What is the Fermi Paradox?
Fermi paradox
The Fermi paradox, or Fermi's paradox, named after physicist Enrico Fermi, is the apparent contradiction between the lack of evidence and high probability estimates for the existence of extraterrestrial civilizations. The basic points of the argument, made by physicists Enrico Fermi (1901–1954) and Michael H. Hart (born 1932), are:
According to this line of reasoning, the Earth should have already been visited by extraterrestrial aliens. In an informal conversation, Fermi noted no convincing evidence of this, leading him to ask, "Where is everybody?" There have been many attempts to explain the Fermi paradox, primarily either suggesting that intelligent extraterrestrial life is extremely rare or proposing reasons that such civilizations have not contacted or visited Earth.
The Fermi paradox is a conflict between the argument that scale and probability seem to favor intelligent life being common in the universe, and a total lack of evidence of intelligent life having ever arisen anywhere other than on the Earth.
Conformal cyclic cosmology
In 2015 Gurzadyan and Penrose also discussed the Fermi paradox, the apparent contradiction between the lack of evidence but high probability estimates for the existence of extraterrestrial civilizations. Within conformal cyclic cosmology, the cosmic microwave background provides the possibility of information transfer from one aeon to another, including of intelligent signals within information panspermia concept.
Fermi paradox
Cosmologist Alan Guth proposed a multiverse solution to the Fermi paradox. This hypothesis uses the synchronous gauge probability distribution, with the result that young universes exceedingly outnumber older ones (by a factor of e for every second of age). Therefore, averaged over all universes, universes with civilizations will almost always have just one, the first to develop. However, Guth notes "Perhaps this argument explains why SETI has not found any signals from alien civilizations, but I find it more plausible that it is merely a symptom that the synchronous gauge probability distribution is not the right one."
Space colonization
A corollary to the Fermi paradox—"nobody else is doing it"—is the argument that, because no evidence of alien colonization technology exists, it is statistically unlikely to even be possible to use that same level of technology ourselves.
Fermi resonance
A Fermi resonance is the shifting of the energies and intensities of absorption bands in an infrared or Raman spectrum. It is a consequence of quantum mechanical mixing. The phenomenon was explained by the Italian physicist Enrico Fermi.
Enrico Fermi
The first paper seemed to point out a contradiction between the electrodynamic theory and the relativistic one concerning the calculation of the electromagnetic masses, as the former predicted a value of 4/3 U/c. Fermi addressed this the next year in a paper "Concerning a contradiction between electrodynamic and the relativistic theory of electromagnetic mass" in which he showed that the apparent contradiction was a consequence of relativity. This paper was sufficiently well-regarded that it was translated into German and published in the German scientific journal "Physikalische Zeitschrift" in 1922. That year, Fermi submitted his article "On the phenomena occurring near a world line" ("") to the Italian journal "I Rendiconti dell'Accademia dei Lincei". In this article he examined the Principle of Equivalence, and introduced the so-called "Fermi coordinates". He proved that on a world line close to the time line, space behaves as if it were a Euclidean space.
Fermi submitted his thesis, "A theorem on probability and some of its applications" (""), to the "Scuola Normale Superiore" in July 1922, and received his laurea at the unusually young age of 20. The thesis was on X-ray diffraction images. Theoretical physics was not yet considered a discipline in Italy, and the only thesis that would have been accepted was one on experimental physics. For this reason, Italian physicists were slow in embracing the new ideas like relativity coming from Germany. Since Fermi was quite at home in the lab doing experimental work, this did not pose insurmountable problems for him.
Fermi problem
Scientists often look for Fermi estimates of the answer to a problem before turning to more sophisticated methods to calculate a precise answer. This provides a useful check on the results. While the estimate is almost certainly incorrect, it is also a simple calculation that allows for easy error checking, and to find faulty assumptions if the figure produced is far beyond what we might reasonably expect. By contrast, precise calculations can be extremely complex but with the expectation that the answer they produce is correct. The far larger number of factors and operations involved can obscure a very significant error, either in mathematical process or in the assumptions the equation is based on, but the result may still be assumed to be right because it has been derived from a precise formula that is expected to yield good results. Without a reasonable frame of reference to work from it is seldom clear if a result is acceptably precise or is many degrees of magnitude (tens or hundreds of times) too big or too small. The Fermi estimation gives a quick, simple way to obtain this frame of reference for what might reasonably be expected to be the answer, giving context to the results.
Fermi Project
A Fermi is an extremely small unit of length equal to one quadrillionth of a meter. It is named after Enrico Fermi, the Nobel Prize winner and physicist who produced the first controlled nuclear chain reaction. Lyons uses this name because they seek to use small, incremental changes to create a series of large changes in how the church views its mission.
Enrico Fermi
Fermi was known as an inspiring teacher, and was noted for his attention to detail, simplicity, and careful preparation of his lectures. Later, his lecture notes were transcribed into books. His papers and notebooks are today in the University of Chicago. Victor Weisskopf noted how Fermi "always managed to find the simplest and most direct approach, with the minimum of complication and sophistication." Fermi's ability and success stemmed as much from his appraisal of the art of the possible, as from his innate skill and intelligence. He disliked complicated theories, and while he had great mathematical ability, he would never use it when the job could be done much more simply. He was famous for getting quick and accurate answers to problems that would stump other people. Later on, his method of getting approximate and quick answers through back-of-the-envelope calculations became informally known as the "Fermi method", and is widely taught.
Fermi paradox
It may be that while alien species with intelligence exist, they are primitive or have not reached the level of technological advancement necessary to communicate. Along with non-intelligent life, such civilizations would be also very difficult for us to detect, short of a visit by a probe, a trip that would take hundreds of thousands of years with current technology.
To skeptics, the fact that in the history of life on the Earth only one species has developed a civilization to the point of being capable of spaceflight and radio technology, lends more credence to the idea that technologically advanced civilizations are rare in the universe.
Purcell effect
One way of seeing why this enhancement arises is by using cavity quantum electrodynamics. Fermi's golden rule dictates that the transition rate for the atom-vacuum (or atom-cavity) system is proportional to the density of final states. In a cavity at resonance, the "density" of final states is enhanced (though the number of final states may not be). The Purcell factor is then just the ratio of the cavity
Liv Boeree
Boeree has written a number of articles and opinion pieces on various scientific and rationality topics. Her publications include a Vox.com article discussing the philosophical implications of Future of Humanity Institute's 2018 Paper "Dissolving the Fermi Paradox", a Vice Media article on a discovered crystalline pattern in prime numbers and an opinion piece in The Independent on the importance of rational thinking classes in mainstream education.
Noogenesis
Therefore, generalizing and summarizing: 
The term "noogenesis" can be used in a variety of fields i.e. medicine, biophysics, semiotics, mathematics, information technology, psychology, theory of global evolution etc. thus making it a truly cross-disciplinary one. In astrobiology noogenesis concerns the origin of intelligent life and more specifically technological civilizations capable of communicating with humans and or traveling to Earth. The lack of evidence for the existence of such extraterrestrial life creates the Fermi paradox.
Fermi arc
In the field of unconventional superconductivity, a Fermi arc is a phenomenon visible in the pseudogap state of a superconductor. Seen in momentum space, part of the space exhibits a gap in the density of states, like in a superconductor. This starts at the antinodal points, and spreads through momentum space when lowering the temperature until everywhere is gapped and the sample is superconducting. The area in momentum space that remains ungapped is called the Fermi Arc.
Extraterrestrial life
The apparent contradiction between high estimates of the probability of the existence of extraterrestrial civilizations and the lack of evidence for such civilizations is known as the Fermi paradox.
Great Filter
The idea was first proposed in an online essay titled "The Great Filter - Are We Almost Past It?", written by economist Robin Hanson. The first version was written in August 1996 and the article was last updated on September 15, 1998. Since that time, Hanson's formulation has received recognition in several published sources discussing the Fermi paradox and its implications.
Fermi paradox
Physiology might also cause a communication barrier. Carl Sagan speculated that an alien species might have a thought process orders of magnitude slower (or faster) than ours. A message broadcast by that species might well seem like random background noise to us, and therefore go undetected.
Great Filter
There are many alternative scenarios that might allow for the evolution of intelligent life to occur multiple times without either catastrophic self-destruction or glaringly visible evidence. These are possible resolutions to the Fermi paradox: "They do exist, but we see no evidence". Other ideas include: it is too expensive to spread physically throughout the galaxy, Earth is purposely isolated, it is dangerous to communicate and hence civilizations actively hide, among others.
Fermi surface
formula_3
Fermi paradox
Humanity's ability to detect intelligent extraterrestrial life has existed for only a very brief period—from 1937 onwards, if the invention of the radio telescope is taken as the dividing line—and "Homo sapiens" is a geologically recent species. The whole period of modern human existence to date is a very brief period on a cosmological scale, and radio transmissions have only been propagated since 1895. Thus, it remains possible that human beings have neither existed long enough nor made themselves sufficiently detectable to be found by extraterrestrial intelligence.
Snell–Hitchcock
On the second floor of section V is the "Fermi Room," where Enrico Fermi is said to have lived while working on the Manhattan Project in the 1940s. It is rumored that he chose that room because it had its own bathroom with tub; though the bathroom remains, the tub was replaced with a shower in 2008. Linked to the Fermi Room is the Fermi Blackboard, which is said to be the same blackboard Fermi used to do his calculations, although this may be an urban legend. This possibility does not, nevertheless, detract from many students' desire to possess it.
Burali-Forti paradox
If we use the von Neumann definition, under which each ordinal is identified as the set of all preceding ordinals, the paradox is unavoidable: the offending proposition that the order type of all ordinal numbers less than a fixed formula_25 is formula_25 itself must be true. The collection of von Neumann ordinals, like the collection in the Russell paradox, cannot be a set in any set theory with classical logic. But the collection of order types in New Foundations (defined as equivalence classes of well-orderings under similarity) is actually a set, and the paradox is avoided because the order type of the ordinals less than formula_1
turns out not to be formula_1.
Fermi paradox
In 1950, while working at Los Alamos National Laboratory, Fermi had a casual conversation while walking to lunch with colleagues Emil Konopinski, Edward Teller and Herbert York. The men discussed a recent spate of UFO reports and an Alan Dunn cartoon facetiously blaming the disappearance of municipal trashcans on marauding aliens. The conversation shifted to other subjects, until during lunch Fermi suddenly exclaimed, "Where are they?" (alternatively, "Where is everybody?"). Teller remembers, "The result of his question was general laughter because of the strange fact that in spite of Fermi's question coming from the clear blue, everybody around the table seemed to understand at once that he was talking about extraterrestrial life." Herbert York recalls that Fermi followed up on his comment with a series of calculations on the probability of Earth-like planets, the probability of life, the likely rise and duration of high technology, etc., and concluded that we ought to have been visited long ago and many times over.
Fermi–Dirac statistics
where      formula_63
Quasi Fermi level
formula_2
Fermi paradox
The greatest challenge is the sheer size of the radio search needed to look for signals (effectively spanning the entire observable universe), the limited amount of resources committed to SETI, and the sensitivity of modern instruments. SETI estimates, for instance, that with a radio telescope as sensitive as the Arecibo Observatory, Earth's television and radio broadcasts would only be detectable at distances up to 0.3 light-years, less than 1/10 the distance to the nearest star. A signal is much easier to detect if the signal energy is limited to either a narrow range of frequencies, or directed at a specific part of the sky. Such signals could be detected at ranges of hundreds to tens of thousands of light-years distance. However, this means that detectors must be listening to an appropriate range of frequencies, and be in that region of space to which the beam is being sent. Many SETI searches assume that extraterrestrial civilizations will be broadcasting a deliberate signal, like the Arecibo message, in order to be found.
Fermi problem
A famous example of a Fermi-problem-like estimate is the Drake equation, which seeks to estimate the number of intelligent civilizations in the galaxy. The basic question of why, if there were a significant number of such civilizations, ours has never encountered any others is called the Fermi paradox.
Fermi paradox
It has been suggested that some advanced beings may divest themselves of physical form, create massive artificial virtual environments, transfer themselves into these environments through mind uploading, and exist totally within virtual worlds, ignoring the external physical universe.
Fermi heap and Fermi hole
formula_11
Curry's paradox
In the 1930s, Curry's Paradox and the related Kleene–Rosser paradox played a major role in showing that formal logic systems based on self-recursive expressions are inconsistent.
These include some versions of lambda calculus and combinatory logic.
Cesare Burali-Forti
Cesare Burali-Forti (13 August 1861 – 21 January 1931) was an Italian mathematician, after whom the Burali-Forti paradox is named.
Fermi's interaction
Similarly,
Burali-Forti paradox
In set theory, a field of mathematics, the Burali-Forti paradox demonstrates that constructing "the set of all ordinal numbers" leads to a contradiction and therefore shows an antinomy in a system that allows its construction. It is named after Cesare Burali-Forti, who in 1897 published a paper proving a theorem which, unknown to him, contradicted a previously proved result by Cantor. Bertrand Russell subsequently noticed the contradiction, and when he published it in his 1903 book "Principles of Mathematics", he stated that it had been suggested to him by Burali-Forti's paper, with the result that it came to be known by Burali-Forti's name.
Fermi heap and Fermi hole
formula_7
Fermi heap and Fermi hole
formula_3
Aestivation hypothesis
The aestivation hypothesis, is a hypothesized solution to the Fermi paradox conceived in 2017 by Anders Sandberg, Stuart Armstrong and Milan M. Cirkovic. The hypothesis, published on April 27, 2017, suggests that advanced alien civilizations may be storing energy and aestivating (hibernating in times of heat instead of cold), until the universe cools to better make use of the stored energy to perform tasks.
Fermi–Pasta–Ulam–Tsingou problem
In the summer of 1953 Enrico Fermi, John Pasta, Stanislaw Ulam, and Mary Tsingou conducted numerical experiments (i.e. computer simulations) of a vibrating string that included a non-linear term (quadratic in one test, cubic in another, and a piecewise linear approximation to a cubic in a third). They found that the behavior of the system was quite different from what intuition would have led them to expect. Fermi thought that after many iterations, the system would exhibit thermalization, an ergodic behavior in which the influence of the initial modes of vibration fade and the system becomes more or less random with all modes excited more or less equally. Instead, the system exhibited a very complicated quasi-periodic behavior. They published their results in a Los Alamos technical report in 1955. (Enrico Fermi died in 1954 and so this technical report was published after Fermi's death.)
Planetarium hypothesis
The planetarium hypothesis, conceived in 2001 by Stephen Baxter, attempts to provide a solution to the Fermi paradox by holding that our astronomical observations represent an illusion, created by a Type III civilization capable of manipulating matter and energy on galactic scales. He postulates that we do not see evidence of extraterrestrial life because the universe has been engineered so that it appears empty of other life.
Fermi's interaction
Fermi first submitted his "tentative" theory of beta decay to the famous science journal "Nature", which rejected it "because it contained speculations too remote from reality to be of interest to the reader." "Nature" later admitted the rejection to be one of the great editorial blunders in its history. Fermi then submitted revised versions of the paper to Italian and German publications, which accepted and published them in those languages in 1933 and 1934. The paper did not appear at the time in a primary publication in English. An English translation of the seminal paper was published in the American Journal of Physics in 1968.
Fermi's interaction
Fermi first introduced this coupling in his description of beta decay in 1933. The Fermi interaction was the precursor to the theory for the weak interaction where the interaction between the proton–neutron and electron–antineutrino is mediated by a virtual W boson.
Curry's paradox
In Zermelo–Fraenkel set theory the axiom of unrestricted comprehension is replaced with a group of axioms that allow construction of sets. So Curry's paradox cannot be stated in ZFC. ZFC evolved in response to Russell's paradox.
Fermi energy
and Fermi velocity
Fermi problem
In physics or engineering education, a Fermi problem, Fermi quiz, Fermi question, Fermi estimate, or order estimation is an estimation problem designed to teach dimensional analysis or approximation, and such a problem is usually a back-of-the-envelope calculation. The estimation technique is named after physicist Enrico Fermi as he was known for his ability to make good approximate calculations with little or no actual data. Fermi problems typically involve making justified guesses about quantities and their variance or lower and upper bounds.
The Dark Forest
Back on Earth, Luo Ji and another contemporary, Da Shi, discover that star 187J3X1 has been destroyed, causing the UN to restore Luo Ji's Wallfacer status. Luo Ji explains to Da Shi the implications he derived from Ye Wenjie's two axioms of cosmic civilization: 1. Each civilization's goal is survival, and 2. Resources are finite. Like hunters in a "dark forest", a civilization can never be certain of an alien civilization's true intentions. The extreme distance between stars creates an insurmountable "chain of suspicion" where any two civilizations cannot communicate well enough to relieve mistrust, making conflict inevitable. Therefore, it is in every civilization's best interest to preemptively strike and destroy any developing civilization before it can become a threat, but without revealing their own location, thus explaining the Fermi paradox.
Existential risk from artificial general intelligence
Nick Bostrom was the first person to suggest that an artificial general intelligence might deliberately exterminate humankind, and invention of artificial general intelligence is the explanation for the Fermi paradox. Bostrom's 2014 book om the artificial general intelligence question stimulated discussion. By 2015, public figures such as physicists Stephen Hawking and Nobel laureate Frank Wilczek, computer scientists Stuart J. Russell and Roman Yampolskiy, In April 2016, "Nature" warned: "Machines and robots that outperform humans across the board could self-improve beyond our control — and their interests might not align with ours."
Fermi's interaction
Fermi's four-fermion theory describes the weak interaction remarkably well. Unfortunately, the calculated cross-section, or probability of interaction, grows as the square of the energy formula_106. Since this cross section grows without bound, the theory is not valid at energies much higher than about 100 GeV. Here is the Fermi coupling constant, which denotes the strength of the interaction. This eventually led to the replacement of the four-fermion contact interaction by a more complete theory (UV completion)—an exchange of a W or Z boson as explained in the electroweak theory.
Fermi paradox
The zoo hypothesis states that intelligent extraterrestrial life exists and does not contact life on Earth to allow for its natural evolution and development. This hypothesis may break down under the uniformity of motive flaw: all it takes is a single culture or civilization to decide to act contrary to the imperative within our range of detection for it to be abrogated, and the probability of such a violation increases with the number of civilizations.
Postbiological evolution
If we consider this possibility of a PBC in our galaxy we are still faced with Fermi's paradox. However many of the proposed solutions for Fermi's paradox also hold true for a PBC. In terms of the search for extraterrestrial life and astrobiology because of the almost infinite possible forms a PBC could take and our lack of understanding of these we would effectively be blind in this search. For this reason even though there is a logical argument for the existence of PBCs our best hopes remain with looking for biological life.
Faraday paradox
The Faraday paradox or Faraday's paradox is any experiment in which Michael Faraday's law of electromagnetic induction appears to predict an incorrect result. The paradoxes fall into two classes:
Fermi point
Fermionic systems that have a Fermi surface (FS) belong to a universality class in quantum field theory. Any collection of fermions with weak repulsive interactions belongs to this class. At the fermi point, the break of symmetry can be explained by assuming a vortex or singularity will appear as a result of the spin of a fermi particle (quasiparticle, Fermion) in one dimension of the three-dimensional momentum space.
Magician's Academy
Fermi
Enrico Fermi
While writing the appendix for the Italian edition of the book "Fundamentals of Einstein Relativity" by August Kopff in 1923, Fermi was the first to point out that hidden inside the famous Einstein equation () was an enormous amount of nuclear potential energy to be exploited. "It does not seem possible, at least in the near future", he wrote, "to find a way to release these dreadful amounts of energy—which is all to the good because the first effect of an explosion of such a dreadful amount of energy would be to smash into smithereens the physicist who had the misfortune to find a way to do it."
Mathematical logic
Skepticism about the axiom of choice was reinforced by recently discovered paradoxes in naive set theory. Cesare Burali-Forti (1897) was the first to state a paradox: the Burali-Forti paradox shows that the collection of all ordinal numbers cannot form a set. Very soon thereafter, Bertrand Russell discovered Russell's paradox in 1901, and Jules Richard (1905) discovered Richard's paradox.
Future of Humanity Institute
A recurring theme in FHI's research is the Fermi paradox, the surprising absence of observable alien civilizations. Robin Hanson has argued that there must be a "Great Filter" preventing space colonization to account for the paradox. That filter may lie in the past, if intelligence is much more rare than current biology would predict; or it may lie in the future, if existential risks are even larger than is currently recognized.
Manifold Trilogy
The third novel, "Origin", is set in a multiverse that is a compromise between the ideals in the first two novels: that life is only on Earth, but at the same time is everywhere. This novel solves the Fermi Paradox by suggesting that intelligent life is segregated into separate parallel universes.
The Crystal Spheres
"The Crystal Spheres" is a science fiction short story by American writer David Brin, originally published in the January 1984 issue of "Analog" and collected in "The River of Time". It won the Hugo Award for Best Short Story 1985. In it, Brin presents an explanation for the Fermi Paradox.
Fermat number
If "N" = "F" > 3, then the above Jacobi symbol is always equal to −1 for "a" = 3, and this special case of Proth's theorem is known as Pépin's test. Although Pépin's test and Proth's theorem have been implemented on computers to prove the compositeness of some Fermat numbers, neither test gives a specific nontrivial factor. In fact, no specific prime factors are known for "n" = 20 and 24.
Temporal paradox
A temporal paradox, time paradox, or time travel paradox is a paradox, an apparent contradiction, or a logical contradiction that is associated with the idea of time and time travel. In physics, temporal paradoxes fall into two broad groups: consistency paradoxes exemplified by the grandfather paradox; and causal loops. More broadly, a variation of the Fermi paradox also applies to time travel.
Search for extraterrestrial intelligence
The Fermi paradox is commonly understood as asking why extraterrestrials have not visited Earth, but the same reasoning applies to the question of why signals from extraterrestrials have not been heard. The SETI version of the question is sometimes referred to as "the Great Silence".
Fermi paradox
Liu Cixin's novel The Dark Forest is based upon such a situation.
Robert Hofstadter
Robert Hofstadter coined the term fermi, symbol fm,
in honor of the Italian physicist Enrico Fermi (1901–1954), one of the founders of nuclear physics, in Hofstadter's 1956 paper published in the "Reviews of Modern Physics" journal, "Electron Scattering and Nuclear Structure". The term is widely used by nuclear and particle physicists. When Hofstadter was awarded the 1961 Nobel Prize in Physics, it subsequently appears in the text of his 1961 Nobel Lecture, "The electron-scattering method and its application to the structure of nuclei and nucleons" (December 11, 1961).
Curry's paradox
Curry's paradox is a paradox in which an arbitrary claim F is proved from the mere existence of a sentence C that says of itself "If C, then F", requiring only a few apparently innocuous logical deduction rules. Since F is arbitrary, any logic having these rules proves everything. The paradox may be expressed in natural language and in various logics, including certain forms of set theory, lambda calculus, and combinatory logic.
The Fermi Paradox Is Our Business Model
Their "business model" consists of the following steps:
Fermi paradox
It may be that alien civilizations are detectable through their radio emissions for only a short time, reducing the likelihood of spotting them. The usual assumption is that civilizations outgrow radio through technological advancement. However, even if radio is not used for communication, it may be used for other purposes such as power transmission from solar power satellites. Such uses may remain visible even after broadcast emission are replaced by less observable technology.
Fermi paradox
Thus to detect alien civilizations through their radio emissions, Earth observers either need more sensitive instruments or must hope for fortunate circumstances: that the broadband radio emissions of alien radio technology are much stronger than our own; that one of SETI's programs is listening to the correct frequencies from the right regions of space; or that aliens are deliberately sending focused transmissions in our general direction.
Philosophy of physics
Many in the scientific community believe that backward time travel is highly unlikely, because it violates causality i.e. the logic of cause and effect. For example, what happens if you attempt to go back in time and kill yourself at an earlier stage in your life (or your grandfather, which leads to the grandfather paradox)? Stephen Hawking once suggested that the absence of tourists from the future constitutes a strong argument against the existence of time travel— a variant of the Fermi paradox, with time travelers instead of alien visitors.
Accelerating change
Applying this vision to the search for extraterrestrial intelligence leads to the idea that advanced intelligent life reconfigures itself into a black hole. Such advanced life forms would be interested in inner space, rather than outer space and interstellar expansion. They would thus in some way transcend reality, not be observable and it would be a solution to Fermi's paradox called the "transcension hypothesis", Another solution is that the black holes we observe could actually be interpreted as intelligent super-civilizations feeding on stars, or "stellivores". 
This dynamics of evolution and development is an invitation to study the universe itself as evolving, developing. If the universe is a kind of superorganism, it may possibly tend to reproduce, naturally or artificially, with intelligent life playing a role.
Fermi paradox
It is possible, however, that present scientific knowledge cannot properly gauge the feasibility and costs of such interstellar colonization. Theoretical barriers may not yet be understood, and the resources needed may be so great as to make it unlikely that any civilization could afford to attempt it. Even if interstellar travel and colonization are possible, they may be difficult, leading to a colonization model based on percolation theory. Colonization efforts may not occur as an unstoppable rush, but rather as an uneven tendency to "percolate" outwards, within an eventual slowing and termination of the effort given the enormous costs involved and the expectation that colonies will inevitably develop a culture and civilization of their own. Colonization may thus occur in "clusters," with large areas remaining uncolonized at any one time.
Fermi paradox
This is the argument that technological civilizations may usually or invariably destroy themselves before or shortly after developing radio or spaceflight technology. Possible means of annihilation are many, including war, accidental environmental contamination or damage, resource depletion, climate change, or poorly designed artificial intelligence. This general theme is explored both in fiction and in scientific hypothesizing. In 1966, Sagan and Shklovskii speculated that technological civilizations will either tend to destroy themselves within a century of developing interstellar communicative capability or master their self-destructive tendencies and survive for billion-year timescales. Self-annihilation may also be viewed in terms of thermodynamics: insofar as life is an ordered system that can sustain itself against the tendency to disorder, the "external transmission" or interstellar communicative phase may be the point at which the system becomes unstable and self-destructs.
Fermi paradox
Exoplanet detection and classification is a very active sub-discipline in astronomy, and the first possibly terrestrial planet discovered within a star's habitable zone was found in 2007. New refinements in exoplanet detection methods, and use of existing methods from space (such as the Kepler Mission, launched in 2009) are starting to detect and characterize Earth-size planets, and determine if they are within the habitable zones of their stars. Such observational refinements may allow us to better gauge how common potentially habitable worlds are.
Manifold Trilogy
Each one of the main novels deals with a possible resolution to the Fermi paradox. The first, "Time", is set in a universe that is completely devoid of intelligent life beyond that of mankind and its creations (i.e. A.I. and uplifted animals).
Fermi level
The term, "Fermi level", is mainly used in discussing the solid state physics of electrons in semiconductors, and a precise usage of this term is necessary to describe band diagrams in devices comprising different materials with different levels of doping.
In these contexts, however, one may also see Fermi level used imprecisely to refer to the "band-referenced Fermi level", "µ" − "ϵ", called "ζ" above.
It is common to see scientists and engineers refer to "controlling", "pinning", or "tuning" the Fermi level inside a conductor, when they are in fact describing changes in "ϵ" due to doping or the field effect.
In fact, thermodynamic equilibrium guarantees that the Fermi level in a conductor is "always" fixed to be exactly equal to the Fermi level of the electrodes; only the band structure (not the Fermi level) can be changed by doping or the field effect (see also band diagram).
A similar ambiguity exists between the terms, "chemical potential" and "electrochemical potential".
Enrico Fermi
Fermi received numerous awards in recognition of his achievements, including the Matteucci Medal in 1926, the Nobel Prize for Physics in 1938, the Hughes Medal in 1942, the Franklin Medal in 1947, and the Rumford Prize in 1953. He was awarded the Medal for Merit in 1946 for his contribution to the Manhattan Project. Fermi was elected a Foreign Member of the Royal Society (FRS) in 1950. The Basilica of Santa Croce, Florence, known as the "Temple of Italian Glories" for its many graves of artists, scientists and prominent figures in Italian history, has a plaque commemorating Fermi. In 1999, "Time" named Fermi on its list of the top 100 persons of the twentieth century. Fermi was widely regarded as an unusual case of a 20th-century physicist who excelled both theoretically and experimentally. The historian of physics, C. P. Snow, wrote that "if Fermi had been born a few years earlier, one could well imagine him discovering Rutherford's atomic nucleus, and then developing Bohr's theory of the hydrogen atom. If this sounds like hyperbole, anything about Fermi is likely to sound like hyperbole".
Fermi problem
Dividing gives
Manifold Trilogy
The second in the series, "Space", proposes the opposite: that life is endemic to the universe, and there is intelligence in nearly all possible places of the cosmos. The solution to the Fermi Paradox in this novel is that intelligent life is continually wiped out by cosmic disasters before it has time to spread too far.
Fermi's interaction
and
Enrico Fermi
At this time, physicists were puzzled by beta decay, in which an electron was emitted from the atomic nucleus. To satisfy the law of conservation of energy, Pauli postulated the existence of an invisible particle with no charge and little or no mass that was also emitted at the same time. Fermi took up this idea, which he developed in a tentative paper in 1933, and then a longer paper the next year that incorporated the postulated particle, which Fermi called a "neutrino". His theory, later referred to as Fermi's interaction, and still later as the theory of the weak interaction, described one of the four fundamental forces of nature. The neutrino was detected after his death, and his interaction theory showed why it was so difficult to detect. When he submitted his paper to the British journal "Nature", that journal's editor turned it down because it contained speculations which were "too remote from physical reality to be of interest to readers". Thus Fermi saw the theory published in Italian and German before it was published in English.
Quasi Fermi level
A quasi Fermi level (also called imref, which is "fermi" spelled backwards) is a term used in quantum mechanics and especially in solid state physics for the Fermi level (chemical potential of electrons) that describes the population of electrons separately in the conduction band and valence band, when their populations are displaced from equilibrium. This displacement could be caused by the application of an external voltage, or by exposure to light of energy formula_1, which alter the populations of electrons in the conduction band and valence band. Since recombination rate (the rate of equilibration between bands) tends to be much slower than the energy relaxation rate within each band, the conduction band and valence band can each have an individual population that is internally in equilibrium, even though the bands are not in equilibrium with respect to exchange of electrons. The displacement from equilibrium is such that the carrier populations can no longer be described by a single Fermi level, however it is possible to describe using concept of separate quasi-Fermi levels for each band.
Fermi paradox
Although astronomers do not usually search for extraterrestrials, they have observed phenomena that they could not immediately explain without positing an intelligent civilization as the source. For example, pulsars, when first discovered in 1967, were called little green men (LGM) because of the precise repetition of their pulses. In all cases, explanations with no need for intelligent life have been found for such observations, but the possibility of discovery remains. Proposed examples include asteroid mining that would change the appearance of debris disks around stars, or spectral lines from nuclear waste disposal in stars. An ongoing example is the unusual transit light curves of star KIC 8462852, where natural interpretations are not fully convincing. Although most likely a natural explanation will emerge, some scientists are investigating the remote possibility that it could be a sign of alien technology, such as a Dyson swarm.
Static forces and virtual-particle exchange
and formula_86 is the Fermi energy
Enrico Fermi
After Wolfgang Pauli announced his exclusion principle in 1925, Fermi responded with a paper "On the quantisation of the perfect monoatomic gas" ("), in which he applied the exclusion principle to an ideal gas. The paper was especially notable for Fermi's statistical formulation, which describes the distribution of particles in systems of many identical particles that obey the exclusion principle. This was independently developed soon after by the British physicist Paul Dirac, who also showed how it was related to the Bose–Einstein statistics. Accordingly, it is now known as Fermi–Dirac statistics. Following Dirac, particles that obey the exclusion principle are today called "fermions", while those that do not are called "bosons".
Sherman paradox
The paradox is named after Stephanie Sherman, who studied the inheritance patterns of people with Fragile X syndrome. Sherman observed that the effects of Fragile X syndrome seemed to occur more frequently with each passing generation. This observation is now known as the Sherman Paradox.
Michael H. Hart
Hart published in 1975 a detailed examination of the Fermi paradox: the contrast between the extreme likelihood of extraterrestrial life somewhere in the universe and the total absence of any evidence for this. Hart’s work has since become a theoretical reference point for much of the research into what is now sometimes known as the "Fermi-Hart paradox". Concerning Hart's contributions to the study of the paradox, Geoffrey A. Landis writes: "A more proper name for [the paradox] would be the Fermi-Hart paradox, since while Fermi is credited with first asking the question, Hart was the first to do a rigorous analysis showing that the problem is not trivial, and also the first to publish his results". Robert H. Gray argues that the term "Fermi paradox" is a misnomer; he argues that it is not the work of Fermi, nor is it an actual paradox (rather an argument). He views Hart as the proper originator of this argument, in his 1975 paper. Gray therefore proposes, that instead of the (standard, but in his view incorrect) name "Fermi paradox", it should be known as the "Hart-Tipler argument"–acknowledging Hart's priority as the argument's originator, but also acknowledging Frank J. Tipler's substantial extension of Hart's arguments in his 1980 paper "Extraterrestrial intelligent beings do not exist".
Time travel
The absence of time travelers from the future is a variation of the Fermi paradox. As the absence of extraterrestrial visitors does not prove they do not exist, so the absence of time travelers fails to prove time travel is physically impossible; it might be that time travel is physically possible but is never developed or is cautiously used. Carl Sagan once suggested the possibility that time travelers could be here but are disguising their existence or are not recognized as time travelers. Some versions of general relativity suggest that time travel might only be possible in a region of spacetime that is warped a certain way, and hence time travelers would not be able to travel back to earlier regions in spacetime, before this region existed. Stephen Hawking stated that this would explain why the world has not already been overrun by "tourists from the future."
Naive set theory
Some believe that Georg Cantor's set theory was not actually implicated in the set-theoretic paradoxes (see Frápolli 1991). One difficulty in determining this with certainty is that Cantor did not provide an axiomatization of his system. By 1899, Cantor was aware of some of the paradoxes following from unrestricted interpretation of his theory, for instance Cantor's paradox and the Burali-Forti paradox, and did not believe that they discredited his theory. Cantor's paradox can actually be derived from the above (false) assumption using for is a cardinal number". Frege explicitly axiomatized a theory in which a formalized version of naïve set theory can be interpreted, and it is "this" formal theory which Bertrand Russell actually addressed when he presented his paradox, not necessarily a theory Cantor, who, as mentioned, was aware of several paradoxes, presumably had in mind.
Fermi–Dirac statistics
In quantum statistics, a branch of physics, Fermi–Dirac statistics describe a distribution of particles over energy states in systems consisting of many identical particles that obey the Pauli exclusion principle. It is named after Enrico Fermi and Paul Dirac, each of whom discovered the method independently (although Fermi defined the statistics earlier than Dirac).
Fermi heap and Fermi hole
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Origin (Baxter novel)
The scenario begins when a portal appears in the sky and transports a select few individuals including Malenfant's wife to a new red moon which has appeared in place of the moon we know. Blaming himself, Malenfant launches a mission to find his wife and solve the Fermi Paradox once and for all.
Fermi paradox
Other names closely related to Fermi's question ("Where are they?") include the Great Silence, and silentium universi (Latin for "silence of the universe"), though these only refer to one portion of the Fermi Paradox, that we see no evidence of other civilizations.
Fermi paradox
Self-replicating probes could exhaustively explore a galaxy the size of the Milky Way in as little as a million years. If even a single civilization in the Milky Way attempted this, such probes could spread throughout the entire galaxy. Another speculation for contact with an alien probe—one that would be trying to find human beings—is an alien Bracewell probe. Such a hypothetical device would be an autonomous space probe whose purpose is to seek out and communicate with alien civilizations (as opposed to Von Neumann probes, which are usually described as purely exploratory). These were proposed as an alternative to carrying a slow speed-of-light dialogue between vastly distant neighbors. Rather than contending with the long delays a radio dialogue would suffer, a probe housing an artificial intelligence would seek out an alien civilization to carry on a close-range communication with the discovered civilization. The findings of such a probe would still have to be transmitted to the home civilization at light speed, but an information-gathering dialogue could be conducted in real time.
Fermi paradox
It may be that non-colonizing technologically capable alien civilizations exist, but that they are simply too far apart for meaningful two-way communication. If two civilizations are separated by several thousand light-years, it is possible that one or both cultures may become extinct before meaningful dialogue can be established. Human searches may be able to detect their existence, but communication will remain impossible because of distance. It has been suggested that this problem might be ameliorated somewhat if contact/communication is made through a Bracewell probe. In this case at least one partner in the exchange may obtain meaningful information. Alternatively, a civilization may simply broadcast its knowledge, and leave it to the receiver to make what they may of it. This is similar to the transmission of information from ancient civilizations to the present, and humanity has undertaken similar activities like the Arecibo message, which could transfer information about Earth's intelligent species, even if it never yields a response or does not yield a response in time for humanity to receive it. It is also possible that archaeological evidence of past civilizations may be detected through deep space observations.
Fermi paradox
The only civilization we know, our own, does not explicitly transmit, except for a few small efforts. Even these efforts, and certainly any attempt to expand them, are controversial. It is not even clear we would respond to a detected signal—the official policy within the SETI community is that "[no] response to a signal or other evidence of extraterrestrial intelligence should be sent until appropriate international consultations have taken place." However, given the possible impact of any reply it may be very difficult to obtain any consensus on "Who speaks for Earth?" and "What should we say?"
Physical paradox
A further set of physical paradoxes are based on sets of observations that fail to be adequately explained by current physical models. These may simply be indications of the incompleteness of current theories. It is recognized that unification has not been accomplished yet which may hint at fundamental problems with the current scientific paradigms. Whether this is the harbinger of a scientific revolution yet to come or whether these observations will yield to future refinements or be found to be erroneous is yet to be determined. A brief list of these yet inadequately explained observations includes observations implying the existence of dark matter, observations implying the existence of dark energy, the observed matter-antimatter asymmetry, the GZK paradox, the heat death paradox, and the Fermi paradox.
Alan Dunn (cartoonist)
A cartoon of his is credited with inspiring the Fermi Paradox.
Fermi paradox
There have been some attempts to find evidence of the existence of Dyson spheres that would alter the spectra of their core stars. Direct observation of thousands of galaxies has shown no explicit evidence of artificial construction or modifications. In October 2015, there was some speculation that a pattern of light from star KIC 8462852, observed by the Kepler Space Telescope, could have been a result of Dyson sphere construction.
Search for extraterrestrial intelligence
The Fermi paradox can be stated more completely as follows:
There are multiple explanations proposed for the Fermi paradox, ranging from analyses suggesting that intelligent life is rare (the "Rare Earth hypothesis"), to analyses suggesting that although extraterrestrial civilizations may be common, they would not communicate, or would not travel across interstellar distances.
Fermi heap and Fermi hole
Fermi heap and Fermi hole refer to two closely related quantum phenomena that occur in many-electron atoms. They arise due to the Pauli exclusion principle, according to which no two electrons can be in the same quantum state in a system (which, accounting for electrons' spin, means that there can be up to two electrons in the same orbital). Due to indistinguishability of elementary particles, the probability of a measurement yielding a certain eigenvalue must be invariant when electrons are exchanged, which means that the probability amplitude must either remain the same or change sign. For instance, consider an excited state of the helium atom in which electron 1 is in the 1s orbital and electron 2 has been excited to the 2s orbital. It is not possible, even in principle, to distinguish electron 1 from electron 2. In other words, electron 2 might be in the 1s orbital with electron 1 in the 2s orbital. As they are fermions, electrons must be described by an anti-symmetric wavefunction which must change sign under electron exchange, resulting in either a Fermi hole (having a lower probability of being found close to each other) or a Fermi heap (having a higher probability of being found close to each other). Since electrons repel one another electrically, Fermi holes and Fermi heaps have drastic effects on the energy of many-electron atoms, although the effect can be illustrated in the case of the helium atom.
Neglecting the spin-orbit interaction, the wavefunction for the two electrons can be written as formula_1, where we have split the wavefunction into spatial and spin parts. As mentioned above, formula_2 needs to be antisymmetric, and so the antisymmetry can arise either from the spin part or the spatial part. There are 4 possible spin states for this system:
Fermi paradox
The theories and principles in the Drake equation are closely related to the Fermi paradox. The equation was formulated by Frank Drake in 1961 in an attempt to find a systematic means to evaluate the numerous probabilities involved in the existence of alien life. The speculative equation considers the rate of star formation in the galaxy; the fraction of stars with planets and the number per star that are habitable; the fraction of those planets that develop life; the fraction that develop "intelligent" life; the fraction that have detectable, technological intelligent life; and finally the length of time such communicable civilizations are detectable. The fundamental problem is that the last four terms are completely unknown, rendering statistical estimates impossible.
Fermi paradox
It may also be that intelligent alien life develops an "increasing disinterest" in their outside world. Possibly any sufficiently advanced society will develop highly engaging media and entertainment well before the capacity for advanced space travel, and that the rate of appeal of these social contrivances is destined, because of their inherent reduced complexity, to overtake any desire for complex, expensive endeavors such as space exploration and communication. Once any sufficiently advanced civilization becomes able to master its environment, and most of its physical needs are met through technology, various "social and entertainment technologies", including virtual reality, are postulated to become the primary drivers and motivations of that civilization.
Fermi's golden rule
Although named after Enrico Fermi, most of the work leading to the Golden Rule is due to Paul Dirac who formulated 20 years earlier a virtually identical equation, including the three components of a constant, the matrix element of the perturbation and an energy difference. It was given this name because, on account of its importance, Fermi dubbed it "Golden Rule No. 2."
Fermi heap and Fermi hole
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