Fermi paradox

Star Rail invited 2019 Nobel Physics Prize winner Didier Queloz to talk about astronomy in Galactic Rhapsody.

One concept mentioned is the Fermi paradox: if there is life in the universe then why can't we see it? There are billions of stars out there. With high probability, some should have planets within the circumstellar habitable zone to support development of liquid water and intelligent life. This is based on the 'goldilocks principle': that there is a habitable zone around star where the temperature is just right, not too cold or too hot (in the words of Stephen Hawking). One can generalize the concept to a galactic habitable zone or regions of galaxy where life can form.

The name Fermi paradox originates from a conversation Enrico Fermi had with Edward Teller (inventor of the hydrogen bomb).

If life developed on these other planets long ago, some of these civilizations may have developed interstellar travel and may have been able to visit Earth within a few million years. However, there is no evidence this has happened.

There are numerous theories trying to explain this. First, we know that there do exist many exoplanets in the universe. The question becomes is there life on these planets? Some say that life is just extremely rare and that our Earth is quite unique in that regard. Some say even if there is life, perhaps that life has not evolved to be as intelligent as humans. After all, it could be that life on other planets could just be bacteria or dinosaurs. In such a case where life is not intelligent enough, perhaps they just have not developed the technology for interstellar travel.

Another theory says that even if there is sufficiently intelligent life that developed such advanced technology, they may have been wiped out before they could get to the point of interstellar travel. The atomic bomb has the power to wipe out whole civilizations. So it is possible that when other civilizations in galaxies far away developed such advanced technology, they destroyed themselves in war or some other disaster. Perhaps there is no 'technological utopianism' and that is natural for civilizations to destroy themselves.

Perhaps such civilizations were destroyed by regularly occurring extinction events such as the meteor that wiped out the dinosaurs. Perhaps other planets follow 'honkai'-like catastrophes, where every once in a while, a great cataclysm wipes out civilization. Even in the three body problem series by Liu Cixin, planets that inhabit a three-body system can experience chaotic, unpredictable fluctuations in climate, which can inhibit the continuous development of civilization.

Dark forest theory

There are other hypotheses such as the dark forest and berserker hypothesis. The berserker theory says that the reason we do not see life is because an alien civilization capable of interstellar travel would have destroyed all other forms of life (hostile von Neumann probe), viewing them as a threat. The dark forest theory is a relaxation of this, saying that alien civilizations would destroy any other form of life that made its presence known. Only if a civilization chose to show signs of life (via things like technosignatures), the von Neumann probes would be sent to destroy it. If the civilization chose not to, then they would survive.

A comment on the berserker and dark forest theories is that they seem to have a cynical assumption that other aliens (if they exist) have a natural instinct or impulse to kill others upon sight. Some can justify this by observing that many animals and species on our own planet have an instinct to kill other foreign, alien species. Moreover, we cannot assume that other aliens are even like us in temperament. They may not even share the same DNA as humans, nevermind even use DNA.

However, even though some humans are crazy, most of humanity is not psychopathic in that they would kill others upon sight. Humans are a bit more tame and civilized, and they possess a certain degree of curiosity about other things insofar that they would not necessarily kill every other living being they see. The point is that if a civilization has developed to the point where they can create advanced technology such as interstellar spaceships, then perhaps they may have required the development of a civilized society where many individuals learn to cooperate with each other rather than kill everything they see.

If an alien species' first instinct was to destroy other lifeforms, then how could it even get to the point of interstellar travel? Would they have not killed themselves and gone extinct before reaching such a stage. Or perhaps somehow there are species that do not kill within their own kind, but only attack everything outside of themselves. So the way they treat their own species is not necessarily how they treat other species.

But still, it seems a bit extreme that aliens would kill everything they see immediately. Observe how the Europeans colonized the Americas: yes, they did genocide the Native Americans. But they also enslaved Africans and brought them to the Americas. Even looking at agriculture, humans have tamed cows, sheep, and other livestock to suit our own needs. Maybe cows and sheep do not constitute the same level of intelligent lifeform. But extending this to extraterrestial beings, it would seem that rather than genocide all other life in the universe, aliens would at least insubordinate other lifeforms or find partnerships that are mutually beneficial.

Time argument

The Drake equation can be used to estimate the number of intelligent civilizations in a galaxy. There is then one more argument, using the dimension of time. So far we have been concerned with the dimension of space at a single instant in time (assuming absolute time rather than relative time as in general relativity). That is, at a given moment we assume there could be several planets with intelligent life. First this may not be the case. It might be extremely rare for multiple planets with life to exist simultaneously. However, if we look at a longer time span, such as millions or billions of years, there may be increased probability that multiple planets with intelligent life have appeared at different points in time. It is just that these planets are spread out so far in time that their lifespan ended long before the next planet with intelligent life could be born. Moreover, none of these civilizations have been able to develop interstellar travel or if they have they are located so far away from others in the universe that it would take much longer than the current age of the universe for them to have visited other planets with intelligent life.

In absence of things like tachyons, wormholes, time travel, there is a universal speed limit on how fast spaceships can travel: the speed of light. And even light can take millions and billions of years to travel from one place in the universe to another. That is how big the universe is: so big that astrophysicists adopt another unit of measurement such as parsecs or lightyears.

Fate of the universe

"If the increase of entropy is a fundamental law of the universe, then the heat death would be the inescapable destiny of the material world. So, why is it that we bother to struggle to survive? Expansion, fusion, and then annihilation. If we wish to welcome the new, then we must first embrace the end." — From a scientist just before pressing the button for nuclear detonation, 2152 AE

The birth of the universe is a mistake. If civilization is a cancer emerging quietly from the boundless stars, then war is the only common language known to all intelligent life. To correct this mistake and to clean up this tainted universe, Nanook became the avatar of entropy.

These are quotes on the path of Destruction.

Entropy

What is entropy? Entropy is a measure of how disordered a system is. In physics, especially thermodynamics, it is usually notated in equations as S. In the field of AI, it is sometimes written as H for the Shannon entropy. For most of the following, we use S for entropy as H can stand for something else in physics.

Entropy can be calculated based on the probability distribution for different configurations of the system. The closer the probability distribution is to a uniform random distribution, the higher the entropy. When a flower vase is broken and shattered into pieces, that is a process that increases disorder (by breaking the crystalline molecular structure holding the vase together), thereby increasing entropy.

Another way to calculate entropy is via the Boltzmann principle, where entropy is proportional to the log of the number of possible states. This formula is related to the first formula mentioned above.

Lastly, entropy can be calculated from a formula involving heat and temperature. In the thermodynamic interpretation, it is natural for heat to spread throughout the system rather than stay concentrated in a single place. Heat (Q) is a measure of energy transfer. It is related to other thermodynamic concepts such as efficiency (e.g. Kelvin's theory of heat as loss of energy). Temperature (T) is a statistical average measurement of kinetic energy.

The 2nd law of thermodynamics, related to the 'arrow of time', states that entropy does not decrease over time within a closed system. One implication is that heat tends to flow from a hotter to a cooler body until eventually both are at the same temperature, in which case equilibrium is reached and there is no net flow between the systems.

In a sense, crowd control abilities such as Venti's vacuum, freezing, petrification can be thought of as things that 'decrease entropy' by making a system more ordered. However, the key point to remember is that it requires energy to make things more ordered. This is not energy in the sense of Genshin or HSR, but energy in the physics sense.

Heat death

The quote above states that the heat death is the inevitable destiny of the universe. The heat death is also called the big chill or freeze. It is a theory that in an expanding universe, energy will become more and more evenly distributed and dissipated across the universe. That is when the universe reaches thermodynamic equilibrium. In equilibrium, there is no net flow of energy between systems.

Another part of this is that the universe will evolve to a point of zero thermodynamic free energy. Gibbs free energy is defined as G = H - TS where H is enthalpy. What does this mean? It is the amount of energy that can be used to perform work at constant temperature.

At this point, the universe will have reached absolute zero and perhaps a state of max entropy.

One implication of the heat death could be that the Sun will be put out, and there will be no civilization left. The average temperature of the universe is way lower than that of Earth and the Sun. The universe is extremely 'cold' in most places. In the heat death, planets like the Earth will be reduced to cold dust and stars will be put out into ashes, so that everything in the universe is uniformly at equilibrium. This is what is behind the name 'big freeze'.

The gas needed for star formation would be exhausted, stars would collapse into black holes, which would dominate the universe. Eventually black holes will go extinct over time due to Hawking radiation. In the heat death, there will be no gradients to do work (no free energy), which are needed for information processing and life.

Incidentally, this concept of equilibrium plays a role in honkai as well, being mentioned several times.

So when the honkai scientist asks 'why we struggle to survive', he is talking about this ultimate fate of annihilation of all life in the end, the erosion and return of all matter to cold dust, particles at equilibrium.

In this context, Nanook, the aeon of destruction, avatar of entropy, is the bringer of the end, the destroyer of civilizations that brings the universe closer to the heat death. When civilization is called a 'cancer' amidst the stars, that is taken to mean an anomaly when considering the ultimate the fate of the universe, where there is no life, no civilization. But the attitude of destruction is not to view life or civilization as something wonderful, to be cherished, but rather as a tumor that must be eradicated to ensure the heat death.

As for the rhetoric, 'the birth of the universe is a mistake', 'war is the common language', this just highlights the attitude that the ultimate fate of the universe is destruction, the whole point of its existence is for it to be 'destroyed' in the end, in the big chill.

A result from cosmology and general relativity is that if the curvature of the universe has hyperbolic or flat geometry ('nonpositive curvature') or if dark energy has a positive cosmological constant, then the heat death will occur. If the cosmological constant is zero, the universe will approach absolute zero over a long time. If positive, it will asymptotically approach a nonzero positive temperature and state of max entropy.

What do we mean by curvature? Something flat like a Euclidean plane would have no curvature. The shortest distance between points (geodesic) would be a straight line. The sum of angles in a triangle is 180 degrees (see parallel transport). Something hyperbolic is related to 'negative' curvature. These are things like horse-saddles. The sum of angles in a triangle is less than 180 degrees. Such manifolds are sometimes called 'open' in that they can expand infinitely in space. On the other hand, something with 'positive' curvature includes things like spheres. The sum of angles in a triangle is more than 180 degrees. Such manifolds are sometimes called 'closed' as they are finite in area.

The above is for 2-dimensional manifolds (embedded in 3-space). We live in 4-dimensional spacetime. General relativity deals with 4-dimensional manifolds. The second thing is that in general curvature can be measured by a tensor rather than a single scalar.

As for the cosmological constant (also called Einstein's constant), it has been interpreted to mean the vacuum energy of the universe, arising from quantum mechanics. This term is added to Einstein's equation in general relativity.

As for how hyperbolic/flat curvature or positive cosmological constant implies a heat death, the derivation is beyond the scope of this article and would take more time.

Implications

Note above the heat death hypothesis is just a theory. There are many other theories describing the ultimate fate of the universe. So then which one is the most probable or most accepted by scientists? Scientists used to believe the universe would end in a big crunch, but now they view the big chill / heat death theory as being the most plausible.

Assuming the heat death is true, how does that impact our view of civilization and humankind? What is the purpose of existence if in the end we will all return to dust, if in the end everything is destroyed? Why do people bother chase material things in life then, pursue wild dreams, knowing that in the end, nothing will matter? Such a nihilistic viewpoint is one way to interpret this fate, to say that life, human values, and much things are meaningless, if the ultimate fate of the universe is the big chill. Another viewpoint is that of the path of destruction: if the universe is going to be chilled to oblivion, then let us accelerate its demise and destroy everything. Time is the ultimate arbiter of the universe. In the end things will return to equilibrium.

The different paths of star rail carry philosophical connotations with them too, with some being connected to the ultimate destiny of the universe.

While the article is not to judge which path or school of philosophy is the correct dao, it should be mentioned that 1) the heat death is still a theory rather than a guaranteed truth, 2) if one wants to be very optimistic, civilization may be able to advance to the point where they can 'evade' the heat death in a number of creative ways such as reversing the flow of entropy, creating another universe using quantum fluctuations, etc. 3) the heat death is so far away in the future. Within our mortal lifespans, the heat death is almost something we do not have to worry about for now, so we can continue to engage in the pursuits, dreams, and goals of our material world. With the time spent learning more about the world and universe, perhaps we can derive greater satisfaction than just sitting around lamenting about the eventual destruction of everything or about the meaningless of it all.

And the more time spent learning more about the universe, perhaps we can one day gain the power to change our destiny and the universe's destiny. The key word is hope. As long as we have the hope that we can control our own destiny and fates, as well as the universe's, then that gives enough purpose to life. As long as one can dream, one does not need to feel confined by theories such as the heat death of the universe.

Dark matter and energy

Dark matter is a type of matter that does not interact with the electromagnetic field. Thus it is 'dark', meaning it does not absorb or emit light, making it hard to see. However, the matter is detected via gravitational effects. Dark matter is thought to comprise 85% of the matter in the universe.

The existence for dark energy arose when it was observed that the universe expansion is accelerating. Einstein originally introduced a cosmological constant term into his gravitational field equations so that it could yield a solution of a static universe. However this equilibrium is unstable (this is a concept from dynamic systems and chaos theory). Slight perturbations could make the universe keep expanding or keep contracting. Because of the uneven distribution of matter in the universe, these perturbations are inevitable. Thus in reality, we do not live in a static universe, but rather a dynamic one (one that is expanding).

Another example of an unstable system involves a ball sitting at the top of a hill (shaped in a dome). If the ball is pushed in any direction, it will accelerate away from its initial position. An example of a stable system involves a ball sitting at the bottom of a spherical valley (take the dome and invert it). If the ball is pushed in any direction, it will eventually return to its initial position (assuming friction dampening any pendulum effects).

In general relativity, the static universe in Einstein's solution is unstable. When perturbed by matter, it will not return to a static configuration, but either expand or contract.

What is the actual value of the cosmological constant? Observations from cosmology indicate a very small positive vacuum energy / cosmological constant. However, quantum field theory (qft) predicts this to be very large instead. This leads to an apparent paradox, and this is one of the many issues faced when trying to reconcile general relativity and qft.

General relativity and QFT are the two main modern theories of physics, discovered in the 20th century. General relativity describes gravity and the theory of large scales and massive objects, whereas QFT describes EM, the strong, and the weak forces as well as the theory of small scales. However, an open problem in physics is how to combine or merge the two theories into one grand unified theory. This is one of the final problems that Einstein himself tried to solve (Einstein having invented to general relativity and contributed much to the founding of quantum theory).

There have been many attempts in history, though a recent attempt called string theory has been gaining more traction. Many predictions of string theory have not yet been experimentally verified. One challenge is where to find a natural phenomena where general relativity and QFT could interact. One example is a black hole, but observing black holes and getting close enough to one is quite tricky.

As it stands, string theory remains a beautiful mathematical construct. Whether reality is actually described by such a symphony of strings remains to be proven.

But this serves to highlight that there are still gaps in our theoretical understanding of the universe. Although we believe the heat death is a probable end to the universe, there is still much that we are trying to learn and figure out about fundamental physics. And who knows, if string theory or some other grand unified theory is finally confirmed, maybe that could completely revolutionize or change our understanding of the fate of the universe. It may even pave the way to a possible solution to change that fate.

antimatter, antiparticles, quantum field theory