This document outlines a theoretical framework for a hypothetical form of matter, termed “magmatter,” which is fundamentally based on the existence and interaction of magnetic monopoles. This framework proposes a dualistic structure to ordinary electrically charged matter, with distinct fundamental particles and binding mechanisms operating at significantly higher energy scales.

Disclaimer: This entire manuscript is created with the help of Gemini 2.5 Flash model.

I. The Magtron: Fundamental Magnetic Fermion

The “magtron” is posited as the fundamental fermionic building block of magmatter, analogous to the electron in ordinary matter.

  • Composition: A magtron is theorized to be a composite particle formed by the “embedding” of a bosonic magnetic monopole (the core constituent) within a very light, neutral elementary fermion.

    • The bosonic magnetic monopole is the primary carrier of the magnetic charge.

    • The neutral elementary fermion (e.g., a neutrino, a hypothetical sterile neutrino, or a neutralino) serves to confer the necessary half-integer spin, thereby making the composite magtron a fermion, without significantly contributing to its overall mass.

  • Magnetic Charge: Each magtron carries a single unit of fundamental magnetic charge, denoted as $1g_D$ (one Dirac magnetic charge).

  • Mass Range: The mass of a magtron is estimated to be around $2 \text{ TeV}/c^2$. This mass is predominantly attributed to the intrinsic mass of the bosonic magnetic monopole itself. This range is consistent with current experimental lower limits for the mass of magnetic monopoles, which have not yet been observed in direct searches.

II. The Magnucleus: Magnetic Atomic Nucleus

The “magnucleus” represents the magnetic analogue of an atomic nucleus, serving as the central, positively charged component of a magatom.

  • Composition: A magnucleus is theorized to be a distinct type of bosonic magnetic monopole that is significantly heavier than the fundamental monopole found in magtrons. Unlike the magtron’s composite nature involving a neutral fermion, the magnucleus is conceived as a fundamental, heavier bosonic monopole capable of carrying multiple units of magnetic charge.

  • Magnetic Charge: Magnuclei can carry multiple units of positive magnetic charge, ranging from 1 to 12 magnetic charges (e.g., $+1g_D$ to $+12g_D$).

  • Mass Range: The mass of a magnucleus scales with its magnetic charge, estimated at approximately $N \times 20 \text { TeV}/c^2$ per magnetic charge unit. Thus, a magnucleus with $N$ magnetic charges would have a mass of approximately $N \times 20 \text { TeV}/c^2$. This substantial mass reflects its role as a dense, multi-charged core.

  • Internal Binding: The stability and integrity of a multi-charged magnucleus imply the existence of an incredibly strong, short-range binding force that overcomes the immense magnetic repulsion between like magnetic charges. This force would be analogous to the strong nuclear force binding protons in ordinary nuclei, but operating at a much higher energy scale due to the significantly larger magnetic charges involved.

III. The Magatom: Magnetic Atom Analogue

A “magatom” is the complete, magnetically neutral analogue of an ordinary atom.

  • Composition: A magatom consists of a magnucleus (carrying a net positive magnetic charge) bound to an equal number of magtrons (each carrying a single unit of negative magnetic charge, $−1g_D$).

    • For example, a magnucleus with $+3g_D$ would be bound to three magtrons, each with $−1g_D$, resulting in a magnetically neutral magatom.

  • Binding Mechanism: The binding between the positively charged magnucleus and the negatively charged magtrons is mediated by the fundamental magnetic force. Due to the exceptionally large magnetic charge ($g_D\approx68.5e$), this magnetic force is orders of magnitude stronger than the electromagnetic force governing ordinary atoms. This strong attraction ensures the formation of stable magatoms.

  • Estimated Size: Based on the proposed masses and binding energies, the calculated radius of the smallest (single-charge) magmatter atom is approximately $0.000189\text{ fm}$ (femtometers). This makes magmatter atoms extraordinarily compact, orders of magnitude smaller than even an ordinary atomic nucleus (which is typically a few femtometers) and vastly smaller than a hydrogen atom (which is around $52,900\text{ fm}$). This extreme compactness is a direct consequence of the high constituent masses (TeV scale) and the significant binding energy (GeV scale) arising from the powerful, short-range interactions within magmatter.

    Estimated Size Calculation Steps

    To estimate the size of the smallest magmatter atom (analogous to a hydrogen atom, with one magnucleus and one magtron), we adapt principles from the Bohr model, connecting the binding energy, the masses of the constituents, and an effective coupling constant.

    Given Parameters:

    • Magtron Mass ($m_{magtron}$): $\approx 2 \text{ TeV}/c^2$

    • Magnucleus Mass (for 1 magnetic charge, $m_{magnucleus}$): $\approx 20 \text{ TeV}/c^2$

    • Overall Binding Energy of Magmatter Atoms ($E_B$): $\approx 300 \text{ GeV} = 0.3 \text{ TeV}$

    Calculation Steps:

    1. Calculate the Reduced Mass ($\mu_{mag}$): For a two-body system, the reduced mass is given by:

      $$ \mu_{mag} = \frac{m_{magnucleus} \cdot m_{magtron}}{m_{magnucleus} + m_{magtron}} $$

      Substituting the given values:

      $$ \mu_{mag} = \frac{(20 \text{ TeV}/c^2) \cdot (2 \text{ TeV}/c^2)}{(20 \text{ TeV}/c^2) + (2 \text{ TeV}/c^2)} = \frac{40 \text{ TeV}^2/c^4}{22 \text{ TeV}/c^2} \approx 1.818 \text{ TeV}/c^2 $$

    2. Determine the Effective Coupling Constant ($\alpha_{eff}$): In a Bohr-like model, the ground state binding energy ($n=1$) for a system with a central charge $Z=1$ is related to the reduced mass and an effective fine-structure-like constant ($\alpha_{eff}$) by:

      $$ E_B = \frac{1}{2} \mu_{mag} c^2 \alpha_{eff}^2 $$

      Rearranging to solve for $\alpha_{eff}^2$:

      $$ \alpha_{eff}^2 = \frac{2 E_B}{\mu_{mag} c^2} $$

      Substituting the given values ($E_B = 0.3\text{ TeV}$ and $\mu_{mag}c^2=1.818\text{ TeV}$):

      $$ \alpha_{eff}^2 = \frac{2 \cdot (0.3 \text{ TeV})}{1.818 \text{ TeV}} = \frac{0.6}{1.818} \approx 0.330 $$

      Taking the square root:

      $$ \alpha_{eff} \approx \sqrt{0.330} \approx 0.574 $$

      This large effective coupling constant reflects the strong binding force at play, as stipulated in the framework (dominant Higgs-boson mediated interaction).

    3. Calculate the Radius of the Smallest Magmatter Atom ($r_{magatom}$): The radius of the ground state ($n=1$) in a Bohr-like model is given by:

      $$ r_{magatom} = \frac{\hbar c}{\alpha_{eff} \mu_{mag} c^2} $$

      Using the value of $\hbar c \approx 0.1973 \text{ GeV} \cdot \text{fm}$ (a fundamental constant relating energy and length in natural units):

      $$ r_{magatom} = \frac{0.1973 \text{ GeV} \cdot \text{fm}}{0.574 \cdot (1.818 \text{ TeV})} $$

      Convert TeV to GeV ($1 \text{ TeV} = 1000 \text{ GeV}$):

      $$ r_{magatom} = \frac{0.1973 \text{ GeV} \cdot \text{fm}}{0.574 \cdot (1818 \text{ GeV})} $$

      $$ r_{magatom} = \frac{0.1973}{1043.772} \text{ fm} $$

      $$ r_{magatom} \approx 0.000189 \text{ fm} $$

IV. Mass and Density of Magmatter Atoms

The properties of magmatter atoms, particularly their mass and density, are vastly different from those of ordinary matter due to the extremely heavy constituents and the strong binding forces involved.

  • Mass of a Magmatter Atom (Hydrogen Analogue): A hydrogen analogue magmatter atom is composed of one magnucleus (with 1 magnetic charge) and one magtron.

    • Mass of magnucleus (1 charge): $\approx 20 \text{ TeV}/c^2$

    • Mass of magtron: $\approx 2 \text{ TeV}/c^2$

    • Total mass of magmatter atom (unbound constituents): $20 \text{ TeV}/c^2 + 2 \text{ TeV}/c^2 = 22 \text{ TeV}/c^2$

    • Considering the binding energy ($0.3 \text{ TeV}$), the actual mass of the bound magmatter atom would be slightly less due to mass defect. However, for an approximate comparison, using the sum of constituent masses is sufficient: $M_{magatom} \approx 22 \text{ TeV}/c^2$

  • Comparison to Normal Hydrogen Atom: The mass of a normal hydrogen atom is approximately 938.78 MeV/c2 (or 0.00093878 TeV/c2). The ratio of the magmatter atom mass to the normal hydrogen atom mass is:

    $$ \text{Ratio} = \frac{M_{magatom}}{M_{Hydrogen}} = \frac{22 \text{ TeV}/c^2}{0.00093878 \text{ TeV}/c^2} \approx 23,434 $$

    Therefore, a single magmatter atom (hydrogen analogue) is approximately 23,434 times heavier than a normal hydrogen atom.

  • Expected Density of Magmatter Material: To calculate the density, we use the formula $\rho = \frac{M}{V}$.

    • Mass of the smallest magmatter atom ($M_{magatom}$): We will use the sum of constituent masses for simplicity, $22 \text{ TeV}/c^2$. Convert to kilograms: $1 \text{ TeV}/c^2 \approx 1.782 \times 10^{-24} \text{ kg}$. $M_{magatom} \approx 22 \times 1.782 \times 10^{-24} \text{ kg} \approx 3.9204 \times 10^{-23} \text{ kg}$

    • Volume of the smallest magmatter atom ($V_{magatom}$): Assuming a spherical shape with radius $r_{magatom} \approx 0.000189 \text{ fm}$. Convert femtometers to meters: $1 \text{ fm} = 10^{-15} \text{ m}$.

    $$r_{magatom} \approx 0.000189 \times 10^{-15} \text{ m} = 1.89 \times 10^{-19} \text{ m}$$

    $$ V_{magatom} = \frac{4}{3} \pi r_{magatom}^3 = \frac{4}{3} \pi (1.89 \times 10^{-19} \text{ m})^3 $$

    $$ V_{magatom} \approx \frac{4}{3} \pi (6.741969 \times 10^{-57} \text{ m}^3) \approx 2.825 \times 10^{-56} \text{ m}^3 $$

    • Density ($\rho_{magmatter}$):

    $$ \rho_{magmatter} = \frac{M_{magatom}}{V_{magatom}} = \frac{3.9204 \times 10^{-23} \text{ kg}}{2.825 \times 10^{-56} \text{ m}^3} $$

    $$ \rho_{magmatter} \approx 1.388 \times 10^{33} \text{ kg/m}^3 $$

    This density is extraordinarily high. To provide context:

    • Density of water: $\approx1000 \text{ kg}/m^3$

    • Density of Earth’s core: $\approx 13,000 \text{ kg}/m^3$

    • Density of a neutron star: $\approx 10^{18} \text{kg}/m^3$ (trillions of times denser than water)

    The calculated density of magmatter is approximately $10^{15}$ times denser than a neutron star, or about $10^{30}$ times denser than water. This implies that magmatter would be an incredibly compact and massive form of matter, far exceeding the densities of any known conventional or exotic matter structures in the universe.

V. Strength of Magmatter Compared to Ordinary Matter

The “strength” of a material can be broadly understood as its resistance to deformation or breaking, often related to the force required per unit area. For magmatter, this strength is derived from the immense binding energies and the extreme compactness of its constituent atoms.

  • Energy Scaling Factor: This factor quantifies how much stronger an individual magmatter bond is in terms of energy compared to a normal chemical bond (e.g., in hydrogen).

    • Binding Energy of Magmatter Atom ($E_{mag}$): $300 \text{ GeV} = 3 \times 10^{11} \text{ eV}$

    • Binding Energy of Normal Hydrogen Atom ($E_{norm}$): $13.6 \text{ eV}$

    • Energy Scaling Factor:

    $$ \text{Energy Scaling Factor} = \frac{E_{mag}}{E_{norm}} = \frac{3 \times 10^{11} \text{ eV}}{13.6 \text{ eV}} \approx 2.206 \times 10^{10} $$

  • Length Scaling Factor (Inverse): This factor quantifies how many times smaller a magmatter atom is compared to a normal hydrogen atom.

    • Radius of Normal Hydrogen Atom ($r_{norm}$): $52,900 \text{ fm}$

    • Radius of Smallest Magmatter Atom ($r_{mag}$): $0.000189\text{ fm}$

    • Length Scaling Factor:

    $$ \text{Length Scaling Factor} = \frac{r_{norm}}{r_{mag}} = \frac{52,900 \text{ fm}}{0.000189 \text{ fm}} \approx 2.7989 \times 10^8 $$

    This implies that a normal atom is approximately 280 million times larger than a magmatter atom.

  • Force per Bond Scaling: The force required to break a single bond is conceptually related to the binding energy divided by the characteristic length over which the force acts.

    $$ \text{Force per Bond Scaling} = \frac{\text{Energy Scaling Factor}}{\text{Length Scaling Factor (Magmatter/Normal)}} = \left(\frac{E_{mag}}{E_{norm}}\right) \times \left(\frac{r_{norm}}{r_{mag}}\right) $$

    Substituting the calculated values:

    $$ \text{Force per Bond Scaling} = (2.206 \times 10^{10}) \times (2.7989 \times 10^8) $$

    $$ \text{Force per Bond Scaling} \approx 6.174 \times 10^{18} $$

    This indicates that a single magchemical bond can withstand approximately $6.174\times10^{18}$ times greater force than a normal chemical bond.

  • Bonds per Unit Area Scaling: Since magmatter atoms are significantly smaller, a much larger number of them can fit into a given area. The number of bonds per unit area scales inversely with the square of the atomic radius.

    $$ \text{Bonds per Unit Area Scaling} = \left(\frac{\text{Radius of Normal Atom}}{\text{Radius of Magmatter Atom}}\right)^2 = \left(\frac{r_{norm}}{r_{mag}}\right)^2 $$

    Substituting the calculated values:

    $$ \text{Bonds per Unit Area Scaling} = (2.7989 \times 10^8)^2 $$

    $$ \text{Bonds per Unit Area Scaling} \approx 7.8338 \times 10^{16} $$

    This means there are approximately $7.83\times10^{16}$ times more bonds per unit area in magmatter compared to normal matter. (This is consistent with the “300 million squared” approximation mentioned, as $(3\times10^8)^2 = 9\times10^{16}$).

  • Overall Strength Scaling: The overall strength of a material (force per unit area) can be estimated by multiplying the force per individual bond by the number of bonds per unit area.

    $$ \text{Overall Strength Scaling} = (\text{Force per Bond Scaling}) \times (\text{Bonds per Unit Area Scaling}) $$

    This can also be expressed as:

    $$ \text{Overall Strength Scaling} = \left(\frac{E_{mag}}{E_{norm}}\right) \times \left(\frac{r_{norm}}{r_{mag}}\right)^3 $$

    Now, substituting the calculated values:

    $$ \text{Overall Strength Scaling} = (2.206 \times 10^{10}) \times (2.7989 \times 10^8)^3 $$

    First, calculate $(2.7989\times10^8)^3$:

    $$ (2.7989)^3 \times (10^8)^3 \approx 21.89 \times 10^{24} = 2.189 \times 10^{25} $$

    Then multiply by the Energy Scaling Factor:

    $$ \text{Overall Strength Scaling} = (2.206 \times 10^{10}) \times (2.189 \times 10^{25}) $$

    $$ \text{Overall Strength Scaling} \approx 4.825 \times 10^{35} $$

    The calculated overall strength of magmatter, relative to its normal matter equivalent, is approximately $4.825\times10^{35}$ times greater. This is an astonishingly high figure, indicating that magmatter, if it could exist and be assembled, would possess a structural integrity far beyond anything known in the universe, consistent with its extreme density and the powerful forces at play at the sub-femtometer scale.

VI. Binding Energy Limitations and Theoretical Considerations

The proposed “magmatter” framework necessitates a re-evaluation of binding energy dynamics, particularly concerning vacuum magnetic polarization and the role of hypothetical new interactions.

  • Vacuum Magnetic Polarization Limits:

    • In quantum electrodynamics (QED), the vacuum is not empty but filled with fluctuating virtual electron-positron pairs. These pairs screen bare electric charges, reducing their effective strength at larger distances. A similar phenomenon, vacuum magnetic polarization, is expected for magnetic monopoles. Due to the large magnetic charge ($g_D$), this effect would be significant, potentially leading to strong screening of the magnetic charge at distances comparable to or larger than the Compton wavelength of the mediating particles.

    • While theoretically, the bare magnetic charge interaction could yield binding energies in the 300 TeV range, vacuum magnetic polarization is expected to significantly restrict the effective strength of pure magnetic forces at larger distances, potentially limiting their direct binding contribution to the MeV range. This means that for the formation of stable magatoms, the primary binding force cannot solely rely on the unscreened magnetic interaction.

  • Higgs Interaction as a Speculative Binding Force:

    • The stability and high mass of magtrons and magnuclei, particularly the ability to overcome the immense magnetic repulsion within multi-charged magnuclei, strongly suggest the involvement of a new, very strong, short-range fundamental interaction beyond the Standard Model.

    • The “Higgs-boson binding” mentioned in the original context is a plausible (though highly speculative) candidate for such an interaction. This would imply a new scalar field (distinct from the Standard Model Higgs) or a novel coupling involving the known Higgs field, mediating an attractive force specifically between magnetic monopoles or their constituents.

    • Crucially, the Higgs-boson mediated field interaction is always attractive and, at the scale of magmatter atoms, is hypothesized to be a stronger and more significant force compared to the vacuum-polarized magnetic forces. This hypothetical interaction would need to generate the substantial binding energies required to form stable composite particles at the TeV scale. Its strength would need to be sufficient to:

      • “Embed” the bosonic monopole within the neutral fermion to form a stable magtron.

      • Bind multiple magnetic charges within a magnucleus, overcoming their mutual magnetic repulsion.

    • The mass scales (2 TeV for magtrons, 20 TeV per charge for magnuclei) are indicative of the energy density and binding strength of this new interaction.

  • Overall Binding Energy of Magmatter Atoms:

    • Considering both the (screened) magnetic forces and the dominant Higgs-boson mediated force, the combined binding energies of magmatter atoms are therefore approximated to be around 300 GeV. This energy represents the stability of the magatom system, resulting from the interplay of these powerful, albeit short-ranged, interactions.

  • Stability and Decay: The stability of these proposed particles (magtrons and magnuclei) is paramount. The existence of such high binding energies would be critical to prevent their decay into lighter, more conventional particles, particularly given the inherent instability of free neutrons (if they were considered constituents, though here we’re using elementary neutral fermions). The stability of magtrons and magnuclei would be governed by the strength of this new binding interaction relative to any possible decay channels mediated by known fundamental forces (weak, strong, electromagnetic).

VII. Closing Statements

This theoretical framework for magmatter represents a significant departure from the Standard Model of particle physics, requiring the existence of magnetic monopoles and at least one new fundamental interaction (e.g., Higgs-boson binding) to explain the formation and stability of its proposed constituents. Further theoretical development would be necessary to derive the precise properties of these particles and interactions from first principles, and experimental verification would be required to validate any aspect of this intriguing hypothesis.