Some critics of the Search for Extra-Terrestrial Intelligence (SETI)—and there are a few—like to bolster their arguments with what they call the Fermi Paradox [1-5]. Legend has it that one day at Los Alamos, shortly after the Alamogordo test, Enrico Fermi abruptly broke the mealtime silence with the question: Where are they? Meaning, of course, that since advanced extraterrestrials presumably have long had nuclear power, why haven't we been visited? Today this so-called paradox—really a syllogism in fuzzy probabilities—is stated this way:

(a) Interstellar travel is easy, at least for advanced extraterrestrial intelligence (ETI).

(b) If the Galaxy is rife with ETI, at least one civilization would have colonized it by now.

(c) We see no evidence of this.

Therefore, say these impeccable logicians, ETI must be rare or, even better, perhaps we are the only intelligent life after all. There are of course many other explanations for our absence of evidence; it is even possible that (a) is false. But none of these appeal to Hart, Tipler, et al. whose main concern seems to be to preserve tlie position of homo sapiens at the very top of the evolutionary ladder—or perhaps as the noblest work of God. It feels so good to be unique even if the cost is shoddy logic!

Years of science fiction have produced a mindset that it is human destiny to expand from Earth, to the Moon, to Mars, to the stars. (Actually Venus used to be in this list until we found it to be too hot.) Very few of us have stopped to analyze what that last step to the stars would really mean in tlie way of resources. And so tlie manned space program continues to receive tlie lion's share of NASA funding while the unmanned craft continue to produce the exciting results. To those of us who have belatedly faced reality, the space-faring myth has begun to fade.

Another misconception that helps sustain the dream of interstellar travel—and it is an exciting dream—is that present day rockets are terribly inefficient. This allows us to believe that some-day, when our technology is up to the task, the cost of interstellar travel will drop dramatically. But even the present space shuttle is about 20% efficient. So only a five-fold improvement would result even from perfect rockets.

The factor most ignored in discussing interstellar flight is the kinetic energy that must be invested in the ship to make its tons of matter move at a substantial fraction of the speed of light. This turns out to be the dominant energy requirement, and is thus a useful lower bound on the total. If, in assessing the cost of interstellar travel, we find this lower bound too big, we can forget about all the other costs, for they will only make matters worse. This saves an enormous amount of detailed analysis. It also keeps a lot of sand out of our eyes.

For simplicity we will assume Newtonian mechanics in our analysis, but we will include the exact relativistic results, which are a few percent worse. We take the kinetic energy, W0, of a mass, m, moving at a velocity v (in the inertial launch frame) to be

          W0 = 1/2 mv2  .          (1)

As an example, a 2 ton (2000 kg) car moving at 60 miles per hour (26.8 meters/sec) has a kinetic energy of about 720,000 joules or 0.2 kilowatt hour. We usually ignore this few cents worth of energy but it accounts for the increased fuel consumption of stop-and-go driving. It also accounts for the wreckage and deaths that occur when cars crash.

A trip to Alpha-Centauri

The sun and its retinue of planets drift as a group through the vast gulfs of space that separate the stars. Our nearest luminous neighbor is Alpha-Centauri, which means the brightest star in the southern constellation Centaurus, the centaur. Actually, Alpha-Centauri is not a single star, it is a multiple system consisting of a visual binary, Alpha-Centauri A and B, and a far flung third component, Proxima, so called because in this epoch it is slightly closer to us than its companions: 4.28 as against 4.38 light years. Proxima Centauri is an M star, probably not a good sun to nurture life on its planets, but Alpha-Centauri A is a G2 star very like our sun. It is separated from Alpha-Centauri B far enough to have stable planetary orbits at about our distance from the sun. Some feel that these planets might harbor life and that makes Alpha-Centauri-Centauri an interesting star system for us. So let us look at the logistics of the shortest interstellar trip of interest: one to the star next door.

If we cruise at 0.2 the speed of light, the trip to our destination will take about 22 years and the round trip, 44 years. Allowing a couple of years or so to explore the planetary system, our crew of 12 (6 couples?), who started out as 20 year olds, would return at age 65 to their heros' welcomes and ample pensions. Two tenths the speed of light is 37,256 miles per second or 5360 times the escape velocity from Earth (6.95 miles/second). This means the kinetic energy of the ship at cruising speed would serve to launch the ship from Earth's surface into deep space (5360)2 or over 28 million times. We have yet to make a single-stage rocket that can do this job once.

Since starship Centaurus hasn't been designed yet) the payload mass is a little difficult to estimate. In our calculations, we will use 4000 tons—about the launch weight of the Saturn V rocket—on the unassailable grounds that it is a nice round number. If you feel it is too small you can easily scale up our results. Compared with our auto going at 1 mile per minute, we now have 2000 times the mass moving at 2.235 million miles per minute. Thus our few cents of energy has now become 0.2 x 2000 x (2.235 x 106)2 = 2 x 1015 kilowatt hours. World energy use in 1986 was 321 quad or almost 1014 kilowatt hours. (This is all energy usage, not just electric.) So the kinetic energy of the payload is about 20 years of world energy consumption.

But this is only part of the story. To explore the worlds of
a-Centauri A, if any, we must stop at the destination. If there are no planets, we might like to return home. Since stopping is the same for our ship as another acceleration to twice the cruise speed, we must be prepared to supply the energy.


for a one-way trip and


for a round trip. This last is over three centuries of present world energy usage. It is important to realize that W2 and W4 are never the actual kinetic energies of the ship. Rather, they are the kinetic energies it would have had after two and four firings had they all be additive. Nevertheless, they remain valid lower bounds for the one-way and round-trip energies, respectively. W is proportional, not to the number of firings) but to the square of that number, because the ship at the outset is laden with the fuel and propellant needed for all future firings. We cannot count on service stations en route.

We can, of course, reduce W2 and W4 by reducing the cruise speed. The trouble with this is that the trip takes too long already. If we reduce W2 and W4 to 1% of the values found, the one-way trip would take two centuries, the round-trip four. Now we will need a larger ship to accommodate nurseries and schools as well as more people; whether the last generation would complete the mission started by their great-grandparents or end up in the plight described in Heinlein's Orphans of the Sky [6] is an open question. One thing is sure, the sponsoring generation that paid for the trip will never live to hear the results. This is likely to make funding difficult.

More ambitious journeys

A relativistic analysis [7] shows that W2 and W4 should be multiplied by gamma2 and gamma4 respectively.*

* In the symbols of special relativity, "c" is the speed of light,
At beta = 0.2, gamma2 = 1.041 and gamma4 = 1.085 so our Newtonian results up to this point are accurate to a few percent. For longer journeys at greater beta , a relativistic analysis should be used, so here we will merely present the results. It is convenient to express W2 and W4 not in joules but in units of the annihilation energy of the payload—that is, we divide W2 and W4 by mc2. We then have


Because of time dilation, the ship time per leg is now


rather that simply r/B, where r is the stellar distance in light years. This means that W2 and W4 may be written:


Figure 1, (next page) taken from reference [7] shows a plot of W2 (marked one-way trip) and W4 (marked single round-trip). Also shown is the energy needed to explore from Earth all good suns out to the radius given by the abscissa.

Energy-Range Graph

Figure 1: Minimum energy needed to complete the indicated trips to a destination at the distance shown on the abscissa. Ship time is twenty years per one-way trip (forty years per round-trip). For twice the time, double abscissa distances. For a four thousand ton ship, energy of one payload mass is a millennium of world energy consumption.

Present annual world energy consumption is about equal to the annihilation energy of 4 tons of matter. For our 4000 ton ship, the ordinates of Figure I could equally well be marked "millennia of world energy." So all it would take to colonize the solar neighborhood out to a radius of only 80 light years is a million millennia—one billion years—of Earths energy usage. This might tax the prowess of even the most advanced ETI, and casts serious doubt on the truth of both propositions (a) and (b). A better strategy would distribute this task over the already colonized worlds. This replaces the raw energy usage with the task of building the needed infra-structure on many worlds.

If interstellar travel is as time- or energy- demanding as the above figures indicate, it is far from obvious what the motive for colonization might be. In the past, on Earth, it has largely been to exploit foreign resources and to expand the domestic territory. Neither of these is valid in the interstellar case. The shipping costs and time are too great to allow a profit in commerce or to permit mass emigration from Earth. Further, we seem to have lost our own lust for domination as the importance of the brotherhood of man has become clearer.

On the other hand, if their desire is not to colonize, but to pool our knowledge, wisdom, and experience we should not expect visitations. Above all, I would not expect a wise race, at great expense, to set loose an army of self-replicating robots. The specter of our Galaxy overrun by robots devastating world after world either by design or because of a software bug, is a nightmare I'd rather not consider likely, despite Tipler.

Antimatter drives and other nightmares

There is nothing new in what we've discussed. Advocates of interstellar flight have devoted many years trying to find answers to these very problems [8]. Confining our attention to solutions that do not violate known physical laws we find a number of hair raising, if not hare-brained ideas. Clearly a powerful new energy source could solve a lot of problems and so we find early on the list the use of matter-antimatter annihilation to drive the propellant. The main problem here is not that we don't known how to contain antimatter, which we don't; its that we don't know how to obtain it—in quantity. The known methods of producing anti-protons require, for their formation, millions of times the energy they will release when they contact protons. Antimatter is not a source of energy for us, it's a method of storing energy, compact but inefficient. No matter where we get the energy originally, we don't want to handle millions of times our already huge final amount.

Further, the problems associated with nuclear power, which many people fear, are present a fortiori in antimatter, which explodes violently on contact with any normal matter. The proverbial powder keg is too weak a simile to use in describing a containment system for antimatter that is potentially unstable. I would not fly to the next airport with one, let alone to the stars.

Light sails and laser driven ships all suffer from unrealistic engineering problems. There simply isn't the rigidity necessary in any possible chemical bond to preserve the shape of a sail miles in diameter and only microns thick against meteoroidal impact, especially if it needs to meet surface tolerances of a fraction of a wavelength, as is required for Robert Forward's ingenious drives [9]. Matter simply isn't stiff enough to produce the mirrors he needs.

Speaking of meteoroidal impact, we have not mentioned one of the real delights of interstellar travel. A one millimeter cube of interstellar dust weighs about three milligrams. When it impacts the hull at two tenths the speed of light, the energy released is more than that of a ton of TNT. Months of boredom are apt to be punctuated with days of frantic activity to restore the integrity of the hull and to rescue the ships precious oxygen.

The essential point we want to make is that interstellar travel, far from being easy, presents problems for which we do not have valid solutions. We had such solutions for the Apollo mission. But this is very different. It is therefore misleading to give the impression that such travel is in our foreseeable future. If that word means anything it means we can foresee a solution, and we can't.

Maybe SETI is the way

No one can deny the excitement of visiting another world. It would almost compensate for a lifetime of travel getting there. But everything we could learn from a visit, we could learn by communication. It would be a pity if, frustrated by the price of travel, we elected to become a society that never made contact, that never gave SETI a fair chance.

The energy, W4 = 32 x 1015 KWH, needed for a round-trip to a-Centauri, would keep a gigawatt beacon shining for a million years, even at 30% efficiency. An array of 100 antennas—already within our capability-could detect an omnidirectional gigawatt beacon within 100 light years. If we are willing to grant the ETI prowess far beyond our own in interstellar travel, why question their ability to do what we can already do? And why not credit them with the good sense to realize that between travelling and signalling the latter is vastly cheaper?

In our eagerness to discover other life it would seem a poor strategy to devote billions to manned interstellar flight before we have thoroughly tested SETI. We have so far spent between 5 and 10 cents per taxpayer per year on SETI. To do an all out effort would take 5 to 10 dollars—still only 10 % of the NASA budget. A longer observation time should be planned, to allow repeated searches as the full system capability is built up. During this period, until a signal unmistakably from another world is detected, the extended SETI system of large arrays around the world would prove its worth for radio astronomy alone. And, when the call is finally heard across the light years, we can rejoice that we have made contact in the sensible, inexpensive way, and that they have anticipated us.

How wonderful to find, at long last, that the same astonishing sequence that has converted the ravening chaos of the early universe into delicate structures like the neural nets that allow us to contemplate this very pageant, how wonderful to find that it has occurred elsewhere. Surely the joining through common technology of these two independent but sentient life forms would be evolution's finest hour.


(1) "An Explanation for the Absence of Extraterrestrials on Earth," Michael H. Hart, Q. Jl. R. Astr. Soc. 16, 128 (1975).

(2) "Extraterrestrial Intelligent Beings do not Exist," Frank J. Tipler, Physics Today, April 1981.

(3) "Extraterrestrials: Where are They?," M.H. Hart and B. Zuckerman, eds. Pergamon Press, New York (1982).

(4) "The Most Advanced Civilization in the Galaxy is Ours," F. J. Tipler, Mercury, Jan.-Feb. 1982.

(5) "We are Alone in the Galaxy," F.J. Tipler, New Scientist, Oct. 7, 1982.

(6) "Orphans of the Sky," R. Heinlein, Putnam Press, New York (1963).

(7) "A Review of Interstellar Rocketry Fundamentals," B.M. Oliver, J.B.I.S. 43, pp. 259- 264 (1990).

(8) "Interstellar Travel: A Review for Astronomers," I.A. Crawford, Q. Jl. R. Astr., Soc. 31, pp. 377-400 (1990).

(9) "Roundtrip Interstellar Travel Using Laser- pushed Lightsails," R.L. Forward, copyright 1982 Hughes Aircraft Company. Presented at AIAA Annual Meeting, Baltimore, MD (May 1982).

Who was Barney Oliver?

Here are the pertinent paragraphs from the 1995 memorial-tribute booklet.

Barney received a host of awards during his life, foremost of which was the National Medal of Science, which he received at the White House in 1986. He served as vice president (1962) and president (1965) of the Institute of Electrical and Electronic Engineers (IEEE), after being made a Fellow of its predecessor, the Institute of Radio Engineers, in 1954 and director-at-large in 1958.

In 1966 he was appointed to the President's Commission on the Patent System. In 1990 he received both NASA's Medal for Exceptional Engineering and the Pioneer Award of the International Foundation for Telemetering in recognition of a lifetime of service to the telecommunications profession. Other significant honors include the Caltech Distinguished Alumnus Award for 1972; IEEE's Lamme Medal for meritorious achievement in the development of electronic instrumentation and measuring devices, 1977; the Halley Lectureship on Astronomy and Terrestrial Magnetism of Oxford University, 1984; and the Harvey Mudd College Wright Prize for Multidisciplinary Scientific or Engineering Accomplishments, 1984. He was an Adjunct Professor of Astronomy at the University of California, Berkeley, and served on the Boards of Directors of the Exploratorium in San Fransisco, Geostar Corporation, and Associated Universities, Inc. He was a founder of the Biosys Corporation, which seeks environmentally sound means to eliminate agricultural pests.

Barney was awarded some 60 patents, with some pending, and he authored some 71 publications in more than seven scientific and technical fields. In 1991, Hewlett-Packard Laboratories established the "Bernard M. Oliver Symposium on the Future," an annual distinguished lecture series in his honor. He received the NASA Group Achievement Award for the NASA SETI project in 1993. Barney also generously donated his time in the service of education and the community. He served on the Palo Alto Unified School District Board from 1961 to 1971, and was a member of the Engineering Advisory Councils at both Stanford and the University of California, Berkeley. He was appointed for ten years as a consultant on the engineering and safety of the new San Fransisco/Oakland Bay Area Rapid Transit (BART) System. He served as a consultant to the Army Scientific Advisory Panel, and a member of the Congressional Review Committee for the National Bureau of Standards. Barney was a member of the Dean's Advisory Council for Natural Sciences at the University of California, Santa Cruz.

As chance would have it, in 1953 at the Bell Telephone Laboratory, I made the acquaintance of someone called "Barney Oliver" when I received calls for him on my laboratory telephone. Barney had occupied this laboratory. When I renewed my acquaintance by moving myself to Hewlett-Packard in 1962, I met one hard-nosed, overwhelmingly competent engineer and scientist. It was worth one's self-respect to engage him in any debate. One simply did not risk that. I would not dream of challenging his analysis in this paper for fear he might come back.

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