Substrate

This is a retroductive account of nature, reasoning from phenomena back to geometric archetypes that generate them. Here, the cause and effect of field and space form a unified figure whose composition necessarily gives rise to reality. Carl Friedrich von Weizsäcker noted in 1971 that “Philosophy as a university discipline commands no authority today… mainly because the task of philosophy is so difficult. Philosophy can be defined as continued questioning. Socrates practiced it thus, in an exemplary manner.”

The nature of matter

What we traditionally call “matter” is re-understood as a self-reinforcing, stable field in which spatial energy is governed by the field’s recursive geometry, whose geometric topology determines its observable properties. This geometry characterizes its point source—the zero-dimensional substrate of matter, mass, charge, and time—and its emergent space—the three dimensions of energy and waves (light and gravity) that, paradoxically, do nothing but give light to measurement. Hence, the principle of causality arises for the recursive field and its space, where the point-source field is always the cause of space, and exists through space but not in space.

Matter is not composed of discrete particles, but rather represents stable, self-sustaining configurations of electric charge density and current density whose field geometry defines the observed properties of different materials. Drawing from Jefimenko’s nonlinear electrodynamics, these configurations exist as non-radiating, stationary electric density structures, where the distributions of charge and current are arranged in a self-consistent equilibrium. The spatial reality of matter itself are not causal agents but secondary effects arising from these underlying electric densities. Such nonlinear coupling provides the stability that prevents radiation loss, allowing each atom or material form to persist as a unique equilibrium of intertwined charge and current densities. In this view, the apparent solidity and diversity of matter emerge entirely from variations in these stable electric-density field geometries, rather than from separate, pointlike particles.

Even so-called neutron phenomena exhibit internal electric structure. Experimental evidence, seen in the nonzero electric form factor, reveals spatially separated regions of positive and negative charge density whose integrals cancel to zero. Within Jefimenko’s framework, this neutrality arises from dynamic balance among intertwined charge and current densities, not from the absence of charge itself. The neutron phenomenon thus represents a self-consistent electrodynamic configuration—a stable equilibrium in which internal motion of charge sustains both its neutrality and persistence without invoking discrete particles.

The nature of the field, point source, and zero-dimensionality

A useful example of recursive geometry that demonstrates a field is the recursive pentagram—the regular pentagram, or more precisely, the dodecahedral star—which has its first layer whose √5-term carries a coefficient of 1 at the minimum subdivision depth of Φ⁻³, as shown in A Fibonacci–Lucas Decomposition of Subdivision Lengths in the Pentagram.

The lines of the pentagram are zero-dimensional, as the space that arises is dimensional. The recursion points correspond to point masses or electric point charges, the connecting lines to “distributed” mass or electric charge densities and current densities, and the emergent spatial structure to the static gravitational, cogravitational, electric, or magnetic spaces—or, in the case of gravitational or electromagnetic wave propagation, to varying gravitational or electromagnetic spaces.

In the context of topology and geometry, a point is a dimensionless, indivisible locus; it has no magnitude, no breadth, no extension—merely existence without form. Contrary to popular understanding, a single connecting line is no different than a point because it lacks space. However, two distinct points can provide a distance length because they are seperated by a space. In nature, there exist only three-dimensions and zero-dimensions, with zero-dimensionality accounting for temporal point-source mass and charge. When a point becomes recursive, it must include space to define the recursion—thus, space emerges as an effect originating from the point-source cause.

When considering mass or electric charge, we refer exclusively to the lines, rather than to the spatial effects that emerge around and from material bodies or geometries. Space itself is massless radiation or gravity—a domain of wave propagation, which serves only to carry energy and bring light to reality. When viewing nature in its entirety, as composed of two fundamental aspects—field and space—the central pentagon, or inner polygon of the pentagram, is the nuclear mass (the lines) and massless space of an atom (the empty space), whereas the surrounding stellated triangles forming the star points are the gravitational or electromagnetic outer shell of an atom or mass. The recursive stellation of the pentagram, through its nested forms, illustrates the infinite subdivision and interrelation of these two natural elements, wherein mass and radiation or gravity coexist within distinct dimensions: the radiation and gravitation as dimensional, the point-source mass or electric charge field as zero-dimensional.

In conventional physics, a field is defined operationally—as a measurable quantity that has a value at every point in space and time—for instance, as an electric, magnetic, or electromagnetic field. Yet these so-called “fields” are in fact spatial manifestations of the underlying source field, not the field itself. In the natural Platonic view, a field represents an invisible source or essence behind physical effects. Jefimenko’s insight was that gravitational and electromagnetic fields are caused by point-source distributions at earlier (retarded) times, not instantaneously. In his words, gravitational, cogravitational, electric, and magnetic fields are not causes—they are effects of changing point mass or electric point charge sources. Although this may seem like mere semantics or logomachy, it is fundamentally important to define the field according to the Platonic view rather than the conventional approach found in textbooks. In this discussion, we depart from the engineering convention by referring to these effects as spaces—that is, gravitational fields as gravitational space, magnetic fields as magnetic space, electric fields as electric space, and propagating gravitational or electromagnetic waves as varying gravitational space or varying electromagnetic space. This offers a clearer exposition and a more formal perspective that connects Jefimenko’s causality with the natural retroductive understanding of the field.

A point-source field has no size (zero-dimensional), which can’t “fill” any space. In mathematical terms, a point source is “distributed” through the Dirac delta function, which lets us treat it as part of a continuous spatial framework, so it can “participate” in integrals. The point source (i.e., point mass or electric point charge) is still the cause in Jefimenko’s view, but technically, it’s always understood as a distribution of a point source because the field’s spaces arise from their spatially extended zero-dimensional points.

The nature of force

Force is the analogy of unification through nature: Force = Field × Space (i.e., F = mg, F = qE, etc.). It is a response equation describing how causes show up through their effects—a response calculating a point source (point mass or electric point charge) showing up through its causal corresponding space (gravitational space, electric space, etc.). In nature, the gravitational and electric spaces don’t cause, and their forces don’t act—both are maps of relationships, not agents. In essence, force itself doesn’t “do” anything; rather, it is a local summary of distant, retarded interactions between sources.

We can’t say gravity is electromagnetism because their mechanical definitions are of different field configurations. But what is obvious is that they both exert the same empirical expression of force that can be seen as unified under analog equations—F = mg, F = qE, etc.—where mass (m) is analogous to charge (q), and gravity (g) is analogous to the electric field (E) (see page 104 in Causality, Electromagnetic Induction, and Gravitation).

Science keeps trying to unify everything with complicated math, but the unification is already there—every force works the same basic way: a kind of field (that we define in this writing as a point source, i.e., a point mass or an electric point charge) interacting with its causal corresponding space (i.e., gravitational space, electric space, etc.); the algebraic form is identical: Force = Field × Space.

The nature of light, gravity, and space

When we describe something as quantum, we are referring to the fundamental, quantifiable electromagnetic fabric of nature. A quantum interaction represents the smallest possible amount by which energy can be transmitted in nature. This does not imply that light is inherently a particle; rather, it means that light interacts with the field in discrete energy packets. The interaction between light and the field—or between space and the field—constitutes this quantum state.

Light is space—a massless effect caused by a zero-dimensional point-source electric charge. The entire propagating electromagnetic spectrum is light; however, the human eye can only visibly perceive a portion of it. We know that where there is space, there is always light, due to quantum vacuum fluctuations, a fact experimentally reinforced by the Casimir effect. Even within the spatial structure of an atom, wave propagation occurs, reinforcing the notion that all space is a light-wave propagation. Likewise, we can say that all space—light itself—carries energy, and that electric and magnetic energies are complementary aspects of a single unified electromagnetic energy.

Gravity is, likewise, space—an analogy of light and massless effect caused by a zero-dimensional point-source mass. All space includes gravity; however, its effect is defined by the energy deficit of the mass, later discussed in the Energy, mass, and gravity in field dynamics section.

Light appears as the spatially extended aspect of a wave oscillation; it is not a particle—not a “photon.” A wave always involves spatial variation—either directly in real space or implicitly through a representation that encodes spatial structure—unlike a mere oscillation, which varies only in time. Light cannot oscillate without being a wave. Contrary to a mainstream popular belief system, the experimental reality of light shows that it is the spatially extended aspect of propagating waves, as evidenced by interference phenomena in which constructive and destructive interference occur—constructive representing the spatial reinforcement and amplification of interfering waves, and destructive representing their spatial cancellation. There is no electric charge or current “inside” of the spatially extended aspect of a wave oscillation, rather the point source is the zero-dimensional cause of the space. This applies analogously to gravity.

Since light is a manifestation of space and thus a massless effect, its physical cause arises from electric charge—a zero-dimensional point. Therefore, we should define light solely as the effect of the point-source field. Space does nothing, and likewise, light does nothing but radiate and expire. Without light, there is no measurement, and without measurement, no visible reality. Again, this applies analogously to gravity.

Light—that is, radiation or propagating electromagnetic waves—surrounds all physical matter and works through it. However, the nature and intensity of this radiation depend on the stability of the matter itself. Stable matter emits only minimal radiation, largely limited to quantum vacuum fluctuations—the transient electromagnetic energy variations that occur even in empty space. In contrast, unstable matter releases significant radiation as it undergoes decay or transformation, making its energetic activity much more pronounced.

The dynamics of energy across the electromagnetic spectrum of light are simple: the smaller the wavelength, the greater the capacitance. This means a gamma wave carries more energy than a radio wave because the gamma wavelength is tiny compared to the radio wavelength.

Energy, mass, and gravity in field dynamics

Mechanical energy—kinetic and potential—is the energy of motion or configuration within matter, while spatial energy resides in the surrounding spaces that mediate forces between masses or charges. In this discussion, energy and mass remain distinct, and gravity is interpreted as arising from the spatial energy deficit of a mass, rather than from relativistic mass–energy equivalence.

If mass and energy are distinct in nature, and changes in potential energy do not affect mass, then what we perceive as gravity is simply the spatial energy deficit of the mass or field–space configuration—a deficit that governs the collapse of space, producing what we call gravity. Although Jefimenko’s equations imply that gravity is an effect of a point mass and its current—which it is, because it is analogous to an electric charge and current causing electric and magnetic fields—the nature of the point mass is defined at the discrete level by its electric charges that make up the entire “distributed” point mass.

The more tightly the recursive knot of a field, and the smaller its spatial region, the greater its capacitance and its capacity to carry energy. As discussed in the section The nature of light, gravity, and space, the behavior of energy within the electromagnetic spectrum follows a simple principle: shorter wavelengths carry more energy than longer wavelengths. Additionally, regions of constructive interference amplify local energy, whereas regions of destructive interference weaken it.

The larger the space, the smaller the capacitance, and the greater the gravitational effect becomes—due to the lack of energy that promotes the collapse of space. In atoms, we observe a mass–energy equivalence: stable space can exist because there is an abundance of energy within such a small region, preventing the collapse of space from occurring.

An atom contains so much localized energy in such a tiny space that it produces virtually no gravitational effect. In contrast, massive gravitational bodies lack energy relative to their spatial scale, which is why they exert such extreme gravitational pull—to compensate for their energy deficit. In the example of nuclear fission, splitting a heavy atom releases excess energy in the form of kinetic energy. Because such a large amount of energy is locked within such a small space, even the excess energy released is tremendous relative to our scale. Consequently, gravity arises when a system’s mass lacks energy—a condition known as an energy deficit of the mass. This is why atoms exhibit no observed gravity, and the energy of a massive gravitational mass is nearing zero—with a large energy deficit.

Artificial magnetism

A strong permanent magnet is not natural in the sense of spontaneously arising in the universe. It is an artificial configuration that involves coherently aligning electric current density (point-source lines) of man-made chemical compounds like Nd2Fe14B in a way that rarely occurs without intervention. Magnets were first discovered in natural minerals like lodestone (a naturally magnetized form of magnetite). Ancient people noticed that lodestone could attract iron and align with Earth’s magnetic space. These were weak natural magnets formed over time, likely by exposure to lightning or Earth’s magnetic space. Modern powerful magnets are made by aligning electric current density in magnetic compound materials artificially using heat, pressure, and external magnetic spaces—engineering a stronger, coherent recursion structure.

Naturally occurring magnetic spaces tend to be weak, broad-scale (like planetary or stellar magnetism), dynamic (changing over time), and not coherent at the domain level. These natural magnetic spaces arise from dynamic processes (like convection currents of molten iron), not man-made recursion alignments. Only in certain rare minerals, as mentioned (lodestone), do we find naturally magnetized regions—but even then they are localized and weak, likely formed under high-energy geological conditions, and they're more like residual fragments of recursive imprinting, not structured artificial magnetic spaces.

An electromagnet generates a magnetic space only when an electric current density is present around a wire, typically wound into a coil. The strength of an electromagnet’s space can be controlled by adjusting the current, making it highly useful in experimental and industrial settings.

Many particle physics experiments use powerful artificial electromagnets to steer and focus high-energy particles. These devices are designed and operated entirely within the framework of classical electromagnetism—or formulations within classical framework such as Jefimenko’s—without reliance on the Standard Model. Nevertheless, much of what we observe in the Standard Model arises from highly controlled artificial magnetic environments, where such electromagnetic instruments are foundational to manipulating and detecting particles.

Magnetism

Magnetism is emergent space and does not appear without an electric current density. It is impossible for a magnetic space to arise without its point source due to its dependence on complete recursion. Consequently, magnetism itself is an effect, not an independent physical interaction.

A magnetic space emerges around a mass when it contains a moving charge—that is, an electric current density.

Magnetic North and South poles are the recursion chirality over a mass space—opposite orientations of recursion. The magnetic "field lines" we see are actually space deformation gradients caused by this oriented line recursion. These poles do nothing.

When a magnetic object becomes magnetized, this can be described as self-coherence resulting from the alignment of its electric current density lines.

When self-coherence is made across a mass—whether in the same self-coherent mode or its chiral inverse—it forms a stable eigenmode: a macroscopic closed-loop magnetic space that manifests as an effect of its electric current density. The greater a mass's self-coherence can become, the more potential energy (magnetic potential) can be locked into its configuration when magnetized, and the smaller and tighter its optical isopotential traces of light appear around the magnetized mass when viewed through a ferrocell instrument. The stored energy of this self-coherent mass is the source of magnetic domain strength and sustains the magnetic space.

Magnetic attraction and repulsion arise from electric current density lines acting upon each other through the spaces they generate at retarded times, with the force direction determined by the Lorentz force law. Current density creates magnetic spaces, and while these spaces are causally related to their sources, they do not themselves propagate until changes occur in the spatial configuration—such as when motion or interaction begins—at which point those changes propagate causally and act on other currents. The resulting magnetic forces pull the current density lines together (attraction) or apart (repulsion) depending on their direction and geometry.

Induction

Induction is the interaction caused by point-source densities, with the emergent electromagnetic space propagating from these changes. A charge influences neighboring charges, generating time-varying electric and magnetic spaces. In practical terms, a moving magnet creates a time-dependent effective current distribution (from the movement of bound current loops), which produces an induced electric space at the location of the conductor. This causes spatial reconfiguration around the conductor—observed as an induced electric space—propagating at the rate of induction, which we recognize as the speed of light.

Mass–energy equivalence

In Newtonian physics, mass and energy are separate, so potential energy changes don't affect mass. Conversely in relativistic physics, total energy determines a system’s rest mass, so potential energy—like electromagnetic or gravitational binding—directly contributes; lowering potential energy reduces the system’s mass.

When two atoms bind to form a molecule, the total energy of the bound system is lower than that of the separated atoms, with the difference corresponding to a decrease in electromagnetic potential energy, or binding energy. Potential energy in relativity is a “real” contributor to the total mass of a system but whether you notice it depends on whether you're doing physics in a framework that keeps strict energy–mass bookkeeping. Hence, how did the relativistic framework end up with a strict mass–energy bookkeeping?

We have not measured an “energy free” mass, and instead we end up measuring the total rest-frame energy per c². Special relativity removed the notion mass and energy were distinct forms. Energy and momentum became components of a single 4-vector.

It was known Einstein did not read A gravitational and electromagnetic analogy, published around 1893 by Oliver Heaviside, and worked in isolation. Einstein's 1905 work grew largely out of German and French sources (Lorentz, Hertz/Maxwell via German channels, Mach/Poincaré), and that the English "Maxwellian" literature (e.g., Larmor, Heaviside) left no trace in Einstein's early papers.

A single atom, having no energy deficit relative to its fully unbound state, exerts no noticeable gravitational influence, while an extreme gravitational object exerts intense gravity due to an immense energy deficit relative to its mass. In this view, potential energy is not a real contributor to the total mass of a system.

The energy deficit refers to the shortfall of spatial energy within a system compared to its maximum possible (unbound) state. In this framing, gravity’s strength arises not from the system’s total relativistic mass–energy, but from the degree to which its spatial energy is deprived.

Maxwell’s classical view of atomic and molecular interactions already recognized that the act of binding releases energy, while separation requires an equal or greater input of energy. In the traditional picture, this release is attributed to a shift toward a lower-energy, more stable configuration, with the binding energy carried away by electromagnetic radiation or kinetic motion. Within the present framework, this same release marks the formation of an energy deficit in the field relative to the unbound state, directly influencing the gravitational strength of the resulting system.

This reinterpretation leaves atomic physics—and by extension, the domains of classical electromagnetism and modern chemistry—entirely intact, as all established principles governing energy changes in binding and unbinding remain valid. At these scales, gravitational effects are negligible, and the proposed shift in coupling from total energy to field–energy deficit would not alter any predictions relevant to atoms or larger structures. Its consequences emerge only in regimes where gravity plays a dominant role, making its primary impact felt in astrophysics.

Standard Model of particle physics

In particle physics, powerful artificial electromagnets are used to steer and focus high-energy ions in experiments. These beams can then be used to probe ions, revealing their internal structure and interactions. While classical electromagnetism is sufficient to design and build the magnets themselves, understanding the results within the framework of the Standard Model requires knowledge of the photon—the quantum carrier of the electromagnetic force—since it mediates the interactions that such probes exploit.

Because the photon is the Standard Model’s mediator of the electromagnetic force, any fundamental error in our understanding of its properties would propagate through the theoretical framework like a fault in the foundation of a house of cards, undermining the interpretation of experiments—such as ion-probing collisions—that rely on electromagnetic interactions to test the model.

Most importantly, the electromagnetic field is the only Standard Model field that can be directly manipulated using instruments. Furthermore, modern engineering is grounded in the classical description of electromagnetic fields, since quantum mechanics and theoretical nuclear physics have no direct practical engineering applications. Even quantum computers, despite operating on quantum-mechanical principles, depend on classical electromagnetic systems for their physical implementation and control.

Electrons in the discussion of electric charge density

The electron is better reinterpreted as an electric charge density—a zero-dimensional point source—capable of "extending" or "contracting" in its field influence, despite lacking spatial extent itself.

The interpretation of the electron in the Standard Model is complex and fundamentally useless when discussing electricity or useful matter. Electrons, as particles endowed with magnetic moments, may exhibit magnetic effects in radiation processes, but they are not themselves the source of electric space; that role belongs to their intrinsic electric charge density. In physical experiments, these visible electrons do nothing but expire.

Meaningful material classes

There are a few key classes of materials that explain many phenomena in engineering: dielectric, diamagnetic, conductive, and superconductive materials.

Dielectricity is the ability to store electric energy. Bound charge densities can displace and store electric potential energy.

Diamagnetism is the ability to resist the storage of magnetic energy. Induced current densities oppose external current geometries, resisting magnetic energy storage.

Conductivity is the ability of charge densities within a material to redistribute in response to surrounding charge and current densities. Free charge densities redistribute to transport energy under external charge and current influence.

Superconductivity is the ability where current density persists indefinitely without resistance; magnetic energy is expelled (Meissner effect). Coherent charge-current geometry sustains current without loss, expelling magnetic energy.

Jefimenko's causal electrodynamics and gravity

In Jefimenko’s electrodynamics, wave propagation is not a mysterious self-perpetuation of electric and magnetic spaces "driving" each other. Instead, every electromagnetic wave, whether static in appearance or varying with time, is rooted in the underlying distributions of electric charge density and current density. These sources—described by charge density and current density at their retarded times—dictate the exact structure, timing, and strength of the spaces that emerge. In this framework, the spaces are effects, not causes, and their behavior can be traced directly to the motion and arrangement of their sources.

Beyond electromagnetism, Jefimenko also developed an extensive theoretical framework for strong gravitational and antigravitational nonlinear fields, proposing analogous source–field relationships in gravitation that could, in principle, account for both attractive and repulsive gravitational phenomena under extreme conditions.

See "Causality, Electromagnetic Induction, and Gravitation".

Jefimenko's modern discussion on the nature of strong gravitaty

Some modern physical merit can be added to our treatment on the disconnect between energy and mass. Physicist Oleg Jefimenko writes in Causality, Electromagnetic Induction, and Gravitation that "all presently known results of the general relativity theory based on Einstein’s field equations cannot be considered reliable when these results involve gravitational fields whose gravitational-energy mass is comparable with the true mass of the system." This appears on page 157, in the discussion on the nature of gravitational fields, following his nonlinear theory for strong gravitational fields and antigravitational fields.

Max Planck and the birth of energy quanta

In 1900, Max Planck introduced the revolutionary idea that electromagnetic energy is not emitted continuously, but in discrete packets—which he called quanta. He developed this concept while studying blackbody radiation and trying to solve the ultraviolet catastrophe. By assuming that oscillators in the cavity walls could only exchange energy in discrete amounts proportional to their frequency (E = hf), Planck derived a formula that matched experimental data.

However, Planck viewed these quanta as a mathematical trick, not as physical particles. He believed the quantization applied to the interaction between matter and radiation, not to the radiation space itself. Planck strongly resisted Einstein’s 1905 proposal that light itself was made of localized particles—photons—with real, independent existence. For Planck, quanta were a statistical artifact of energy distribution, not evidence that light was fundamentally granular. He maintained a classical view of the electromagnetic space and accepted Einstein’s quantum interpretation only reluctantly—viewing quantization as a feature of emission and absorption by matter, not a property of the electromagnetic space itself.

Double-slit experiment misconception

The double-slit experiment was first performed by Thomas Young in 1801, long before quantum mechanics, as a demonstration that light behaves like a wave. By shining light through two narrow slits and observing the resulting interference pattern of bright and dark fringes, Young provided clear evidence against Newton’s particle theory of light and in favor of wave theory, helping to establish the foundation of classical electromagnetism. It wasn’t until more than a century later, with the ability to generate extremely weak beams of light or electrons and to detect their arrival one event at a time, that the experiment revealed its quantum character.

A common misconception in popular science presentations of the double-slit experiment is that it somehow shows human consciousness or the act of “looking” with the eye directly causes the collapse of the wavefunction. In reality, the interference pattern disappears because any attempt to determine which path the propagation takes through the slits requires a physical interaction with a detector, and that interaction disturbs the system enough to wash out the interference. The effect is not mystical or psychological—it arises from the unavoidable influence of measurement devices on spaces.

Imagine you have a tire filled with air. If you want to measure its pressure, you insert a gauge. But as soon as you connect the gauge, a little bit of air escapes into the instrument. That means the act of measuring changes the tire slightly. That’s the idea behind quantum measurement: it’s not that “looking” with your eyes changes the outcome. It’s that in order to determine which path the propagation takes through the slits, you need to set up a detector—and that detector must interact with the propagating wave itself. The interaction unavoidably disturbs the wave pattern, washing out the interference.