June 21, 2021
The butterfly effect 3/5
Irreversibility, memory and entropy
Butterfly effect, further investigation ! Before continuing your reading, it is still time to explore the history of chaos theory and broaden your perspective by looking at chaotic systems from the perspective of interdependence. Are you ready ? So keep this information in mind, we will put it in perspective with the notions of irreversibility and entropy.
The irreversibility of the phenomena
Course of time, arrow of time
There is no consensus in physics on the concept of time. Or in philosophy, for that matter. This subject probably deserves a full article. Lack of time… I’d settle for a shortcut here ! In an attempt to shed light on the mystery of time and to lay the foundations for this article, I borrow from the french physicist and philosopher of science Etienne Klein the distinction between the course of time and the arrow of time.
« To put it in one sentence, the course of time ensures the continuity of the world — it prevents the world from disappearing — while the arrow of time produces stories whose epilogue is never the same than the beginning. » 
« Let’s say that the course of time will prevent you in the future from having a lower age than your present one, and the time arrow will prevent you in the future from looking like the child you were. » 
Etienne Klein’s words are easily conceivable on our scale : we experience the irreversibility of phenomena. Our experience continually teaches us that we cannot go back in time. You can’t put the eggs that were used to make the omelette back in the box.
What about at the microscopic level ? The answer is far from obvious because things are not really comparable. On this scale, in fact, one cannot have a direct experience of time, nor any other, one can only observe phenomena. And our observation leads to a completely different interpretation.
Experiment Vs Observation
All the equations of microscopic physics, such as the Schrödinger equation, are reversible in time. Which means that whatever they allow to be done, they also allow to be undone. Thus, particle collisions can be performed in the laboratory… and also reverse collisions. But let’s be clear : it’s the phenomenon that is reversible, not time !
Let us note all the same that a particle collision, even if it is reversed, does not make much sense for us, it is the case to say so ! Because we never experience it. Therefore, whether time at the microscopic level flows one way or the other, whether time and phenomena are independent of each other, it remains for us only an observation unrelated to our experience. However, are we sure what we’re looking at ? We’ll come back to that.
If for reversible phenomena, there is therefore no time arrow, then how can we explain the emergence of this arrow at the macroscopic level ? Or, in other words, how can macroscopic irreversibility be explained from microscopic physical laws that are all reversible ?
« It is not excluded that the course of time and the time arrow are ultimately the result of one and the same, deeper reality, that they are both products of underlying phenomena that a « new physics » may bring to light (…). » 
It would seem that Nassim Haramein’s « new physics » reveals an underlying phenomenon. First of all, for him, time is a human concept. And not a feature of the universe : what characterizes the universe is memory.
An underlying phenomenon…
« Without memory, there is no time. If you can’t remember the previous moment, you have no sense of time. » 
In his theory of the unified field (connected universe), Nassim Haramein shows that the universe encodes information on the surface of space-time. The encoding is so meticulously done consecutively that it gives us that familiar feeling of « time passing ». Thus is assured « the continuity of the world » of which Etienne Klein speaks.
The information stored by the universe forms a regular progression that we interpret as the passage of time, with its beginnings and its epilogues. Beginnings and endings that are never the same because their respective space-memory coordinates  can never be identical. The only way for us to distinguish an epilogue from a beginning is to remember the beginning. And what differentiates a beginning from an epilogue is the learning that takes place between the two . Each system learns about itself and progresses. Since no system is isolated in the connected universe, everyone participates equally in the learning of others. Thus, at any scale, no system can ever return to the space-memory coordinates it was at, and in that sense there is a time arrow. An arrow of time that, so to speak, crosses scales.
Therefore, while the laboratory reverse collision does not take us back in time, it is not incompatible with a time arrow. The particles are in fact continuously informing themselves, encoding each time information that little by little accumulates to form their memory. In the same way, we can believe that the trajectory of a classical oscillator, like a pendulum, always passes through the same points again and again. In reality, each time the pendulum passes, these points are located at different spatio-temporal coordinates .
… for an emerging property
Moral : The storage of information allows both the continuity of the world to be assured and the epilogues to be always different from the beginnings. In other words, it explains both the course and the arrow of time, and thus the irreversibility of phenomena.
Our age and appearance will not more change with the notion of memory than with the notion of time. But storing offers an interesting possibility : connecting to a known age or physical state in the past. Such a possibility exists because of the holographic nature of the universe , which makes all information available at every point in space. Then, from there, it is possible to modify the information encoded to precise coordinates, and thus our feeling of this information in the present and for the future.
Finally, the dynamics that construct the timeline of the universe logically follow the dynamics that underlie the universe. This dynamic constantly does, undoes and redoes the material world. Through this feedback between emptiness and matter, it creates the illusion of movement, and therefore of time and irreversibility that we experience. Then, time becomes an emergent property  of the dynamics of the universe.
If for the physicist Ilya Prigogine, « there is an arrow of time at the macroscopic level, but the microscopic level creates the illusion that there is none » , for Nassim Haramein, there is an arrow of time, from the microscopic to the macroscopic scale, because the universe stores information.
« Entropy is the essential element introduced by thermodynamics, the science of irreversible, i.e. time-oriented processes. » 
Complexity rather than chaos
What is entropy ?
Entropy is defined in a closed system, i.e. a portion of space that has no interaction with the outside. Here I approach this concept from the angle of the notion of heat .
Heat refers to a flow of energy between two systems. It is a thermal agitation transfer  which, as its definition indicates… is messy ! Shocks between particles create an agitation that propagates in all directions, with heat transfer always taking place from the hottest to the coldest system.
An example ? You put a cup of hot tea in a cold closed room. The tea and the room form an isolated system, which evolves as follows :
- In its initial state, tea, due to its high temperature, has the most important thermal agitation.
- Gradually, and irreversibly, the tea will transmit its thermal agitation to the room. Its temperature will therefore decrease, while that of the room will increase, until the temperature between the tea and the room is finally homogenized.
- The system will never spontaneously return to its initial state. For the tea to warm up, it would have to provide work (a bring of energy). The equivalence between the heat received (Q) and the work done (W) is : W + Q = 0, i.e. W = — Q (which means : the work produces heat, which is transferred to the outside).
What does entropy measure ?
Entropy measures the tendency of energy to disperse. It quantifies two things :
- the degree of dispersion of energy (in all its forms : thermal, chemical, electrical) among the particles of a system,
- and the degree of distribution of these particles in all directions throughout the accessible volume.
Entropy is a macroscopic phenomenon that only makes sense if there is a high number of particles, a sine qua none condition for the appearance of irreversibility. Over time, the entropy can only increase. There are more ways to distribute energy than to concentrate it. You’ve probably noticed that it’s very easy to create chaos in a Rubick’s Cube, but there’s only one way to put it in order (even if there are several methods to do so)!
Any closed system eventually reaches the state of maximum entropy, in which energy is uniformly distributed. A state also known as « thermodynamic equilibrium ».
A pendulum story
Thermal energy is one of the various forms that energy can take in the universe. There is also electrical energy, chemical energy and mechanical energy. The latter also occurs in two forms : potential energy (related to altitude) and kinetic energy (related to speed).
Thermodynamics, which appeared in the nineteenth century, is historically the science of heat. Because thermodynamicists have demonstrated the irreversible transformation of kinetic energy into thermal energy, called « entropy production », it can also be defined as the science of large systems in equilibrium, or the science of irreversibility.
Potential energy, kinetic energy, entropy… are you lost ? Stay with me, I’ll get my pendulum and explain ! If I place the mass of the pendulum in the high position, it has a maximum potential energy, because of its altitude, and zero kinetic energy since it is immobile. Careful, I’m dropping everything ! When it passes through its lowest point, the mass has, in fact, zero potential energy. On the other hand, its speed, and thus its kinetic energy, are maximum. As the mass moves up on the other side, it loses speed and, at the same time, kinetic energy. But as it gains height, its potential energy increases.
As the pendulum swings, it is braked by air resistance. It then loses in kinetic energy, or more precisely, its kinetic energy is transformed into thermal energy : entropy increases.
Quality energy… or not…
What one has to understand is that not all energies are equal. Thermal energy is much less « useful » than others, in the sense that it can never be fully transformed into work, whereas the opposite is possible.
Thermodynamics thus teaches us the following two principles :
1st principle : In an isolated system, the total amount of energy, including thermal energy, is conserved.
In the universe, energy can neither be produced from nothing nor destroyed. It can only change form, or be transmitted from one system to another. In the case of the pendulum, so we have : Mechanical energy + Thermal energy = Constant
2nd principle : If the amount of energy is conserved, this does not mean that the system is stable. For the quality of energy, on the other hand, is deteriorating : more and more energy is dispersed into unusable thermal energy.
I’ll take my pendulum back and explain ! While the mass is in motion, it is subjected to air resistance. This causes a microscopic disordered agitation of the atoms that make up the mass, and a transfer of this thermal agitation from the system to the outside environment. The mass loses speed, its kinetic energy is transformed into thermal energy which is dispersed and becomes unusable.
So there is still as much energy in the system, but of lesser quality : the entropy increases until the system reaches thermodynamic equilibrium (the state of maximum entropy). It can also be said that the second principle establishes the irreversibility of phenomena.
Between order and disorder
According to thermodynamics, entropy can therefore only increase in the universe, considered by standard physics as an isolated system. So be it. However, we have seen an irreversible increase in complexity since the « Big Bang ». The universe has indeed evolved from a « plasma soup » close to thermal equilibrium to the formation of galaxies, planets and even human beings. That is to say, structures that are as orderly as possible.
It would seem that order does not therefore contradict the tendency of the general movement of the universe to disorder. Does this mean that organization has a cost and disorder is the price to pay for the organization of the universe ? From a thermodynamic point of view, it’s not so strange. One can indeed conceive the appearance of ordered structures as long as disorder developed simultaneously.
So everything would be for the best in the best of isolated systems… if dissipative structures did not exist !
Dissipative structures are open systems. Far from thermodynamic equilibrium, they are the seat of spontaneous organization. The physicist and chemist Ilya Prigogine named them so in 1969.
Associating the terms structure and dissipation is like associating order and chaos : a bit paradoxical, isn’t it ? Not if we look at the second principle of thermodynamics from a new angle. Not the one where irreversibility leads the system to the state of maximum entropy, but the one where irreversibility becomes a source of coherence and self-organization.
Unlike chaotic systems, which depend only on initial conditions, dissipative structures are conditioned by permanent disturbances or fluctuations.
« Our world presents persistent interactions (…) Classical mechanics considers isolated movements whereas irreversibility only makes sense when we consider particles immersed in an environment where interactions are persistent. » 
In this sense, an aneurysm is more of a dissipative structure than a chaotic system .
The division of the large swirls that make it up into smaller swirls allows a transfer of energy from large to small scales. We talk about energy cascades, which cause high energy dissipation, and thus lead to an increase in entropy.
This state of non-equilibrium is nevertheless stabilized thanks to the energy that the vortex system draws from its environment. Precisely, it accumulates energy by resonance , and thus compensates for entropy. Finally, it self-feeds and maintains the organization of its structure… to some extent, however. In the case of an aneurysm, in fact, the natural evolution is towards the inevitable increase in its caliber. Eventually, every aneurysm is threatened with rupture. Indeed, the more the blood pressure increases, the larger the radius of the aneurysm, the higher the pressure on the wall, the less it can resist…
Entropy and negentropy, a great love story
Before Ilya Prigogine, Erwin Schrödinger  had already pointed out the physical possibility of « negative entropy » processes. Schrödinger wanted to mark the difference between physical thermodynamic processes and life processes. Along these lines, the french mathematician and physicist Léon Brillouin coined the term « negentropy » in 1956 to replace the term negative entropy .
Thermodynamics teaches us that the tendency of energy is to go from order to disorder. Experience shows, however, that irreversibility is rather a source of coherence in the universe. Through dissipative structures, and at the cost of a large amount of energy, certainly. Because the increase of order inside a structure leads to an increase of disorder outside and vice versa.
Rather than being opposed, entropy and negentropy are in fact complementary. They are part of the same dynamic, that of self-organization, that which builds order out of disorder.
As we will see in the next article Gravity, entropy and self-organization, the difference between physical thermodynamic processes and vital processes is not as clear-cut as it seems. The notions of feedback and resonance, highlighted by Nassim Haramein and essential to the constitution of a hierarchical level of organization, are valid for all processes !
Notes and references
The irreversibility of the phenomena
 KLEIN Etienne, Faut-il distinguer cours du temps et flèche du temps ? [Is it necessary to distinguish between the course of time and the arrow of time?], p. 9 (in French)
 KLEIN Etienne, Le temps, son cours et sa flèche, [Time, its course and its arrow], L’université de tous les savoirs, conférence n°188, 6 juillet 2000 (in French)
 KLEIN Etienne, Faut-il distinguer cours du temps et flèche du temps ?, op.cit., p.10
Memory rather than time
 HARAMEIN Nassim (2015, 20 juin), L’univers connecté [The connected universe]
 Since we are talking more about memory than about time, it is more accurate to speak of memory-space rather than space-time.
 The notion of feedback was discussed in particular in the section Chaotic systems in the connected universe of article 2.
 See the helical dynamics of the solar system : the planets and stars never pass through the same coordinates, because they move in a spiral around the sun according to Nassim Haramein’s model
 The holographic principle will be developed in the article Gravity, entropy and self-organization. You can also read the article The holographic universe : the underlying unit.
 « An emergent property is a characteristic that is unpredictable (or at least invisible) at the local level and that appears at the global level. It results from the collective activity of the system’s constituents ». ZWIRN Hervé, Les systèmes complexes [Complex systems], Paris, Editions Odile Jacob, 2006, p.35
 PRIGIGINE Ilya quoted by Etienne KLEIN, Faut-il distinguer cours du temps et flèche du temps ?, op.cit., p.11
 PRIGOGINE Ilya, La fin des certitudes [The end of certainties], Paris, éditions Odile Jacob, 1996
Complexity rather than chaos
 We will see in the next article Gravity, entropy and self-organization that entropy can also be approached from an information perspective.
 Thermal agitation, or microscopic agitation of molecules and atoms, is measured by temperature.
 PRIGOGINE Ilya, La Fin des certitudes, op.cit., p.133
 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. See also the section on aneurysm as a chaotic system in Article 2.
 The concept of resonance has already been discussed in article 1 Chaotic systems and will also be detailed in article 4 Gravity, entropy and self-organization.
 In his book What is Life ?, Londres : Cambridge University Press, 1944
 The term « syntropy » proposed by L. Fantappie in 1944 is sometimes used, but it was not adopted.