Energy as a Fundamental Reality: From Points to Processes

Abstract

The article proposes a fundamental reconsideration of the ontological foundations of physics, where the primary entity of the universe is not matter or field, but energy understood as a dynamic process. By analyzing the limitations of the point-particle model and purely mathematical fields, the author develops an approach that interprets all physical phenomena—from elementary particles to cosmological structures—as different forms of organization within a unified energy continuum. The work does not reject the existing mathematical framework (GR, QFT), but offers a new physical interpretation, deepening the understanding of gravity, the “dark” components of the universe, and the phenomenon of mass. The concept finds strict mathematical expression in the author’s wave model of matter, which derives the spectrum of stable particles and predicts possible variations of fundamental constants. The article is not speculation but a coherent theoretical program aimed at restoring the ontological integrity that physics has lost.

In this article, the term “longitudinal wave” is used in an extended sense: it is not a new type of wave, but rather a part of the process associated with the front and the finite “thickness” of the electromagnetic wave. Essentially, it is the same field, only considered not separately but as an integral part of the wave itself. This perspective makes it possible to unify the description of the wave and the field, and to propose a mechanism of quantization through the equal work of space in the formation of each half-wave.

The text was structured and refined with the help of ChatGPT and DeepSeek to enhance its academic clarity.

Introduction

Modern physics has reached impressive heights in predictive accuracy and mathematical description of phenomena, but in the process it has lost part of the intuitive and physical understanding of processes. At the heart of most theories still lies the model of point particles and abstract fields, which are treated as mathematical entities rather than as physical processes. This simplification made calculations easier and allowed the development of quantum mechanics, electrodynamics, and general relativity, but also created a barrier to intuitive comprehension of the nature of matter, energy, and space.

The history of science shows that every major theory was born as an attempt to explain phenomena through simple and fundamental ideas. Newton formalized mechanics through the laws of motion and gravity, Maxwell united electricity and magnetism into a single system of equations, Einstein abandoned absolute space and time, introducing their dynamic nature. Each step was accompanied by a revolution in thinking but also its own limitations: for example, relativity theory was developed under the assumption of an “ideal vacuum” and does not contain a direct physical description of the carrier of fields. These assumptions simplified the mathematics and made theory development possible, but over time many of them have come to be seen as absolute truths rather than working models.

Today, physics relies on the complex apparatus of quantum field theory and the Standard Model. These theories predict experimental results extremely well but essentially describe the world as a set of mathematical objects — operators, fields, symmetries. The fundamental properties of particles (mass, charge, spin) are introduced as constants, while their nature remains hidden. This situation resembles Ptolemaic astronomy: the complex system of epicycles allowed prediction of planetary motion but did not reveal the essence of what was happening. Modern physics has reached a similar level of formalism — powerful and precise, but not always explanatory.

The approach proposed in this article is based on a different philosophy: energy as a process of change is primary, rather than particles or fields as static objects. Everything we observe is different forms of organization of energy: from stable configurations (particles) to large-scale distributions (gravity, electromagnetism). Fields should be regarded not as “attributes” of particles, but as dynamic manifestations of energy. In this context, the “point-like” nature of particles is just a convenient abstraction that hides their internal structure and dynamics.

This perspective opens new possibilities. If we abandon the rigid point as the basic model, the limitations of Heisenberg’s Uncertainty Principle can be seen differently: uncertainties become a natural consequence of the dynamics of wave configurations, rather than a strange property of “point-like objects.” Similarly, the phenomena of “dark matter” and “dark energy” cease to appear mystical: we already observe their indirect manifestations on galactic scales, but conventional particle-search methods cannot “catch” them directly. These phenomena should be regarded as forms of energy organization that manifest not in local measurements, but in large-scale dynamics.

An important example is the approach to waves in electrodynamics. Classical interpretation reduces them mainly to transverse modes, but retarded potentials and the effect of self-induction directly indicate a longitudinal component, which is often referred to as a “subtle effect” and discarded in calculations. This example shows: the familiar mathematics is convenient, but it can conceal important aspects of physical reality.

This work proposes to unite two directions:

• Preserve the existing mathematical apparatus as a computational tool.
• Complement it with a new level of understanding, where energy acts as the fundamental reality, and particles and fields as manifestations of dynamic processes.

This approach does not contradict the existing scientific picture but continues its logical development. At one time, Einstein made a decisive step by showing that space and time are not absolute but dynamic. Today, returning to a process-based understanding of energy may become a similar step toward deepening our worldview — but now on a new level.

Problem Statement

Physics of the 20th–21st centuries has achieved exceptional success in quantitatively describing nature. Quantum field theory, general relativity, the Standard Model — these are fundamental achievements of science. However, they are built on assumptions that were historically taken as working simplifications and over time came to be seen as absolute truths.

One of these assumptions is the representation of a particle as a point object. In modern theory, particles have no internal structure, and their properties — mass, charge, spin — are specified as constants. Fields are treated as something that “arises” around particles, but their nature is not disclosed. This is a convenient mathematical model, but it does not explain why these quantities exist as they do or where they come from.

A similar situation is observed in other areas. For example, waves in electrodynamics are often considered only transverse, whereas retarded potentials and the effect of self-induction directly indicate the existence of a longitudinal component, which is usually considered insignificant and excluded from consideration. This practice is justified in a number of tasks, but it creates the illusion that these phenomena are absent.

As a result, a paradoxical situation has arisen: physics has a powerful predictive apparatus, but remains philosophically incomplete. It describes “what” and “how,” but rarely answers the question “why.”

An example is Heisenberg’s Uncertainty Principle. It is treated as a fundamental property of nature rather than a consequence of the dynamic structure of energy. This turns it into an axiom rather than an explanation. Similar axiomatic approaches pervade modern science: dark matter and dark energy are described as unknown entities, but they may turn out to be manifestations of the same energy in other scales or forms of organization.

The problem is that excessive emphasis on mathematical formalization with insufficient physical interpretation has led to a gap between theory and intuitive understanding. To move forward, it is necessary not to abandon existing models but to complement them with a new level of conceptualization: to consider energy as the primary reality, and particles and fields as its manifestations.

Proposed Approach

The goal of this approach is to move from the representation of particles and fields as static objects to understanding them as various forms of energy organization. In this context, energy is not seen as an abstract quantity but as a process of change and interaction, from which the phenomena we observe follow.

• Energy as the fundamental element of the physical picture of the world. All observed objects and interactions can be regarded as different configurations of energy. Particles are stable wave formations, fields are energy distributions in space, and interactions are dynamic changes of these configurations.
• Rejection of strict point-likeness. The concept of “point particles” simplifies calculations but hides important aspects of their internal dynamics. Real objects have structure and extent, and their parameters (mass, charge, spin) may be the result of a complex distribution of energy.
• Fractality of nature. Space and matter may have multi-level structure, where each scale reflects similar laws of energy organization. What we call “particles” may be the result of processes at a larger level. Galaxies and black holes may represent stable configurations of energy on a larger scale.
• Longitudinal waves as an underestimated phenomenon. Modern electrodynamics mainly emphasizes transverse waves, but phenomena of self-induction, Larmor radiation, and retarded potentials indicate the presence of a longitudinal component. This component is often considered “small” and discarded, but its influence can be critical at small scales.
• Preservation of the existing mathematical apparatus. The new approach does not require abandoning QFT or GR but proposes to consider them as particular cases of a broader picture, where energy is not just a quantity but a dynamic reality.

Such a view can help to look at “dark matter” and “dark energy” in a new way, considering them not as unknown entities but as energy configurations not yet incorporated into existing models.

Maxwell’s Equations

In SI units:

1. ∇·E = ρ/ε₀ — Gauss’s law for electric field.
2. ∇·B = 0 — absence of magnetic charges.
3. ∇×E = −∂B/∂t — Faraday’s law of induction.
4. ∇×B = μ₀J + μ₀ε₀∂E/∂t — Ampère’s law with displacement current.

Self-Induction and Radiation Reaction

Self-induction is one of the most vivid manifestations of the presence of longitudinal components of the electromagnetic field. When current changes in a circuit, the changing magnetic field induces an EMF opposing the change in current (Lenz’s law). This effect cannot be explained by considering current as an instantaneous motion of charges without delays: for the magnetic field to change, a finite propagation time of the disturbance in space is required. Thus, self-induction is a direct consequence of the finite propagation speed of electromagnetic interactions.

Consider an inductor. With a rapid change in current, the energy of the magnetic field does not have time to reorganize instantly. A reaction of the circuit arises, expressed as the EMF of self-induction:

E = −L · dI/dt

where L is inductance. This equation reflects the fact that the change of the field lags behind the change of current: the physical system resists accelerated changes, which corresponds to the presence of a longitudinal component of the field in the near zone.

Radiation reaction is a more subtle effect, manifested in the accelerated motion of a charge. An accelerating charge radiates an electromagnetic wave and, at the same time, experiences a “radiation reaction” or radiation recoil, which is described by the Larmor and Lorentz–Abraham–Dirac formulas. This recoil arises because the changing field cannot instantly reorganize: the charge “interacts” with its own field through retarded potentials.

These effects demonstrate:

• Electromagnetic interactions are not instantaneous.
• Longitudinal components of the field exist and play a key role in the near zone.
• Classical models often discard these effects as small, but at high accelerations or rapid current changes their contribution becomes decisive.

Thus, self-induction and radiation reaction are direct confirmations that longitudinal waves not only exist but are critically important for the exact understanding of processes.

Geometry and Energy: Rethinking Einstein

Einstein’s brilliant step was to abandon Newtonian gravity as action at a distance and replace it with the geometry of spacetime. Mass and energy determine the curvature of this spacetime, and the trajectories of particles and light rays become merely geodesics in the curved field — a manifestation of this curvature. General Relativity (GR) became a triumph of mathematical physics, uniting gravity, mechanics, and geometry within a single framework.

However, from the standpoint of the energy paradigm proposed in this work, this achievement opens the way for the next step. Geometry is a brilliant language of description, but not a fundamental entity. What exactly “curves”? And what is the carrier of this curvature?

It is proposed to shift the focus from geometry to energy as the primary reality. In this interpretation:

• Curvature is a consequence, not a cause. The effect we describe as “curvature of spacetime” is a macroscopic manifestation of a complex redistribution of energy density in a given region. The presence of mass or energy distorts the fundamental energy state (“background”) of the Universe. Riemannian geometry is an ideal mathematical apparatus for describing the consequences of this distortion for the motion of bodies and the passage of time, but it does not describe the internal mechanism of the distortion itself.
• Geometry as an emergent property of energy. Geometry of space-time does not disappear from the picture of the world; on the contrary, it retains its fundamental role but becomes derived from deeper energetic processes. Just as temperature and pressure of a macroscopic gas arise from the chaotic motion of molecules, the geometry of space can be understood as an expression of the symmetries of the energy continuum. Space is isotropic and symmetric in all directions, which is why fundamental relations are naturally linked to circles and angular characteristics. In this sense, Einstein’s equations are effective equations describing the averaged behavior of energy, while geometry itself reflects the symmetry and structure of the energy field.
• Deepening the physical meaning of field equations. Einstein’s equation links the curvature tensor (geometry) with the energy–momentum tensor (matter and energy): in the standard interpretation this is read as “matter tells space how to curve, and space tells matter how to move.” In the energy interpretation, this equation acquires a deeper meaning: it describes the dynamic equilibrium between different forms and configurations of a single substance — energy. The energy–momentum tensor Tμν describes localized, condensed forms of energy (particles, fields), while the Einstein tensor Gμν describes the consequences of their presence for the surrounding energy continuum. These are not two different subjects in dialogue but self-interaction of a single energetic reality.

This approach does not cancel or refute General Relativity. On the contrary, it generalizes and deepens its physical interpretation, moving beyond a purely geometric metaphor. It raises new questions: what is the microscopic structure of this energetic continuum? Which processes at the quantum level give rise to an effective description in terms of smooth geometry? The birth of each particle indeed alters the energy distribution throughout space, but because this contribution is negligible compared to the overall background, gravity manifests as a smooth process. This suggests the possibility of a deeper theory that would describe the transition from discrete events at the micro level to a continuous gravitational picture. However, it is too early to speak of a fully developed “quantum gravity” — this is merely a potential direction for further research.
Thus, Einstein’s legacy can be viewed not as a final truth but as a powerful bridge from the physics of forces to the physics of states and processes. The next step is a shift from describing the geometry of space to understanding the physics of the energy that gives rise to this geometry.

Perhaps this path points toward a quantum theory of gravity, where the key insight may lie in separating the source from the manifestation. It is important to understand that it is not the macroscopic manifestations of gravity (the smooth curvature of spacetime) that should be quantized, but the primary processes of energy redistribution that give rise to these manifestations.

• The source is discrete. A particle, being a stable standing wave of energy, represents a quantized, discrete node of disturbance in the energy continuum. It is the source of gravitational influence.
• The manifestation is continuous. However, this influence itself propagates and dissipates in a continuous energy continuum, manifesting on the macro-level as a smooth gravitational field. We do not observe the quantized source directly, but its “response” in the medium. Just as a stone thrown into water (a discrete act) creates spreading waves (a continuous field), a quantized particle creates a continuous gravitational field.

Thus, the contradiction between the discreteness of the quantum world and the continuity of gravity proves to be apparent. It arises from the attempt to describe the source and propagation within the same mathematical model. Quantization belongs to the processes of forming stable configurations (particles), while continuity is a property of their dynamic interaction with the fundamental energy reality. This separation allows reconciling the two approaches: the microworld is described by quantum theory of energy perturbations, and the macro-manifestations of these perturbations — by an effective theory in terms of continuous geometry.

Einstein described gravity as curvature of spacetime — a grand step forward that united mass and energy into a single system. Today we can go further: instead of “curved space” it is more accurate to speak of redistribution of energy causing the observed effects. Geometry is a language of description, not a fundamental entity. This approach does not diminish Einstein’s achievement but continues his path, deepening the physical meaning of mathematical models.

Field, Energy, and Medium: From Forbidden Topic to New Paradigm

Historically, physics discarded the concept of ether after the Michelson–Morley experiment and the triumph of Einstein’s special relativity. This was a necessary step: rejection of the hypothesis of a rigid, mechanical ether serving as an absolute reference frame allowed science to make a giant leap forward. However, with the bathwater the baby was thrown out too: the very idea that fields may be not just mathematical abstractions but manifestations of some fundamental physical reality.

As a result, modern physics finds itself in a paradoxical position: we deal with fields (electromagnetic, gravitational, quantum) that are successfully and ubiquitously used in calculations, yet their nature remains ontologically undefined. What oscillates in an electromagnetic wave? What “curves” in a gravitational field? The standard answer is “spacetime,” but this is again a geometric, not a physical, interpretation.

The proposed energy approach allows us to lift this taboo by offering a modern, self-consistent replacement for the concept of “ether.”

• Not “medium” but “continuum.” We propose to speak not of a “medium” in its classical, mechanistic sense (a substance consisting of particles through which waves propagate), but of a fundamental energy continuum. This is not matter in its usual sense but a deeper reality, a primary entity whose states and perturbations we perceive as both matter and fields. The key property of this continuum is its dynamic nature: it is not an absolute reference frame, and its properties may change locally under the influence of the same perturbations that exist in it (directly resonating with GR).
• Energy as the only substance. In this paradigm, a “particle” is not a foreign body moving through the continuum. It is a localized, stable perturbation of the continuum itself, its specific state. A “field” is a dynamic, propagating disturbance or gradient of energy in this continuum. Thus, the dualism of “matter” and “field” disappears — there is only energy in different forms of its organization.
• Mathematical consistency. This approach does not require revising Maxwell’s or Einstein’s equations. On the contrary, it gives them new physical meaning. The equations describe the behavior of this continuum. For example, the speed of light c is not the speed “relative to ether,” but the critical speed of propagation of perturbations in this energy continuum, its fundamental property.
• Solution to the problem of gravity. In this model, gravity ceases to be a mysterious “force.” It becomes a manifestation of the gradient of energy density in the continuum. A massive body (a large, stable perturbation) creates around itself a region with altered energy density. Other perturbations (particles) are forced to change their motion in this non-uniform continuum, which we interpret as attraction. This directly agrees with the reinterpretation of GR proposed above: geometry is the language describing the energy topography.

Thus, this approach does not attempt to revive the old concept of the ether. Instead, it proposes an evolutionary development of the idea: a transition from a mechanical medium to a dynamic energetic continuum. This is not a step backward but a step forward — toward an ontologically complete physical picture of the world, where mathematical objects acquire their physical essence without contradicting the vast body of experimental data and existing theories.

Fractality and the Birth of Matter: The Universe as a Self-Similar Energy Network

One of the deepest consequences of the energy paradigm is the fractal, or self-similar, structure of reality. If the fundamental entity is energy rather than matter, then the forms of its organization may repeat at different scales. Within this model, a radical yet elegant view of the nature of “dark” components and matter itself is proposed.

• Dark matter and energy as density imbalance. In this interpretation:
  Dark matter is not invisible matter but a region of space on a galactic scale with anomalously high energy density of the fundamental continuum. It is not particles, but a “condensation” of the energy substance itself, which manifests gravitationally; it is mass in itself — an amplitude of increased energy.
  Dark energy is, conversely, a region with decreased energy density of the same continuum — a kind of “rarefaction,” producing the effect of accelerated expansion of the Universe.
• Galaxies as analogs of particles. This model allows that some types of galaxies, possessing specific sizes, mass, and other characteristics (such as morphological type and the presence of active nuclei — black holes), may be large-scale analogs of elementary particles. If a particle is a stable standing wave of energy on the micro-level, then such a galaxy is a stable wave configuration (“standing wave”) of energy on a mega-scale. Their stability and structure are governed by the same principles of dynamic equilibrium in the energy continuum.
• Birth of matter through energy redistribution.The key mechanism for the emergence of ordinary (“baryonic”) matter is linked to a change in the state of these large structures. According to relativistic effects (Lorentz transformation), a change in the velocity of a galaxy (as a large wave configuration) should lead to a change in its effective “size” and “mass” in its own frame of reference. This process requires a large-scale redistribution of energy within the continuum. The excess energy released during such “compression” or “restructuring” does not disappear but is localized as stable perturbations on the next lower scale — giving rise to stars, planetary systems, and, most importantly, baryonic matter itself. Thus, matter is not a primary given, but a byproduct of the dynamics of larger energy processes.
• The Universe as multi-level interaction. This model does not require all galaxies to be analogs of elementary particles. Many of them may be the result of other processes — interaction of regions with different energy density (dark matter and dark energy). Their “overlap” and interference may generate a wide variety of structures. Moreover, this principle works on all levels. The collision of two truly elementary particles in a collider (such as CERN) in this paradigm is an analog of the collision of two galaxies at their own scale. And it is equally likely that the result of such a micro-collision may not simply be the birth of new particles, but the formation of a complex, hierarchical structure — a whole “microcosm” (for us — just a particle or atomic nucleus), which for a hypothetical observer inside it might appear as a whole universe or galaxy.
• Black holes as energy accumulators and transformers. Within this model, black holes play a key role not as “cosmic garbage collectors,” but as critical nodes in the network of energy redistribution. This process forms a closed cycle:
  Accretion and concentration: Baryonic matter born as a result of galactic dynamics (stars, gas, planets) gradually migrates toward the center of the gravitational potential — the black hole — and is absorbed by it. This is not destruction, but accumulation and transformation of energy at the most extreme level. Energy previously distributed in the form of matter at the periphery is concentrated and “compressed” in the central singularity (or its vicinity, within the model).
  Reverse process and release: The accumulated and transformed energy does not remain trapped in the black hole forever. Certain conditions (e.g., reaching a critical density, interaction with powerful magnetic fields, or quantum-gravitational effects) can trigger the reverse process — powerful outflows (jets) of energy and matter (in the form of relativistic plasma) back into the galaxy. Thus, the black hole acts as the heart of the galaxy, “pumping” energy through itself: absorbing it in one form (matter) and releasing it in another (radiation, accelerated particles).
• Rethinking the Big Bang. Such an approach naturally calls into question the standard cosmological model. The Big Bang may not have been the absolute beginning of everything. Within the fractal paradigm, it can be interpreted as:
  A local event — the birth of a new “elementary particle” the size of our observable Universe within a larger Metaverse.
  A moment of phase transition — a sudden change in the state of the energy continuum (its density or level of perturbation), which we perceive as a singularity.
  A consequence of a change in cosmic acceleration, causing large-scale restructuring and redistribution of energy, rather than a “point of creation from nothing.”

It is crucial that at the moment of this event, baryonic matter might have already existed as a product of previous cycles or processes at super-large scales. The Big Bang in this case did not necessarily create all matter but catalyzed its transformation and redistribution.

Inflation and the Speed of Light Limit: A New Perspective. In standard cosmology, the origin of the Universe is linked to inflation — an instantaneous superluminal expansion of space from a “point.” In the proposed approach, such an interpretation is unnecessary. The Universe is considered as a distinct energetic element, possessing boundaries and an internal tension of energy balance. At the moment of acceleration, the redistribution of energy occurs simultaneously throughout its entire volume — not through the transfer of matter across space, but as a change in the energetic state of the system. Thus, the speed of light limit is not violated: matter emerges as a process of energy redistribution within the “Universe-particle,” while space already exists as a geometrical structure.

• Spooky Interaction as a Manifestation of the Paired Nature of Energy

One of the most puzzling phenomena of quantum mechanics remains the so-called "spooky interaction" (entanglement), where the change in the state of one particle instantly reflects on its partner, regardless of distance. Within the point-particle model, this seems paradoxical: how can information be "transmitted" faster than the speed of light?

In the wave model of energy, the situation finds a natural explanation. Particles are never born in isolation: every real particle arises in a pair — matter and antimatter. Their energy configurations are initially connected through a common process, and a change in one does not "send a signal" to the other, but simply manifests as a change in the shared wave system. The rotation of energy creates an effect of localization into a point, and for this point distance itself does not exist. Therefore, the connection between paired particles persists regardless of their spatial separation.

This is especially clear in the case of neutral particles. A neutron and an antineutron differ only by the direction of energy rotation. Their interaction leads to instability and, consequently, to the phenomenon of radioactive decay. Thus, "spooky interaction" ceases to be a mystery: it becomes a direct consequence of pair creation and the wave-like nature of matter.

• Matter and Antimatter: Apparent Asymmetry and Hidden Symmetry

One of the oldest questions in physics remains the problem of matter–antimatter asymmetry: why do we observe almost exclusively matter in the Universe? Within the proposed approach, the very formulation of the question requires revision. There is no asymmetry in creation: matter and antimatter always arise in pairs, in equal amounts.

The difference lies in their dynamics. Matter tends to concentrate toward centers — regions of high energy density such as black holes, where it is processed and transformed. Antimatter, on the contrary, gravitates toward regions of lower density, where it is likewise redistributed and transformed, acting as a kind of “counterpole” to the processes involving matter.

Thus, the observed “asymmetry” is an illusion caused by the limitations of our observational level. In reality, there exists a dynamic symmetry in which both matter and antimatter participate in the overall cycle of energy redistribution, ensuring the stability of the Universe’s energy continuum.

Thus, the proposed perspective erases the boundaries between the micro- and macroscopic worlds. The paired nature of particles, the phenomenon of entanglement, and the apparent “asymmetry” of matter and antimatter turn out not to be local oddities but universal principles of energy dynamics. Matter and antimatter participate in the same cycle of redistribution, yet manifest at different density levels, ensuring the balance and stability of the energy continuum.

Matter, dark matter, and dark energy appear not as three distinct entities, but as forms of organization of a single energetic process. The Universe emerges as a fractal, self-similar network where processes at every level — from quantum correlations to cosmic accretion — nourish and sustain one another. The birth of matter, its transformation, and its subsequent accretion into black holes form a closed cycle of energy redistribution from the periphery to the center and back, with black holes acting as key dynamic nodes.

This approach provides a new perspective on inflation, gravity, and the origin of mass. It does not reject the existing mathematical apparatus of physics but offers it a different interpretation: to see behind the formulas not abstractions, but real processes of energy dynamics. This opens the way toward a more coherent and ontologically consistent understanding of the structure of the Universe.

Conclusion

This work proposes a conceptual revision of the foundations of modern physics, aimed at addressing its key paradox: unprecedented predictive power combined with a growing loss of intuitive and ontological understanding of the nature of reality. As a way to resolve this crisis, it is proposed to return to a fundamental principle, placing at the foundation of the world picture energy — not as an abstract scalar quantity, but as a primary dynamic reality, the only true substance of the universe.

Such an approach allows a series of fundamental shifts in perception, which find not only qualitative but also strict mathematical expression in the author’s developed “Theory of the Wave Model of Matter and the Fractal Structure of the Universe” [5]. The key conclusions of this work provide a philosophical and theoretical justification for the results already obtained in that theory:

• From objects to processes. Particles and fields appear as secondary manifestations — stable wave configurations of a single energy continuum. The mathematical model, based on the principle of standing waves and the Pythagorean theorem, derives the possible spectrum of masses and sizes of stable elementary particles, explaining why there can be only a limited number of them (four main types), and linking their parameters to the speed of light and the gravitational constant.
• From static constants to dynamic relations. In the model, the fine-structure constant loses its status as an absolute constant. It appears as a coefficient reflecting the properties of the energy continuum — possibly its “viscosity” or the degree of damping of gravitational perturbations. This hypothesis, which has a concrete mathematical representation, is experimentally testable through the search for variations of fundamental “constants.”
• From disparate phenomena to a fractal network. The micro- and macro-worlds are united by the principle of self-similarity. The mathematical apparatus describing the birth of particles as wave processes is logically extrapolated to the mega-scale, allowing galaxies to be viewed as analogs of elementary particles and the “dark” components as manifestations of energy density redistribution in the continuum.
• From singularity to cyclicity. This view calls into question the uniqueness of the Big Bang, suggesting that it be seen as a local event in an eternal and self-similar Universe, which naturally follows from the fractal hierarchical model.

Thus, the philosophical paradigm presented here acquires a strict mathematical body in a separate work by the author [5]. Further development lies not in beginning formalization but in deepening and expanding the existing model:

• Developing a mathematical description of the processes of energy redistribution between scales.
• Accurate calculation of the predicted variations of the fine-structure constant and planning experiments to detect them.
• Building a bridge between the wave model of particles and the formalism of quantum field theory, starting from the primacy of the energy continuum.

Ultimately, the proposed approach is not speculation but an alternative theoretical program possessing internal coherence, mathematical apparatus, and most importantly — the ability to make testable predictions. It is a decisive step toward a theory that not only predicts “how,” but explains “why,” returning to physics its lost integrity and ontological depth.

References

1. J. C. Maxwell. A Treatise on Electricity and Magnetism. 1873.
2. A. Einstein. The Foundations of the General Theory of Relativity. Annalen der Physik, 1916.
3. W. Heisenberg. On the Visualizable Content of Quantum Theoretical Kinematics and Mechanics. Zeitschrift für Physik, 1927.
4. J. D. Jackson. Classical Electrodynamics. 3rd Edition.
5. S. N. Skrynnik. Model of the Wave Structure of Matter and the Fractal Structure of the Universe. Zenodo, 2025. https://zenodo.org/records/17170052