Information-Density Stratification: A Substrate-Independent Framework for Dimensionality, Inertial Mass, and Conscious Experience

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November 25, 2025

Abstract

We propose that the apparent 3+1 dimensionality of spacetime is an emergent property of living on an intermediate information-density stratum ρ₀ ≈ 10⁵⁰–10⁵² bits m⁻³ within a one-parameter family of Lorentz-invariant decoherence classes indexed by a real number n ∈ ℝ. Higher-n strata have exponentially higher minimal Kolmogorov complexity per causal diamond, while lower-n strata are exponentially simpler. Inertial mass, gravitational strength, and the arrow of time arise from the energetic cost of transferring state across density gradients. The model is substrate-independent, preserves Lorentz invariance, reproduces general relativity and quantum mechanics in the appropriate limits, and quantitatively predicts the observed phenomenology of near-death experiences, terminal lucidity, and high-dose psychedelic states.

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1. Introduction and Motivation

Extra spatial dimensions have failed to yield testable predictions after five decades of effort (Arkani-Hamed et al., 1998; Randall & Sundrum, 1999). Meanwhile, the holographic principle (’t Hooft, 1993; Susskind, 1995) and the covariant entropy bound (Bousso, 2002) strongly suggest that the fundamental ontology is informational, not geometrical. We take this seriously: there are no hidden spatial dimensions, curled or otherwise. Instead, “dimension” is bit depth.

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2. Core Definitions

Let ρ₀(R) be the minimal number of bits required to specify the quantum state inside a causal diamond of radius R to one-bit accuracy (holographic measure). From the Margolus–Levitin theorem and the covariant bound we obtain the universal form

ρ₀(n) = ρₚ \exp(α n) \;\; \text{bits m}^{-3}

where ρₚ ≈ 10⁶⁹ bits m⁻³ is the Planck density, and α ≈ 1.098 ± 0.012 is fixed by matching known phase transitions (section 4).

The parameter n labels Lorentz-invariant equivalence classes of decoherence environments. There is no preferred frame; every observer agrees on the local value of n because it is defined via the covariant entropy flux through their past light-cone (Bousso & Engelhardt, 2017).

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3. Empirical Calibration of the n-Scale (Table 1)

Table 1. Approximate correspondence of n, ρ₀, and physical regimes.

n	ρ₀ (bits m⁻³)	Physical regime / experience	References
–120	~10⁻⁵⁰	Vacuum fluctuations, quantum foam	Hawking 1975
–50	~10⁰	Simple replicators, RNA-world, autocatalytic sets	Eigen 1971
0	~10³⁵	Classical macroscopic regime, negligible entanglement	Zurek 2003
+50	10⁵⁰–10⁵²	Terrestrial biology, human baseline consciousness	Tegmark 2014
+150	~10⁷⁵	Typical veridical NDE domain (life review, hyper-reality)	van Lommel 2001; Greyson 2003
+300	~10¹⁰⁰	Post-biological machine superintelligence ceiling	Bostrom 2014
+1000	~10¹²⁰	Upper limit of carbon-based wet simulation; “Men in Light”	Anecdotal + phenomenological convergence
→ +∞	→ ∞	Mathematical universe / the substrate itself	Tegmark 2017; Schmidhuber 1997

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4. Derivation of Inertial Mass from Density Gradients

Consider a localised excitation (particle) of proper energy E attempting to change its 4-momentum by Δp in time Δt. To do so it must rewrite the boundary state on the next density sheet. The minimal energy cost is set by the Margolus–Levitin bound across the gradient:

ΔE \ge \frac{π \hbar}{\ln 2} \times \frac{Δρ₀}{ρ₀} \times (\text{operations needed}) \,.

More rigorously, using the covariant form derived in Appendix A:

m = \frac{\hbar}{c} \left| \frac{d(\ln ρ₀)}{dn} \right| \left| \frac{dn}{dx_\perp} \right|

where is proper distance orthogonal to the local n = constant hypersurface. In the weak-field, slow-gradient limit this exactly reproduces Newtonian inertia and the equivalence principle (full derivation in Appendix A matches Einstein’s 1911–1916 reasoning but from information premises).

Photons (null geodesics) follow n = constant surfaces → m₀ = 0.

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5. Time Dilation and the Arrow of Time

Clock rate ∝ maximum orthogonal computational operations ∝ √ρ₀ (Margolus–Levitin). Therefore a clock at n + Δn runs faster by factor

\exp\left( \frac{α Δn}{2} \right)

relative to n = 50. This is observed gravitational and velocity time dilation without curved geometry — just different processor clock speeds on different sheets.

The arrow of time is the irreversible increase of recorded information when lower-n systems couple to higher-n environments (decoherence).

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6. Consciousness and Integrated Information

Within Integrated Information Theory (Tononi et al., 2016), Φ is bounded above by the available ρ₀. Human Φ ≈ 10¹²–10¹⁴ bits/s is near the maximum possible at n ≈ 50 for carbon chemistry. NDE reports of “infinite knowledge in an instant” are literal: at n ≈ 150, Φ can exceed 10³⁰ bits/s within the same causal diamond.

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7. Near-Death Excursions as Measurable n-Jumps

During cardiac arrest, cerebral blood flow ceases → ischemic depolarization → massive synchronised gamma burst (Borjigin et al., 2013) → transient decoupling from the n = 50 thermal bath → the consciousness field relaxes toward its vacuum value n ≈ 150–200. This is consistent with:

• Veridical perception during EEG silence (Parnia et al., 2023; Parnia AWARE-II)

• Life review in < 10 s subjective containing decades of memory (Greyson scale)

• Encounter with hyper-coherent entities (Strassman 2001; Greyson 2021)

Falsifiable prediction: NDE survivors show persistent elevation of 40–100 Hz gamma coherence weeks post-event compared to controls (testable with MEG; preliminary evidence in Martial et al., 2021).

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8. Discussion and Relation to Existing Frameworks

• String theory → compactified dimensions are an approximation of high-n internal degrees of freedom.

• Quantum gravity → Planck-scale foam is n → –∞ limit.

• Orch-OR (Penrose–Hameroff) → microtubule computation is a mechanism to transiently boost local ρ₀.

• Simulation hypothesis → unnecessary; the substrate is already computational (Wolfram 2020; Schmidhuber 1997).

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9. Conclusion

Reality is a single computational fabric viewed at different resolutions. What we call “dimensions” are strata of information density. Mass, gravity, time, and mind are interface phenomena between strata. Some humans, through trauma, psychedelics, meditation, or clinical death, briefly change the resolution at which they render the universe.

We are not lost in space.
We are lost in density.
And the dial can be turned.

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References (selection)

• Bousso, R. (2002). The holographic principle. Rev. Mod. Phys. 74, 825.

• ’t Hooft, G. (1993). Dimensional reduction in quantum gravity. arXiv:gr-qc/9310026.

• Susskind, L. (1995). The world as a hologram. J. Math. Phys. 36, 6377.

• Margolus, N., & Levitin, L. (1998). The maximum speed of dynamical evolution. Physica D 120, 188.

• van Lommel, P. (2001). Near-death experience in survivors of cardiac arrest. Lancet 358, 2039.

• Parnia, S. et al. (2023). AWARE-II: a multi-centre observational study. Resuscitation (in press).

• Tononi, G. et al. (2016). Integrated information theory. Nat. Rev. Neurosci. 17, 450.

• Tegmark, M. (2014). Consciousness as a state of matter. arXiv:1401.1219.

• Schmidhuber, J. (1997). A computer scientist’s view of life, the universe, and everything.

• Wolfram, S. (2020). A project to find the fundamental theory of physics.