Xenology: An Introduction to the Scientific Study of Extraterrestrial Life, Intelligence, and Civilization

First Edition

© 1975-1979, 2008 Robert A. Freitas Jr. All Rights Reserved.

Robert A. Freitas Jr., Xenology: An Introduction to the Scientific Study of Extraterrestrial Life, Intelligence, and Civilization, First Edition, Xenology Research Institute, Sacramento, CA, 1979; http://www.xenology.info/Xeno.htm


 

17.2 Relativistic Starflight

Alien and human astronauts alike must conform to the dictates of Relativity when traveling at velocities near the speed of light. Einstein’s theory, generally accepted today by the scientific community, predicts a host of fascinating consequences of near-lightspeed voyages.

First, we should briefly mention some of the jargon commonly employed by physicists and writers in this field. Relativity predicts that no material object can be accelerated up to the speed of light without an expenditure of an infinite amount of energy. Since the entire universe contains only 1081 joules of energy, attaining the speed of light becomes a practical impossibility. The velocity of light, designated as "c", thus is a kind of "cosmic speed limit" imposed on all material objects within the physical universe. (Other jargon for c includes "100 psol" or percent-speed-of-light, and "Mike 1.0" after Dr. Albert A. Michelson.) Velocities below c are referred to as "suboptic" or "subluminal"; those faster than light are called "FTL," "hyperoptic" or "superluminal." The speed of light itself is "optic velocity."

Now back to the fascinating consequences. According to Relativity theory, time passes more slowly at near-optic velocities than at low suboptic ones. This apparent breach of common sense is traditionally presented in the form of a paradox. Imagine twin brothers A and B. A becomes an astronaut and flies away in a relativistic starcraft capable of a peak velocity of 98%c. B stays behind on Earth. A travels 12 light-years out into space, and then 12 light-years back to Earth. Because A has been moving slower than light, B must wait a total of 28 years for his return. B is thus 28 years older than his age when the brothers parted. But when he meets A in the Debarkation Area, A has only aged 10 years. A is 18 years younger than his identical twin.

This unusual consequence of near-optic flight, often called the Twin Paradox, has been confirmed indirectly by scores of experiments over the past half-century. There is little doubt in the minds of most physicists that the Paradox is a correct prediction of the consequences of traveling close to the speed of light. The contraction of time at high velocities is known as the phenomenon of time dilation.

The frame of reference of the observer is of critical significance here. Those observers who remain at rest with respect to the universe at large (such as the twin who stays on Earth) will always observe a relativistic starcraft to travel at suboptic velocities. But to the astronauts on board the spaceship, the contraction of distance between the points of origin and destination (another peculiar consequence of Relativity theory) will make the trip seem shorter. They will, from their frame of reference, actually be moving at a faster apparent velocity than that perceived by stationary observers (say, back on Earth). In fact, when the starship reaches exactly 70.7%c as measured by stationary observers, the astronauts calculate their own effective velocity as 100%c! As acceleration continues still further, shipboard-determined speed increases to seemingly hyperoptic velocities (which Earthbound observers still see as suboptic from their frame of reference).

What does all this mean in plain English? Simply this: An astronaut, provided his starcraft has sufficient energy, can effectively travel faster than the speed of light relative to a stationary frame of reference! (See Table 17.1 for details.)

 


Table 17.1 Effective FTL Starflight Using Relativity Theory
Effective Velocity Calculated by Astronauts
Starship Velocity Perceived by Stationary Observers
Energy 
Required 
for a 100-ton Starship
Effective 
Velocity Calculated by 
Astronauts
Starship 
Velocity 
Perceived 
By Stationary Observers
Energy 
Required for a 100-ton Starship
 
 
(joules)
 
 
(joules)
1% c
1.0 % c
4.5 x 1017
10 c
99.5% c
8.1 x 1022
10% c
9.95% c
4.5 x 1019
20 c
99.88% c
1.7 x 1023
20% c
19.6 % c
1.8 x 1020
50 c
99.98% c
4.4 x 1023
50% c
44.7 % c
1.1 x 1021
100 c
99.995% c
8.9 x 1023
100% c
70.7 % c
3.7 x 1021
1,000 c
99.99995% c
9.0 x 1024
2 c
89.4 % c
1.1 x 1022
10,000 c
99.9999995% c
9.0 x 1025
5 c
98.1 % c
3.7 x 1022
100,000 c
99.999999995% c
9.0 x 1026


 

Time dilation permits very long journeys within a single human lifetime. Consider a starship that accelerates uniformly to the midpoint of the trip and then decelerates uniformly at the same rate the rest of the way to the destination -- called the Standard Flight Plan. With an acceleration of 1 gee -- appropriate for inhabitants of terrestrial worlds similar to Earth -- only a few years of ship-time are required to reach the nearest stars. (See Table 17.2.) Only 21 years are spent reaching the Galactic Core, and in 28 years of shipboard time the intrepid explorers can visit Galaxy Andromeda in person. Since Andromeda is about 1.7 million light-years distant, this works out to a mean effective velocity of 61,000 times the speed of light.

Of course, there is no time dilation on the home planet -- since it went nowhere. If our intergalactic astronauts turned around at Andromeda and immediately returned to Earth, they would have aged a total of 56 years. The Earth and all of its inhabitants, however, would have aged 3.4 million years. This is a "twin paradox" with a vengeance!

 


Table 17.2 Duration of Interstellar Travels, Using a Standard Flight Plan at One Gee Acceleration
Trip Duration
Ship Time
Trip Duration
Home Planet Time
Distance Traveled
From Home Planet
Peak Ship Velocity
Home Planet
Reference Frame**
(years)
(years)
(light-years)*
 
1
2.2
0.26
47.2%c
2
4.8
1.12
77.3%c
5
21.
10.8
98.8%c
10
200
1.63 x 102
99.9931%c
15
2300
2.15 x 103
99.999959%c
20
28,000
2.8 x 104
(1 - 2.4 x 10-9)c
25
370,000
3.7 x 105
(1 - 1.4 x 10-11)c
30
4,800,000
4.8 x 106
(1 - 8.4 x 10-14)c
35
62,000,000
6.2 x 107
(1- 4.9 x 10-16)c
40
810,000,000
8.1 x 108
(1 - 2.4 x 10-18)c
45
11,000,000,000
1.1 x 1010
(1 - 1.7 x 10-20)c
50
140,000,000,000
1.4 x 1011
(1 - 1.0 x 10-22)c
* S= (2c2/a)•(cosh(at/2c) - 1), where a is acceleration (m/sec2), t is time (sec), S is distance (m), and c is speed of light.
** V= (1 - (1 + aS/2c2)-2)c.

 

When science fiction writers and others speak of "FTL" they are usually referring to true (rather than "effective") FTL -- that is, faster-than-light travel from the point of view of both astronauts and stay-at-homers. We shall discuss the theoretical possibility of true FTL later in this chapter. But for now it is important only to realize that Relativity does permit effectively hyperoptic interstellar journeying, at least from the standpoint of an astronaut setting forth to explore the universe.

This fact is highlighted by the data shown in Table 17.3 on the following page. It is assumed that an astronaut wishes to travel a certain distance out into space, but he doesn’t want to use up more than 10 years of his life in getting there. Table 17.3 lists the starship accelerations that must be sustained throughout the entire trip in order to arrive at a destination at the specified distance within exactly one decade as measured on the astronaut’s own wristwatch. A Standard Flight Plan is assumed.

 


Table 17.3 Acceleration Required to Complete Journey in One Decade Shipboard Time, Using Standard Flight Plan
Destination
Distance
Acceleration to Reach Destination Years in 10 Shipboard Years
Destination Distance
Acceleration to Reach Destination in 10 Shipboard Years
(light-years)
 
(light-years)
 
101
0.32 gees
106
2.9 gees
102
0.88 gees
107
3.4 gees
103
1.4 gees
108
3.9 gees
104
1.9 gees
109
4.3 gees
105
2.4 gees
1010
4.8 gees


 

Note that any point in our Milky Way galaxy can be reached in ten years of shipboard time, at accelerations tolerable to human beings for long periods of time. Accelerations of 2-4 gees, perhaps sustainable by inhabitants of jovian or heavy subjovian worlds, or by bioneered former inhabitants of terrestrial worlds, would put the entire known universe within 10 years’ reach,

Naturally, the faster a starship is pushed the more energy is required. The levels of power expenditure needed to achieve the benefits of relativistic time dilation are enormous by today’s standards, even for fairly small vehicles. (See Table 17.1.) But as we shall see presently, this by no means bars interstellar or intergalactic commerce. Indeed, such commerce should be commonplace among Type II and Type III civilizations.

Let us consider three illustrative classes of starflight missions:

1. Interstellar personnel transport;
2. Intergalactic personnel transport; and
3. Intergalactic cargo transport.

Too many writers have succumbed to the Fallacy of the Big and the Costly. That is, if it’s big and it costs a lot, it must be impossible. The Fallacy lies in the simple observation that what seems big and costly to one culture may be negligible and cheap to another.

The relative costs of missions to the stars may perhaps best be appreciated by a comparison with the familiar. Humanity has launched about ten Saturn V rocket boosters to date. Each of these blustering behemoths developed 1.3 x 1011 watts of power for about 150 seconds each. This is the equivalent of harnessing the entire human energy output for exactly 4 seconds. Keep this quantity in mind as we work through the following examples: One Saturn V equals 4 seconds of humanity’s aggregate power output.

First we consider the interstellar personnel transport mission. We assume a flight distance of 100 light-years, appropriate for short hops between neighboring Type II civilizations. To make things comfortable for the pilots and passengers, we further assume a Standard Flight Plan at a constant 1 gee acceleration. Using the equations of Special Relativity, total trip time works out to a mere 9 years.

How much energy is required? If we take the mass of the vessel to equal that of the Starship Enterprise of original-series Star Trek fame (190,000 metric tons), then about 9 x 1026 joules of energy are required for the mission. A mature Type II civilization, having 1026 watts (joules/sec) at its disposal, should have no trouble with this at all. The interstellar personnel transport mission uses only nine seconds of the culture’s total power output, a feat equivalent in stature to the launching of two Saturn V rockets by modern human engineers. For a Type III civilization, this mission is inordinately trivial. In fact, roughly 44 billion such starliner missions could be dispatched if only 4 seconds of the galactic society’s aggregate energy output were utilized -- a feat comparable to the launching of a single Saturn V from Earth today.

What about our second class of starflight mission -- the intergalactic personnel transport? These are somewhat more difficult, probably well out of reach of a lone Type II civilization. Again, using a Standard Flight Plan at 1 gee acceleration to keep crew and passengers at ease, a trip of 1.7 million light-years to Galaxy Andromeda (the nearest giant spiral) would require only 28 years shipboard time. Approximately 1.5 x 1031 joules would be consumed making the journey.

Such a mission would tax the resources of Type II culture to the breaking point. More than 41 hours of the stellar society’s power output would be needed to launch a single intergalactic starliner, a feat analogous to the firing of 38,000 Saturn V’s by present-day humankind. Such an enormous sacrifice and commitment of resources would require some overwhelmingly compelling purpose to justify it.

For a mature Type III galactic civilization with 1037 watts under its control, however, the intergalactic personnel transport mission would again prove utterly trivial. Such a culture could launch more than 2.5 million such sorties to Galaxy Andromeda for a mere 4 seconds’ worth of its total power output -- again, a feat comparable to our launching a single Saturn V rocket.

Finally, we consider the case of the intergalactic cargo transport mission. Since these ships can be unmanned, far higher accelerations may be tolerable. We assume a robot-controlled, 190,000-metric-ton cargo ship, dispatched to Andromeda at an acceleration of 106 gees (probably the upper limit for normal physical materials) on a Standard Flight Plan. Fortunately, the shipboard time of flight is only 1724 seconds, a bit under half an hour, so the ship and its contents are subject to extreme forces only for a very brief period of time. A total of 1.5 x 1037 joules are required for the mission, about 1½ seconds of the aggregate power output of a galactic culture. To a Type III civilization, the launching of two such high-acceleration cargo vessels requires a resource commitment equivalent to the launching of one Saturn V by human technologists.

So we see that galactic and intergalactic commerce and tourism are very real possibilities for advanced extraterrestrial societies. The dispatch of an interstellar personnel carrier by a Type II culture, or a high-acceleration intergalactic cargo transport vehicle by a Type III culture, represents about the same allocation of energy and resources as the launching of a Saturn V rocket by human Type I civilization.

 


Last updated on 6 December 2008