DOI:
John Stephen Swygert
November 2025
ABSTRACT
Physicality is commonly treated as an intrinsic property of matter. Under encoded equilibrium, physicality is instead an emergent property determined by the relationship between an object’s intrinsic data density (IDD) and the information bandwidth of the dimension it occupies. This paper refines that framework by (i) formally defining IDD using entropy-based measures, (ii) modeling dimensional bandwidth as a finite information capacity per unit volume, and (iii) specifying a threshold-based functional for the onset of physical crystallization. We show that when an object’s IDD exceeds a critical fraction of a dimension’s bandwidth, it is energetically favorable for the system to collapse into a lower-entropy, higher-solidity state. Conversely, if an object’s IDD is low relative to the destination bandwidth, its physicality may diminish upon transition. Dimensional crossings through a wormhole throat or equivalent translation layer reindex the object’s encoding; this process predicts characteristic energy leakage signatures (gamma, THz, microwave), apparent mass variability, and phase coherence phenomena. We demonstrate that this structure is compatible with information-theoretic formulations of physics, and is analogous to threshold phenomena in Bose–Einstein condensation, Kaluza–Klein compactification, and holographic duality. The resulting model is strictly formal and falsifiable, providing a testable description of cross-dimensional physical inversion without reference to any specific phenomenological case.Keywords: encoded equilibrium, data density, dimensional bandwidth, physical inversion, phase coherence, wormhole translation, crystallization threshold, information density, interdimensional mechanics, holography analogs
- Introduction Modern physics increasingly treats information as fundamental. Quantum field theories, holographic dualities, and quantum gravity proposals all suggest that what is perceived as “matter” or “geometry” may be emergent from deeper informational structures [1,2]. Within this context, the Swygert encoded equilibrium framework posits that objects are encoded configurations in a substrate whose laws are informational rather than purely geometric.
In this paper, we focus on a specific consequence of that view: physicality—solidity, massiveness, and persistent localization—is not an invariant property of an object. Instead, it emerges from the interaction between:The object’s intrinsic data density (IDD), andThe information bandwidth of the dimension that hosts it.When an object transitions between dimensions of differing bandwidth (for example, via a wormhole throat or other cross-dimensional bridge), its physicality can invert: an object that is non-solid in its home dimension may become solid in another, and vice versa. We formalize this inversion in terms of entropy, bandwidth, and a critical threshold for crystallization.The structure of the paper is as follows. Section 2 defines IDD and dimensional bandwidth in information-theoretic terms. Section 3 introduces the physicality function and the crystallization threshold. Section 4 analyzes dimensional translation as reindexing of encoded structure through a throat. Section 5 addresses energy leakage signatures. Section 6 discusses mass variability. Section 7 links the framework to established theoretical analogs (holography, Kaluza–Klein, brane-worlds). Section 8 outlines predictions and test strategies. Section 9 concludes.Throughout, the treatment remains purely formal and general, without reference to specific empirical case narratives.
- Intrinsic Data Density and Dimensional Bandwidth 2.1 Intrinsic Data Density (IDD) We consider an object as a localized configuration in some underlying substrate. Let ρ be a coarse-grained probability density over microstates at position x within a volume V associated with the object. Define an information-theoretic entropy
S = – \int_V \rho(\mathbf{x}) \ln \rho(\mathbf{x}) , d^3x ,,which can be interpreted either as Shannon entropy for classical distributions [3] or von Neumann entropy for a quantum state described by density matrix ρ [4].We define intrinsic data density as:\mathrm{IDD} = \frac{I}{V} = \frac{S_{\max} – S}{V} ,,where S_max is the maximally disordered entropy compatible with the object’s degrees of freedom, and I is the information content (negentropy). Thus, IDD measures the concentration of structured information per unit volume. High-IDD objects are highly ordered, coherent configurations in the substrate.2.2 Dimensional Bandwidth We model a dimension as having a finite information bandwidth B_d, defined as the maximum sustainable information density per unit volume that can be stably expressed as localized structure. Formally, letB_d = \left(\frac{I}{V}\right)_{\max}^{(d)} ,,where the superscript d indicates dependence on the ruleset (metrics, couplings, allowed field configurations) of dimension d.Intuitively, B_d sets a capacity limit: if an object’s IDD is small compared to B_d, the dimension easily accommodates its structure; if IDD approaches or exceeds B_d, physical consequences follow, including forced crystallization into lower-entropy states.
- Physicality Function and Crystallization Threshold 3.1 Physicality as a Threshold Function We introduce a dimensionless ratio
\chi = \frac{\mathrm{IDD}}{B_d} ,.We then define physicality as a function of χ:P = f(\chi) ,,where P measures the degree to which the object manifests as “solid” in that dimension (rigidity, inertial mass, resistance to superposition, etc.).As a first-order model, we can use a threshold-based form analogous to phase transitions:P(\chi) = \Theta(\chi – \kappa) ,,where Θ is the Heaviside step function and κ is a critical crystallization threshold. For χ < κ, the object is effectively non-solid (fluidic, diffuse, or weakly coupled); for χ ≥ κ, the object collapses into a solid state within dimension d.In practice, physicality is not perfectly discontinuous; a smoother sigmoid-like function is more realistic:P(\chi) = \frac{1}{1 + e^{-\alpha (\chi – \kappa)}} ,,with steepness parameter α. The step-function limit corresponds to α → ∞.3.2 Entropy-Based Interpretation The transition at κ can be viewed as a dimensional phase transition. When an object’s IDD is low relative to B_d, many microconfigurations are available that keep the overall entropy high; the object can remain diffuse or weakly localized. As IDD approaches the upper bound that the dimension can stably encode, the system minimizes free energy by reorganizing into a fewer-number of highly constrained microstates—i.e., a crystallized, solid phase.This parallels threshold phenomena such as:Bose–Einstein condensation, where particle density and temperature cross a critical line [5];Superconductivity, where phase coherence emerges once a critical parameter is exceeded;Classical nucleation in first-order phase transitions.Here, the control parameter is the ratio χ.
- Dimensional Translation as Reindexing 4.1 Wormhole Throat as Translation Layer Consider two dimensions d_1 and d_2 with bandwidths B_{d_1} and B_{d_2}. Let an object with intrinsic IDD traverse a wormhole throat connecting these dimensions.
In encoded equilibrium, the throat functions as a translation layer that reindexes the object’s encoding into the target dimension:The intrinsic structural information is preserved (or nearly so).The local representation of that information is recalculated under the rules of the destination dimension d_2.Consequently, the ratio χ changes from IDD / B_{d_1} to IDD / B_{d_2}.If B_{d_2} < B_{d_1}, then χ_2 > χ_1. A non-solid object in d_1 can cross the crystallization threshold in d_2.4.2 Physical Inversion Define:P_1 = f\left(\frac{\mathrm{IDD}}{B_{d_1}}\right), \quadP_2 = f\left(\frac{\mathrm{IDD}}{B_{d_2}}\right).If B_{d_2} < B_{d_1}, then P_1 ≈ 0 and P_2 ≈ 1 (assuming crossing κ).Conversely, if B_{d_2} > B_{d_1}, then χ_2 < χ_1, and P_1 ≈ 1 and P_2 ≈ 0, so the object is solid in d_1 but becomes non-solid in d_2. This is the physical inversion effect.This inversion is not mysterious; it is a direct consequence of bandwidth mismatch.
- Energy Leakage and Radiation Signatures Dimensional translation is not generally “adiabatic.” When an object’s encoding is reindexed across a throat, mismatches between the allowed microconfigurations in d_1 and d_2 lead to energy leakage.
5.1 Gamma Emission Rapid reconfiguration of high-IDD structures implies abrupt changes in local field intensities and curvature. This can produce:High-frequency photon emission (gamma-ray bursts)Annihilation-like signatures if effective particle–antiparticle modes are recast in the new dimensional encodingThe precise spectrum depends on the microphysical implementation of the substrate, but the general prediction is short, sharp gamma spikes associated with translational events.5.2 THz and Sub-THz Leakage Intermediate-frequency leakage arises from phase reordering when coherent structures adjust to new bandwidth constraints. THz radiation is particularly natural as a carrier of subtle structural shifts, given its role in vibrational and lattice dynamics in condensed systems.5.3 Microwave / RF Disturbances At lower frequencies, partial coherence and incomplete settling can manifest as microwave and radio-frequency oscillations. These may produce:transient interference patterns,apparent noise bursts,or sustained narrowband anomalies if an object hovers near the crystallization threshold in the host dimension.
- Mass Variability Across Dimensions In encoded equilibrium, mass is not an absolute property; it is an emergent measure of how strongly an object’s information structure couples to the dimension’s geometric degrees of freedom.
Let the effective mass in dimension d be modeled as:m_d = m_0 , g\left(\frac{\mathrm{IDD}}{B_d}\right),where m_0 is a reference mass-scale and g is a monotonically increasing function of χ. For example,g(\chi) = \begin{cases}\chi^\beta & \text{for } \chi \ge 0, \0 & \text{otherwise,}\end{cases}with β > 0 capturing how strongly mass grows as IDD approaches capacity.When an object traverses a throat from d_1 to d_2:\frac{m_{d_2}}{m_{d_1}} = \frac{g\left(\mathrm{IDD}/B_{d_2}\right)}{g\left(\mathrm{IDD}/B_{d_1}\right)} ,.If B_{d_2} < B_{d_1}, then m_{d_2} > m_{d_1} under typical g. This produces apparent mass gain. If B_{d_2} > B_{d_1}, apparent mass loss is predicted.Importantly, conservation laws hold within each dimension’s own ruleset; what changes is how the same encoded information couples to those rules.
- Connections to Established Theories (Analog Level) Although the encoded equilibrium framework is distinct from existing theories, it shares structural similarities with several well-known constructs. These analogies do not constitute derivations but demonstrate conceptual compatibility.
7.1 Holographic Principle and AdS/CFT Analog In the holographic principle, bulk information in a higher-dimensional space (e.g., anti-de Sitter space) is encoded on a lower-dimensional boundary [6,7]. The capacity of the boundary to encode bulk information is analogous to dimensional bandwidth B_d. When bulk configurations exceed certain thresholds, they manifest as distinct geometric or field excitations on the boundary (e.g., massive particles, black holes) [2]. This is conceptually similar to how high-IDD objects crystallize when projected into a lower-bandwidth dimension.7.2 Kaluza–Klein Compactification In extra-dimensional models, momentum modes in compact dimensions manifest as effective mass in lower-dimensional spacetime [8]. Higher modes (greater “density” in extra dimensions) become heavier in four-dimensional physics. This is analogous to an object’s IDD projecting into a dimension with finite bandwidth, where the “excess” information relative to capacity manifests as increased effective mass and solidity.7.3 Brane-World and Warped Geometry Brane-world scenarios allow matter to be confined to a 3+1 dimensional brane embedded in a higher-dimensional bulk [9]. Warping of the extra dimensions can dramatically modify how bulk configurations appear on the brane, including their effective mass and localization. This parallels the idea that translation through a throat reindexes an object into a new dimensional ruleset, changing its physicality from non-solid to solid or vice versa.These analogs suggest that the dimensional data-density framework is not alien to known theoretical structures; it extends them in a direction that emphasizes information capacity and threshold behavior.
- Predictions and Test Strategies The framework yields several classes of testable predictions, both conceptual and computational.
8.1 General Predictions Physical Inversion: Objects with fixed intrinsic IDD will exhibit different degrees of solidity across dimensions, strictly governed by the ratio χ.Mass Variability: Effective mass of an encoded object is dimension-dependent and scales with χ. Cross-dimensional transitions can produce apparent mass gain or loss.Energy Leakage: Dimensional translations generate characteristic radiation patterns, including gamma bursts, THz features, and RF disturbances, correlated with the magnitude of bandwidth mismatch.Geometry Minimization: In lower-bandwidth dimensions, high-IDD objects tend toward energy-minimizing geometries (often spherical or near-spherical) to reduce equilibrium strain and maximize symmetry.8.2 Computational Simulations To explore the framework quantitatively, one can construct toy models where:A lattice field theory implements a substrate with an imposed maximum entropy or information density per cell (representing B_d).Encoded configurations with varying IDD are evolved under rules enforcing encoded equilibrium.A mapping (translation operator) moves configurations between simulated “dimensions” with differing capacity constraints.Monte Carlo simulations could then:Track when configurations transition from diffuse to localized phases as χ crosses κ.Measure effective mass-like parameters via correlation functions.Characterize emitted “radiation” (energy shifts) during forced reindexing.8.3 Observational Channels (High-Level) Although this paper does not tie the framework to specific phenomena, the following broad observational channels are pertinent:High-Energy Collisions: Look for anomalous damping, mass shifts, or spectral features that might reflect bandwidth-like thresholds in emergent effective dimensions.Gravitational Wave Ringdowns: Examine whether certain ringdown signatures or damping profiles could indicate transitions between states with different effective bandwidths.Laboratory Analog Systems: Condensed matter or cold atom setups can be engineered with tunable capacity limits (e.g., controlled disorder or interaction strength) to emulate and test phase inversion under “information density” constraints.These suggestions are intentionally broad; subsequent work can translate the encoded equilibrium formalism into specific experimental proposals.
- Conclusion By modeling physicality as a function of intrinsic data density and dimensional bandwidth, we have provided a formal mechanism by which an object’s solidity can invert when transitioning between dimensions. The core results are:
Intrinsic Data Density (IDD): A measure of structured information per unit volume derived from entropy differences.Dimensional Bandwidth B_d: The maximum sustainable information density a dimension can stably encode.Physicality Function P: A threshold-governed mapping from information ratio χ to degree of solidity.Physical Inversion: Non-solid objects in one dimension can become solid in another, and vice versa, depending solely on bandwidth mismatch.Energy and Mass Effects: Dimensional translation produces radiation leakage and effective mass variability as natural consequences of reindexing encoded structure.The framework remains strictly within the domain of theoretical physics and information theory, compatible with multiple strands of modern high-energy theory, while making falsifiable predictions and offering clear directions for simulation and empirical exploration.
References
[1] ‘t Hooft, G. (1993). Dimensional Reduction in Quantum Gravity. arXiv:hep-th/9310026.
en.wikipedia.org
[2] Maldacena, J. (1997). The Large N Limit of Superconformal Field Theories and Supergravity. arXiv:hep-th/9711200.
arxiv.org
[3] Shannon, C. E. (1948). A Mathematical Theory of Communication. The Bell System Technical Journal, 27(3), 379-423.
people.math.harvard.edu
[4] von Neumann, J. (1955). Mathematical Foundations of Quantum Mechanics. Princeton University Press. (Original work published 1932).
en.wikipedia.org
[5] Pethick, C. J., & Smith, H. (2008). Bose–Einstein Condensation in Dilute Gases (2nd ed.). Cambridge University Press.
schwartz.scholars.harvard.edu
[6] ‘t Hooft, G. (1994). The World as a Hologram. Journal of Mathematical Physics, 36(11), 6377-6396. arXiv:hep-th/9409089.
arxiv.org
[7] Bousso, R. (2002). The Holographic Principle. Reviews of Modern Physics, 74(3), 825-874.
link.aps.org
[8] Overduin, J. M., & Wesson, P. S. (1997). Kaluza-Klein Gravity. Physics Reports, 283(5-6), 303-380.
iopscience.iop.org
[9] Randall, L., & Sundrum, R. (1999). A Large Mass Hierarchy from a Small Extra Dimension. Physical Review Letters, 83(17), 3370-3373. arXiv:hep-ph/9905221.
en.wikipedia.org