(zenodo.org)

of March 11

Introduction

Modern physics is based on quantum mechanics and general relativity theory (GRT), but their unification remains an unsolved problem. We propose an alternative model in which the frequency of oscillations is the primary concept determining the energy density. Within this model, Planck’s constant plays the role of the fractalisation coefficient, determining the scale of physical processes.

1. basic principles of the theory

1.1 Frequency as a fundamental quantity

In the Universe, the frequency of oscillations determines all physical processes, and its gradients create gravitational and quantum effects. We assume that the change of frequency generates interactions, and space remains unified, but its properties depend on the frequency of interactions.

1.2 Quantisation of velocity, mass and dimensions

The energy density is determined by the frequency of oscillation. The higher the frequency, the energy becomes denser and the scale decreases. In our model, the speed of light, the mass of objects and their size change depending on the level of fractality. The scaling occurs as follows:

The laws of physics and fundamental constants remain unchanged and identical at every level of organisation of matter. The speed of light determines the limiting speed of electromagnetic interactions, depending on the energy density at a given scale.

With this approach, the Universe acquires a potentially infinite fractal structure. In mathematical expression, the variable n has no strict restrictions and can take both positive and negative values. At the moment, the fundamental principles imposing restrictions on n are unknown.

The relative frequency at all levels remains the same, but the speed of light changesc . The wavelength is related to these parameters by the equation:

If we denote the parameters in our level as c0, ν and​ R0, and in another level as c, ν and R, then, since the relative frequency does not change, we are left with:

Wavelength ratio:

If we assume that the scaling dimension R is proportional to the wavelength λ, then

Then the relative scale will be:

Whence it follows that the size ratio between levels is defined as:

Thus, quantisation is expressed in stepwise change of speed of light, which automatically sets scale transitions and energy density.

1.3 Scaling between the neutron and the Milky Way

The size of the Milky Way:

• Diameter: estimates range from 100,000 to 120,000 light-years (about 30-37 kiloparsecs). znanierussia.ru
• Thickness: about 1,000 light years. techinsider.ru

The mass of the Milky Way:

• Total mass: estimates range from 1 to 2 trillion (10¹²) solar masses, including dark matter. ru.wikipedia.org
• Mass of the stellar component: about 50-60 billion (5-6 × 10¹⁰) solar masses.

1.3.1 Application to the Milky Way

When going from the neutron to the Milky Way, the level changes towards a lower frequency, i.e. n=− 1. Then the scaling of the radius is as follows:

The size of a neutron is about 1 femtometer (fm), which is equivalent to 10⁻¹⁵ metres. elementy.ru

Substituting the values:

The diameter of the Milky Way in metres:

• Minimum estimate: ≈ 9.46×10²⁰ m
• Maximum score: ≈ 1.14×10²¹ m

The calculated radius of the Milky Way within this model differs slightly from the values accepted in astrophysics (~ 1×10²¹ m). This may be a consequence of several factors:

1. Experimental error in determining the size of both neutron and galaxy.
2. The effect of speed of movement on the size of objects, which is important to consider when comparing scales.
3. The calculation methods in astrophysics are based on the expansion models of the Universe, which may introduce additional deviations. In the future we will consider the question of how correct it is to take into account the expansion when determining the sizes of objects.

1.3.2 Mass scaling

If the mass of a neutron is (ru.wikipedia.org):

That’s the mass of the galactic analogue of the neutron:

Milky Way mass derived from observations:

• Lower estimate: 1.99×10⁴² kg
• Upper estimate: 3.98×10⁴² kg

The mass was slightly less than expected (~ 3×10⁴² kg). This may be due to several factors:

1. Measurement errors arising in the determination of both neutron and galaxy masses.
2. Dependence of mass on speed of motion, which can play an important role in comparing objects at different scales.

Analysing the results obtained

The calculated values of the radius and mass of the Milky Way galaxy, obtained on the basis of the fractal coefficient, showed a surprising correspondence with the data of modern astrophysics. The radius calculated using the formula is R=6.626×10¹⁹ m, which is comparable to the observed value of about metres 1×10²¹. The mass obtained considering the fractal coefficient is M=1.109855×10⁴² kg, while astrophysical estimates give a range of (1.99-3.98)×10⁴² kg. These results confirm that the proposed calculation method takes into account the fundamental principles of matter and space.

However, the question of the accuracy of current measurement methods remains important. In quantum physics, the mass of particles is determined through interaction with fields and depends on the environment. If spatial structures have fractal properties, this can influence the measurement results by introducing systematic errors.

The results obtained indicate that the current methods of mass and size estimation both at the microscale and at the level of galaxies may need to be revised taking into account the fractal structure of the Universe. This opens prospects for refining experimental data and for a deeper understanding of the fundamental processes that shape the world at all scale levels.

1.3.3 Scaling the speed of light

This shows that the speed of light — the limiting speed of electromagnetic interactions — is much smaller at the level of galaxies than at our scale, corresponding to a more rarefied state of energy.

1.3.4 The Fractal Structure of the Universe: Galaxies as Elementary Particles

The calculated data on the Milky Way, obtained using standard physical formulas with slight modifications and utilizing the well-known physical constant – Planck’s constant, cannot be mere coincidence. One might assume it is just a random match, but only if it were observed for a single parameter. However, the fact that two parameters (mass and size) align almost perfectly rules out the possibility of coincidence. There is a high probability that the UNIVERSE is fractal. The fact that the fractalization formula worked with remarkable precision for the Milky Way suggests that the Milky Way is analogous to a neutron. This is a very strong correlation. Now, this analogy can be used to study and describe the surrounding space. The Milky Way can be taken as a reference model.

The next step is to determine how to explain the vast variety of galaxy types. It is important to establish whether they are all analogs of elementary particles or if some arise as a result of interactions between fundamental structures.

1.3.4.1 Analogy Between Spiral Galaxies and Neutrons

The Milky Way and the Andromeda Galaxy have similar masses but different sizes. This may be related to their motion: at lower speeds, a galaxy becomes larger, while at higher speeds, it becomes more compact. This distinction explains the observed differences in their sizes and masses. Spiral galaxies are particularly interesting because their structure and mass distribution follow certain patterns. When considering galaxies formed as standing waves with an even number of nodes (charged particles), determining the actual size of the structure becomes challenging. Such galaxies consist of alternating regions of increased and decreased energy density. Matter can accumulate in regions of higher energy density. Interactions with such structures can lead to the formation of various types of galaxies, which may only indirectly represent fundamental structures.

Some spiral galaxies have significantly greater masses than the Milky Way. For example, ISOHDFS 27 is a spiral galaxy with a mass four times that of the Milky Way, yet its size has increased only slightly. This behavior may indicate that its mass increases in discrete steps, each proportional to the mass of a neutron (or proton), while its size remains nearly unchanged. This resemblance is akin to nuclear interactions: ISOHDFS 27 is similar to a helium nucleus, where the energy density is higher, and the mass increases in multiples of the neutron mass.

1.3.4.2 Compact Dwarf Galaxies and Electrons

If spiral galaxies can be compared to neutrons or their interactions with protons, then compact dwarf galaxies may represent analogs of electrons. An electron can be viewed as a standing wave, with a central region of increased energy density. Matter may form in this high-energy-density region, which is perceived as a compact dwarf galaxy. It is important to note that an electron’s size is usually defined as its effective size, determined through scattering experiments. Interestingly, the difference between the size of an electron and a neutron is approximately three orders of magnitude. If the size of the Milky Way is estimated to be between 10²⁰ and 10²¹ meters, then the size of its electron analog should be around 10¹⁷ to 10¹⁸ meters, which corresponds to the observed size range of compact dwarf galaxies.

1.3.4.3 Formation of Additional Galaxies

The universe contains many galaxies that may not be direct analogs of elementary particles but instead arise from interactions. Just as temporary clusters form in quark-gluon plasma, regions of increased energy density on cosmic scales can lead to the formation of additional galaxies. Such galaxies may appear as independent objects, but they are likely just a consequence of energy redistribution among more fundamental structures.

Thus, analyzing the sizes and masses of galaxies, as well as their interactions, can provide insight into the fundamental structure of the Universe and its analogy with the micro-world.

1.3.5 Calculating the sizes of elementary particles based on their masses using the neutronas examples, neutrino and electron

1.3.5.1 Calculating the size of a neutron based on its mass

This part of the paper deals with the calculation of the size of a neutron, based on its known mass, under the assumption that elementary particles are standing waves of energy in space. The de Broglie wave in this context is interpreted as a mathematical description of this standing wave.

If the neutron is a standing wave with three nodes, its size can be determined by knowing its mass.

Calculation of neutron size

In the limiting case of motion at the speed of light, the de Broglie wavelength is determined by the relation:

Where:

• h is Planck’s constant,
• c is the speed of light,
• E is the rest energy of the neutron, defined as E= mc ².

Substituting this into the equation, we get:

Since the neutron is treated as a standing wave with three nodes, its diameter will be equal to two wavelengths:

Substituting the values of the physical constants:

• h=6.626×10⁻ ³⁴ J-s,
• c=2.998× 10⁸ m/s,
• m=1.675×10⁻ ²⁷ kg,

we get it:

D≈2.64×10⁻ ¹⁵ m.

At rest transition, the neutron size is about D≈2.07×10⁻ ¹⁵ m

Analysing the result obtained

The calculated neutron size can be in the range of (2.07 — 2.64)×10⁻ ¹⁵ m.

Experimental data estimate the neutron size to be in the range of (1-2) ×10⁻ ¹⁵ m. Thus, the result obtained is:

1. Found in the same order of magnitude as the experimental measurements.
2. Confirms that the calculation method via de Broglie wave and standing waves gives a reasonable estimate of particle sizes.
3. Indicates the possibility of refining the experimental data taking into account the principles of the wave nature of particles.

Calculation of the Neutrino Size

If the neutrino is a standing wave with one node, its diameter corresponds to one wavelength:

According to recent experimental data, the neutrino mass is estimated to be (ru.wikipedia.org):

m≈1.43×10⁻³⁶ kg

Substituting the values:

We obtain:

Dv≈1.55×10⁻¹⁰

Analysis of the Obtained Result

1. The size of the neutrino is found to be approximately 10⁻¹⁰m, which corresponds to the size of an atom.
2. This aligns with experimental estimates suggesting that neutrinos may have sizes exceeding atomic scales.
3. This calculation supports the standing wave hypothesis, as the obtained result logically fits into the concept of elementary particle scaling.

Thus, the proposed approach not only confirms the correctness of the standing wave model but also provides a tool for verifying experimental measurements of elementary particle sizes.

1.3.5.3 Calculation of the size electron

If a electron is a standing wave with two nodes, its diameter corresponds to three second wavelengths:

According to recent experimental data, the mass of an electron is estimated to be (ru.wikipedia.org):

m≈9.109×10⁻³¹ kg

Substituting the values:

We get it:

Dₑ≈3.64×10⁻¹² m

Analysing the result obtained

In modern physics, an electron is regarded as a point particle with no internal structure or size. However, there are various characteristics related to its size:

• Classical electron radius: This parameter, based on classical electrodynamics, is defined as ru.wikipedia.org:

This radius is related to the charge distribution and the scale of the electromagnetic interaction.

• The Compton wavelength of an electron:

This length characterises the scale on which quantum effects are manifested in the scattering of photons on electrons.

• Experimentally determined radius limit: modern experiments show that the radius of the electron does not exceed 10⁻¹⁸ m, but its exact structure remains unclear.

Theoretical calculation within the framework of the hypothesis

If we consider the electron as a standing wave with two nodes, its limiting size can be estimated through its wavelength:

Dₑ≈3.64×10⁻¹² m

This result agrees well with the Compton wavelength, but does not coincide with the experimental constraints. This can be explained by the peculiarities of the electron structure:

• Density boundary: if there is a region of reduced energy density at the boundary of an electron, the interaction with other particles will occur mainly in the central region. This creates an effect in which particles pass through the outer region, leading to overestimates of its compactness by experiment.
• Charge and density gradient: the classical radius of the electron is related to its charge, which is determined by the energy density gradient at the boundary. At distances close to this radius, electrostatic effects can manifest themselves to explain the electron interaction.
• Influence of particle energy in scattering: in high-energy experiments, most particles pass through the electron without interacting with its centre region, making it difficult to accurately determine its size.

Thus, the discrepancies in the definitions of the electron size can be explained in terms of the standing wave hypothesis and the energy density gradient. Theoretical calculations predict a size related to the Compton wavelength, but experimental methods based on scattering may not take into account structural features of the energy density distribution in the electron.

1.3.6 Refinement of the concept of energy density and fractalisation

In the framework of the proposed model, space itself remains unchanged, and all dynamics of observable phenomena is related to the energy density that fills this space. This makes it possible to consider an alternative explanation of fundamental processes.

1.3.6.1 Energy as a medium

It is commonly believed that the curvature of spacetime in the general theory of relativity (GR) describes gravitational effects. However, if we assume that space itself is invariable and energy density determines its occupancy, then:

• The higher the energy density, the smaller the space it occupies.
• The lower the energy density, the greater its propagation in space.
• Thus, the curvature of space can be interpreted as a change in the structure of energy distribution in space.

This leads to the fact that the transition between fractal levels changes the size of the area occupied by energy, but not the space itself.

1.3.6.2 Standing wave with variable volume

If energy is compressed at increasing density and expands at rarefaction, then a standing wave in such a medium behaves nontrivially:

• Its geometry becomes variable because the energy density in different parts of it can be different.
• The electron, represented as a standing wave of length 3/2 of the main wave, is not divided into three equal parts. Due to the change in energy density, the boundaries of these parts shift.
• In high-energy states the particle becomes more compact and in low-energy states it expands.

1.3.6.3 Gravitation and electromagnetism through density gradient

If the energy density varies in space, it gives rise to gradients, which we interpret as forces:

• Gravity arises as a consequence of the global gradient of energy density. Mass deforms the energy structure, creating a directional flow of density.
• Electromagnetic forces are local changes in energy density that can attract or repel particles depending on the configuration of their gradients.
• Quantum entanglement can be explained by the fact that the energy density in entangled particles remains wave-bound, and a change in one element instantly affects another point in the structure.

1.3.6.4 Transfer of space curvature to the concept of energy density

Within the framework of the proposed model we can leave the mathematical principles of space curvature, but interpret them differently: it is not the space itself that is curved, but the structure of energy density in it.

• Space remains unchanged, and all effects previously attributed to its curvature arise from energy density gradients.
• Mass does not curve space, but creates a local change of energy density, which leads to the same results as in GR.
• Energy behaves like a medium and its redistribution leads to gravitational effects.

From the point of view of an observer, it is completely equivalent to the concept of curvature of space in GR. However, in the proposed interpretation gravitation becomes more clearly a consequence not of geometry, but of energy distribution.

1.3.6.5 Implications for understanding matter

This approach allows you to:

• Describe the fractal structure of the universe through energy density without changing the geometry of space.
• Link quantum and macroscopic effects through a unified concept of energy compression and rarefaction.
• To offer a more visual explanation of the effects of quantum mechanics, including the uncertainty principle and the nature of standing waves.

Thus, space remains unchanged, but the very distribution of energy density shapes all observable physical processes.

1.3.6.6 Explanation of the small electron radius in high-energy experiments

If the energy density inside the electron is not uniformly distributed, the region where the main interaction with scattered particles takes place appears compact.

The result:

1. In scattering, the outer regions of the electron, where the energy density is lower, may not contribute significantly to the interaction, causing the measured size to be smaller than expected.
2. Experiments with high-energy particles are more likely to interact with the dense central region of the electron rather than its «sparse» outer regions.
3. The energy density gradient creates an effect in which the main energy is concentrated closer to the centre, while the peripheral regions may participate slightly in scattering.

Thus, the model of variable energy density in standing wave explains the small experimental electron radius observed in scattering.

1.3.7 Effect of energy density and frequency

If the frequency of oscillation affects the energy density, we can assume that on the galactic scale the energy density is so small that objects within it can move faster with respect to the local value of the speed of light without violating the limits existing in their own reference frame.

In other words, if space for a given scale behaves differently (because of the change of frequency), then for the matter in it the speed of 220 km/s is not perceived as «high» relative to local physics. It is as if for us the speed of 1 m/s suddenly turned out to be significant in relation to the new fundamental constant of the speed of light.

1.3.8 Connection with dark matter

Suppose that dark matter is not matter in the usual sense, but a manifestation of differences in frequencies between fractal levels. Then the rotation speed of matter in the galaxy is the result of balancing at the boundary of fractal levels.

Recent studies show that a volume of space equivalent to the volume of the Earth contains less than 1 kilogram of dark matter. This supports the hypothesis of its low density and difficulty in detection, which is consistent with the fractal model.

1.3.9 Galactic orbits and curvature of space

If the fractality of space changes the properties of the metric, then objects can move «faster» with respect to the reduced speed of light, but at the same time their motion through space remains consistent with the overall dynamics of the Universe. In such a picture gravity at the galactic level is manifested not only through mass, but also through the structure of space itself, which changes with the change of frequency.

1.3.10 Effect of frequency on scaling

Since mass and size are frequency dependent, the discrepancies in the calculations can be explained by the fact that different fractal levels have different oscillation ranges. This corresponds to the relativistic effects, where:

• An increase in frequency leads to a decrease in size and an increase in energy density;
• A decrease in frequency leads to an increase in size and a decrease in energy density.

Thus, the fractal structure of the Universe naturally unites the macro- and micro-worlds through frequency dependences, explaining why objects of different scales can coexist in a single space.

2. Standing waves of energy density and particle structure

Introduction

Modern physics describes elementary particles as point objects or perturbations of quantum fields, but another interpretation is possible. This chapter considers the hypothesis that particles are standing waves of energy density and their properties can be explained through de Broglie waves.

We will also consider how particle birth can be explained within this model and why the law of conservation of energy leads to the symmetry of matter and antimatter.

2.1 Standing waves of energy density and particles

2.1.1 De Broglie waves as the basis of particle structure

In the framework of the hypothesis of standing waves of energy density particles can be considered as nodes of such waves. The de Broglie wave associated with a particle does not simply describe its motion, but is its structural element. The de Broglie wavelength is determined by the relation:

Where:

• h is Planck’s constant,
• m is the mass of the particle,
• c is the speed of light.

If a particle is a standing wave, its size must correspond to an integer number of half-waves, which explains quantisation of energy and charge.

2.1.2 Fractal structure of particles

Earlier we proposed a model according to which the energy density scales with frequency. This means that at different levels of fractality particles can appear as macroanalogues of each other. For example, if a neutron is a standing wave with three nodes, a similar structure can appear on larger scales, for example, in the form of a galaxy.

2.2 Particle birth and the law of conservation of energy

2.2.1 How particles are born

In the framework of the proposed model the birth of particles can be represented as a process of local redistribution of energy density. When in vacuum there arise fluctuations of energy density, they can lead to formation of stable standing waves, which are perceived as particles.

The birth of particles is accompanied by the formation of particles matter and antimatter. This follows from the law of conservation of energy: any local fluctuation must be compensated by an equal and opposite fluctuation.

2.2.2 Why there is no symmetry breaking of matter and antimatter

It is usually considered that in the Universe there is an excess of matter over antimatter, but in the framework of this model symmetry breaking is not required. If a particle is a standing wave of energy density, its antipode may be a wave with opposite phase. The difference between matter and antimatter may lie in where the maxima and minima of energy density are located.

In a confined space, the redistribution of energy density will be due to the structure of the particles themselves:

• In the centre of particles matter (with an even number of nodes) there is a region with increased energy density, which leads to the effect of creating macro-objects and the emergence of gravity.
• In the centre of particles antimatter (with even number of nodes) there is a region with reduced energy density, which leads to their scattering from each other and formation of antigravity effect.
• Neutral particles are standing waves with an odd number of nodes. There is no density change at their centre, but they have the property of rotation. The antiparticle in this case differs only in the direction of rotation.

Antimatter is not capable of forming macroobjects because of the peculiarities of its structure. While matter particles tend to combine and can lead to the formation of black holes, antimatter is probably not capable of forming atoms more complex than antihydrogen. Instead, it would be distributed in a sphere around the forming black hole, contributing to the balance of energy in space.

3. Why do particles interact? Nature of quantisation and electromagnetic forces

Introduction

In standard physics, particle interactions are explained through the fundamental forces: electromagnetic, strong, weak and gravitational interactions. However, if we consider particles as standing waves of energy density, we can offer an alternative explanation of why particles interact, why the electron does not fall on the nucleus, why charges attract and repel, and what causes quantisation.

3.1 Why do particles interact?

In the framework of the proposed model, the particles are standing waves of energy density. The interaction between them is caused by gradients of energy density in the surrounding space.

• The particle creates a around itselfperturbation of energy density, similar to a gravitational or electromagnetic field.
• When two particles are brought close together, their wave structures can interfere, creating regions of increased or decreased energy density.
• This interference results in forces of attraction or repulsion, depending on the phase shift of their waves.

Thus, the interaction of particles is a manifestation of the energy density distribution in space.

3.2 Why doesn’t the electron fall on the nucleus?

In classical physics, the orbital motion of the electron around the nucleus should lead to the emission of energy and its inevitable fall. However, this does not happen, which is explained by quantum mechanics. In the framework of our model, the reason lies in standing waves of energy density.

• An electron is a standing wave of energy density associated with a nucleus.
• Its position is determined not by orbital motion but by wave nodes and interference with the energy density of the nucleus.
• At certain distances from the nucleusarise, stable states in which energy density gradients compensate for possible energy losses.
• These states correspond to the energy levels known in quantum mechanics.

Thus, the electron does not fall on the nucleus because its wave nature forms stable energy levels where the energy density is stable.

3.3 Why do charges attract and repel?

The attraction and repulsion of charges can also be explained through the energy density and phase interference of their wave structures.

• The charge is related to the energy density along the boundary of the standing wave.
• A negative charge (such as an electron) occurs if there is a region of at the boundary of particlereduced energy density the.
• A positive charge (such as a proton) occurs if there is a region of at the boundary of particlehigher energy density the.
• Charges of the same name repel because their wave structures create a region of increased energy density between them, which creates a repulsion effect.
• Dissimilar charges are attracted because their wave structures complement each other, creating a region of reduced energy density between them, resulting in a pulling effect.

This explains the electromagnetic forces without the need to introduce virtual particles, but through fundamental changes in energy density.

In addition, this explanation clarifies why protons can form nuclear bonds while electrons cannot. Since the proton has a region of lower energy density at the boundary, it is able to unite with other protons through neutrons, which stabilise their interaction in the nucleus. The electron, on the other hand, having a higher energy density at the boundary, is not capable of such bonds.

3.4 What is the reason for quantisation?

Quantisation within this model naturally follows from the structure of standing waves of energy density.

• For each particle there are only certain stable wave states corresponding to the nodes and bunches of standing waves.
• These states determine the energy levels and the possible values of momentum and spin.
• The scaling of the energy density causes different levels of fractality to repeat the same patterns, which explains the universality of quantum effects.

Thus, quantisation is not an artificial restriction, but a natural consequence of formation of stable standing waves of energy density.

4.Standing waves of energy density and nature of fundamental forces

Introduction

In modern physics, the fundamental forces (gravitational, electromagnetic, strong and weak) are described through fields and carriers of interactions. However, if we consider particles as standing waves of energy density, an alternative explanation of the nature of fields and interactions can be proposed. This chapter examines how energy density determines the properties of fields and fundamental forces.

4.1 What is a field in terms of energy density?

From the point of view of this theory, the field is a gradient of energy density in space. Any particle is a localised standing wave of energy density creating density changes around itself. These changes define the interaction field.

• A gravitational field is a gradient of energy density throughout space caused by mass objects.
• The electromagnetic field is localised changes in energy density associated with standing waves of charges.
• Strong and weak interactions are special forms of energy density changes acting on small scales due to peculiarities of particle structure.

Thus, the field is not a separate entity, but a manifestation of the non-uniform distribution of energy density in space.

4.2 Why do interactions between particles occur through fields?

If particles are standing waves of energy density, they can interact through changes in energy density in the surrounding space. Such interaction occurs by several mechanisms:

1. Wave superposition — the wave structures of particles overlap, creating regions of increasing and decreasing energy density.
2. Density gradient — the motion of particles is caused by the desire to equalise the energy density.
3. Resonance states — if the energy density of two particles are matched, they can form stable states (e.g. atomic levels or nuclear bonds).

Thus, interaction through fields is a natural consequence of the fact that particles are localised changes in energy density.

4.3 Why are the fundamental forces so different?

The fundamental forces differ in range and intensity, but in the framework of the proposed model they are all manifestations of one phenomenon — redistribution of energy density.

• Gravity is a consequence of the global energy density gradient and acts on any mass.
• Electromagnetic forces are related to the local redistribution of energy density at the standing wave boundary and can be both attractive and repulsive.
• The strong interaction arises from the compression of the energy density within particles, making it extremely powerful at small distances.
• Weak interactions are associated with changes in the energy density structure within particles, as manifested in nuclear decays.

Thus, the differences between the fundamental forces are due to the scale and peculiarities of energy density redistribution.

4.4 Why do strong and weak interactions act only at small distances?

4.4.1 Strong interaction

The strong interaction occurs within the atomic nucleus and holds protons and neutrons together. Within this model:

• Interactions between nucleons occur through very high energy density gradients.
• External energy density gradients interfere with long-range action, causing the force to weaken exponentially with distance.
• Nucleons are held in the nucleus because the energy density inside it is higher than in the surrounding space.

4.4.2 Weak interaction

The weak interaction is responsible for the decay of particles and changes in their structure. Within this theory:

• It is related to local fluctuations of the energy density inside the particles.
• Such fluctuations can lead to changes in the state of particles and their disintegration.
• Due to the very local nature of the energy density, the weak interaction only acts at short distances.

Thus, strong and weak interactions are limited to small distances because they are due to local changes in energy density that do not propagate far away.

5. Standing waves of energy density and the nature of mass

Introduction

Mass is a fundamental characteristic of matter, but its origin remains one of the key questions in physics. In the Standard Model, the mass of particles is explained by the mechanismHiggs , but this chapter considers an alternative approach: mass as a manifestation of energy density in standing waves. We explain why mass is proportional to energy, how inertia is related to energy density, and why particles have different masses.

5.1 How do standing waves of energy density explain mass?

In the framework of the proposed model particles are standing waves of energy density which possess steady states. The mass in this case is determined by a local gradient of energy density:

• The greater the energy density inside a standing wave, the greater its mass.
• Mass is a measure of resistance to change in energy density, which corresponds to the inertial properties of matter.
• Different particles have different masses because their standing wave structure is different and hence their energy density is different.

Thus, mass is not an entity in its own right, but a manifestation of the energy density within the standing wave.

5.2 Why is mass proportional to energy?

From the special theory of relativity we know that energy and mass are related by the equation:

In our model, this relation follows naturally from the standing wave structure:

• The energy of a particle is determined by its energy density and frequency of oscillation.
• Mass arises as a parameter characterising the local energy density in a standing wave.
• The speed of light at this scale sets the limiting speed of energy transfer within the system.

Thus, mass is proportional to energy because the energy density determines the properties of the standing wave that makes up the particle.

5.3 Why does inertia depend on mass?

Inertia is resistance to changes in the state of motion. Within the framework of this model, inertia occurs for the following reasons:

• The higher the energy density in a standing wave, the more difficult it is to change its structure.
• Any change in the state of a particle requires a redistribution of the energy density in space.
• This redistribution obeys wave processes, which are constrained by the law of conservation of energy.

Hence, inertia is proportional to mass, since more massive particles have higher energy density and require more energy to change their state.

5.4 Why do particles have different masses?

The mass of different particles depends on the structure of their standing wave:

• Different oscillation frequencies result in different energy densities.
• The more nodes in the standing wave, the higher the energy concentration and the larger the mass of the particle.
• The mass scaling occurs according to fractal energy density levels, which may explain similar particle structures at different scales.

Thus, the masses of particles are different because their wave structure is formed by different energy density conditions.

5.5 Is the necessaryHiggs mechanism ?

In the standard model the mass of particles is explained by their interaction with the fieldHiggs . However, in the framework of our theory the mass naturally arises as a consequence of the energy density in standing waves. This leads to the following conclusions:

1. The Higgs field can be interpreted as a manifestation of energy density at a certain fractal level. In this case it is not a separate mechanism, but only reflects the existence of the energy density gradient.
2. If mass is determined by the standing wave structure, then the mechanism is Higgs unnecessary, since particles acquire mass simply by having an energy density at a given point in space.

Thus, the Higgs field may be unnecessary in the fundamental understanding of mass. It can be a convenient mathematical tool, but the mass itself is determined by the energy density structure without the necessity to postulate an additional field.

6. Speed of Light, Fractality and Expansion of the Universe

Introduction

The speed of light is considered a fundamental constant of physics, but why does it remain unchanged in different frames of reference? Within the framework of our theory, in which space is characterised by energy density and standing waves, the speed of light is a local characteristic of energy density. This explains not only its constancy, but also phenomena such as redshift.

6.1 Why is the speed of light a local constant?

In classical physics, the speed of light is considered to be a universal quantity, but within the framework of the proposed model:

• The speed of light determined by the islocal energy density.
• It remains unchanged for observers within a given energy density level.
• This is analogous to how the speed of sound depends on the density of a medium, but remains constant within that medium.

Thus, the speed of light is a local characteristic of the energy density of space.

6.2 Why do we see redshift, why do we observe the expansion of the Universe?

Redshift is traditionally explained by the Doppler effect or the stretching of space, but within the framework of our theory it may be a consequence of changes in energy density and gravitational effects:

• The frequency of light depends on the density of the surrounding space.
• When passing through regions with different energy densities, not only the speed of light changes, but also its frequency, which leads to a shift in the spectrum.
• Gravitational disturbances bend the trajectory of light, causing it to move along a curve, which creates a centripetal force.
• This force does the work of causing the photon to lose energy.
• Since frequency is responsible for the energy density, this results in a shift to the red region of the spectrum.

Thus, the redshift and expansion of the Universe can be considered as a consequence of the expenditure of light energy to overcome gravitational perturbations and changes in the density of the medium.

6.3 Why is the speed of light important to the structure of the universe?

The speed of light plays a key role in shaping the structure of the universe:

• It limits the maximum transmission rate of interactions.
• It defines the energy density and the boundaries of possible levels of fractality.
• Gravitational effects, which depend on energy density, affect the propagation of light, creating the observed effects of cosmology.

Thus, the speed of light is not just a constant, but a key parameter governing the energy density and structure of the Universe.

7. Gravitational time dilation and energy density

Introduction

Gravitational time dilation is traditionally explained within the framework of the General Theory of Relativity (GTR) through the curvature of spacetime. However, if we consider space not as a geometrical structure but as a distribution of energy density, an alternative explanation of this effect can be proposed. This chapter considers whether the concept of time dilation is really necessary or whether it can be replaced by a change in the velocity of electromagnetic wave propagation in a medium with different energy density.

7.1 Gravitational time dilation or change in the speed of processes?

In GR the gravitational time dilation is explained by the fact that near massive objects space-time is curved and the clocks go slower. However in the framework of the proposed model:

• Time as an independent physical entity does not change.
• Near massive objects, the energy density is higher, which slows down the speed of propagation of electromagnetic oscillations.
• All physical processes, including the operation of atomic clocks, are slower, not because of a change in time, but because of a change in environmental conditions.

Thus, gravitational time dilation can be replaced by a change in the rate of electromagnetic processes in a medium with high energy density.

7.2 Is curvature of space necessary?

GR uses the mathematical concept of curvature to describe gravitation. However, in the framework of our model:

• Space itself remains unchanged, only the changes energy density.
• The curvature of object trajectories can be explained not geometrically, but through energy density gradients.
• Gravitational forces are not a consequence of curvature, but a result of the tendency of objects to move towards the lowest energy density.

Thus, it is possible to replace the concept of curvature of space by a change in energy density without violating the known laws of physics.

7.3 Why can energy density replace curvature?

• All observed gravitational effects can be expressed through the energy density and its gradients.
• GR uses the energy-momentum tensor, which already describes the energy density, but through a geometrical interpretation.
• In the framework of the proposed approach, there is no need for curvature of space, since the motion of objects and time dilation are fully explained by energy density.

So the curvature of space is a mathematical tool and the real physical quantity is energy density.

7.4 Can Einstein’s equations be replaced by energy density equations?

Einstein’s equations describe the dependence of the curvature of space on the distribution of energy and momentum. However, if we replace curvature by energy density, we can obtain an alternative approach:

• The gravitational field can be expressed as a gradient of energy density.
• The motion of objects is determined by changes in energy density, not geometry.
• In the framework of quantum gravity this approach can be more convenient, since quantum fields are already described through the energy density.

Thus, Einstein’s equations can be rewritten in terms of changes in energy density, which simplifies the understanding of gravitation and its relation to quantum mechanics.

8. Spooky interaction and Heisenberg uncertainty via energy density

Introduction

Quantum mechanics describes many phenomena that seem counterintuitive to classical intuition. Some of the most puzzling are quantum entanglement (spooky interaction) and Heisenberg’s uncertainty principle. In the framework of our theory, where energy density determines the structure of particles and interactions, these effects can be more clearly explained. The plays a special role in this process rotation of the energy density inside the particle.

8.1 How do you explain the spooky interaction?

Quantum entanglement (spooky interaction, to quote Einstein) implies that two particles can instantaneously affect each other at any distance. In standard physics this seems like a paradox, but if we consider particles as standing waves of energy density with internal rotation, an alternative explanation can be proposed:

• Entangled particles are a single standing wave distributed in space.
• The rotation of the energy density within the particle creates a centripetal force that moves the energy to a point where the concept of distance becomes meaningless.
• Thus, changes in the state of one particle are instantly reflected on another because they are a single rotating wave formation.

This explains why the spooky interaction does not require information to be transmitted at superluminal speed — it is a consequence of a uniform distribution of energy density and its rotation.

8.2 Energy density rotation and its role

• Neutral particles (e.g. neutron and neutrino) have an odd number of standing wave nodes, which causes the energy density inside the particle to rotate.
• Spiral galaxies have a similar process — their structure reflects the rotational distribution of energy density.
• Photons can also rotate due to the mismatch between the centre of mass and the geometric centre of the wave structure., which explains polarisation
• The rotation of the energy density creates localised changes in density gradient the, resulting in instantaneous transmission of changes in the entangled particle system.

Thus, the spooky interaction can be seen as the effect of moving energy into a region where distance becomes meaningless due to the rotational compression of the energy density.

8.3 How can the Heisenberg uncertainty be explained?

The Heisenberg uncertainty principle states that it is impossible to measure the momentum and coordinate of a particle simultaneously accurately. In the framework of our model this effect can be explained as follows:

• A particle is produced by the propagation of an electromagnetic wave, which is an energy density wave structure travelling through a sphere.
• The generated wave in space is related to the wave on the sphere through the number π, which is irrational.
• If we know exactly the boundary of the sphere, it is impossible to calculate its centre accurately even mathematically.
• If the centre is known, it is impossible to calculate the length of the sphere accurately, even mathematically.
• The mass of a particle is formed due to the spherical structure, and it is the geometry of the wave process that creates the fundamental uncertainty.

Thus, the Heisenberg uncertainty is not just a mathematical constraint, but a consequence of the spherical wave structure of particles and the properties of the π number.

8.4 Relation of entanglement, rotation and uncertainty

If particles are standing waves of energy density with spin, entanglement and the uncertainty principle may be related:

• Entangled particles are a single wave structure with rotational components in which the uncertainty of coordinate and momentum is propagated to the whole system.
• The rotation of the energy density leads to centripetal effects in which the distance between entangled particles becomes meaningless.
• Measuring one of the particles changes the entire wave, thereby instantly changing the state of the second particle.

9. Measurements in the context of energy density theory

Introduction

Measurement plays a key role in physics, defining the boundaries of our understanding of reality. In the standard interpretation of quantum mechanics, the measurement process is associated with the collapse of the wave function, which leads to many paradoxes. However, in the framework of energy density theory, in which particles are considered as standing waves of energy density, measurement acquires a new physical explanation related to the structure of space, rotation and geometry constraints.

9.1 Measurement limitations and energy density geometry

Measurement is not possible without the interaction of the system with the environment. Within the framework of our model this is related to:

• Spherical energy density structure: the particles are standing waves, and their boundaries and centre are related through the π number.
• Uncertainty of the boundary and centre: since the number π is irrational, it is impossible to precisely determine both the boundary of the particle and its centre at the same time.
• The relationship between wave and spatial dimensions: any attempt to fix coordinates or momentum upsets the balance of energy density, changing the system itself.

Thus, the measurement limitations are not just a statistical consequence, but a result of fundamental properties of energy density.

9.2 Measurement process and interaction with energy density

In traditional quantum mechanics, measurement leads to the collapse of the wave function. In the framework of the energy density theory this can be explained differently:

• A measurement is a redistribution of energy density: when a system interacts with an instrument, the local energy density changes.
• Changing the wave structure: the measurement captures one of the possible configurations of energy density, changing the system.
• Inability to measure coordinate and momentum simultaneously: due to the spherical nature of wave structures, measuring one characteristic changes the other.

Measurement is a process involving the redistribution of energy density, not the abstract collapse of a wave function.

9.3 How does energy density affect measurement accuracy?

If the particles are standing waves of energy density, the accuracy of the measurements is limited by several factors:

• Frequency of energy density fluctuations: higher energy density creates sharper gradients, reducing uncertainty.
• Gravitational field: changes in energy density in space can alter the trajectories of measured particles, creating additional distortions.
• Influence of energy density rotation: particles with intrinsic rotation create dynamical position uncertainty.

Thus, measurement in physics is the process of interacting with a dynamic system of energy density rather than static determination of parameters.

10. Space, time and mass: three fundamental quantities

Introduction

In physics it is common to consider many fundamental quantities such as length, mass, time, electric charge and others. However, within the framework of energy density theory, three key fundamental quantities can be identified — space, time and mass, each of which is responsible for a different aspect of reality. This chapter explains why these three characteristics are the basic ones, and why the other parameters can be derived from them.

10.1 Space as the basis of structure

Space determines the coordinates of objects and their relative position. Within the framework of our theory, space can be represented as a wave medium with different energy density:

• Space defines the boundaries of the possible arrangement of particles.
• Standing waves of energy density are formed in it, defining the structure of matter.
• The change in energy density in space creates gravitational effects.

Thus, space is not just a background, but an active environment in which energy redistribution takes place.

10.2 Time as a characteristic of dynamics

Time is traditionally considered as an independent quantity, but within the framework of energy density theory it can be related to the frequency of energy density fluctuations:

• The frequency of wave processes determines the local speed of the processes flow.
• Time can be viewed as a parameter that depends on energy density but does not vary by itself.
• Time is not a changeable entity, but a characteristic of the rate of interactions in a medium with a certain energy density.

Thus, within the framework of this theory there is no need for time warp, and its manifestations are explained by changes in the properties of the medium.

10.3 Mass as a measure of energy density

Mass in classical physics is defined through inertia and gravitational interaction. In the framework of our model, mass is a local compactification of energy in a standing wave:

• Mass arises due to the concentration of energy density in a certain area.
• The higher the energy density, the greater the mass of the object.
• Mass is the source of gravity because it creates a gradient of energy density in the surrounding space.

Thus, mass is a consequence of the wave structure of energy density, not a separate property of matter.

10.4 Other parameters as derivatives

If space, time and mass are fundamental quantities, then other physical parameters can be expressed through them:

• Velocity is the ratio of coordinates to time.
• Impulse is the product of mass times velocity.
• Electric charge can be associated with energy density gradients at standing wave boundaries.

Thus, other quantities can be viewed as derivatives of space, time, and mass.

Conclusion

This paper considers a new concept that explains fundamental physical processes through the energy density, frequency and fractal structure of the Universe. Within the framework of this model it was possible to link such phenomena as quantum uncertainty, gravitation, electromagnetism and the structure of matter, without the need to introduce additional entities such as spacetime curvature.

The key achievements of this paper are:

1. The fractal relationship between scales of matter has been revealed— from elementary particles to galaxies. Calculations of the Milky Way radius and mass based on neutron parameters and coefficient fractalisation gave values close to the observed ones.
2. A new interpretation of the de Broglie wave is proposed as a mathematical description of standing waves forming elementary particles. This made it possible to theoretically determine the dimensions of the neutron and neutrino based on their mass. The calculations showed that:
   • The neutron size (~2.64 × 10⁻¹⁵ m) is consistent with experimental data.
   • The size of the neutrino (~1.55 × 10⁻¹⁰ m) has been found to be comparable to the atomic scale, as confirmed by recent studies.
3. Methods of measuring sizes and masses at different scale levels have been clarified. If standing waves determine the structure of matter, then the existing methods for estimating the sizes of particles and astrophysical objects may require correction taking into account their wave nature.
4. It is shown that dark matter can be a consequence of a smooth gradient of energy density. In this model dark matter is not a separate substance, but is a distributed energy creating gravitational effects.
5. An alternative explanation of the accelerated expansion of the Universe is proposed. The gravitational influence of rarefied energy at large distances can cause an additional redshift of photons, which is perceived as an effect of accelerated expansion of galaxies.
6. The possibility of using the fractal approach to predict physical parameters was confirmed. Scaling of sizes and masses from neutron to galaxy confirmed the applicability of the model at different levels of matter organisation.

Thus, this paper offers a new perspective on the nature of matter, gravity and the structure of the Universe, unifying quantum mechanics and astrophysics through the principle of fractality.

Future steps include:

1. Further development of the model, including its application to more complex physical systems.
2. Developing new predictions that can be tested by observations and experiments.
3. To popularize the theory among the scientific community and a wide audience.

Thus, this paper does not simply propose a new hypothesis, but forms the basis for further study of the laws of nature through the principles of energy density and fractal structure.

PS:)

I deeply respect Einstein and his contributions to science. He did the right thing for his time. Experiments showed that the speed of light remains constant, and he had no choice but to introduce the concept of curvature of space. However, Einstein himself emphasised that it is in an absolute vacuum that the speed of light is constant.

Similarly, at this stage I cannot definitively determine which of the constants — the Planck constant or the reduced Planck constant — should act as a factorfractalisation. The available experimental data are still not precise enough to make an unambiguous choice. Therefore, this question remains open and requires further study.

This approach offers a new perspective on the nature of mass and its relationship to electromagnetic processes. A more detailed discussion of this hypothesis and its philosophical implications can be found in the following works:

— (Dzen)

— (Zenodo)