeman for
filtering out some
of my worst errors
and most obtuse wording. But most
particular thanks to Robin Hanson, for jointly starting and working with me on this project, and
specifically for pointing out how empire-time follows from time- dilation. Needless to say none of the above share any responsibility for, or
with, some of
my conclusions, nor any of my errors.
Feinberg. Physics and Life
Prolongation. _Physics Today_ 19(11) 45
(1966). The full quote is: "A good approximation for such predictions is to assume that everything will be
does not violate known fundamental laws
of science as
well as many things that
do violate these laws."
 Frank J Tipler.
Beings Do Not Exist. _Quarterly Journal
of the Royal Astronomical Society_ 21(3) 267 (1980). Additional Remarks on
_Quarterly Journal of the Royal Astronomical Society_ 22(3) 279
(1981). See also Chapter 9 
 Frank J Tipler & John D Barrow. _The Anthropic Cosmological Principle_, Clarendon Press,
Oxford (1986) ISBN 0198519494 Provides lots of evidence against the notion that the universe is crawling
with aliens, Chapter 9
 K Eric Drexler. _Engines of Creation_, Anchor
Press/Doubleday, (1986) ISBN 0385199724. _Nanosystems: Molecular Machinery,
Manufacturing, and Computation_, Wiley-Interscience, (1992) ISBN
0471575186. See also _Extropy_#10 4(2)
44 (1993) for a review by J. Storrs Hall
 Hans Moravec. Pigs in cyberspace, _Extropy_#10 4(2) 5
 Gerald Feinberg. Possibility of Faster-Than-Light Particles. _Physical Review_ 159(5) 1089 (1967) Tachyons
can always be re-interpreted as moving
forwards in time, with positive energy, by all observers, so that emission predates
absorption. The inability to distinguish
emissions from absorptions vitiates communication.
 Charles Bennett. Teleporting an Unknown Quantum State via Dual
Classical and Einstein-Podolsky-Rosen Channels.
_Physical Review Letters_ 70, 1895 (1993) How to use a split EPR experiment to
make a perfect
quantum copy of
a system - but the original is destroyed during classical signal assembly.
 Werner Israel & Eric
Poisson. Internal Structure of
Black-Holes. _Physical Review D_ 41(6)
1796 (1990) Infalling radiation (including
gravitational) blue-shifts at the internal Cauchy horizon forms an infinite, hidden energy barrier (called
blue-sheets) blocking passage to travelers.
 Charles W Misner, Kip S Thorne &
John A Wheeler. _Gravitation_ WH Freeman (1973) ISBN 0716703440. Simply the best book on
general relativity. See section 31.6 for
 Carl Sagan. _Contact_, Arrow and Legend,
(1985) ISBN 0099469502 The novel that, amongst other things,
features a fictional account of travel through a traversable wormhole. Quite
good story, so
 Michael S Morris & Kip S Thorne.
Wormholes in Space-time and Their Use for Interstellar Travel. _American Journal of Physics_ 56(5), 395
(1988) The article that
started all the fuss. Good historical
overview of the status
of various energy conjectures. Outlines
the requirements for traversable wormholes: violation of the averaged weak energy condition and the presence of exotic states.
 Matt Visser. Traversable Wormholes:
Some Simple Examples. _Physical
Review D_ 39(10), 3182, (1989) Non-spherically symmetric traversable wormholes
permit passage without collision with exotic material.
 Ian H Redmount & Wai-Mo Suen.
Is Quantum Space-time Foam Unstable?
_Physical Review D_ 47(6), 2163, 15-March-1993 The authors show that we'd expect small, Planck scale, negative-
energy wormholes to inflate to observable dimensions. Since we don't observe this instability, perhaps, (i) the
Wheeler quantum foam, with planck-scale wormholes popping into and out of
existence, doesn't exist, or (ii) wormholes are constrained by as- yet-unknown
energy conditions - for instance
if they only had net positive energies.
 Thomas Schneider. Channel Capacity
of Molecular Machines. _Journal of
Theoretical Biology_, 148(1) 83 (1991) Draws the parallels between a molecular assembly and
Shannon's concept of channel capacity.
 Claude L Shannon. Communication in the Presence of Noise. _Proceedings of the IRE_ (now the IEEE), 37,
 Thomas Schneider. Energy
Dissipation from Molecular Machines.
_Journal of Theoretical Biology_, 148(1) 125 (1991) A general derivation
of the thermodynamic limits
 Ian Nicolson _The Road to the
Stars_, Westbridge Books (1978), ISBN 0-7153-7618-7 Has some nice artistic impressions
of Bussard ramscoops and more references
for the space-faring
 RW Bussard. Galactic Matter and
Interstellar Flight. _Astronautica Acta_
6 179 (1960) Contains
plans for a
1000-tonne, 1-gee ramscoop with 10^5 - 3.10^6 metre radius magnetic scoops.
 Fernando Echeverria, John Friedman, Gunnar Klinkhammar, Michael S Morris,
& Ulvi Yurtsever. Cauchy Problem in Spacetimes with Closed Timelike Curves. _Physical Review D_ 42(6) 1915 (1990) Shows
how the Feynman path integral,
sum-over-histories approach to quantum field theory might remove time-travel causality paradoxes, an approach pioneered
by Igor Novikov. See especially figure
11 for how wormhole clock synchronisation works.
 EV Mikheeva & Igor D Novikov.
Inelastic Billiard Ball in a Spacetime with a Time Machine. _Physical Review D_ 47(4) 1432 15-Feb-1993 An
extension of  which covered the elastic
collisions of a billiard ball with itself, to include inelastic collisions.
 Stephen W Hawking. Chronology
Protection Conjecture. _Physical Review D_ 46(2) 603 (1992) Provides
plausibility 'proof' of CPC. The
back-reaction of the gravitational metric opposes conditions which permit
 Matt Visser. From Wormholes to Time
Machines: Remarks on Hawking's Chronology Protection Conjecture. _Physical Review D_ 47(2), 554 15-Jan-1993
Hawking's CPC is expanded
upon and fleshed out. Wormholes are shown to enable FTL travel, but
not time travel. The back reaction of
the gravitational metric and vacuum
both act to block the formation of CTLs.
Note: this work,
impressive, is not complete.
 Gary W Gibbons & Stephen W Hawking.
Selection Rules for Topology Change. _Communications
of Mathematical Physics_ 148(2) 345 (1992) Wormholes may have to be
created/destroyed in pairs.
 Enrico Fermi, quoted by Carl Sagan.
_Planetary and Space Science_
11(5) 495 (1963), quoted by Tipler & Barrow, 578 
 Dani Eder (private communication)
Models the occurrence time of galactic and
intergalactic civilisations on a normal distribution, bell curve. The time between the first and second civilisations, in a
large volume, is an appreciable fraction of the standard deviation or sigma,
which is related to biological and galactic formation time scales of many
billions of years. The time between the arising of the first
and second civilisations, in an arbitrary
volume, scales with the standard
deviation, but is very insensitive to other factors. Assuming
the galaxy could
millions or billions of civilisations (as is conventional, via the Drake
equation), but that
sigma is of the order
of billions of years, gives the statistical time between the first and second
civilisations as hundreds of millions of years.
This may be a gross
underestimate, if life is much rarer (although time to Contact is not much altered
unless we are completely
 Sir Isaac Newton. On the Gravity
and Equilibrium of Fluids (1668+) Translated in _Unpublished Papers of Isaac
Newton_ ed AR and Marie Boas Hall (1962) Newton preferred the term Universal
Ruler to describe God. The divine
time-frame was the Universal Ruler's view of its creation.
central was this to Newton's theology that he equated the relativism espoused by Leibnitz
as tantamount to atheism.
 Thomas Roman. Inflating Lorentzian
Wormholes. _Physical Review D_ 47(4),
1370 15-Feb-1993 Speculation on inflating planckian wormholes to macroscopic
and astronomical dimensions. Also that naturally occurring
wormholes from the inflationary era, may link our habitable post-inflationary
bubble to other bubbles.
 Andrei D Linde. An Eternally
Self-Reproducing Cosmos? _Scientific
American_, 268(5) 10 (1993) Computer simulation of some eternal inflation models.
 Dalia S Goldwirth & Tsvi Piran.
Inflation - an Alternative to the Singular Big Bang. _General Relativity and Gravitation_ 23(1) 7
(1991) More detailed presentation of eternal inflation , and how it may
arise from quantum gravity, based on generic, dimensional arguments. Habitable post-inflationary bubbles continually nucleate within an
eternally inflating, expanding
sea. The observable universe is contained within one such bubble.
 Matt Visser. Wormholes, Baby
Universes and Causality. _Physical
Review D_ 41(4) 1116 (1990) Banning topological transformations preserves
causality. Baby universes created by
inflation, for instance,
are constrained to be linked with the parent universe by a wormhole. Superseded
by , to some
extent, which introduces other mechanisms for preserving causality. The possibility of topology changes to space-time (which the
creation of wormholes require) is addressed
 Katherine A Holcomb, Seok Jae Park & Ethan T Vishniac. Formation of a "child" universe in
an inflationary cosmological model. _Physical Review D_ 39(4) 1058 15-Feb-1989
Basement universe formation modelled by number-crunching the Einstein equations.
 Alan H Guth, SK Blau & EI Guendelman.
of False Vacuum
Bubbles. _Physical Review D_ 35(6) 1747
(1987) Localised inflation is modeled, leading to the creation of baby universes.
 Jacob D Bekenstein & Marcelo Schiffer.
Proof of the Quantum Bound on Specific Entropy for Free Fields.
_Physical Review D_ 39(4) 1109, (1989) Do Zero-Frequency Modes
contribute to the Entropy? _Physical Review D_ 42(10) 3598 (1990), an
extension to the above
 Jacob D Bekenstein. Entropy Content and Information flow in Systems with Limited Energy. _Physical Review D_ 30(8) 1669, (1984). Entropy Bounds and the 2nd Law for Black-Holes. Physical Review D 27(10) 2262 (1983). See also _Physical Review D_ 23 287 (1981).
The Bekenstein upper bound for information,
in a system, is I = 4 pi^2 E R / h c
ln2, where E = energy, R = euclidean radius Note: also valid for black-holes
 Freeman J Dyson. Time without End:
Physics and Biology in an open Universe.
_Reviews of Modern Physics_, 51(3), 447 (1979). Suggests
ways in which intelligences can survive indefinitely in an open, expanding universe. See also Chapter 10 
 Gary T Horowitz. Topology Change in Classical and
Quantum-Gravity. _Classical and Quantum
Gravity_ 8(4) 587 (1991) How topology transformations can be naturally handled
by classical general relativity. The
singularities imposed by  need not be physically significant since no physical
quantity, like intrinsic curvature, becomes
 Robert P Geroch. Topology in
General Relativity. _Journal of
Mathematical Physics_ 8(4) 782 (1968) Creation of a wormhole requires either
CTLs or a "mild"  singularity, according to classical general
relativity. If we exclude CTLs, a la
Visser, then wormhole creation implies a mild, physically permissible,
14. FURTHER READING
Apart from the references
accounts are available. None, yet, incorporate Visser's work on the chronology
Paul Halpern. Cosmic Wormholes: The
Search for Interstellar Shortcuts.
Dutton Press (1992) ISBN 0525934774.
Very good presentation of the arguments against time-travel and FTL through black-holes.
John Gribbin. In Search of the Edge of
Time. Black Swan (1992) ISBN 0552994626. Covers a lot of the relativity background material assumed here, with useful
Thomas Donaldson. The Holes of
Space-Time. Analog Science Fiction and Fact, July
1993, ISSN 10592113. Covers most of the wormhole basics, but
not any of the CPC material
and implications - i.e. empire and universal time.
LETTER BY KEVIN SCHWARTZ
Send dialogue on time travel.
Here's Harding's address
if you wanna write him direct--P.O. Box 5271, Rockhampton Mail Centre,
Queensland 4702, Australia.]
AD (?) FROM KEVIN SCHWARTZ
[Editor's comment on next
letter: The GRE is a test people take to be considered for admission to graduate school. It's supposed to show your level of something like knowledge compared to other
applicants. Only one school that I know of uses it to grant undergraduate credit. Under the semester system, 30 units equal one year of classes; 120 units is
the minimum for a BA. Some schools run on trimesters. For them, 45 units equal a year and 180 units
are the minimum for a degree.
Under the semester system, a
student is (was) expected
to take 15
semester, which is supposed to equal 15 hours a week spent in class.]
A LETTER AND A TEST FROM MARCEL FEENSTRA