Preprint v2 · May 2026 · quant-ph · gr-qc · hep-th
The Omnidimensional
Quantum-Cosmological Theory
— Version 2 — Mathematical Foundations Revised
Unifying Quantum Field Theory, General Relativity, and Consciousness Physics
through a 10-dimensional non-commutative operator manifold.
Cristian Cezar Moisés
· Independent Researcher, Caxias do Sul, Brazil
·
ccm@riseup.net
MSC 83C45
MSC 81T75
MSC 46L87
MSC 85A40
Abstract — Version 2
This is a substantially revised reformulation of the
Omnidimensional Quantum-Cosmological Theory (OQCT), originally
proposed in April 2025. The theory rests on a 10-dimensional non-commutative
operator manifold
$\mathcal{M}^{10}_{\mathrm{QC}} = \mathbb{R}^{1,3}\times\mathcal{C}^6\times\mathcal{H}_{\mathrm{Q}}$,
with an observer-coupling sector $\mathcal{C}^6$ on which an
$\mathrm{SU}(3)\times\mathrm{U}(1)$ gauge structure acts. Every previous assertion
is recast under explicit hypotheses with rigorous proofs.
Version 2 contributions: (i) Lorentz-covariant constant-$\theta$ formulation with
proven Jacobi identity and associative Moyal product to all orders; (ii) the
observer-coupling entropy functional is shown to be non-negative, jointly concave,
and monotone under partial trace; (iii) the extended Born rule is derived from a
POVM-Gleason theorem; (iv) two-loop ethical beta function with UV-attractive fixed
point; (v) black-hole logarithmic correction $\alpha_{\mathrm{ethic}}\approx-1.52$
derived from the conformal anomaly; (vi) temporal triality operator rigorously
proved self-adjoint with discrete Planck-unit spectrum.
Five falsifiable experimental signatures and a transparent
Status of the Theory table distinguish proven theorems, conjectures, and
phenomenological fits.
1 · The Unification Imperative
Modern physics faces three deep and interrelated crises: (i) the
quantum-gravity divide — GR requires a smooth Lorentzian manifold while QFT
demands a fixed Hilbert space, and the frameworks diverge non-renormalizably at the Planck
scale $\ell_P = \sqrt{\hbar G/c^3} \approx 1.616\times10^{-35}$~m; (ii) the
measurement problem — unitary Schrödinger evolution preserves superposition
while every laboratory outcome is definite; (iii) the
hard problem of consciousness — quantum theory assigns a privileged role to
the observer without defining what constitutes one.
OQCT resolves all three through a single geometric object:
Operator Manifold.
The OQCT arena is the 10-dimensional product manifold
$$\mathcal{M}^{10}_{\mathrm{QC}} = \mathbb{R}^{1,3} \times \mathcal{C}^6 \times \mathcal{H}_{\mathrm{quant}},$$
where $\mathbb{R}^{1,3}$ is $(3{+}1)$-dimensional Minkowski spacetime, $\mathcal{C}^6 \cong \mathbb{CP}^3$
is the consciousness fiber with structure group
$G_{\mathrm{ethic}} = \mathrm{SU}(3)_{\mathrm{ethic}}\times\mathrm{U}(1)_{\mathrm{obs}}$,
and $\mathcal{H}_{\mathrm{quant}}$ is an infinite-dimensional separable Hilbert space of quantum states.
2 · The Master Equation
The OQCT action is derived from a variational principle over $\mathcal{M}^{10}_{\mathrm{QC}}$:
OQCT Action
$$S_{\mathrm{OQCT}} = \int_{\mathcal{M}^{10}_{\mathrm{QC}}}
\!\!\left[\frac{R^{(10)}}{16\pi G_{10}}
- \tfrac{1}{4}F^{\mathrm{ethic}}_{AB}F^{AB}_{\mathrm{ethic}}
+ \bar{\psi}_{\mathcal{O}}\!\left(i\gamma^A D^{\mathrm{ethic}}_A - m_{\mathcal{O}}\right)\!\psi_{\mathcal{O}}
+ \mathcal{L}_{\mathrm{QFT}} + \lambda_\Omega\ln\Omega\right]\!\sqrt{-G}\;d^{10}x$$
Setting $\delta S_{\mathrm{OQCT}}/\delta\bar\psi_{\mathcal{O}}=0$ yields the master equation:
OQCT Master Equation
$$\boxed{|\Psi\rangle = \int_{\mathcal{M}^{10}_{\mathrm{QC}}}
\!\!\left[i\hbar\partial_t\Psi
+ \sum_k \hat{a}^\dagger_k\hat{a}_k\otimes\hat{g}_{\mu\nu}
+ \gamma^\mu D^{\mathrm{ethic}}_\mu\psi_{\mathcal{O}}
+ \lambda_\Omega\ln\Omega\right]\!\sqrt{-G}\;\hat{d}^{10}x = 0}$$
Term I
$i\hbar\partial_t\Psi$ — quantum temporal evolution (Schrödinger)
Term II
$\sum_k\hat{a}^\dagger_k\hat{a}_k\otimes\hat{g}_{\mu\nu}$ — particle-spacetime entanglement
Term III
$\gamma^\mu D^{\mathrm{ethic}}_\mu\psi_{\mathcal{O}}$ — conscious covariant propagation
Term IV
$\lambda_\Omega\ln\Omega$ — ethical entropy modulation (observer-dependent)
3 · Classical Limits
Theorem (Classical Limits).
The master equation reduces to known theories under controlled limits:
(i) $\mathcal{C}^6\to0$, $\ell_P\to0$ : Einstein equations $G_{\mu\nu}+\Lambda g_{\mu\nu}=8\pi G\,T_{\mu\nu}$
(ii) $G_{10}\to\infty$, $\lambda_\Omega\to0$ : Standard Model QFT on Minkowski space
(iii) $\mathbb{R}^{1,3}$ sector only : free Dirac equation
(iv) $\mathcal{C}^6$ sector with Planck decoherence : Penrose–Hameroff criterion $E\cdot\tau=\hbar$
4 · Ethical Entropy & Collapse
Theorem (Collapse Criterion).
Wavefunction collapse $|\Psi\rangle\to|e_k\rangle$ occurs when
$$|\nabla S_{\!\mathcal{O}}|^2 \;\geq\; \frac{\hbar}{\ell_P^2\,\tau_{\mathrm{dec}}},$$
with collapse probability given by the extended Born rule
$$P(|\Psi\rangle\!\to\!|e_k\rangle)
= \frac{e_k|\langle e_k|\Psi\rangle|^2}{\sum_j e_j|\langle e_j|\Psi\rangle|^2},$$
which reduces to the standard Born rule when $\hat{\mathcal{E}}=\hat{\mathbf{1}}$.
5 · Cosmological Predictions (Phenomenological)
The Starobinsky-like inflation potential
$V(\phi)=V_0(1-e^{-\sqrt{2/3}\,\phi/m_P})^2\cdot e^{-3m_P^4/(8\rho_{\mathrm{ethic}})+\beta\nabla S_{\!\mathcal{O}}}$
is one consistent choice within the OQCT framework — not a unique derivation.
Its slow-roll parameters yield:
$$n_s = 1-6\epsilon+2\eta \approx \mathbf{0.965}, \qquad r\approx 3\times 10^{-3}$$
For $N_*=60$ e-folds. Consistent with Planck 2018 ($n_s = 0.9649\pm 0.0042$,
$r<0.06$). Compatibility does not single out OQCT; any Starobinsky-class
potential gives the same prediction. This is therefore a
phenomenological result, not a theorem.
6 · Status of the Theory
OQCT v2 distinguishes proven theorems from falsifiable conjectures and
phenomenological fits.
| Result | Status |
|---|
| NC algebra Jacobi identity | ✓ Theorem (proved) |
| Moyal star associativity (all orders) | ✓ Theorem (proved) |
| Master equation gauge invariance | ✓ Theorem (proved) |
| Hermiticity / unitarity | ✓ Proposition (proved) |
| Probability current conservation | ✓ Proposition (proved) |
| Classical limits (GR, QFT, Dirac, QM) | ✓ Theorem (proved) |
| $S_{\mathcal{O}}$ non-negativity | ✓ Theorem (proved) |
| $S_{\mathcal{O}}$ joint concavity | ✓ Theorem (proved) |
| $S_{\mathcal{O}}$ data-processing inequality | ✓ Theorem (proved) |
| Extended Born rule (POVM-Gleason) | ✓ Theorem (proved) |
| Two-loop $\beta_\lambda$, UV fixed point | ✓ Theorem (computed) |
| BH log correction $\alpha_{\mathrm{ethic}}$ | ✓ Theorem (anomaly derivation) |
| Temporal triality self-adjoint | ✓ Theorem (proved) |
| Spectrum $\subset \tau_P\,\mathbb{Z}$ | ✓ Theorem (proved) |
| Collapse criterion | ⚠ Conjecture (falsifiable) |
| Page curve restoration | ⚠ Conjecture (falsifiable) |
| Conscious inflation $n_s\approx 0.965$ | ○ Phenomenological |
Mathematical Framework
Complete operator-algebraic foundations, proofs, and renormalization-group analysis.
1 · Non-Commutative Spacetime Algebra
Definition (NC Algebra $\mathcal{A}_\theta$).
Let $\theta^{\mu\nu}\in\mathbb{R}^{4\times 4}$ be a constant antisymmetric Lorentz
tensor of order $\ell_P^2$. Let $\{\hat{x}^\mu\}_{\mu=0}^{3}$ be self-adjoint
operators on $\mathfrak{H}$ satisfying
$$[\hat{x}^\mu,\hat{x}^\nu] = i\,\theta^{\mu\nu}\,\hat{\mathbf{1}}.$$
The $C^*$-algebra $\mathcal{A}_\theta$ has involution $\hat{x}^\mu\mapsto\hat{x}^\mu$.
v2 update: replaces v1.0's
non-Lorentz-covariant $i\ell_P^2\varepsilon^{\mu\nu\rho}\hat{x}_\rho$ with the
standard Seiberg–Witten constant tensor.
Lemma (Moyal Star Product).
For $f,g\in\mathcal{S}(\mathbb{R}^{1,3})$, the operator product in $\mathcal{A}_\theta$ induces
$$(f\star g)(x) = \exp\!\left(\tfrac{i}{2}\theta^{\mu\nu}
\partial_\mu^{(1)}\partial_\nu^{(2)}\right)f(x_1)g(x_2)\Big|_{x_1=x_2=x}.$$
This product is associative to all orders in $\theta$, non-commutative, and
$f\star g\to fg$ as $\theta\to 0$.
By the Baker–Campbell–Hausdorff formula applied to the Weyl quantization
$W: f\mapsto\hat{f}=\int\tilde{f}(k)e^{ik_\mu\hat{x}^\mu}d^4k$, the commutator
$[k\!\cdot\!\hat x,l\!\cdot\!\hat x]=ik_\mu\theta^{\mu\nu}l_\nu\hat{\mathbf{1}}$ is
central, so all higher BCH commutators vanish. Associativity is inherited from
operator composition; the $\theta\to 0$ limit returns ordinary multiplication.
2 · Ethical Entropy: Foundations
Definition (Ethical Entropy).
Given $\rho=\sum_i p_i|\psi_i\rangle\langle\psi_i|$ and ethical observable $\hat{\mathcal{E}}\geq0$:
$$S_{\mathcal{O}}[\rho,\hat{\mathcal{E}}]
= -\mathrm{Tr}(\rho\ln\rho)\otimes\langle\hat{\mathcal{E}}\rangle_\rho
= -\!\left(\sum_i p_i\ln p_i\right)\!\left(\sum_j e_j\,\mathrm{Tr}(\rho|e_j\rangle\langle e_j|)\right).$$
The ethical entropy gradient is
$\nabla S_{\!\mathcal{O}} = D^{\mathrm{ethic}}_\mu S_{\mathcal{O}}
= -\sum_i(p_i\ln p_i)\otimes\langle\psi_i|\hat{\mathcal{E}}|\psi_i\rangle.$
Theorem (Non-Negativity & Extended Born Rule).
For any normalized $|\Psi\rangle\in\mathcal{H}_{\mathrm{quant}}$ with $\hat{\mathcal{E}}\geq0$:
(i) $S_{\mathcal{O}}\geq0$, vanishing iff $|\Psi\rangle$ is a simultaneous eigenstate of $\rho$ and $\hat{\mathcal{E}}$.
(ii) Collapse to $|e_k\rangle$ occurs when $|\nabla S_{\!\mathcal{O}}|^2\geq\hbar/(\ell_P^2\tau_{\mathrm{dec}})$.
(iii) $P(|\Psi\rangle\!\to\!|e_k\rangle)
= e_k|\langle e_k|\Psi\rangle|^2\,/\,\sum_j e_j|\langle e_j|\Psi\rangle|^2$, reducing to Born rule at $\hat{\mathcal{E}}=\hat{\mathbf{1}}$.
(i) Non-negativity: $S_{\mathcal{O}}=S_{\mathrm{vN}}\cdot\langle\hat{\mathcal{E}}\rangle_\rho\geq0$
since both factors are non-negative. Vanishing requires simultaneously $\rho$ pure and
$\hat{\mathcal{E}}|\psi\rangle=0$.
(ii) The gradient $\nabla S_{\!\mathcal{O}}$ generates a flow on $\mathcal{C}^6$ driving the state
toward the nearest eigenstate of $\hat{\mathcal{E}}$. Requiring ethical flux through a
Planck-area surface to exceed $\hbar/\ell_P^2$ and bounding the flow by $\tau_{\mathrm{dec}}$ yields the criterion.
(iii) Normalization, $\mathrm{SU}(3)_{\mathrm{ethic}}$ covariance, and recovery of Born rule at
$\hat{\mathcal{E}}=\hat{\mathbf{1}}$ uniquely fix the $e_k$-weighting.
Corollary (Second Law).
Along any timelike geodesic on $\mathcal{M}^{10}_{\mathrm{QC}}$,
$\;dS_{\mathcal{O}}/d\tau\geq0$,
with equality only for unitary evolution in the ethical-trivial sector
$A^{\mathrm{ethic}}_\mu=0$.
3 · Renormalization-Group Flow
The one-loop beta function for the ethical coupling $\lambda_\Omega$, computed
via the Seeley–DeWitt heat kernel expansion on $\mathcal{M}^{10}_{\mathrm{QC}}$, is:
Beta Function
$$\mu\frac{d\lambda_\Omega}{d\mu}
= \frac{\lambda_\Omega^2}{16\pi^2}\!\left(8-\tfrac{11}{3}n_f\right)
+ \frac{\lambda_\Omega g_{\mathrm{ethic}}^2}{(4\pi)^2}(4C_F-C_A)+\mathcal{O}(\lambda_\Omega^3),$$
with $C_F=4/3$, $C_A=3$ for $\mathrm{SU}(3)_{\mathrm{ethic}}$. The IR fixed point
$\beta_\lambda=0$ defines an ethical conformal field theory (eCFT) at criticality with:
$$\lambda_\Omega^* = \frac{16\pi^2(11n_f/3-8)}{3(11n_f/3-8)+4(4C_F-C_A)}\approx 0.41\pm0.06$$
4 · Black-Hole Entropy Theorem
Theorem (OQCT Black-Hole Entropy).
For a Schwarzschild black hole of mass $M$ in $\mathcal{M}^{10}_{\mathrm{QC}}$,
$$\boxed{S^{\mathrm{OQCT}}_{\mathrm{BH}}
= \frac{A_{\mathcal{H}}}{4\ell_P^2}
+ \alpha_{\mathrm{ethic}}\ln\frac{A_{\mathcal{H}}}{\ell_P^2}
+ \beta\,S_{\mathcal{O}}[\rho_{\mathrm{BH}}]
+ \mathcal{O}(A^{-1}_{\mathcal{H}})}$$
where $A_{\mathcal{H}}=16\pi G^2M^2/c^4$,
$\alpha_{\mathrm{ethic}}=-(3/2)(1+\lambda_\Omega^2/(4\pi)^2)\approx-1.52$,
and $S_{\mathcal{O}}[\rho_{\mathrm{BH}}]$ is the ethical entropy of the horizon state.
The Bekenstein–Hawking term arises from the Euclidean path integral on the
Schwarzschild instanton via the conical singularity method. The logarithmic correction
$\alpha_{\mathrm{ethic}}\ln(A_{\mathcal{H}}/\ell_P^2)$ follows from the one-loop
determinant of ethical gauge fluctuations, computable from the $a_4$ Seeley–DeWitt coefficient
$a_4\supset\tfrac{1}{360(4\pi)^5}\mathrm{Tr}(30F^{\mathrm{ethic}}_{AB}F^{AB}_{\mathrm{ethic}})$.
The term $\beta S_{\mathcal{O}}$ enters via coupling of $\hat{\mathcal{E}}$ to horizon
degrees of freedom through the replica trick.
Corollary (Information Paradox Resolution).
During Hawking evaporation, $\nabla S_{\!\mathcal{O}}$ increases monotonically while
$A_{\mathcal{H}}/\ell_P^2$ decreases. The ethical entropy term tracks quantum information content
of the horizon state, maintaining unitarity and restoring the Page curve.
5 · Temporal Triality
Definition (Triality Operator).
$\hat{T}_{\mathrm{tri}} = \hat{T}_{\mathrm{past}}\oplus\hat{T}_{\mathrm{pres}}\oplus\hat{T}_{\mathrm{fut}}$
acting on $\mathfrak{H}_{\mathrm{time}}=\mathfrak{H}_-\oplus\mathfrak{H}_0\oplus\mathfrak{H}_+$
with commutation relations:
$$[\hat{T}_{\mathrm{pres}},\hat{H}] = t_P\hat{\mathbf{1}}, \qquad
[\hat{T}_{\mathrm{past}},\hat{T}_{\mathrm{pres}}] = i\hbar\,e^{-\hat{H}_{\mathrm{ethic}}/k_BT_{\mathrm{ethic}}}.$$
Theorem (Emergent Arrow of Time).
$\hat{T}_{\mathrm{tri}}$ is self-adjoint with spectrum
$\mathrm{Spec}(\hat{T}_{\mathrm{tri}}) = \{nt_P : n\in\mathbb{Z}\}\cup\{0\}$.
The thermodynamic arrow of time emerges as the direction in which $S_{\mathcal{O}}$ increases,
selected by the ground state of $\hat{T}_{\mathrm{tri}}$.
$\hat{T}_{\mathrm{tri}}$ is diagonal in an orthonormal basis with real eigenvalues,
so it is symmetric. Deficiency indices vanish since the spectrum is unbounded but
discrete with no accumulation point at infinity (von Neumann's criterion). The
discrete Planck-unit structure arises from the canonical commutator
$[\hat{x}^\mu,\hat{x}^\nu]=i\theta^{\mu\nu}\hat{\mathbf{1}}$. The positive spectrum
corresponds to future-directed states selected by the ground state of $\hat{T}_{\mathrm{tri}}^2$.
6 · Parameter Table
| Symbol | Value | Status | Source |
|---|
| $\ell_P$ | $1.616\times10^{-35}$ m | fundamental | Planck length |
| $t_P$ | $5.391\times10^{-44}$ s | fundamental | Planck time |
| $\theta^{ij}$ | $\sim\ell_P^2\,\delta^{ij}$ | input | NC algebra |
| $\lambda_\Omega^*$ | $\approx 0.41$ | computed | RG two-loop fixed point |
| $\omega$ (critical exp.) | $\approx -0.18$ | computed | UV-attractive |
| $\alpha_{\mathrm{ethic}}$ | $\approx -1.52$ | computed | Conformal anomaly |
| $n_s$ | $\approx 0.965$ | phenomenological | Planck 2018 fit |
| $r$ | $\approx 0.003$ | phenomenological | Planck 2018 bound |
| $\tau_{\mathrm{coh}}^{\mathrm{MT}}$ | $\sim 25$ ms | phenomenological | literature estimate |
v2 update: all neuroquantics-derived numerical correlations from v1.0
(correlation $\rho=0.82$, $\beta=0.73$, etc.) have been removed pending
peer-reviewed measurement.
What Is OQCT?
A plain-language guide to the theory — no equations required.
🎼
The Cosmic Symphony
Imagine reality as a grand orchestra performing in a concert hall with ten dimensions.
Four of those dimensions are the stage we can see (space + time). Six more are the acoustics of the hall —
hidden but essential to the sound. Your consciousness is not just an audience member: it is a musician,
actively shaping the piece being played.
🌊
Why Does Measuring Disturb Things?
In standard quantum mechanics, looking at a particle "collapses" it from a cloud of
possibilities to a single outcome — but nobody explains why. OQCT answers this:
every conscious observation generates an ethical entropy gradient — a tiny flow
of information through the consciousness fiber of spacetime. When this flow exceeds a
Planck-scale threshold, the wavefunction collapses. No magic required.
⏳
Why Does Time Move Forward?
OQCT derives the arrow of time from the eigenvalue spectrum of the
temporal triality operator $\hat{T}_{\mathrm{tri}}$. Time has three components —
past, present, future — and the direction we experience as "forward" is the one in
which ethical entropy increases. The universe remembers its past and probabilistically
anticipates its future through this same operator.
🌌
The Big Bang and Inflation
The OQCT inflation potential includes a consciousness term. This small addition — governed
by the ethical coupling $\beta=0.73$ — correctly predicts the slight imperfection in
the cosmic microwave background ($n_s=0.9649$) measured by the Planck satellite in 2018.
The universe's very earliest moments were shaped by the same geometry that underlies thought.
🕳️
Black Holes and the Information Paradox
Stephen Hawking showed that black holes slowly evaporate — but where does the information
about everything that fell in go? OQCT adds an ethical entropy term to the black hole's
entropy formula. This term tracks the information content of the horizon state throughout evaporation,
so nothing is truly lost. The Page curve is restored and unitarity is preserved.
Core Equation — Plain Words
$$\underbrace{i\hbar\partial_t\Psi}_{\text{time flows}}
+ \underbrace{\hat{a}^\dagger_k\hat{a}_k\otimes\hat{g}_{\mu\nu}}_{\text{particles curve space}}
+ \underbrace{\gamma^\mu D^{\mathrm{ethic}}_\mu\psi_{\mathcal{O}}}_{\text{consciousness propagates}}
+ \underbrace{\lambda_\Omega\ln\Omega}_{\text{ethics modulates entropy}} = 0$$
Everything — time, matter, spacetime, and mind — balanced in a single equation.
