**Considerations on the subject of chaos**

*A few phrases at the beginning*…in the beginning was chaos …. from chaos arose order ….. or chaos is the basis for the principle of self-organization which explains the present universe with its complex structures … etc.

**What is the meaning of chaos? How can chaos exist? Where did chaos come from?**

Chaos can´t exist by itself, by its inner power, by its nature. It can´t hold together by its own properties. Chaos cannot sustain itself in chaotic behavior. Chaos must be sustained, allowed to behave chaotically, by limiting conditions from the outside. See particles of gas. These particles must be limited in closed space or limited by gravitational field. In the other hand particles of gas must be in constant motion.

Upper two conditions defined the chaotic behaviour of gas. The limited space and the motion (the change).

How to determined the gas? Firstly, the gas must be bound. By gravity or anything else – boxes, vessels. etc.

Where did such boxes come from? *Imagine only the gas – how to form it into solids like boxes?***The gas without bonds – such gas could not exist There must be bounds for interaction – reciprocal collisions among particles of gas. **

*The situation with the chaotic behaviour not only of the gas but also of the quantum fluctuations is similar to the probability calculus. Particles with no external limits would expand to infinity. Thus, there is no chance of at least two particles meeting. Likewise in probability – there must be limits (edges of the dice, sides of the coin, given possibilities, etc.). If there were no limits we cannot evaluate probability. It is hard to calculate the probability of one hard-to-differentiate event out of an infinity of possibilities of hard-to-differentiate events.* *However, we know that when we look more closely we discover still new details, and likewise when we go the other way, to a great distance – still new and different structures.*

**How to cancel chaotic behaviour?** How to cancel gas properties? Very easy. Put the gas into closed box. After that let´s fly to intergalactic space. Open the box and all chaotic behaviour will be over. Gas will not exist from this moment. But each particles of the gas had some movement (*mass times speed*). The movement didn´t dissappear. The particles are free to move freely through space, each in the direction of its velocity after leaving the box. At some distance from the box, the particles will occasionally collide, but at multiples of the distance from the box, each particle will fly to its own side without ever colliding with another particle. Until particles reach the nearest galaxy with their stars and planets.

**Go on!** Imagine only particles in closed box in empty space (without galaxies) – imagine material particles of chaotic gas motion. Every particle has its own mass. Every particle weighs something. We will open the box and what will happen? The particles are free to move freely through space, each in the direction it had after leaving the box. But we are in the empty space without galaxies. In other words, the particles fly into free space and **if their velocity is less than the escape velocity** they collide again at the starting point. But the gas will no longer exist. The particles will be motionless together, at most oscillating due to internal atomic motions.

**If their velocity is greater than the escape velocity**, then the particles will move away to “infinity”. But we already know from inertia and spacetime that the slightest matter deforms spacetime. In short, the free particles will move for a long time through the gently deformed spacetime until they come together again at another place – after many orbits of the curves of the deformed spacetime. *See Inertia*

Imagine our universe which is filled by moving particles. Every particle has its own mass. These particles interacts with each other by collisions among them. They are attracted to each other, but they will never be away from each other. The range of their appearance defines the dimension of the universe. It doesn’t have to be just particles, but perhaps the basic vacuum fluctuations of the quantum field. *The universe must be limited and changeable, otherwise chaos could not exist. See condensation nuclei of clumps of matter based on exciations of omnipresent quantum field.*

**Conclusion:**

**The gas as such exists only in closed space or with gravity forces. Without gravity forces or without closed space there is no gas as we understand it – colliding particles.** **To stretch the space infinitely – there are no collisions, no gas, no random fluctuations, no chaotic behaviour. Chaos without collisions is not the chaos.** Collisions are given by external forces – gravity or closed space like vessels or anything else. *We quietly postulate this, but it’s important to think about it in more detail.*

**Without a closed space or gravity forces, there is not only no gas, but there is no chance to condense into a liquid or solidify into a solid.**See phase transitions.

**Chaotic behaviour needs bounds. Chaos needs boundary conditions. Without bonds, without boundary conditions there is no chaos, no chaotic behaviour.**

**In the beginning of the universe there was no chaos. In the beginning there were primordial origins of boundary conditions.*** The result of boundary conditions is the chaotic behaviour of everything inside the boundary conditions. Not mention wildly „bubbling“ quantum fluctuations.*

It is impossible for ours (humans) to explain the subject of primordial origins of bounding conditions (gravity, closed space) by derived thermodynamical equations describing behaviour of bounded chaotic gas which depends on upper mentioned bounding conditions.

*If the chaos can´t support itself then the chaos is unable to form itself to higher structures. Especially organized organism. The flow of energy through chaos doesn´t solve anything. See self-organization theory. We need chaos and the difference of an energy levels, after that there are some germs of organized structures.*

the well-known thermodynamic equation for the behaviour of an ideal gas for a given pressure, temperature and volume** pV = nRT** needs closed space, it doesn´t matter if the universe, the atmosphere of the Earth or closed vessel or a cylinder with a piston inside that.

For thermodynamics we need at least two different chaotic environments. One of which is closed. See a closed volume of gas in the atmosphere. Two differently chaotic environments in terms of the intensity of chaos. Only then does thermodynamics begin with its equations. As in physics or mathematics, we must have at least two different dimensions or values – distance, volume, area, force, speed, time, intensity, voltage, etc. Then we can compare, measure and solve. Then we can generalize and predict and verify by measurement, etc.

To have energy we must have at least two or more wavelenghts. Only one wavelenght there is no ratio – only one value equals to 1 (or anything else as we wish). The value of energy is given by ratio of measured energy to base unit for energy.

Conservation of energy (matter) is valid only for isolated space like in second law of thermodynamics. The sum of total energy before the experiment in isolated space is equal with the sum of total energy after the experiment.

**The law of conservation energy or of conservation shapes or structures like pots or artworks at all. The law of conservation of information? **The question is the category of space – open, closed or isolated space. There could be a change in the category of space in the universe.

Not only the law of conservation energy, but conservation of frequency or shapes, space, volume or artworks which are sometimes broken? Where is the point of view? What about the frequency. What does the frequency mean? Regular changes or nearly regular changes? See probabilistic distribution with peak in the middle. How long the frequency must to be or how many? Where is the point of view for valuating what is frequency, how many are there parts and so on. What about the part of frequency? Like the part of the pot which is created by the potter. Such laws are valid only for isolated space. And what does it mean the isolated space? Is it even possible to have that kind of space in the universe?

**Where did the information come from? Where did all “regular” changes come from in such indescribable random cirmcumastances of quantum foam. ****new m****usic songs, art works, inventions, new ideas, etc. The law of conservation of new music songs, art works, inventions, new ideas, etc. information? See entropy – informations, shapes and structures.**

Very important short remark about temperature. Briefly – the zero point degree celsius (0°C) temperature was chosen by A. Celsius as the temperature at which ice melts or water freezes at a defined atmospheric pressure. 100°C means the temperature of boiling water at a defined atmospheric pressure. These two points are determined by the temperature scale. As well as two points in mathematics, a straight line is determined. O.K. Go on. Scientists (Boyle, Mariott, Gay-Lussac, Pascal, etc.) investigated the behaviour of gases. Change in their volume depending on temperature and pressure. At constant atmospheric pressure, they found a reduction in the volume of gases studied. Air, nitrogen, hydrogen, etc. The reduction in temperature leads to a reduction in the volume of gas. Expressed mathematically — we get a linear dependency — a line with a given direction. How many different gases so many different directions. That was the premise – see the figure below.

But what was a tremendous surprise was that these divergent directictions after their extrapolation meet at a single point, or in a given area, according to the accuracy of the measurement. See next image.

Furthermore, it has been developed on the basis of passed measurements of the theory of ideal gas. this theory works with a gas that behaves ideally – without interfering with internal particles. Light gases such as hydrogen and helium are closest to the ideal gas. But these gases condense at a sufficiently low temperature. Whereas the ideal gas does not condense until temperature, when its volume is reduced to zero. This is equivalent to a temperature of -273.15°C. Temperature absolute zero.

It should be added that this temperature was determined only and only by extrapolating to the ideal gas on the basis of measurements made for real gases.

**Thus we have a common point at which the directives of all light gases meet – so close to the ideal gas.**

But this point is only and only our extrapolation. We know nothing about how the gas behaves in the close approach to absolute zero. In fact, a real gas at such a low temperature does not exist – whether hydrogen or helium is in the liquid or solid phase at such a low temperature. There is another question – **does absolute zero temperature even exist?** I mean absolute nothingness.

Out of nothingness the our universe was created. However, we already know that our universe did not have to have a nothingness, i.e. zero beginning, but there were still “zero” vacuum fluctuations in an infinite ocean of quantum field. And at some point, some vacuum fluctuation “did” for itself, and we have the origin of our universe with all that accompanies it – including ” inflated” inhomogeneities from the original “disturbed” states of infinite and indescribable vacuum fluctuations. We are modulated on the errors of the failure states. Better said, on the chaos of the failure states.**It can be the same with temperature.** Absolute zero temperature in the strict mathematical sense does not exist in real nature. To consider infinitesimally small temperatures is not yet of much use. *Compare with the basic vacuum fluctuations of the quantum field. This state is a result of Pauli’s exclusion principle. Not to mention the Heisenberg uncertainty principle. *

See **thermodynamics**There are a large number of equations of state for real gases. These equations become more complicated the higher the accuracy required and the wider the range of pressures and temperatures we want to describe and the closer the real gas state is to the critical point.

In the beginning we have chaos – the gases expand as they want, one more, one less, each time differently – at first sight we have no chance to describe the behaviour of the gases.

A few scientists (**Boyle, Mariott, Gay, Lussac, Pascal, Torriceli**, … ) start to take a closer look at the behavior of the gases. They enclose the gases in containers with a piston, measure (using their chosen units of temperature) what has changed (temperature, pressure, volume), isolate the gases from their surroundings and lo and behold very simple elementary math formulas come out.

** pV = nRT**

After next time, we find when we go into detail that the calculated values differ. Let’s refine our equations with more measurements. We get more complex formulas – not so simple.

**van der Waals **

And if we go into even more detail – we have a choice – very complex formulas with a certain accuracy for a given region of physical conditions.

**the BWR equation (Benedict, Webb and Rubin) **

In the beginning there is a chaos of the gases behaviour. In the first time there is a pretty simple equation for ideal gases. In the middle there is quite complicated but also beauty equation. In the end there is an chaos of very complicated equations which are valid for very narrow range of pressures and temperatures. There is again a chaos, but in descriptiveness. See a curve below.

**See below – brief remarks waiting for word processing to articels**