The Indirect Fermi Paradox
In June, two years ago, an investigation promoted by Harry Reed, the former speaker of the House, released a report of what the government knows about UFO’s (UAPs?). Recent documentaries like Phenomenon and Out of the Blue have highlighted several former directors of the CIA, including John Brennan and James Woolsey, who hinted that the government has convincing evidence of UFOs. Recently, John Ratcliffe, ex-intelligence director has hinted that convincing undisclosed evidence of UFOs exists. However, since 1950 a more substantive debate about intelligent extra-terrestrial life has been taking place among scientists who believe better evidence of intelligent extra-terrestrial life could be established by receiving radio signals from extra-terrestrial beings. The assumption is that in the hundred billion stars of our Milky Way galaxy a substantial number should have planets, and of those a significant number of planets could occupy orbits in the the so-called habitable zone where conditions allow liquid water to exist, an assumed necessity for life. During the last decade we have confirmed the existence of over 4000 exoplanets. In fact, based on Kepler space mission data, some estimates put the number of earth-like planets at 40 billion in our galaxy alone, which means as many as 40% of the stars in our galaxy by nominal estimates may have earth-like planets. We have good reason to believe that chemistry, and in particular bio-chemistry, works the same way throughout the universe implying that most of those planets develop life and at least some should develop intelligent life at a level of sending and receiving radio messages.
In 1961, Frank Drake, an astronomer, came up with the Drake equation, a quantitative way of estimating the number of civilizations reaching the technological benchmark of radio. Drake’s estimates, and the estimates of other scientists using this methodology, have come up with numbers ranging from 1000 to 100,000,000 for the number of radio competent civilizations in the Milky Way, depending on the assumption of factors (guesses) put into the Drake equation. Note that the high estimate is about 0.25% of the current high estimate of earth-like planets in our galaxy. Earlier, a conversation among Enrico Fermi, Edward Teller, and others asked the question, “where is everybody?” Given estimates using the Drake equation, and the discovery of exoplanets made this past decade, the “where are they” sentiment has haunted scientists and others: there should be all these civilizations, but our radio telescopes are quiet (SETI). This is the basis of the Fermi Paradox — something doesn’t compute, or does it? Could we really be the only radio-competent life in the galaxy? This version of the Fermi Paradox is the so-called indirect Fermi Paradox that confirms the existence of intelligent life by other than direct contact, which was Fermi’s original thought. This version of the paradox was further explored by Frank Tipler, a particle physicist, in an article in Physics Today in 1981. In his article Extraterrestrial intelligent beings do not exist, Tipler posits that if even one advanced civilization existed in the galaxy capable of launching von Neumann probes with modest rocket technology, they could expand throughout the galaxy in about 300 million years. This is the direct Fermi Paradox that is well explored in the medium article Fermi and the Hart-Tipler Conjecture and in a video by Cool Labs . In this article we explore the indirect Fermi Paradox.
In 1977, at Ohio State University’s big-ear radio telescope, Jerry R. Ehman, an astronomer examining the output of the automated telescope discovered a signal 30 times background at a significant frequency for ET searches and circled it in red with the annotation WoW! The signal had some very distinctive features. It lasted for 72 seconds and was very strong, 30 times background — something seldom if ever seen in an astronomical source. It was constant over the 72sec it took the telescope to track it across the sky due to the rotation of the Earth (the telescope was fixed) making a perfect Gaussian line-shape. It was at around 1.42 Ghz in frequency, which is the hyper-fine transition of excited hydrogen, a frequency so anticipated for ET signals that it is restricted by world-wide agreement (so it is quiet — no one transmits at the hydrogen frequency). And the signal was extremely narrow band, only 10kHz wide, which is very unusual. By the line-shape, whatever it was was stationary in the sky in the direction of the constellation Sagittarius. In the following 40 years it has never appeared again. It was not there the next day, meaning that it lasted for anywhere from 72sec to 24hrs — nobody knows.
This leads me to the point of this article. How many ET signals should we expect to find in any period of time? This assumes we’re looking all the time and that the signal is where we expect to find it (at the hydrogen frequency?) — none of this is necessarily true. But let’s make a toy model anyway. The galaxy is about 100,000 light years across. This means that any signal at any given time has a maximum duration of 100,000 years to be seen if transmitted inside the galaxy by someone else inside the galaxy. Let’s assume that the duration of the signal is about zero compared to it’s transit time, making it a wavefront. Let’s also assume it’s omni-directional. Let’s take Earth as a baseline model of chemistry’s ability to develop life. By our experience on Earth with its many species, we might conclude that life results from chemistry in a robust way given enough time, but radio-capable life is rare since there is only one example of this on Earth. Earth is about 4 billion year old, let’s say (roughly) that intelligent life develops any time during a billion years after the first 3 billion (giving chemistry time to develop life from inorganics) to reach the radio stage, so in this toy model 1 billion years is our statistical universe. Further, we assume that transmissions from alien civilizations are uniformly distributed over time and independent of each other. That means that at any given time one expects a 100,000/1,000,000,000 = 1/10,000 chance (at most) of detecting a signal from 1 civilization. Now assume that the signal can be degraded by ionized conductive gases like ionized hydrogen, which attenuate signals by 50%, 90%, and 99%, and that the number of civilizations range from 1 to 10,000 at any time in the billion year period. Under these assumptions, the table below is the chance of detecting a signal at any given time (in increments of a year).
So for 10,000 civilizations with a signal attenuation of 50%, there is a maximum chance of detecting a signal every two years on average. We’ve been listening for, let’s say 100 years (more or less), then with a signal attenuation by 99% (1% signal), one would expect (by luck) to find 1 signal in a 100 years, on average, if there were 10,000 civilizations capable of radio and the signal was originally transmitted from an outer arm of the galaxy making the transit time approximately 100,000 years. And maybe we’ve found one — -the WoW signal. So in this toy model finding the WoW signal, and assuming it is not of natural origin, is consistent with 10,000 technologically advanced civilizations in our galaxy. We could further assume that after a 100 years, relatively zero time in this scenario, most if not all advanced civilizations would communicate over tight-beam laser or maser channels and most planet-wide communications would take place over a closed network. Or, as the Drake investigators might assume, many advanced civilization annihilate themselves due to the instincts of their evolutionary origins. All these advancements or tragedies would greatly decrease the chances of detecting a signal unless that was expressly the purpose of the transmission and by great random chance transmitter and receiver overlapped in (transmission) time. Given a model like this, the Fermi Paradox becomes very weak indeed, and maybe by great luck we’ve actually found what we’d expect to find.
