Written 1990, Revised 1998
From time to time there are reports of sightings of unidentified flying objects. A flurry of news articles follows. Witnesses claim talking with visitors from outer space and being beamed into their spaceships. The government is accused of suppressing evidence. It is alleged that hidden away in secret vaults are the bodies of aliens, killed when their craft crashed. The remnants of wrecked ships are stored in well-guarded hangers. The X-files are created.
The modern age of science fiction dates from the end of World War II, when humanity had not only to cope with the economic and social problems engendered by the war but also suddenly and unexpectedly to face the perils of the nuclear era. While there had always been reports of strange lights in the skies, such sightings now took on a new significance. If humankind on earth could harness the energy of the nucleus of the atom, might not an alienkind in a distant stellar system do even better and perfect a spaceship which could traverse the vast distances between stars. Might not such an alienkind, far superior in intelligence to us mere mortals, see our unleashing of nuclear energy as a threat to the stability of the universe? Might not this alienkind decide that intervention was demanded? Such is the grist on which movie cameras grind, and a motion picture, The Day the Earth Stood Still, released in 1951, 6 years after the end of the war and many sightings, was the best of its genre.
If aliens have invaded our air-space, if they have landed and taken over the bodies of innocent victims, if they are now secretly planning the overthrow of our civilization, they are doing so only on television and in the theaters. There is no physical evidence that they have arrived.
The argument I wish to pursue here is that they have not in fact arrived, and it is extremely
unlikely that they ever will arrive. But if they do, we shall surely know it, and know it far before
they have landed.
Assuming aliens we must assume an alien home. It goes without saying, of course, that the alien home could not be on one of the other planets in our solar system. None of these could harbor even the smallest element of life, much less an intelligent species. But the universe is populated with thousands of billions of galaxies. A galaxy consists of hundreds of billions of stars. Surely among all these stars, there are billions of planetary systems containing worlds upon which life could have evolved. The vastness of the numbers, the laws of nature and of probability demand it. But wait. Is it really all just a questions of numbers?
About half the stars are binaries or multiple systems. If there are two or more stars orbiting about
one another, there is little possibility that stable planetary orbits could exist near enough to the
suns to provide the warmth needed to generate life. The varying tugs of the two (or more) suns
on an earth-sized planet, assuming one had formed, would eventually plunge it into one sun or the
other, or fling it far out into space. It might be that a planet could exist in a stable orbit far from a
pair of close stars, which it would see as one, but its distance would be so great that its surface
temperature would be near absolute zero. Let us therefore drop all binary and multiple stellar
systems from consideration. There are still many stars left.
But stars are not alike. The bright stars which dominate our night skies are not at all like the sun. Their most significant feature for this discussion is that they are generally large and very hot, with surface temperatures of 8000, 9000, 10,000 kelvins, as compared with the sun's 5700 kelvins, and with radii considerably larger than that of the sun. These numbers in themselves do not preclude the possibility of life-sustaining planets orbiting large, hot stars. Rather it is the life-expectancy of the star itself. The larger and hotter the star, the more rapidly its nuclear fires burn at its core and the more quickly those fires consume the available fuel.
A star like the sun is stable for about 9 billion years. At the conclusion of this long period of quiescence, the sun is expected to begin expanding, eventually becoming a red giant. It may go through periods of pulsation, as its energy oscillates between nuclear burning at its core and gravitational collapse. Whatever the sun does, the earth will not be a pleasant place on which to live. Life will be quickly extinguished. A star 1.5 times as massive as the sun enjoys a period of stability of only 1.6 billion years before expanding and pulsing. Long enough? The evidence of the rocks is that the earth solidified from the original gas and dust cloud now seen as our solar system 4.5 billion years ago. The human species has been around only 1 or 2 million years. And our species has been technologically competent to begin even seriously contemplating interplanetary travel only in the last few decades. Let us therefore require that an upper limit on the mass of the proposed home star of an alien species be not much greater than the mass of the sun, if only to provide a duration of stability long enough to allow for the evolution of a technically capable species.
But what of stars which are less massive than the sun. The nuclear fires in these smaller stars burn slowly, and their periods of stability can be longer than the present age of the universe. There are many such stars about. Of the 55 stars nearest the solar system--out to a distance of 16.6 light years--42 are considerably smaller and cooler than the sun. Would these not be suitable home stars for an alien culture? Unlikely. The reason is based not upon the amount of warmth such stars might provide but upon the kind of light they radiate.
The sun, whose surface temperature is 5700 kelvins, radiates photons of all energies, from the lowly radio-wave photons to the dangerous x-ray photons. The very great maximum number of photons emitted, however, lies in the visible spectrum, in the blue-green region to be precise--not surprising, since one assumes vision evolved to take advantage of the greatest number of photons. But there is more significance to this maximum than evolutionary opportunism. Rather, its importance is in the energy of the visible photons, an energy which spans the narrow range of 2.9 to 4.7x10-19 joules, or in units which may be more meaningful, 1.8 to 2.9 electron volts. These are the energies of ordinary chemical interactions. We see light of this photonic energy perhaps not so much because that light from the sun happens to be most intense but because that light happens to be of the energy needed to excite the kinds of chemical reactions in our eyes which constitute the sense of sight.
Would photosynthesis have evolved on a planet bathed in the infrared light of a small star? From such a star, the number of photons whose energies lie in the range of chemical reactions would be meager indeed, and photosynthesis, which requires energetic photons--but not too energetic-- would be hard pressed to evolve. Let us therefore discard the small star along with the large star as possible central stars of a thriving alien civilization. We look then only for stars like the sun, the so-called G-stars in the spectral classification of stars.
The most promising nearby star is in the constellation of Cetus, the whale, which is seen lying low in the our southern skies at midnight in mid-autumn. This star, whose catalog name is Tau-Ceti, is, on the basis of spectroscopic measures, very much like the sun, and is but a mere 11.8 light years distant. The nearest star, Alpha Centauri, at 4.3 light years, is a G-star a little larger than the sun. It loses out as a candidate because it is accompanied by a white dwarf whose surface, at a temperature of 10,000 K, radiates enough lethal x-rays to wipe out any budding life on otherwise acceptable planets. There is also the problem of the stability of orbits.
Thus the number of stars to choose from dwindles quickly. Even so, when there are billions, what
difference does a factor of 1000 or so make? We are still left with millions. Let us admit then,
that there are suitable stars.
There is only one known planetary system in the universe, and that is the one we live in. Every other system is hypothesized. Our ignorance of others is blamed on our inability to detect them, not on their non-existence. In our system of nine planets, only one fosters life. The others not only would not succor it should life be transported to them, they would be fatally hostile. But this planet on which life thrives is indeed remarkable in possessing, out of all possible attributes, precisely those which engender and nourish life.
First, as we noted above, it has a suitable sun. Secondly, it moves in a nearly circular orbit about that sun at a distance which provides just the right average surface temperature to encourage the functioning of living processes, temperatures which lie for the most part between 0 and 100 F. Below 0, salt water freezes. The chemistry of living processes grinds to a halt. Above 100, the chemical stability of living processes cannot easily be maintained. The range on the scale of absolute temperatures at which life can flourish is narrow indeed, from about 255 K to 315 K--not much when one considers how cold and how hot are the other planets in the solar system.
Since this is a paper submitted under the aegis of physics, it is worthwhile illustrating the use to which the methods of physics can be put in anticipating the average surface temperature of a planet as a function of its distance from its primary and the surface temperature of the primary. And because of the severe font limitations imposed by hypertext, I am writing out Greek and mathematical symbols.
We start with Stefan's law: The intensity I of radiation emitted at the surface of a black body whose surface temperature is T is given by
|(1)||I = (sigma)T4|
where sigma = 5.670x10-8 W/m2K4. (Though it shines brightly, we of course regard the sun as a black body because any radiation falling on it is absorbed.) Next let us surround the sun by a black spherical shell whose radius is r. Since the intensity of radiation is inversely proportional to the square of the distance from a point source, and since we may regard the intensity of radiation at the surface of the sun as arising from a point source at its center, we write that
|(2)||Isun/Ishell = r2/R2.|
Here Isun is the intensity of radiation at the surface of the sun, Ishell is the intensity of the sun's radiation at the shell, and R is the radius of the sun.
The black shell absorbs radiant energy from the sun and re-emits it. In a state of equilibrium, the temperature of the shell is at that temperature at which the intensity of radiation radiated by the shell outward equals that received by the shell from the sun. Using Stefan's law, we thus find that
|(3)||Tsun4/Tshell4 = r2/R2.|
|(4)||Tshell = Tsunsqrt(R/r).|
Letting r be the distance of the earth from the sun, namely 1.496x1011 m, and using Rsun = 6.961x 108 m and Tsun = 5700 K, we find that Tshell = 389 K, which is 16 K above the boiling point of water. Lest we wonder about this result, we remind ourselves that the earth is happily shrouded in an atmosphere of clouds and water vapor which shield us from an unmitigated solar radiation. The surface of the moon is not so protected, and temperatures there can rise to the maximum provided by law.
An equally important equation concerns the average temperature of the earth's surface attained under the light from the sun. We now must account for the radiation of the earth on its dark side. To do so, we note first that the earth's surface presents a circular disk of area pi(Rearth2) to the sun's rays. On the other hand, the earth radiates over its entire spherical surface, whose area is given by 4pi(Rearth2). At equilibrium, the power radiated by the earth's entire surface, namely 4pi(Rearth2)Iearth, equals the power received by the sun, namely pi(Rearth2)Iearth,. Using Stefan's law to replace intensities of radiation with absolute temperatures, we have that
|(5)||Tearth = Tshell/sqrt(2)|
a result which yields a value for Tearth of 275 K, or 36 F, a temperature which is surely not far from the average temperature of the globe.
Moving the earth closer to the sun clearly results in a rise in average temperature. If r is 0.723 of the present orbital radius, which is the radius of the orbit of Venus, the average temperature is 122F. On the other hand if the earth is moved out to the orbit of Mars, whose orbital radius is about 1.524 that of the earth's, the average temperature is -58F.
Differentiating Eq. (1) provides a means of finding the effect of changing by a small amount the radius of the earth's orbit on the average temperature of the earth's surface. We thus have
|(6)||dTearth/Tearth = dTshell /Tshell = -dr/2r.|
A variation in the earth's average temperature of one Kelvin (Celsius) degree involves changing the radius of the earth's orbit by 0.73 percent. (As the earth swings around the sun in an elliptical orbit, its distance from the sun varies by 1.7 percent from the average distance.) A ten-degree change in the Celsius temperature would occur if the radius of the earth's orbit changed by 7.3 percent. It is clear that the surface temperature of the earth is highly sensitive to the distance of the earth from the sun.
These calculations suggest that it might not be so easy after all to find a planet at just the right distance from its primary to produce an average surface temperature amenable to the growth of living forms. Is the alien planet at such a distance from its primary to nourish life?
There are other problems. Consider the importance of water, not so much as an essential compound in the structure of protoplasm, but as a regulator of planetary temperatures. Without our huge oceans, which store vast amounts of thermal energy during the day and which release that energy at night, the temperature of the earth might well fluctuate between intolerable extremes. At noon the surface temperatures would exceed those of our present-day deserts. At night the temperatures would drop well below freezing. Does the alien planet have large oceans?
Consider the moon, a satellite large enough in comparison to the earth that the earth-moon system
may be properly regarded as a double planet. Without the moon, there would be no tides. And
without the ebb and flow of the tides, which might strand struggling water-born creatures on
rocky beaches, would life have ever left the oceans? Does the alien planet have a large moon?
Consider the radius and mass of the earth, two properties which determine the acceleration of
gravity at its surface. Were the gravitational acceleration too great, could living structures
withstand the force of their weights. Were the gravitational acceleration too small, could the
planet retain an atmosphere? Is the acceleration of gravity at the surface of the alien planet in the
neighborhood of 10 m/s2?
Finding the range of suitable planets quickly narrowing, the defender of alienkind might well protest that alien life evolved on the alien planet in accordance with the physical conditions present there. What may be intolerable for earth-bound life could be a Garden of Eden for alien forms. But how much leeway does life of any form have?
First we must accept that the molecular basis of life is necessarily complex. Otherwise life would be no different from say a snowflake, which while complex, is not complex enough. Next we ask what atoms might fit the need. There is but one. Only carbon possesses the four bonds of just the right binding energy to make long chains and rings without being overly disrupted by the presence of other atoms. For example, silicon, a sister to carbon in the periodic arrangement of the elements, also has four chemical bonds, but it cannot form long chains with itself because its binding energies are such as to cause it instead to unite strongly with other atoms. Most of the silicon on the earth is tightly bound to oxygen, the compound we see as sand on our beaches. Carbon, on the other hand, may be found both as pure carbon, as carbon dioxide and as the backbone of complex organic molecules. The differences in the binding energies of organic compounds are not so great that wood cannot burn to form carbon dioxide or that photosynthesis cannot turn carbon dioxide eventually into wood. The small differences in the binding energies of carbon with itself and with other elements are essential to the processes of life, which would otherwise not occur were these compounds of carbon extremely stable.
We are thus forced to the conclusion that if aliens live, they are built of the same kind of weakly
interacting organic molecules of which earth-life is made. And as such, they must come from a
planet very much like the earth in a circular orbit about a star very much like the sun.
Not long ago the radio telescope at Arecibo, Porto Rico, turned itself toward Tau Ceti and listened. Not a whisper of an alien "I Love Lucy." If a technologically competent living form lives on a planet about that star, it is not using electromagnetic radiation with which to communicate.
Let us forego Tau Ceti and look beyond for sun-like stars. Unfortunately, my catalogue of stars lists only those whose brightnesses are about that of Tau Ceti or greater. Tau Ceti, we recall, is at a distance of 11.8 light years. A sun-like star beyond 20 light years would be too dim to make the list. We shall have to estimate. In a sphere of 20 light years centered at the sun, there are three such stars: the sun itself, Alpha Centauri, and Tau Ceti. Assuming this is the density of sun-like stars throughout the immediate solar neighborhood, we see that doubling the distance to 40 light years octuples the number of candidates to 24, doubling again to 80 light years yields 192. Of these 192 might not one star other than the sun possess an earth-like satellite at an earth-like distance? For the sake of argument, let us suppose that such exists.
Which brings us to the problem of space travel. One of the characteristics of flying saucers reported again and again by observers is their unusual motion. Flying saucers seem to defy the laws of physics, shooting this way and that without the least regard for gravitation or inertia. Proponents of alien visitation argue that these creatures have learned how to nullify both gravitation and Newton's second law. Is such an argument reasonable? I think not. Let me explain.
Mankind has delved deeply into the mysteries of the universe, making marvelous discoveries which have given us command over much of nature herself. But have we ever truly discovered anything which was not already manifest in nature? We generate and harness electromagnetic forces. But so has nature, not only in the ordinary processes of atomic interactions but in the more dramatic lightning bolts of a summer storm. We explode hydrogen bombs. So also does the sun. Is it reasonable to suppose that alien creatures have truly suspended gravity and the laws of inertia when nothing, absolutely nothing, indicates that such is possible? Indeed, the contrary holds, namely that our understanding of nature indicates that such suspensions are impossible.
Let us therefore require that aliens adhere to confirmed physical laws in flitting from one stellar system to another.
If the aliens are to travel, they need roads, and since a universal department of transportation has not seen fit to build roads connecting stars, the aliens must carry their roads with them. They would do this in a rocket ship. Instead of using wheels to push back against an asphalt surface, thrusting their vehicle forward, they would eject massive particles from the rear of the ship so as to propel the ship forward. Furthermore they cannot dawdle. When light years are to be spanned, one should move at the speed of light. Once again it is interesting from the view-point of physics to note a few equations and make a few calculations. Because of the high speeds demanded, we are thrust into the realm of relativity.
A ship that is accelerated at a constant rate a relative to its momentary inertial rest frame attains a proper speed u which grows very nearly exponentially with the passage of time t kept on the ship. The relationship can be shown to be given by
|(7)||u = csinh(at/c)|
Here u is the ratio of the infinitesimal distance ds traveled relative to the initial inertial frame of the alien planet to the infinitesimal lapse of time dt, and c is the speed of light. The distance s traveled by the ship also grows approximately exponentially with ship time . The equation of motion is
|(8)||s = (c2/a)(cosh(at/c)-1).|
These speeds and displacements do not come without cost. The mass m of material which must be ejected from the ship during the lapse of ship time t is given by
|(9)||m = M0(1-exp(-at/V))|
where V is the velocity of the ejected material relative to the ship, and M0 is the initial mass of the ship and its fuel. Clearly the greater the speed V the smaller the mass of fuel needed for any given product of acceleration a and lapse of ship time t. Thus the most efficient rocket material are photons themselves, and so we repace V with c in the above equation to obtain
|(10)||m = M0(1-exp(-at/c))|
The engines of an ideal alien ship would consist of a chamber into which are fed quantities of matter and antimatter, the antimatter having been generated in high energy machines on the alien planet. Since antiprotons annihilate only protons, antineutrons only neutrons, and so forth, we shall give the aliens the technical ability to manufacture storage containers for antimatter which are impervious to annihilation. United in the annihilation chamber of the ship, matter and antimatter vanish in a deluge of gamma-ray photons which are directed by mirrors into a sharp coherent beam out the rear of the ship. The interaction between mirrors and photons pushes the ship forward, and the rate of annihilation is adjusted so as to produce the constant acceleration a.
The rate at which the energy of matter must be converted into the energy of photons to produce the constant acceleration a is given by
|(11)||dE/dt = acM|
where M is the mass of matter remaining.
We next apply these equations and ideas to an example. We assume a distance between the alien system and the earth of 100 light years, a not unreasonable separation considering the small likelihood of finding a suitable planet in that range. We assume also an acceleration of 10 m/s2 and require that this acceleration hold for 2 years at the beginning of the journey and 2 years at the end, between which times the ship drifts at the constant speed attained at the end of its initial acceleration. Substituting these numbers into the above equations, we find that the final proper speed of the ship at the end of the initial acceleration is 4.04 lt-yr/yr and that the distance it has traveled is 3.01 lt-yr. The ship also travels 3.01 lt-yr at the end of its journey during its deceleration. Hence it travels 93.08 lt-yr at the proper speed of 4.04 lt-yr/yr, which requires a travel time of 23.28 years. The total travel time on the ship is thus 27.28 years. Of course, on the earth, the corresponding lapse of time is much greater, exceeding 100 years, since, from the point of view of the earth, the speed of the ship cannot exceed the speed of light. But lapses of time on the earth are of no concern to the aliens. We assume a travel time of about 27 years to be well within the endurance of these creatures.
We next consider the initial ratio of fuel to payload. Using an accelerating duration of four years, we find that 98.51% of the initial mass of the ship must consist of equal parts of matter and antimatter.
Finally we inquire into the rate of energy transformation from matter to photons as the ship approaches the solar system. Using the above formula we see that dE/dt = 3 billion watts for each kilogram of ship remaining to be decelerated. If the payload is 100,000 kg, the power expended toward the end of the journey, as the alien ship enters the solar system, is 100 thousand billion watts. Could such an arrival, accompanied, by a continuous blast of 100 thousand billion watts of gamma-ray photons directed toward the sun, go unnoticed by astronomers on the earth? I think it is highly unlikely.
It is worthwhile in conclusion to wonder about the behavior of such aliens, assuming they have journeyed through the solar system undetected. If they are so advanced technologically as to have traversed the many light years separating our systems, would not the discovery of this technology imply a certain curiosity and aggressiveness in their psychological makeup? Could we really expect them to be secretive about their arrival and avoid contact with the very civilization we assume they came to investigate? It is rather like expecting Columbus, having landed on that Caribbean shore, to hide from the natives.
I think then it is safe to believe that they have not arrived and that if and when they do, we shall know about it long before they set foot on our world. But why wait for them? The theory, if not the technology, is there, telling us that it is not out of the realm of possibility to travel among the stars. Let us begin.