# From renormalization to fractals

FEBRUARY 20, 2019 (updated on September 7, 2023)

## Table of contents

At the cosmological level as well as at the quantum level, **the equations predict infinity**. Yet our standard theories of physics do not reflect these predictions. Either they ignore infinity if it comes from the singularities of the cosmological level. Or, at the quantum level, they try to eliminate it by renormalization, i.e. to make it finite, accessible, measurable. This is what I propose to discover in this article.

“Quantum field theory, to date, [eliminates] through a process of renormalization, (…) an energy density that would be formally infinite if it were not excluded from calculations through renormalization.”

JOHN ARCHIBALD WHEELER [1]

## Zero point

Zero-point energy, or quantum vacuum energy, is **the energy that remains when all other forms of energy have been removed**. The calculation shows that this energy – the lowest of the quantum field – is infinite. Therefore, it cannot be differentiated from higher energy. Unless renormalized to zero at the lowest level, allowing for the observation and measurement of **energy variations** with respect to this floor.

This renormalization is not incompatible with an estimation of the value of the vacuum energy. To make this estimate, physicists use **Planck distance**: 1.616 x 10^{-33} cm. Far from being the smallest thing that exists in the universe, this value is the fundamental boundary condition that defines our **relationship** to it. Planck distance is used to calculate the density of 1 cm^{3} of vacuum, which is equivalent to 10^{93} g/cm^{3} (see also the article Unity from ether to space). Thus infinity is artificially made finite.

## Zero pointing

If it belongs to the field of physics, renormalization, in principle, finds a certain echo in the medical field and in the way fields of consciousness are considered. In this way, consciousness is renormalized in order to enter into boxes that correspond to certain mental processes, beyond which it has almost no **more reality**.

This is not the way of thinking of Nassim Haramein. Neither in terms of physics, nor in terms of consciousness. For him:

“For more than 100 years – ever since we discovered that there is an infinite amount of energy at every point – instead of saying “we found the source of creation”, we’ve been looking for a way to stop the infinite…. Planck distance became the end of the equation.”

NASSIM HARAMEIN [2]

One could say that infinity does not scare him, and consider his approach much more objective. In fact, it is just much more conscious. But how does he **take infinity into account** in his unified field theory? To find out, we have to be interested in fractals!

## Fractals

### Fractal and aneurysm

On a human scale, an aneurysm [3], for example, makes it possible to observe what fractal dynamics are. It contains a turbulent blood flow which, while at first glance it gives an impression of disorder and complexity, is on the contrary **very structured** when you look at it more closely. The “vortices” that make it up follow a fractal process. The division of large eddies into smaller ones allows **energy transfer** from large to small scales, such as energy cascades.

As an interdependent part of the human body, the aneurysm is also in a fractal relationship with it. More generally, at the biological level, there is an **interdependence between the parts and the toddlers**, the toddlers themselves always being parts of a larger whole. Thus, in order to exist, the human body depends on organs, which depend on cells, which depend on DNA and so on. Each higher level takes over the characteristics of the previous one while adding additional functions.

### The strong link

This is called **holarchy**, after Arthur Koestler’s term [4]. A holarchy contains elements – holons (here DNA, cells, organs…) – that function both as a self-regulating whole and as part of a larger whole (the human body). The holons are connected to the whole, which depends on them. Thus, a holarchy implies a hierarchical relationship in which each level functions autonomously, and where **the smallest level is the most important** because it conditions all the higher levels. All levels are involved in a dynamic of information feedback, thus influencing each other.

This point of view is close to that of Nassim Haramein, for whom looking at infinity and finite systems as opposites leads our physics into an impasse. It would be better, in his opinion, to consider them as **complementary**, and to do so, use fractals.

## An order behind the mess

The term “fractal”, derived from the eponymous adjective, was coined by the French-American mathematician **Benoît Mandelbrot** in 1974. This term comes from the Latin *fractus,* which means “broken, irregular”. Irregularity or fragmentation characterizes fractal shapes and prevents their description in traditional geometric terms.

It may seem paradoxical that a mathematician would be interested in such forms, which seem by their complexity and irregularity to be the very opposite of mathematics. The fact is that Benoît Mandelbrot did not see an irregular shape when he looked at a fractal, but a structure, **a pattern that was repeated ad infinitum through an iterative process**. This characteristic is called self-similarity and can be stated as follows: an enlargement of a part of the fractal structure invariably causes the whole structure to reappear. A fractal is constructed by homothety, i.e. **its structure reproduces itself identically at all scales**, and this to infinity. In other words, a fractal tends towards infinity, and yet each of its levels generates a limit, hence the notion of complementarity between finite and infinite.

For Benoît Mandelbrot, many forms present in nature can be described by fractals. From then on, mathematics no longer applies only to smooth shapes (circles, triangles, squares…), but includes roughness. This is how **mathematical laws can be applied** to objects or phenomena that seem to escape them. And there are quite a few of them! These include: structure of lungs, rocks, lightning, distribution of tree branch structures, distribution of galaxies… There is therefore an order behind the apparent disorder.

## Fractals and golden section

Nassim Haramein talks about **highly organized systems** that generate fractal structures everywhere in nature. Even though each of these structures seems particular, they *“actually obey [all] the same Phi [golden ratio]: 1.618″. Always 1.618 times smaller or larger” *[5]. Following this logic, we will never find the “particle of God” that quantum physics is looking for because there will always be a smaller particle. And eliminating infinity won’t change that.

## A fundamental model of division

It would be better to look for a fundamental model of the division of space. Fractals offer this possibility because, as he explains, *“by means of infinite divisions we can generate a “singularity”, a connection with everything else”* [6]*. *This fundamental model actually gives us the **key to understanding the creative process**. Therefore, it doesn’t matter on what scale we look at things because:

“Each point contains everything, each point contains all the information. Each point is connected to the rest of the points in the universe.”

Thus, each fractal boundary is produced by dividing space and generates a specific structure, **specific coordinates in space-time**. Each of these limits can therefore be defined as a very specific set of information. As this process is iterative from one level to another, it means that an **infinite amount of information** can be integrated at each level into a finite structure.

Want to know something even more interesting? Fractals are the patterns that emerge when we study the behaviour of **chaotic systems**, such as an aneurysm. To learn more, you can read the articles about the butterfly effect.

Key points

- Quantum theory eliminates by renormalization the
**infinite value of vacuum energy**predicted by the equations. - The unified field theory reintroduces infinity through
**fractals**. Thus, finite and infinite are not opposed but complementary. - Fractals provide a
**fundamental model of the division of space**rather than a fundamental particle.

#### Notes & references

[1] MISNER Charles W., THORNE Kip S., WHEELER John Archibald, Gravitation, London: W.H. Freeman, “Physics Series”, 1973, quoted by HARAMEIN Nassim, *L’univers décodé ou la théorie de l’unification*, Québec: Editions Louise Courteau, 2012, p.24, free translation

[2] HARAMEIN Nassim. (April 23, 2016). [Video]. *L’Univers connecté : la solution de masse holographique et la source de la conscience* *[The Connected Universe: the holographic mass solution and the source of consciousness]*, free translation

[3] An aneurysm is a dilation of the wall of an artery, resulting in the creation of a pocket inside which the blood changes its behavior. Read My Story to understand why I chose this unlikely example.

[4] The term “holarchy” was coined by Arthur Koestler in his 1967 book The Ghost in the Machine (Hutchinson ed.). The title of the book refers to an expression of the English philosopher Gilbert Ryle, for whom the mind is no different from the activity of the body.

[5] HARAMEIN Nassim. (2003). [Vidéo]. *Nassim Haramein at Rogue Valley Metaphysical Library (1)*

See also the scaling law he wrote.

[6] Ibid.

[7] Ibid.

On the same theme