July 15, 2021
The butterfly effect 4/5
Gravity, entropy and self-organization
After exploring the history of chaotic systems and beginning to put chaos theory into perspective with Nassim Haramein’s theory of the connected universe, I continue my exploration of the links between entropy and self-organization that can be observed throughout the universe.
Ilya Prigogine opened the box of isolated systems by proposing a physics of dissipative structures. Nassim Haramein has shown that there is no box to get out of ! Because in a universe where everything is connected, nothing is isolated from nothing. So, if the universe is not a closed system but is interacting with other universes, what happens to the notion of entropy, which is intimately linked to closed systems ?
In this article, I invite you to examine the idea that in a universe made up of black holes connected at all scales by a feedback of information, the notion of entropy is entangled with that of gravity. In other words, I am exploring the possibility of reconciling the increase in entropy predicted by the second law of thermodynamics with the increase in self-organization in the universe. Let’s go !
A formula for entropy
« You start with a random group of atoms, and if you light it long enough, it shouldn’t be so surprising that you get a plant. » 
An article  published in 2014 in Quanta Magazine describes how the physicist Jeremy England  developed a simple mathematical formula describing entropy. It explains the ability of certain groups of atoms to capture energy from their environment and dissipate it in the form of heat, under certain conditions :
- Being driven by an external energy source (such as the sun for example)
- Being surrounded by a bath of heat (like the ocean or the atmosphere)
These atoms manage to gradually self-structure themselves in order to dissipate more and more energy. To develop his formula, England relied on the work of physicist Chris Jarzynski and chemist Gavin Crooks. These scientists have shown that the entropy produced by a thermodynamic process corresponds to a simple ratio : the probability that atoms undergo this process divided by their probability of undergoing the opposite process. This ratio increases as the production of entropy increases : the behaviour of the system then becomes more and more « irreversible ».
According to this formula, in principle applicable to any thermodynamic process, systems far from equilibrium can therefore keep their entropy low by considerably increasing the energy of their environment.
Example with photosynthesis. During this phenomenon, a plant absorbs sunlight, which is extremely energetic. It uses it to make sugars and then rejects infrared light, which is much less concentrated. Thus, as sunlight dissipates, the overall entropy of the universe increases. However, during its lifetime, the plant will prevent itself from decomposing by keeping its internal structure in order.
Jeremy England shows that the absorption and emission of light are due to resonance phenomena.
For optimised energy dissipation
« We can show very simply from the formula that the most likely evolutionary outcomes will be those that absorb and dissipate the most energy from external environmental inputs to achieve them. » 
« This means that clusters of atoms surrounded by a bath at a given temperature, such as the atmosphere or the ocean, should tend to organize themselves to resonate better and better with the sources of mechanical, electromagnetic or chemical work in their environment. » 
Jeremie England talks about dissipation-induced matter adaptation. He identified two mechanisms that allow an increasing amount of energy to be dissipated over time (increasing entropy):
- Self-replication : According to him, the theoretical minimum dissipation that can occur during the self-replication of RNA molecules and bacterial cells is very close to the actual amounts that these systems dissipate during replication .
- Structural organization : under certain conditions, particle systems will spontaneously organize themselves by adapting their structure to better dissipate energy. For non-living systems, we can cite the vortices of turbulent fluids. They reproduce spontaneously (self-replication) according to a fractal law (structural organization).
On the right frequency
As I explained in article 2, these vortices form in an aneurysm 
when blood rushes into it because its behavior becomes turbulent. There are many spatial and temporal scales in the aneurysm sac. The size, location and orientation of twirls are constantly changing.
However, these vortex dynamic systems behave more like dissipative structures than chaotic systems. In fact, they reproduce spontaneously by drawing their energy from the surrounding fluid. Precisely, they accumulate energy by resonance. And in doing so, they also dissipate a large amount of it. Thus, the increase in order inside the structure appears in dependence with the increase in disorder outside.
Dynamic systems are ultimately sensitive not to initial conditions but to resonances. Henri Poincaré highlighted it with the problem of the three bodies, Ilya Prigogine developed it with the dissipative structures : resonances invite us to think differently than in terms of trajectories.
« The notion of resonance characterises a relationship between frequencies (…) Resonance occurs when (…) two frequencies (…) correspond to a simple numerical ratio (one frequency is an integer multiple of the other) (…) Frequencies, and in particular the question of their resonance, are at the heart of the description of dynamic systems. » 
Turbulent fluids behave as such because the rotational forces due to gravity outweigh the frictional forces due to viscosity. And they even have a link with black holes !
Towards black hole entropy
Indeed, a black hole can be described as a bubble of viscous fluid, then its behavior being close to that of a turbulent fluid. We’re talking about a fluid-gravity match.
Moreover, in the holofractographic model, a black hole behaves as such because the rotational forces of space-time exceed the frictional forces. The fractal character of a turbulent fluid is found in the geometry of the horizon of a black hole when it is modified by the absorption of a material object. The black hole emits gravitational waves, whose dissipation by cascades of energy allows it to return to its equilibrium form.
Jeremie England’s work shows that particles tend to dissipate more energy when they resonate with a driving force. Could the source of the electromagnetic work that this physicist is talking about be the gravity that Nassim Haramein is talking about ? Indeed, what better than a black hole in the theory of the connected universe to absorb and dissipate energy ?
Let us add that this theory establishes that black holes are linked by a fractal law from the infinitely small to the infinitely large, and this dynamic can be explained at all scales !
Information, gravity and entropy
At first glance, talking about entropy for a black hole isn’t very intuitive. In the standard model at least. Entropy is related to temperature. Black holes do not emit radiation. Therefore, they have no temperature and no entropy.
In 1972, Stephen Hawking showed that the surface area bounded by the horizon of a black hole cannot decrease. Jacob Bekenstein then saw an analogy with the second principle of thermodynamics and, in 1973, he argued that black holes do indeed possess entropy, represented by their event horizon.
At the time, this theory was unacceptable to Stephen Hawking, who set out to prove that it was false… until his own calculations proved it to be correct. Using quantum physics to explain the mechanism of radiation, he showed that the shape of this radiation is exactly that of an object in thermal equilibrium. And that its temperature is proportional to surface gravity. Finally, in 2004, he recognized that black holes have entropy, that information can be retained, and that black hole horizons absorb and emit coherent information.
According to Bekenstein, the information has a minimum size equivalent to a Planck surface, a quantum pixel the size of a Planck length of side. Based on this work, Gerard ‘t Hooft showed in 1993 that all the information contained in the volume of a black hole can be expressed in terms of information on the black hole horizon. The information is then stored in the form of a fingerprint. This is what Hooft called the « holographic principle » . The information absorbed by a black hole is fully restored during the quantum evaporation process. The holographic solution found represents the entropy of the black hole, it’s equivalent to the temperature.
The quantification of information
The entropy of black holes is a measure of the amount of information they contain, but to which we do not necessarily have access . The interpretation of this definition is debatable according to :
- The theory and therefore the frame of reference used (standard or holofractographic)
- The basic unit used to quantify the information (area or volume)
The entropy of a black hole is less than a quarter of the surface of its horizon.
In the standard theory, a Planck area is used as the fundamental unit of information. Thus, a black hole whose horizon consists of Planck’s areas A has a maximum entropy of A/4 units. From an information point of view, it is as if the entropy is written on the black hole horizon and each bit of information, as 0 or 1, corresponds to four Planck areas.
Nassim Haramein’s model is much more elegant. By using spheres and not surfaces as units of information, he establishes a direct relationship between the volume of a black hole and its surface, and thus its entropy :
- The volume of a black hole is a sphere made of small Planck spheres.
- There is a natural ratio of 1/4 between a sphere and its equatorial surface  (4πr² / 4 = πr²).
- The surface of the black hole is lined with equatorial surfaces arranged in the pattern of the flower of life.
Entropy can thus be quantified in a very simple way .
« Information is the interconnected fabric of our universe. What are the dynamic processes involved ? Feedback systems (like a fractal), which lead to non-linear evolution and local unpredictability . The interactivity (intercommunication) of such a system, with its creative and innovative aspects, leads to exponential assimilation and syntropy. Far from the random and mechanical processes foreseen by the law of entropy, which is in itself a highly theoretical case of an isolation and division scenario. » 
Order and disorder coexist thanks to this feedback dynamic. Information is always trying to organize itself, it tends tirelessly towards more complexity and towards the advancement of consciousness. The feedback of information is established by constant to-and-fro between the infinitely small and the infinitely large : it goes from the quantum vacuum to matter and vice versa. Particles appear and disappear continuously through the fundamental process of materialization/dematerialization of the vacuum. The origin of the material « order » is the feedback between matter and vacuum. This exchange happens in such a short time that it eludes us.
But if each interaction with the vacuum permanently breaks the continuity of the manifestation of matter, how can we explain that forms are preserved in time ? Thanks to the encoded information about the structure of space, which, as it interacts with matter, provides a memory for the structure. In the end, from moment to moment, every structure is recreated fast enough and close enough to the previous one that it gives us the illusion of experiencing continuity in form.
So be it. But in this case, shouldn’t there be a pattern, a structure at the base of all the others, which would serve as a reference ? What if it’s the vacuum structure…
The vacuum structure
Vacuum is not only random, it also has a structure. Which grows in a… fractal fashion. From then on, we can better understand how certain privileged physical quantities — such as the mass of the proton, the speed of light or the gravitational constant — keep their respective values no matter what happens. Why are the constants constant after all ? Because they obey a precise and perpetually renewed division of the structure - and therefore of the energy — of the vaccum. It is not the value of these privileged magnitudes that is constant, it is the dynamics of the universe to which they obey.
And here are the notions that have just been discussed in infographics :
- The universe is an open system.
- The universe is an expanding black hole.
- It is made up of black holes distributed according to a fractal law, from the infinitely large to the infinitely small.
- A fractal is an open equation that allows feedback from one scale to another (or from one black hole to another).
- The exchange of information in the universe is based on the principle of resonance (similar frequencies attracting and « working » together).
- The information is stored in memory, encoded on the space-time structure.
- The exchange of information in a region of space creates an energy called mass.
- Mass energy creates gravity.
- Gravity is the result of an exchange between the information contained in the volume of a black hole and that present on its surface.
- The entropy of a black hole is a measure of the amount of information it contains.
- The volume of a black hole is made up of Planck spheres (the smallest unit of information that defines our relationship to the universe).
- The information contained in the volume of a black hole is projected onto its surface (holographic principle).
- The surface of a black hole is lined with Planck’s equatorial surfaces.
- An equatorial surface of Planck is precisely one quarter the surface of a Planck sphere (4πr² / 4 = πr²).
- The totality of the equatorial surfaces represents the necessary and sufficient surface to quantify the entropy of the black hole.
- As the universe expands, the surface area of our black hole-universe increases.
- Thus the entropy of the universe increases. However, its gravitational field is also increasing.
- Since gravity is a ratio between the volume and the surface of a black hole, entropy is proportional to volume and inversely proportional to gravity.
- So yes, the entropy of the universe is increasing, but it can never increase disproportionately because it interacts with gravity, which constantly balances it by creating order.
- Gravity is a source of resonance and self-organization ; it keeps structures in an ever-changing order.
- Entropy and self-organization appear in dependence.
This is how the universe organizes itself, at the cost of a large amount of energy. In the next and last article of the series on the butterfly effect, we will go back down to Earth and see how this dynamic applies to the scale of the MeToo movement.
Notes and references
A formula for entropy
 ENGLAND Jeremie, quoted by Natalie Wolchover, A new physics theory of life, in : Quanta magazine, 2014
 WOLCHOVER Natalie, op.cit.
 Jeremie England is an assistant professor at the Massachusetts Institute of Technology. Its theoretical results are generally considered valid, but the interpretation of its formula has not been proven.
 Jeremie ENGLAND, quoted by Natalie WOLCHOVER, A new physics theory of life, op. cit.
 September 2013 article published in the Journal of Chemical Physics
 An aneurysm is a dilation of the wall of an artery that causes the creation of a pocket inside which the blood changes its behavior.
 PRIGOGINE Ilya, La Fin des certitudes[The end of certainties], Paris, ed. Odile Jacob, 1996, p.45
Information, gravity and entropy
 See also the article The holographic universe : the underlying unity to understand the link with holography, from which the principle takes its name by analogy.
 To get an idea of what I mean, you can read this alternative interpretation of Schrödinger’s Cat experience.
 The equatorial surface is the flat surface obtained when cutting a sphere perfectly in two.
 Note that this approach also allows us to find a quantum solution to gravity, as well as a solution to the information paradox.
 Authors’ note : « A local phenomenon appears to be unpredictable when it depends on the global evolution of the universe. »
 BROWN William and HARAMEIN Nassim (2014, January 23) Space-time as Information — An Ordering Principle of Living Systems