Are we alone in the Universe?
The Fermi Paradox: Definition, some Solutions,...
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Of the plurality of worlds yesterday:
For a long time, our Earth was considered the center of a Universe created by God for Man and only for man.
This concept was for a long time dominant, even if some wondered, sometimes at the risk of their lives, about its "reality". Thus:
- Epicurus (~342-270 BC) defended the thesis of plurality, even infinity, of the worlds.
- Aristarchus of Samos (~310-230 BC) hypothesized an Earth describing a circle around a fixed Sun, as Archimedes then recounted.
- Hypatia of Alexandria (fourth century AD) saw the Earth rotate around the Sun in a "two-centre circle" -an ellipse-.
- Giordano Bruno (1548-1600) acquired at the thesis of Nicolas Copernicus described an infinite and center-less Universe.
- In 1686, Bernard Le Boutey de Fontenelle, in his Entretiens sur la pluralité des mondes, stated that
the other planets of the solar system were inhabited and that the stars were so many suns illuminating a world identical to ours.
Then came Johannes Kepler, the Copernican revolution,
Albert Einstein,... and beyond.
Of the plurality of worlds today:
Even if we still do not know if our Universe is finite or infinite, what is certain is that it is immense.
Visible matter is grouped into structures: stars, galaxies, clusters of galaxies, super clusters of galaxies,.
There seem to be several hundred billion visible galaxies, often containing several hundred billion stars themselves.
Even if we believed for a long time that our Sun was unique with its procession of planets, we know since 1995 with the discovery of
the first extra-solar planet by Michel Mayor and Didier Queloz (Nobel Prize in Physics 2019), that most stars must have a planetary procession.
Today we know many thousands of such planetary systems and their observations have shown that our solar system was in no way representative.
This is how we discovered, for example, giant gas planets close to their star contrary to what we could imagine by observing Jupiter, Saturn,...
What is intelligent life? We could perhaps define it as the existence of entities made of an assembly of elementary particles
(in very large numbers, complexity being perhaps a necessity for the emergence of a consciousness) capable of:
- to reproduce more or less identically (but not in an absolute manner in order to allow the evolution)
by simultaneously propagating information -heredity-,
- to evolve,
- to communicate with their fellow creatures and with other beings,
- to memorise and transmit experiences and experiences,
- being aware of the environment (this means having several senses for which electromagnetism plays, as far as we are concerned,
an essential role -it is sight and touch-).
- act and interact with their environment,
- perhaps to move,
- but also likely to question themselves and the Universe.
Such entities appeared on our Earth.
It is obvious that the situation of our cradle around the Sun allowed and facilitated this emergence, then promoted it:
- An almost circular trajectory around the sun (and thus stable conditions)
at a distance compatible with temperatures allowing water to be liquid.
- The existence of a satellite -the Moon- stabilizing its axis of rotation.
- A protective magnetic field.
- A strong gravitational field in order to hold an atmosphere, but weak enough in order to allow tridimensional
displacements as well as the building of structures.
Even if it is obviously impossible for us to know what are all possible life forms , it is clear that life must be able
to take forms that completely elude us but despite everything, a favorable environment 
seems to be a sine qua none condition.
One of the great principles of Physics is the absence on a large scale of places, moments or even privileged directions.
In these conditions, the Copernican reasoning must be extended which implies that the Earth has nothing special and
that life must therefore exist elsewhere because, indeed, otherwise it would make
our planet a unique place! Nevertheless, life must be rare, if not very rare .
The Fermi paradox:
The only example of life(s) we have is that of the one(s) we can observe on Earth.
It seems that one of its driving principles is that of expansion and conquest.
If one extrapolates this to the Universe and if extraterrestrial civilizations exist elsewhere, then it must be the same for these:
just as European settlers crossed the oceans on their sailboats to seize distant territories , so intrepid explorers must cross the interstellar or intergalactic spaces.
In 1950, Enrico Fermi, Nobel Prize winner in Physics in 1938, then at the laboratories of Los Alamos in the USA,
was having lunch with several of his colleagues.
Noting that our solar system was much less aged  than the Universe , Enrico Fermi found it surprising that no trace of aliens
was found if they exist and if they are well expansionists.
Indeed, in hundreds of millions of years they could have conquered our Galaxy and we should have at least found traces, electromagnetic in particular.
However, in 1950 it was not and it is still true today.
This question remains current under the name of Fermi paradox...
How to solve this paradox? Several non-exclusive responses can be advanced:
- We are alone in the Universe!
But as was said above it would be contrary to the Copernican principle and the Universe being
so vast, it would be logical that the processes that led to life on our Earth are at work elsewhere, even if they are certainly rare, very rare.
- The life "cradles" are (very) rare!
It is very likely that life (as defined earlier), for it to emerge,
requires a protective and stable environment. This certainly implies a magnetic field diverting particles from space. But most of the stellar systems
are binary and under these conditions the trajectories of the plantes can be
chaotic and therefore create an unstable environment.
- To live happily, let us live hidden!
So do not manifest, but this does not correspond to our own behaviors since our electromagnetic
emissions have left the Earth for more than a century and are currently traveling in interstellar space at the speed of light.
It is also worth noting the explicit sending of messages to other species  either issued or engraved on space probes.
- Every civilization has a (very) limited lifespan.
The history of Humanity illustrates this: the Egyptians, the Greeks, the Romans,... have disappeared as civilizations.
And today the widespread violence, the proliferation of nuclear weapons, the wars of religion, environmental problems,.
jeopardize our very existence! Would this not be a universal behavioural law?
- The lack of "synchronization".
Special relativity published in 1905 by Albert Einstein revealed that the notion of simultaneity was relative.
This implies that it makes little sense to wonder what is happening today in any galaxy.
To illustrate this particular point, let us return to the solar system so that these relativistic problems can be ignored
and suppose that two billion years ago a highly evolved civilization developed on Mars and then disappeared completely after a few thousand years of existence.
It is obvious that we would not have been able to meet.
Extrapolating this to the Universe, there is no reason why many civilizations appear in the Universe in such a way that they can communicate, meet,.
There is no reason for them to be "synchronous".
- The "chasms" of the cosmos: space travel cannot be fast the scale of the Universe.
Our Physics has given us constants and laws  which seem to be.
This is particularly evident in the measurements made on distant objects . In particular, nothing can move faster than light .
And despite this dizzying speed, the light set by Alpha Centauri C  takes 4,244 years to reach us. To cross the Milky Way  light needs
more than 100.000 years and finally, it is more than 2,5 million years that it takes the light of Androm, the galaxy closest
to the Milky Way, to reach us. A priori
materiel objects (spacecraft) can only move (much) more slowly. This means that going from stars to stars could certainly only be done
with the help of "spaceship-worlds" within which many generations would live, the majority of travellers having not known
the point of departure and so many dead well before to arrive at their destination .
How to select the travelers and how to avoid the consanguinity?
The populations of these ships would evolve like any civilization and would necessarily know violence, evolutions,...
But more are they capable of scientific progress and how to train the new generations (of physicians, teachers, engineers, plumbers,...)?
During these journeys, would they not diverge from the civilizations of
those who would have sent them to the conquest of galaxies. And what about the relativistic effects on the flow of time on the edge
of these ships? Finally, are the "Galactic Empires" such as those offered by Isaac Asimov (Foundation) or Frank Herbert (Dune) possible?
- It may not be possible to "circumvent" the known laws of Physics.
The speed of light seems to be a fundamental limit.
But Science-Fiction based on Physics sometimes proposes to "bypass" it by exploiting, for example, the wormholes of General Relativity.
But they certainly would not have the "flexibility" required for a means of transport: it is not a journey in space that they would allow,
but a journey in space-time.
Would they bring us to our Universe or to another? How do I get back? And above all, would it only be possible to enter it?
Let us also mention, to finish this point, warping the space-time dear to Star Trek or "passing" through
the possible "hidden" dimensions.
- The Dark Forest.
The Universe, if finished, therefore possesses a limited amount of resources.
If we again make the hypothesis of the will to expand civilizations, then necessarily a problem arises and that we meet
in our ecology when studying the evolution of populations: that of the prey-predator struggle.
The Universe would then be similar to a dark forest (Dark Forest) populated by beings (the "civilizations").
Then these beings have no choice but to hide, to escape the sight of others because otherwise, as soon as they appear
they are eliminated without hesitation and without notice.
So there is only one way to promote survival: discretion.
This was staged in 2006 by Cixin Liu, a talented Chinese science fiction author, in his trilogy The Three-Body Problem.
- What if we're the aliens?
These various remarks and questions obviously do not answer the question of whether we are alone in the Universe.
But what would happen tomorrow if a contact were made?
- Would communication be possible? As an illustration of this question, can we communicate with ants?
- Is such a meeting desirable? Let us remember the fate of indigenous peoples when European settlers arrived on American continents.
And besides, do we care about the insects that we crush during a country walk?
- The nature of Mathematics finally known?
The existential question of whether Mathematics is created or discovered might at last find its answer:
they would most certainly be independent of us -and therefore discoveries- if
our "visitors" used the same "tools" of access to knowledge.
But if not, it would be fascinating to discover perhaps that we can understand the Universe without needing the numbers.
- The future of religions.
Religions would resist such "pressure".
Would God (which one?) still have meaning? And who would have been the "Son of God" sent to Earth to save men?
- What about unidentified aerial phenomena?
Recent visual testimonies declassified by the Americans show machines with exceptional and inexplicable performances (acceleration and change of direction in particular).
It seems difficult to imagine that the Chinese or the Russians would have had it for a long time, without them boasting about it.
Then what is it? They are probably not aliens for the various reasons mentioned above.
What if they were observers  from our future?
Are we alone in the Universe?
Maybe the answer will never come , but, if yes, then
our Earth would be at last the center of Everything !
The (good) authors of Science Fiction can be consulted about.
This is how Stephen Baxter
in Flux convincingly describes beings living on the surface of a neutron star.
It should be noted in passing that the author then neglects the effects on the passage of time of General Relativity which in all rigor cannot be ignored in these circumstances.
Extra-solar planets very close to their star have been discovered and for which surface temperatures of several thousand degrees are probable.
It is difficult to imagine that perennial assemblies could appear there and last long enough.
Frank Drake, an American astronomer, proposed in 1961 an equation giving the probable number of civilizations in our Galaxy, the Milky Way.
It is of little use given the large number of relatively arbitrary parameters it contains.
Sometimes (always?) at the expense of the lives of Indigenous peoples.
The solar system is about 4,6 billion years old.
In the Big Bang model our Universe was "born" 13,8 billion years ago.
Very naive indeed.
These are Special Relativity, General Relativity and Quantum Mechanics.
Quasars in particular.
Light moves at a speed of 299.792.458 metres per second in a vacuum.
Alpha Centauri C is the closest planetary system to the solar system.
The Milky Way is our Galaxy.
Unless you trust hypothetical reliable hibernation systems throughout the millenia of travel.
And what about the consciousness of travelers when waking up?
In order to avoid the paradoxes of the type "kill his parents before his conception", even if the Physics does not allow it today,
traveling in time could perhaps be envisaged on condition of being limited to the observation WITHOUT interaction
(but doesn't observing involve interacting as we learn from Quantum Mechanics?)...
The only certitude that we could have one day would be that we are not alone, following an encounter.
But as for the negation, don't forget that the absence of proof is not the proof of absence.
But then, what a waste of space (Contact, 1985, Carl Sagan)...
Copyright © Jean-François Colonna, 2021-2022.
Copyright © CMAP (Centre de Mathématiques APpliquées) UMR CNRS 7641 / Ecole Polytechnique, 2021-2022.