Information entropy

Information entropy. Things tend to get messy. We know this truth intuitively, but over the past 200 years, physicists have also understood it mathematically. The enigmatic property known as entropy, which roughly describes the degree of confusion among the elements of a system, tends to continually increase. In other words, everything becomes increasingly chaotic and jumbled over time. Can information entropy be applied to describe our universe?

Entropy is a scientific concept, most commonly associated with states of disorder, randomness, or uncertainty. The term and the concept are used in diverse fields, from classical thermodynamics, where it was first recognized, to the microscopic description of nature in statistical physics, and to the principles of information theory. It has found far-ranging applications in chemistry and physics, in biological systems and their relation to life, in cosmology, economics, and information systems including the transmission of information in telecommunication. And what about Entropy in cosmology? And what could Entropy be for the first moment of existence?

At first, assuming that a finite universe is an isolated system, the second law of thermodynamics states that its total entropy is continually increasing. It has been speculated, since the 19th century, that the universe is fated to a heat death in which all the energy ends up as a homogeneous distribution of thermal energy so that no more thermodynamic work can be extracted from any source.

If the universe can be considered to have generally increasing entropy, then – as Roger Penrose has pointed out – gravity plays an important role in the increase because gravity causes dispersed matter to accumulate into stars, which collapse eventually into black holes. The entropy of a black hole is proportional to the surface area of the black hole's event horizon. Jacob Bekenstein and Stephen Hawking have shown that black holes have the maximum possible entropy of any object of equal size.

This makes them likely end points of all entropy-increasing processes, if they are totally effective matter and energy traps. However, the escape of energy from black holes might be possible due to quantum activity (see Hawking radiation). On the other hand, there are theories that the passage of an object through the event horizon is associated with the complete disappearance of the information contained within that object. Mathematically, this boils down to the statement that to describe a black hole, one simply needs to specify its mass, electric charge, and angular momentum.

Information Entropy – The Universe as an Isolated System

According to our Concept — ToE–Quantum Space, our Universe must be an isolated system. The Universe can exist within an Initial Singularity. According to our Concept — ToE–Quantum Space, for the Universe to exist, some reason had to occur — we called this reason the Root Cause. Otherwise, existence in nothingness would be meaningless. One can only exist within something. An Initial Singularity creates an environment; it is a reason for existence. So, can an Initial Singularity create an isolated system in which the Universe exists?

Let us assume for a moment that the Universe had a beginning. In that case, the Universe probably came into being for some reason. Something must have happened to create the specific circumstances for the creation of the Universe. Here we refer to our intuition – the creation of the Universe is the result of some Cause – in our opinion, the Root Cause of Everything. In our opinion, this Root Cause could be interpreted as a friendly environment for the existence of anything. What would be the point of something coming into being for no reason in the middle of nothing? Something can only exist in something, and that “something” provides isolation.

Information Entropy. Is our Universe an isolated system? If our Universe can exist, it can only exist within the territory of the Root Cause. This reason for existence determines the area of ​​isolation, meaning that the Universe must exist within an environment that can isolate it from areas where it cannot exist. The animation presents the symbolic existence of the Universe marked with a green circle. The Universe can only exist within the blue circle. The blue circle symbolizes the Initial Singularity – according to our concept, this Singularity is the Root Cause of the Universe's existence, the creation of the Universe, therefore, the Universe cannot exist outside the singularity.

Source: Krzywe Stożkowe

Our Root Cause – the Initial Singularity – is an interpretation of the structure of Quantum Space. The structure of Quantum Space is a medium within which information about various objects can be generated. Such information is a representation of the energy states stored within the structure of Quantum Space. This means that such a structure of Quantum Space is an interpretation of a matrix that can, using Primary Information, represent any state of the Universe.

According to our Concept — ToE–Quantum Space, the Universe must exist somewhere, in a specific environment that surrounds its existence and allows it to expand according to the laws of physics. Such an environment is a description — it is information, which we call Primary Information. Therefore, in our opinion, information is a key factor in describing the Universe. So, does Information Entropy exist? Let's start to put the question: How is entropy viewed?

The Physical Reason Why Things Fall Apart

Author: Charlie Wood

Each week Quanta Magazine explains one of the most important ideas driving modern research. This week, physics staff writer Charlie Wood explains how one core physical idea — entropy — determines the fate of all things.

Information entropy. The Physical Reason Why Things Fall Apart

Source: https://mailchi.mp/quantamagazine.org/the-physical-reason-why-things-fall-apart?e=386c697863

Things tend to get messed up. We know this truth intuitively, but over the last 200 years, physicists have come to understand it mathematically, too. An enigmatic property known as entropy, which roughly describes how mixed-up a system’s parts are, tends to always increase. In other words, things get messier and more mixed up as time goes on. Physicists call this tendency the second law of thermodynamics, but it’s more a matter of statistics than physics. Entropy increases because there are more ways to be messy than to be tidy.

Take a drop of ink in a pool of water. Imagine all the possible ways of arranging the ink and water molecules. The arrangements in which the ink molecules all happen to sit together in a tiny teardrop shape are rare, in comparison with all the configurations in which the ink molecules can sit anywhere throughout the pool. The second law is simply the statement that the molecules, as they jitter and push each other around, are bound to end up in one of the more likely arrangements (ink molecules dispersed evenly) rather than a special and rare one (ink molecules all clustered together).

Essentially all known systems behave in a similar way. Sugar cubes dissolve into coffee. Scents disperse throughout a room. Waves mix a sandcastle’s grains back into the beach.

Physicists first started getting to grips with entropy’s rise in the mid-1800s, but now there is a more modern way of thinking about it. The way to understand entropy, as Zack Savitsky discussed in his long-form exploration of the concept last year, is as a measure of uncertainty or ignorance.

This alternative definition traces to the American mathematician Claude Shannon’s 1948 paper establishing a theory of communication. In Shannon’s theory, a low-entropy message is one with recognizable structure, analogous to the ink drop. The message abababab…, for instance, is low entropy, and therefore low uncertainty. After learning the first few characters, you can guess how the message continues. A random jumble of characters like fkale93xh..., by contrast, has high entropy. You are much less certain how this will continue.

This more general notion of entropy as uncertainty provides further insight into why systems mix themselves up in accordance with the second law of thermodynamics. Consider a deck of cards. When it’s fresh out of the package, you can predict the order with total certainty: ace, two, three, et cetera. But as you shuffle the deck, you’re less likely to know what card will follow an ace. Our ignorance is bound to increase with each shuffle as the deck finds those vastly more likely patternless orderings.

The same is true of the universe overall. The most common arrangements of atoms and molecules are uniform ones, where no part contains any information that will help reveal the arrangement somewhere else. So as the universe changes, we’re all but guaranteed to find the more likely situations of bland, structureless states. 

What's New and Noteworthy

Some physicists feel dissatisfied with the looseness of the second law of thermodynamics. The present should lead to one future, they say, so why are we talking about statistics of many possible futures? In recent years, these researchers have made progress on deriving the statistical nature of the second law from absolute quantum principles. 

The inexorability and universality of the second law has focused attention on cases that seem to defy it. In 2017 physicists discovered “quantum scars,” where patterns in strings of particles break down but then spontaneously reappear. And other groups have recently constructed a strange type of magnetic order that persists at high temperatures, where entropy typically erases all patterns. Then there’s life itself: a highly ordered arrangement of molecules.

But these examples merely exploit the second law’s fine print. Quantum scars amount to a very special deck of cards and a very special shuffling technique that allows order to recur — not a general decrease in entropy. And the magnetic order persists by allowing another type of disorder to grow at a greater rate. It survives increasing entropy, rather than defying it. Biophysicists say that living organisms do something similar, keeping their own entropy low by greatly increasing entropy in the world around them. Thus, the apparent exceptions help prove the law.

Entropy has also served as a crowbar to crack open one of the universe’s blackest of boxes: black holes. In the 1970s, the physicist Jacob Bekenstein noticed that black holes seemed to be second-law-violating machines. They could swallow teacups and planets, deleting the entropy of those objects and therefore reducing the entropy of the universe outside. But one should never bet against the second law, Bekenstein reasoned, so black holes must have an entropy of their own that grows as they grow.

Many physicists take this to mean that black holes should be made of many pieces that can be rearranged, much as a gas is made of many molecules. Puzzlingly, however, those pieces appear to live on the black hole’s surface rather than inside it — a mystery that many physicists consider to be their most promising clue to the quantum behavior of gravity.  

But entropy’s most enduring legacy may prove to be the way it helps us define the future itself. One can argue that the “arrow” of time points in the direction of increasing entropy. This insight has fueled research into the quantum origins of time and timekeeping. 

The physicist Sean Carroll gives a thorough overview of entropy and the second law with just a touch of math in this entry of his video series, The Biggest Ideas in the Universe. 

Source: https://mailchi.mp/quantamagazine.org/the-physical-reason-why-things-fall-apart?e=386c697863

Here is an example from our Reality. Take a drop of ink in a pool of water. Imagine all the possible ways of arranging the ink and water molecules. The arrangements in which the ink molecules all happen to sit together in a tiny teardrop shape are rare, in comparison with all the configurations in which the ink molecules can sit anywhere throughout the pool. The second law is simply the statement that the molecules, as they jitter and push each other around, are bound to end up in one of the more likely arrangements (ink molecules dispersed evenly) rather than a special and rare one (ink molecules all clustered together).

Information Entropy – interpretation of the description of the Universe

According to our current knowledge, entropy is the average amount of information (Quantities of information) per single message from an information source. In other words, it is the weighted average of the amount of information (Weighted arithmetic mean) carried by a single message, where the weights are the probabilities of sending individual messages. Entropy can be interpreted as the uncertainty of a given Sample space occurring in the next moment. If an event in a set of events occurs with a Probability equal to 1, then the entropy of the system is 0, because it is known in advance what will happen – there is no uncertainty.

The information definition was originally an attempt to express the traditional concept of entropy known from thermodynamics in terms of information theory. However, it turned out that this definition is useful within information theory itself. Entropy is a state function, which means that its value depends solely on the state of the system (on the current values of its parameters). The change in the state function does not depend on the path, but only on the initial and final states of the system. From a mathematical point of view, the entropy Differential of a function dS is a Exact differential, and the result of its integration does not depend on the path of integration.

According to our Concept — ToE–Quantum Space, Primary Information is an element that describes the state of the Universe at a given moment in time. Such information contributes to the sequence of descriptions of Reality. This description of Reality occurs at each current moment. At each moment, we are dealing with the phenomenon of entropy.

Information entropy. Our Universe is described using Primary Information. Does this mean that if the Universe collapses due to increasing entropy, our Primary Information will also degrade until it can only describe the final moment of our Universe's existence? This could mean that the dispersion of Primary Information interprets the cessation of our Universe's existence. This illustration was generated by AI Gemini (CreatedbyAI).

The entire Universe strives for equilibrium while simultaneously undergoing entropy. Our description of the Universe is made using Primary Information, so perhaps this description — our sequence of existence — will, in our future, strive for a certain repeatability — for the ordering of descriptive data. Perhaps this description will force such a sequence to converge toward a single ending.

Can this also be applied to black holes, where an object passing through the event horizon is associated with the complete disappearance of the information contained in that object? Could this mean that inside a black hole, the information description disappears through the ordering of Primary Information? How? This requires a specific explanation.

Well, according to our Concept — ToE–Quantum Space, inside a black hole there is information gathered from the beginning of our Universe to the moment of its end. The question is, can this information be useful? What if the information inside a black hole tends toward a single state of the Universe — toward a description of the first moment of our Universe's existence? Could it be that in the first moment of existence, it was possible to exist without basic attributes: without time, without space, without energy and without matterr? Perhaps at that time there was only unity, a mysterious bond between time, space, energy and matter.

If the first moment described by Primary Information presented an interpretation of the unification of time, space, energy and matter, then this description must converge to a single point—the moment of the first Primary Information. Therefore, if our Universe has a Beginning and an End, then according to our Concept — ToE–Quantum Space, the Primary Information for the First and Last Moments are convergently the same — even though their values ​​are different. This means that the sequence for the End of the Universe must converge to a single value. This value appears to be the same, although in reality they are not equal.

Information entropy – different concept of time

Entropy is central to the second law of thermodynamics, which states that the entropy of an isolated system left to spontaneous evolution cannot decrease with time. As a result, isolated systems evolve toward thermodynamic equilibrium, where the entropy is highest. A consequence of the second law of thermodynamics is that certain processes are irreversible.

Geometry for relativity theory can play a key role for our concept of gravity. Does this mean that today’s mathematical models based on geometry will have an impact on the development of what Albert Einstein started? We don’t know exactly how geometry will change if our concept of time changes.

Quantum Mechanics has its own rules. One of the rules is the uncertainty principle. It seems that the indeterminacy principle must have different rules for the concept of time – time at the quantum level functions quite differently. This means that the concept of time in quantum mechanics can usefully introduce a different description of phenomena at the quantum level. If that were the case, then we would also have to factor in macro-scale phenomena.

In order for a feature, an attribute of the Universe to appear, which will enable the description of our Universe using laws, information must first appear. Information was the first trigger for subsequent features of the Universe, which can be used to describe our Universe. It was information that united four attributes: time, space, energy and matter. Information originally had to be some form of energy of a type unknown to us. Only then, were the individual attributes of the description of our Universe released from information. The first attribute to be released was time.

At the beginning of everything there had to be Information.

It seems that the origin of our Universe must have been consistent and coherent. This means that what was primordial – at the beginning of our Universe, must be consistent with our current perception of the Reality around us. Something that once began must be consistent and coherent with today’s picture of our Reality. If it were not, our Reality would be unstable, to say the least. It all boils down to one thing – at the beginning of our existence there could have been Information (Primary Information). It was information that gave rise to everything. The only question that remains is. In what form could such information have appeared at the beginning.

Our concept of time takes into account our ToE-Quantum Space. The concept of Quantum Space incorporates a new approach to the concept of „time” – this was discussed in the ToE-time concept. The new concept of time assumes that our concept of time in our surrounding Reality, is an incomplete concept. Therefore, a new interpretation of time has been proposed – this is the concept of expanded time. Extended time has been described by a complex time function. This means that our time has a completely different dimension, so „time” must be described in a completely different way. The mathematical description of time was made using the Time Quaternion.

Information entropy. Does uncertainty already begin with our perception of time? An artistic depiction of the Time Quaternion that was generated by AI CHATGPT (CreatedbyAI). If our concept of time has a completely different dimension, then perhaps we should separate space-time into time (a complex description of time) and space (a complex space for parallel realities)

The above examples of scientific research can also apply to our concept of „Time”. This means that „time” must not have existed before the Big Bang, if the age of the Universe is finite, then it must have started at some point. This is especially important for the process of observing distant objects – distant in both time and distance. See more information in article Observing the visible Universe and Observation rights. 

To understand the Universe and its creation according to the interpretation of our Concept – ToE-Quantum Space, it is necessary to know our concept of time, interpretation of gravity and interpretation of matter. However, everything started with the concept of the emergence of Quantum Space. 

According to our conception, “time” does not exist, and if it does, then perhaps gravity has a completely different meaning as well. This led us to our concept of the Theory of Everything.

My interpretation of the Universe – The Theory of Everything is not a single mathematical formula, nor is it a way to combine several other theories, nor is it a proof of the connection between gravity and quantum mechanics – so what is QST? Quantum Space Theory is an energy state that can express every possibility, every quantum of time – everything. 

Imagine a Theory of Everything – EVERYTHING. A theory that explains what is TIME, the COORDINATE of space, taste, hair color, the movement of planets, the Big Bang, Parallel Worlds and explains all your choices. A theory that explains why you have dreams and, at the same time, how matter was created. A theory that does not exclude what we know, what we have come to know but perhaps looks at things a little differently. 

A theory that takes into account philosophy, mathematics, physics – Everything. A theory that bridges the worlds of physics and metaphysics. The theory that starts from wherever your perception, experience and imagination apply. You can’t go deeper, we are at the limits of abstraction.

It is an energy state that maps time, space, matter, the Universe…. and at any point in time – So does „time” exist? It is impossible to prove certain phenomena, we have problems with both the micro-world and the macro-world, what we present here is the boundary between Knowledge and Philosophy. Some claim that everything began with the Big Bang – we do not dispute this, but we look at it differently.

Marek Ożarowski