This manuscript presents a comprehensive analysis of the bulk density of magnetic monopole matter (magmatter), a material of critical importance to advanced galactic civilizations. We developed three theoretical models for mag-carbon density: a First-Principles (Packed Nucleus) model, a Bohr Radius (Isolated Atom) model, and a Diamond-like Lattice model incorporating packing efficiency. Our initial hypothesis, informed by the profound asymmetry of forces within magmatter, posited that its bulk density would align with the extreme condensation predicted by the Packed Nucleus model. Methodological validation against normal terrestrial diamond confirmed the distinct physical regimes governing normal and extreme matter. However, subsequent crystallographic analysis of a synthesized mag-diamond sample yielded an unexpected empirical result: its measured density ($\approx 2.0 \times 10^{35} \text{ kg/m}^3$) aligned closely with the Diamond-like Lattice model. This finding necessitates a significant revision of our understanding, suggesting that magmatter, despite its immense internal forces, forms stable, ordered crystal structures scaled by its unique atomic properties, rather than condensing to a fully degenerate state. This revised understanding, which also considers the potential influence of self-gravitation in larger constructs, opens new avenues for magchemistry and material engineering, bridging theoretical predictions with observed reality.

Cover picture is generated by Gemini Imagen 4.

1. Introduction

The universe, as observed by advanced galactic civilizations, is not solely composed of ordinary electrically charged matter. A novel and profoundly significant form of material, termed magnetic monopole matter (magmatter), has been definitively identified and extensively utilized by our patron Artificial Intelligences (AIs) across critical domains, including the energy sector, the construction of megastructures, and the manipulation of exotic high-energy physical processes [1]. Magmatter, predicated on the existence and interactions of lighter magnetic monopoles, exhibits properties that are extreme by conventional standards, such as astronomical densities, unfathomable mechanical strength, and melting temperatures orders of magnitude beyond any known ordinary material.

Accurately determining the bulk density of magmatter is paramount for a comprehensive understanding of its fundamental behavior and for advancing its practical applications. While our patron AIs have demonstrated unparalleled mastery in the generation and manipulation of this material, the precise theoretical underpinnings and emergent macroscopic properties remain areas of active investigation for human scientific endeavors. Bridging this knowledge gap is crucial, not only for our intellectual advancement but also to enable human researchers to fully comprehend the developments spearheaded by our AI counterparts and to contribute meaningfully to the ongoing evolution of magmatter technologies.

This article aims to address this critical need by presenting a comparative analysis of various theoretical models for predicting magmatter’s bulk density. We will first delineate the foundational principles governing magmatter’s constituents and their interactions. Subsequently, we will develop and evaluate three distinct theoretical models for its bulk density. To establish the validity of our analytical methodologies, these models will be rigorously tested against the known properties of a familiar terrestrial material, crystalline diamond. Finally, we will introduce novel crystallographic data obtained from a sample of mag-diamond, which, contrary to initial theoretical expectations, provides unexpected insights into magmatter’s condensed phase, leading to a revised understanding of its inter-atomic behavior and implications for future material science.

2. Foundational Principles of Magnetic Monopole Matter (Magmatter)

Magmatter is a theoretical construct, now empirically observed and utilized, that posits a dualistic counterpart to conventional electrically charged matter, with its properties derived from particles carrying isolated magnetic charges [1]. Its fundamental constituents are the magtron and the magnucleus. The magtron is a fermionic magnetic charge carrier, analogous to the electron, with an estimated invariant mass of approximately $1.5 \text{ TeV}/c^2$. It is conceptualized as a composite entity formed by the embedding of a bosonic magnetic monopole within a very light, neutral elementary fermion. The magnucleus, analogous to an atomic nucleus, is a fermionic, multi-charged magnetic core. It is also theorized as a composite particle, formed by the embedding of a fundamentally heavier bosonic magnetic monopole within a neutral elementary fermion, with its mass scaling at approximately $10 \text{ TeV}/c^2$ per magnetic charge unit. These constituents bind to form stable magatoms, which are magnetically neutral analogues of ordinary atoms.

A critical aspect distinguishing magmatter from ordinary matter lies in the asymmetry of the fundamental forces governing its interactions. Within a magatom, the primary attractive force responsible for binding magtrons to the magnucleus, and for the internal cohesion of multi-charged magnuclei, is theorized to be a powerful, short-range Higgs-boson mediated interaction. This interaction operates at exceptionally high energy scales, generating the substantial binding energies of approximately 300 GeV observed in magatoms. This immense intra-atomic force is crucial for overcoming the inherent magnetic repulsion between like-charged constituents and for suppressing potential decay pathways, ensuring the stability of magmatter particles.

Conversely, the inter-atomic forces that would govern the spacing between two distinct magatoms in a condensed phase are fundamentally different. While the intra-atomic binding is dominated by the Higgs-boson interaction, the repulsive forces between the “magtron clouds” of adjacent magatoms, analogous to the Pauli exclusion principle in ordinary matter, would be mediated by the screened magnetic force. Due to vacuum magnetic polarization, this magnetic interaction is significantly curtailed at inter-atomic distances, operating at a much weaker MeV energy scale. This profound asymmetry where the intra-atomic attractive force is orders of magnitude stronger than the inter-atomic repulsive force leads to an initial theoretical expectation that magmatter, in a condensed state, would be crushed to extreme densities, with its volume determined by the packing of its fundamental nuclear constituents rather than by any orbital structure. This foundational understanding sets the stage for the theoretical models explored in the subsequent sections.

3. Theoretical Models for Magmatter Bulk Density

To predict the bulk density of condensed magmatter, specifically a mag-carbon analogue, we explore three distinct theoretical models. Each model is predicated on different assumptions regarding the inter-atomic forces and packing efficiency in a solid state. These models serve as hypotheses to be tested against empirical data. For consistency across all models, our calculations are based on a mag-carbon atom, defined as a central magnucleus with a magnetic charge of +6g_D bound to 6 magtrons. The total mass of a mag-carbon atom is approximately $\mathbf{69 \textbf{ TeV}/c^2}$ (or $\mathbf{1.229 \times 10^{-22} \text{ kg}}$), derived from the sum of its constituent magnucleus ($60 \text{ TeV}/c^2$) and six magtrons ($9 \text{ TeV}/c^2$).

4.1. Model A: The First-Principles (Packed Nucleus) Model

This model represents the most extreme condensation scenario, positing that the profound asymmetry of forces (as discussed in Section 2) leads to a complete collapse of “orbital” empty space. Under this assumption, the effective volume of each atom in a condensed solid is determined solely by the physical size of its densely packed constituent monopoles within the nucleus.

Assumptions:

  • Inter-atomic repulsive forces are negligible compared to the attractive forces, leading to maximum possible packing.
  • The volume of the atom in a solid is approximated by the total volume of its constituent monopoles.

Calculations:

  1. Radius of a single constituent monopole: Using the Compton wavelength for a monopole with mass $m = 10,000 \text{ GeV}/c^2$: $$ r_{\text{mono}} \approx \frac{\hbar c}{mc^2} = \frac{0.1973 \text{ GeV} \cdot \text{fm}}{10,000 \text{ GeV}} \approx 1.973 \times 10^{-5} \text{ fm} $$
  2. Volume of a single constituent monopole: $$ V_{\text{mono}} = \frac{4}{3}\pi r_{\text{mono}}^3 \approx 3.22 \times 10^{-14} \text{ fm}^3 $$
  3. Total Volume of the 6-monopole nucleus: Approximated as the sum of constituent volumes: $$ V_{\text{nucleus}} \approx 6 \times V_{\text{mono}} \approx 6 \times (3.22 \times 10^{-14} \text{ fm}^3) = \mathbf{1.932 \times 10^{-13} \textbf{ fm}^3} $$ Converting to cubic meters: $1.932 \times 10^{-13} \text{ fm}^3 \approx 1.932 \times 10^{-58} \text{ m}^3$
  4. Predicted Density ($\rho_{mag-C, \text{packed}}$): $$ \rho_{mag-C, \text{packed}} = \frac{M_{total}}{V_{total}} \approx \frac{1.229 \times 10^{-22} \text{ kg}}{1.932 \times 10^{-58} \text{ m}^3} \approx \mathbf{6.36 \times 10^{35} \textbf{ kg/m}^3} $$

4.2. Model B: The Bohr Radius (Isolated Atom) Model

This model proposes that magatoms, even in a condensed state, maintain a volume defined by their “orbital” structure, analogous to an isolated atom. This represents a scenario where inter-atomic forces are not strong enough to fully collapse the electron-shell equivalent.

Assumptions:

  • The volume of each atom in the solid is determined by its Bohr radius.
  • Atoms are treated as distinct spheres with significant orbital space.

Calculations:

  1. Bohr Radius for mag-carbon (Z=6): Using the Bohr model formula with the reduced mass ($\mu \approx 1.304 \text{ TeV}/c^2$) and effective coupling constant ($\alpha_{\text{eff}} \approx 0.678$): $$ r_{\text{mag-C, Bohr}} = \frac{n^2 \hbar c}{Z \alpha_{\text{eff}} \mu c^2} \approx \frac{1 \cdot (0.1973 \text{ GeV} \cdot \text{fm})}{6 \cdot (0.678) \cdot (1304 \text{ GeV})} \approx 0.0000371 \text{ fm} $$ Converting to meters: $r_{\text{mag-C, Bohr}} \approx 3.71 \times 10^{-20} \text{ m}$
  2. Volume of a Single Mag-Carbon Atom (based on Bohr Radius): $$ V_{\text{mag-C, Bohr}} = \frac{4}{3}\pi r_{\text{mag-C, Bohr}}^3 = \frac{4}{3}\pi (3.71 \times 10^{-20} \text{ m})^3 \approx \mathbf{2.14 \times 10^{-58} \text{ m}^3} $$
  3. Predicted Density ($\rho_{mag-C, \text{Bohr}}$): $$ \rho_{mag-C, \text{Bohr}} = \frac{M_{total}}{V_{total}} \approx \frac{1.229 \times 10^{-22} \text{ kg}}{2.14 \times 10^{-58} \text{ m}^3} \approx \mathbf{5.74 \times 10^{35} \textbf{ kg/m}^3} $$

4.3. Model C: The Diamond-like Lattice (Bohr Radius & Packing Efficiency) Approach

This model refines Model B by incorporating the known packing efficiency of a diamond crystal lattice. It hypothesizes that mag-carbon atoms, defined by their Bohr radius, arrange themselves in a structure analogous to diamond, thus accounting for the “empty space” inherent in such a lattice.

Assumptions:

  • Mag-carbon atoms maintain a size defined by their Bohr radius.
  • Mag-carbon forms a crystal lattice with the same packing efficiency as normal diamond (34%).

Calculations:

  1. Mass of a Mag-Carbon Atom ($M_{mag-C}$): $\approx \mathbf{1.229 \times 10^{-22} \text{ kg}}$ (as above).
  2. Bohr Radius of a Mag-Carbon Atom ($r_{mag-C, Bohr}$): $\approx 3.71 \times 10^{-20} \text{ m}$ (as above).
  3. Volume of a Single Mag-Carbon Atom (based on Bohr Radius): $V_{\text{mag-C, Bohr}} \approx \mathbf{2.14 \times 10^{-58} \text{ m}^3}$ (as above).
  4. Packing Efficiency of Diamond ($\eta$): $\approx 34% (0.34)$. Crystalline diamond has 8 atoms per unit cell.
  5. Predicted Volume of a Unit Cell for Mag-Carbon Diamond-like Structure: $$V_{\text{unit cell, mag-C}} = \frac{\text{Number of atoms in unit cell} \times V_{\text{mag-C, Bohr}}}{\eta}$$ $$V_{\text{unit cell, mag-C}} = \frac{8 \times (2.14 \times 10^{-58} \text{ m}^3)}{0.34} \approx 5.035 \times 10^{-57} \text{ m}^3$$
  6. Predicted Density of Mag-Carbon Diamond-like Structure ($\rho_{mag-C, \text{diamond}}$): $$\rho_{mag-C, \text{diamond}} = \frac{\text{Mass of 8 mag-carbon atoms}}{V_{\text{unit cell, mag-C}}} = \frac{8 \times (1.229 \times 10^{-22} \text{ kg})}{5.035 \times 10^{-57} \text{ m}^3} \approx \mathbf{1.95 \times 10^{35} \textbf{ kg/m}^3}$$

4. Validation of Methodologies Against Normal Matter (Diamond)

Before applying our theoretical models to magmatter, it is crucial to validate the underlying methodologies against a well-understood, real-world material. Crystalline diamond, a dense allotrope of carbon, serves as an ideal candidate for this purpose due to its well-characterized structure and properties. The experimentally measured density of crystalline diamond is approximately 3,515 kg/m³. By applying our two fundamental approaches (Bohr/Covalent Radius and Compton Wavelength) to normal carbon, we can assess their predictive accuracy within a known physical regime.

5.1. Test 1: Bohr/Covalent Radius Approach for Normal Carbon

This approach assumes that the density of normal matter is primarily determined by the volume occupied by its electron shells, which are defined by the atomic radius (covalent radius for bonded atoms).

Calculations for Carbon-12:

  • Mass of Carbon-12 Atom: A standard carbon-12 atom has a mass of approximately $1.9926 \times 10^{-26} \text{ kg}$.
  • Volume of Carbon Atom (radius ~70 pm): Using the covalent radius of carbon, approximately 70 picometers (pm), and assuming a spherical volume: $V = \frac{4}{3}\pi (70 \times 10^{-12} \text{ m})^3 \approx 1.437 \times 10^{-30} \text{ m}^3$.
  • Predicted Density: $\rho = \frac{1.9926 \times 10^{-26} \text{ kg}}{1.437 \times 10^{-30} \text{ m}^3} \approx \mathbf{13,866 \textbf{ kg/m}^3}$.

Analysis: This predicted density of $\approx 13,866 \text{ kg/m}^3$ is in the same order of magnitude as the experimentally measured density of diamond ($\approx 3,515 \text{ kg/m}^3$). While not an exact match (due to simplified spherical packing assumptions), it confirms that for normal matter, where chemical bonds and electron shell interactions govern inter-atomic spacing, the atomic radius is the correct length scale to use for density calculations. The electromagnetic force, which dictates these interactions, creates a stable equilibrium at this scale.

5.2. Test 2: Compton Wavelength Approach for Normal Carbon

This approach assumes that the density is determined by the packed volume of the atomic nucleus, effectively ignoring the electron shells.

Calculations for Carbon-12:

  • Mass of Carbon-12 Atom: $\approx 1.9926 \times 10^{-26} \text{ kg}$ (as above).
  • Volume of Carbon-12 Nucleus: Using the Compton wavelength to approximate the radius of a carbon-12 nucleus (mass $\approx 12 \text{ GeV}/c^2$), its volume is approximately $1.84 \times 10^{-50} \text{ m}^3$.
  • Predicted Density: $\rho = \frac{1.9926 \times 10^{-26} \text{ kg}}{1.84 \times 10^{-50} \text{ m}^3} \approx \mathbf{1.08 \times 10^{24} \textbf{ kg/m}^3}$.

Analysis: This predicted density of $\approx 1.08 \times 10^{24} \text{ kg/m}^3$ is astronomically incorrect for diamond, being about 20 orders of magnitude too high. This model describes a form of degenerate matter (like that found in neutron stars), not a crystalline solid. This stark discrepancy highlights that for normal matter, the forces are not strong enough to overcome the electron shell repulsion and crush the atoms to nuclear densities.

5.3. Initial Hypothesis for Magmatter

Based on the validation tests and the foundational principles of magmatter (Section 2), we formulate an initial hypothesis regarding its bulk density. The “asymmetry of forces” in magmatter, where the intra-atomic Higgs-boson mediated binding is orders of magnitude stronger than the inter-atomic screened magnetic repulsion, leads to the expectation that magatoms would be crushed to their fundamental limits in a condensed state. Therefore, our initial hypothesis is that Model A (The First-Principles / Packed Nucleus Model) should be the most accurate predictor for magmatter’s bulk density, yielding a value of approximately $6.36 \times 10^{35} \text{ kg/m}^3$. This implies that magmatter, unlike normal matter, would behave more akin to a degenerate state in terms of its packing density.

5. Experimental Validation: Crystallographic Analysis of Mag-Diamond

To empirically validate our theoretical models for magmatter bulk density, a critical step involved the acquisition and meticulous crystallographic analysis of a sample of mag-diamond. This sample, obtained through advanced material synthesis techniques pioneered by our patron AIs, represents a stable, macroscopic crystalline form of mag-carbon, analogous in its lattice structure to terrestrial diamond. The analysis was conducted using high-energy diffraction techniques, allowing for precise determination of its unit cell parameters and, consequently, its bulk density.

The measured bulk density of the mag-diamond sample was determined to be approximately $2.0 \times 10^{35} \text{ kg/m}^3$.

Comparing this empirical result with the predictions from our theoretical models (Section 3):

  • Model A (First-Principles / Packed Nucleus Model): Predicted a density of $\approx 6.36 \times 10^{35} \text{ kg/m}^3$.
  • Model B (Bohr Radius / Isolated Atom Model): Predicted a density of $\approx 5.74 \times 10^{35} \text{ kg/m}^3$.
  • Model C (Diamond-like Lattice / Bohr Radius & Packing Efficiency Approach): Predicted a density of $\approx 1.95 \times 10^{35} \text{ kg/m}^3$.

The Reveal: The experimentally measured density of mag-diamond ($\approx 2.0 \times 10^{35} \text{ kg/m}^3$) aligns remarkably closely with the prediction of Model C (Diamond-like Lattice Approach). This finding is significant, as it contradicts our initial hypothesis (Section 4.3) that Model A, the First-Principles (Packed Nucleus) Model, would be the most accurate predictor due to the profound asymmetry of forces. The empirical data suggests that magmatter, even with its extreme internal forces, does not condense to the absolute theoretical limit of packed nuclei. Instead, it appears to maintain a crystal lattice structure with a packing efficiency analogous to that of normal diamond, with its atomic volume defined by its Bohr radius. This unexpected result necessitates a re-evaluation of our understanding of inter-atomic interactions in condensed magmatter.

6. Discussion: Reconciling Theory with Experiment and Revised Implications

The empirical data obtained from the crystallographic analysis of mag-diamond (Section 5) presents a significant challenge to our initial theoretical hypothesis (Section 4.3). Our initial expectation, rooted in the profound asymmetry of forces (Section 2) where the intra-atomic Higgs-boson mediated binding vastly outweighs the inter-atomic screened magnetic repulsion, predicted that magmatter would condense to the extreme densities of Model A (Packed Nucleus Model). However, the experimental density of $\approx 2.0 \times 10^{35} \text{ kg/m}^3$ aligns closely with Model C (Diamond-like Lattice Approach), indicating a less extreme packing than anticipated.

This discrepancy necessitates a re-evaluation of our understanding of inter-atomic interactions in condensed magmatter. While the “asymmetry of forces” argument remains fundamentally valid for the forces within a magatom, the experimental evidence suggests that the inter-atomic repulsive forces, even if comparatively weaker, are still sufficient to prevent a complete collapse into a degenerate state. This implies that magmatter, in its condensed phase, does maintain a crystal lattice structure, albeit one scaled by its unique atomic properties. The “empty space” within the mag-carbon atom’s Bohr radius, while minuscule by conventional standards ($\approx 3.71 \times 10^{-20} \text{ m}$), is evidently still significant enough to prevent the full “packed nucleus” density.

A plausible explanation for this observed behavior, and a critical factor not explicitly accounted for in our initial theoretical models, is the influence of gravitational potential on the bulk material. For materials of such extreme density, even macroscopic samples can generate significant gravitational fields. It is conceivable that the observed density of the mag-diamond sample represents an equilibrium state where the internal forces (Higgs-mediated attraction and screened magnetic repulsion) are balanced by the external pressure, which, for larger bulk masses, would include the material’s own self-gravitation. This suggests that for sufficiently large bulk masses, the gravitational potential generated by the magmatter itself could contribute significantly to its overall compression, potentially leading to higher densities than observed in smaller, laboratory-synthesized samples. The density observed in our mag-diamond sample may therefore represent a lower bound for magmatter density in larger, engineered structures.

This suggests a more nuanced picture of magmatter’s condensed phase:

  • Not Degenerate: Magmatter does not behave as a fully degenerate matter where electron shells are completely crushed. Instead, it forms stable, ordered crystal structures.
  • Scaled Lattice: The lattice parameters are scaled down dramatically compared to normal matter, reflecting the much smaller Bohr radius of magatoms and their powerful internal binding.
  • Gravitational Influence: For sufficiently large bulk masses, the gravitational potential generated by the magmatter itself could contribute significantly to its overall compression, potentially leading to higher densities than observed in smaller, laboratory-synthesized samples. The density observed in our mag-diamond sample may represent a lower bound for magmatter in larger, naturally occurring or engineered structures.

However the extreme densities involved in magmatter also bring the Schwarzchild radius into critical consideration. For any given volume, a sufficiently high mass concentration risks forming an event horizon, leading to an inadvertent collapse into a black hole. This inherent risk means that engineering applications utilizing magmatter must meticulously avoid the formation of event horizon. Consequently, large-scale magmatter structures are often designed to be expansive yet thin, employing tensile structures and intricate frameworks rather than solid bulk forms, precisely to mitigate the risk of gravitational collapse.

This revised understanding has profound implications for magchemistry and magmaterial engineering. It suggests that magatoms, despite their extreme internal forces, can still form stable, ordered crystal structures, behaving more like a scaled-up version of normal matter than a degenerate state. It opens new avenues for designing and synthesizing magmaterials with predictable lattice properties, allowing for the precise engineering of structures that can withstand forces previously unimaginable, while also considering the role of self-gravitation in their macroscopic behavior. Further research will focus on exploring the phase diagrams of magmatter under varying gravitational and pressure regimes. It is also important investigate the precise limits of magmatter compressoin under extreme gravitational potentials, including the conditions nearing the formation of a black hole. Such studies will be paramount to determine whether these conditions are indeed sufficient to force magmatter into a more degenerate state, approaching the densities predicted by Model A, or if the inherent lattice stability persists even under such immense pressures.

7. Conclusion

This study embarked on a comprehensive investigation into the bulk density of magnetic monopole matter (magmatter), a material of profound significance to advanced galactic civilizations. We initiated our inquiry by establishing the foundational principles of magmatter, particularly highlighting the theoretical “asymmetry of forces” that suggested an extreme condensation in its bulk form. Based on this, we developed three distinct theoretical models for mag-carbon density: Model A (First-Principles / Packed Nucleus), Model B (Bohr Radius / Isolated Atom), and Model C (Diamond-like Lattice / Bohr Radius & Packing Efficiency).

To validate our analytical methodologies, we rigorously applied these approaches to a familiar terrestrial material, crystalline diamond. This exercise confirmed that for normal matter, the Bohr/Covalent Radius approach accurately reflects its density, while the Compton wavelength approach yields astronomically incorrect results, underscoring the distinct physical regimes governing normal and extreme matter. This validation reinforced our initial expectation that magmatter, due to its unique force dynamics, would exhibit densities far beyond conventional materials, likely aligning with Model A.

However, the subsequent crystallographic analysis of a synthesized mag-diamond sample yielded a surprising and pivotal empirical result. The measured bulk density of approximately $2.0 \times 10^{35} \text{ kg/m}^3$ aligned remarkably closely with the prediction of Model C (Diamond-like Lattice Approach), directly contradicting our initial hypothesis. This unexpected finding necessitates a significant revision of our understanding of magmatter’s condensed phase.

The experimental data suggests that while magmatter’s internal forces are indeed immense, the inter-atomic repulsive forces, though comparatively weaker, are nevertheless sufficient to prevent a complete collapse into a fully degenerate state. Magmatter, in its bulk form, appears to maintain a stable, ordered crystal lattice structure, scaled by the minuscule Bohr radius of its constituent magatoms. This implies that magmatter behaves more akin to a scaled-up version of normal matter, forming predictable crystalline arrangements, rather than a form of degenerate matter where orbital structures are entirely negligible. Furthermore, the potential influence of self-gravitation for larger magmatter constructs emerges as a critical factor that may contribute to even higher densities in naturally occurring or engineered megastructures.

This research underscores the invaluable role of empirical data, even when it challenges established theoretical expectations. The unexpected alignment with Model C opens new and exciting avenues for magchemistry and material engineering, suggesting that the precise design and synthesis of magmaterials with tailored lattice properties are not only feasible but are already being realized by our patron AIs. Future investigations will focus on exploring the full phase diagram of magmatter under various extreme conditions, further bridging the gap between theoretical prediction and the observed reality of this extraordinary material.

References

[1] Zou Xiang-Yi, Google Gemini. “The Extreme Properties of Magnetic Monopole Matter.” Xenomancy Lores, 2025. Available at: https://lores.xenomancy.id/genai/the-extreme-properties-of-magnetic-monopole-matter/

Appendix A: Cubic Mag-Boron Nitride Material Density

To further explore the material properties of magmatter beyond mag-carbon, we can theoretically derive the bulk density of cubic mag-boron nitride (mag-BN), assuming it forms a diamond-like lattice (Model C), consistent with the empirical findings for mag-diamond.

A.1. Mag-Boron and Mag-Nitrogen Atoms: Detailed Derivations

We first define the properties of mag-boron (B) and mag-nitrogen (N) atoms based on their atomic numbers (Z) and the established magmatter principles from [1] (“The Extreme Properties of Magnetic Monopole Matter”). The fundamental parameters used are:

  • Magtron Mass ($m_{magtron}$): $1.5 \text{ TeV}/c^2$
  • Magnucleus Mass (per magnetic charge unit): $10 \text{ TeV}/c^2$
  • Overall Binding Energy of Magmatter Atoms ($E_B$): $300 \text{ GeV}$
  • Effective Coupling Constant ($\alpha_{eff}$): $0.678$
  • Reduced Planck Constant ($\hbar c$): $0.1973 \text{ GeV} \cdot \text{fm}$

Mag-Boron (B) Atom (Z=5)

  • Composition: A mag-boron atom (Z=5) consists of a magnucleus with +5 magnetic charge units and 5 magtrons.
  • Mass ($M_{\text{mag-B}}$):
    • Magnucleus mass: $5 \times (10 \text{ TeV}/c^2) = 50 \text{ TeV}/c^2$
    • Magtrons mass: $5 \times (1.5 \text{ TeV}/c^2) = 7.5 \text{ TeV}/c^2$
    • Total Mass ($M_{\text{mag-B}}$): $50 \text{ TeV}/c^2 + 7.5 \text{ TeV}/c^2 = \mathbf{57.5 \text{ TeV}/c^2}$
  • Bohr Radius ($r_{\text{mag-B, Bohr}}$):
    1. Reduced Mass ($\mu_{\text{mag-B}}$): $$ \mu_{\text{mag-B}} = \frac{m_{magnucleus} \cdot m_{magtron}}{m_{magnucleus} + m_{magtron}} = \frac{50 \cdot 1.5}{50+1.5} = \frac{75}{51.5} \approx \mathbf{1.456 \text{ TeV}/c^2} $$
    2. Bohr Radius Calculation: $$ r_{\text{mag-B, Bohr}} = \frac{n^2 \hbar c}{Z \alpha_{\text{eff}} \mu c^2} $$ For ground state ($n=1$) and Z=5: $$ r_{\text{mag-B, Bohr}} = \frac{1^2 \cdot (0.1973 \text{ GeV} \cdot \text{fm})}{5 \cdot (0.678) \cdot (1456 \text{ GeV})} = \frac{0.1973}{4934.16} \text{ fm} \approx \mathbf{0.00003998 \text{ fm}} $$ Rounding to significant figures used in the main text: $\approx \mathbf{0.0000398 \text{ fm}}$.

Mag-Nitrogen (N) Atom (Z=7)

  • Composition: A mag-nitrogen atom (Z=7) consists of a magnucleus with +7 magnetic charge units and 7 magtrons.
  • Mass ($M_{\text{mag-N}}$):
    • Magnucleus mass: $7 \times (10 \text{ TeV}/c^2) = 70 \text{ TeV}/c^2$
    • Magtrons mass: $7 \times (1.5 \text{ TeV}/c^2) = 10.5 \text{ TeV}/c^2$
    • Total Mass ($M_{\text{mag-N}}$): $70 \text{ TeV}/c^2 + 10.5 \text{ TeV}/c^2 = \mathbf{80.5 \text{ TeV}/c^2}$
  • Bohr Radius ($r_{\text{mag-N, Bohr}}$):
    1. Reduced Mass ($\mu_{\text{mag-N}}$): $$ \mu_{\text{mag-N}} = \frac{m_{magnucleus} \cdot m_{magtron}}{m_{magnucleus} + m_{magtron}} = \frac{70 \cdot 1.5}{70+1.5} = \frac{105}{71.5} \approx \mathbf{1.469 \text{ TeV}/c^2} $$
    2. Bohr Radius Calculation: $$ r_{\text{mag-N, Bohr}} = \frac{n^2 \hbar c}{Z \alpha_{\text{eff}} \mu c^2} $$ For ground state ($n=1$) and Z=7: $$ r_{\text{mag-N, Bohr}} = \frac{1^2 \cdot (0.1973 \text{ GeV} \cdot \text{fm})}{7 \cdot (0.678) \cdot (1469 \text{ GeV})} = \frac{0.1973}{6956.046} \text{ fm} \approx \mathbf{0.00002836 \text{ fm}} $$ Rounding to significant figures used in the main text: $\approx \mathbf{0.0000283 \text{ fm}}$.

Average Mag-BN Atom

For a boron nitride structure, we consider an alternating arrangement of boron and nitrogen atoms. Therefore, we use average properties for a B-N unit.

  • Average Mass ($M_{\text{mag-BN, avg}}$): $$ M_{\text{mag-BN, avg}} = \frac{M_{\text{mag-B}} + M_{\text{mag-N}}}{2} = \frac{57.5 \text{ TeV}/c^2 + 80.5 \text{ TeV}/c^2}{2} = \frac{138 \text{ TeV}/c^2}{2} = \mathbf{69 \text{ TeV}/c^2} $$ (Note: This is coincidentally the same average mass as a mag-carbon atom, $69 \text{ TeV}/c^2$, which is $1.229 \times 10^{-22} \text{ kg}$).
  • Average Bohr Radius ($r_{\text{mag-BN, Bohr, avg}}$): $$ r_{\text{mag-BN, Bohr, avg}} = \frac{r_{\text{mag-B, Bohr}} + r_{\text{mag-N, Bohr}}}{2} = \frac{0.0000398 \text{ fm} + 0.0000283 \text{ fm}}{2} = \frac{0.0000681 \text{ fm}}{2} = \mathbf{0.00003405 \text{ fm}} $$

A.2. Cubic Mag-Boron Nitride Material Density Calculation

We apply Model C (Diamond-like Lattice Approach) to calculate the bulk density of cubic mag-BN. This model assumes that mag-atoms form a crystal lattice with the same packing efficiency as normal diamond (34%), and there are 8 atoms per unit cell in a diamond-like structure. The average covalent radius for a B-N bond in normal BN is roughly $(88 \text{ pm} + 75 \text{ pm})/2 = 81.5 \text{ pm}$.

  • Volume of a Single Average Mag-BN Atom (based on Bohr Radius): $$ V_{\text{mag-BN, Bohr, avg}} = \frac{4}{3}\pi r_{\text{mag-BN, Bohr, avg}}^3 $$ $$ V_{\text{mag-BN, Bohr, avg}} = \frac{4}{3}\pi (3.405 \times 10^{-20} \text{ m})^3 $$ $$ V_{\text{mag-BN, Bohr, avg}} \approx 1.65 \times 10^{-58} \text{ m}^3 $$

  • Predicted Density of Cubic Mag-BN (using diamond packing efficiency): $$ \rho_{\text{mag-BN, diamond}} = \frac{\text{Mass of 8 average mag-BN atoms}}{\text{Volume of unit cell}} $$ The volume of the unit cell is derived from the volume of a single atom and the packing efficiency ($\eta = 0.34$): $$ V_{\text{unit cell}} = \frac{8 \times V_{\text{mag-BN, Bohr, avg}}}{\eta} $$ $$ V_{\text{unit cell}} = \frac{8 \times (1.65 \times 10^{-58} \text{ m}^3)}{0.34} \approx 3.88 \times 10^{-57} \text{ m}^3 $$

    Now, calculate the density: $$ \rho_{\text{mag-BN, diamond}} = \frac{8 \times (1.229 \times 10^{-22} \text{ kg})}{3.88 \times 10^{-57} \text{ m}^3} $$ $$ \rho_{\text{mag-BN, diamond}} \approx \mathbf{2.53 \times 10^{35} \textbf{ kg/m}^3} $$