Quantum Matrix: A Critical-Point Autonomous Computational Universe

Abstract

We propose a fresh framework in which all mass organizes around a critical line/point and light acts as the global read/write mechanism. A local quantum mirror resolves an indeterminate quantum state into a definite record by sampling according to quantum probabilities; General Relativity (GR) then carries that record deterministically along null geodesics. The critical line separates particle and anti-particle symmetry sectors; mass clustering toward the line amplifies gravitational effects while preserving GR geometry and the value of \(c\). The universe functions as an outcome-agnostic, massively parallel computer: matter stores state/history, radiation performs read/write, and local mirrors perform stochastic internal updates without altering the GR mesh. We outline postulates, minimal derivations, falsifiable predictions (GW ringdown envelopes, photon-ring contrast vs frequency, curvature-scaled phase noise), and a compact roadmap. Time and space are treated as emergent order from the composition of resolution events, enabling infinite variability within finite capacity.

Synopsis

• Critical line (CL): a universal interface hosting mass organization; across the CL lies anti-particle symmetry.
• Quantum mirror (QM): at each "read" event, QM converts indeterminacy to a definite state by Born sampling, then writes to matter & radiation.
• GR mesh: GR fixes null cones/geodesics, tethering propagation at \(c\) and preserving causal order globally.
• Gravity: mass clustering toward the CL amplifies pull while keeping GR's geometry and angularity intact.
• Universe as computer: matter = memory; light/GWs = read/write; QM = local compute; GR = deterministic routing.

Core Postulates

1. Common origin & CL: all quantum states share a singular origin; the critical line (CL) is the ubiquitous interface separating particle/anti-particle symmetry sectors.
2. Mirror resolution: a quantum mirror at event \(x\) samples an outcome \(a\) with \(p(a|x)=\mathrm{Tr}(E_a\rho_x)\) and writes it to matter/radiation; this does not alter \(T_{\mu\nu}\).
3. GR preservation: Einstein's equations \(G_{\mu\nu}=8\pi G\,T_{\mu\nu}\) fix \(g_{\mu\nu}\), null cones, and geodesics; the mirror is null-supported and retarded, so causality and \(c\) are preserved.
4. Mass clustering & gravity: mass tends to organize around the CL; the closer the clustering, the stronger the gravitational effect—without violating GR.
5. Light as read/write: photons/GWs carry records along null geodesics; horizons act as amplified mirrors without path changes.
6. Finite basis, infinite variety: a few hundred interacting state subdivisions (basis modes) can generate unbounded complexity when composed over the GR mesh.

Emergent Time, Mass, Space & Scale from Hyperlocal Observation

Claim (operational). What we call time, mass, space, and scale are emergent descriptions of hyperlocal resolution (the quantum mirror) composed over GR's global mesh. The mirror resolves indeterminate microstate into a definite record locally; GR carries that record along null geodesics. The "illusions" are not unreal—they are the macroscopic bookkeeping we infer from many such local resolutions.

• Time ≡ ordering of resolutions. Proper time operationally arises as the causal order of resolution events along worldlines (null/timelike reachability defines the arrow).
• Mass ≡ persistent record that bends routes. Mass is the durable part of state that sources curvature via the observed stress–energy; it's the memory left by repeated resolutions.
• Space ≡ relational separation in the mesh. Spatial distance is an emergent relation from the null-cone structure (how many lightlike hops/latency between nodes), not a primitive container.
• Scale ≡ local resolution length. A single parameter \(\ell\) (mirror width) sets the effective "pixel size" of observations; apparent scale changes with \(\omega \ell\) (frequency vs resolution).

Minimal formal sketch

Let \(\mathcal{E}\) be the set of resolution events and \(\prec\) the GR causal order. Then: (i) time is the partial order \((\mathcal{E},\prec)\) restricted to worldlines (proper time is path length defined from observed \(g_{\mu\nu}\)); (ii) mass is the persistent component of the observed state that contributes to \(T_{\mu\nu}\) and thus to \(G_{\mu\nu}=8\pi G\,T_{\mu\nu}\); (iii) space is the relational structure induced by null reachability/latency on spacelike slices; (iv) scale follows from the null-supported kernel \(K_\ell\) via a form factor \(\mathcal F(\omega\ell)\).

Observable corollaries

• Null-preserving envelopes: high-frequency content shows a universal roll-off \(\mathcal F(\omega\ell)\) with no change to GR arrival times or lensing paths.
• Resolution-set scale: feature contrast (e.g., photon ring) varies with frequency as \(\omega\ell\), identifying \(\ell\) as an operational "scale."
• Clock building: any physical clock is a stabilized sequence of resolution events; its rate is set by the local null geometry (gravitational redshift) and \(\ell\)-limited readout.

Minimal Derivations (geometry kept narrow)

1) Mirror chooses; GR delivers

At event \(x\) with local state \(\rho_x\) and POVM \(\{E_a\}\), the mirror draws \(a\) with \(p(a|x)=\mathrm{Tr}(E_a\rho_x)\) and updates

\(\rho_{x\to a}=M_a\rho_x M_a^\dagger / p(a|x).\)

The observed field is a null-preserving, retarded map:

\(\Phi_{\rm obs}(x)=\int d^4y\sqrt{-g}\;K_\ell(x,y;g)\,\Phi(y),\)

\(K_\ell \propto \Theta(t_x{-}t_y)\,\delta(\sigma(x,y))\,f_\ell.\)

\(\delta(\sigma)\) pins support to the null cone: GR causality and \(c\) are preserved while the mirror only changes internal labels (phases/chirality).

2) Internal reflection leaves geometry intact

For a complex scalar with \(\mathcal L=-g^{\mu\nu}\partial_\mu\phi^*\partial_\nu\phi - V(|\phi|^2)\), the internal reflection \(\phi\mapsto \phi^*\) flips the Noether current but leaves \(T_{\mu\nu}\) unchanged, hence leaves \(g_{\mu\nu}\) and geodesics unchanged by Einstein's equations.

3) Event horizons as amplified mirrors

Near trapped surfaces the effective kernel acquires near-returns (no new paths), yielding a local reflection gain while null geodesics remain those of GR. Observable consequence: frequency-scaled envelopes on ringdowns without shifting arrival times.

Gravity from CL clustering (heuristic)

Let \(\rho\) denote mass density clustered at proper distance \(d\) from the CL. A simple monotone "pull" functional is

\(\Gamma(d)=\int_0^d \alpha(u)\,du,\quad \alpha'(u)\!\ge\!0,\)

with \(\alpha\) increasing as clustering tightens. GR still governs metric curvature via \(T_{\mu\nu}\); the CL hypothesis states that physical processes organize \(T_{\mu\nu}\) to increase \(\Gamma\), amplifying gravity while preserving GR's equations and angular structure.

The Universe as an Outcome-Agnostic Computer

• Routing (GR): null cones/geodesics define a global, deterministic mesh; curvature sets latency and path diversity.
• Compute (QM): local stochastic kernels act on internal labels at resolution events; spacelike updates commute (safe parallelism).
• Memory (matter): stress–energy and quantum numbers store persistent state/history; horizons act as reflective caches.
• I/O (light & GWs): read/write carriers moving at \(c\) along the mesh; no path changes under the mirror.
• Capacity: a finite modal basis (hundreds of modes) suffices to generate infinite apparent variety by composition; time/space emerge as ordering and separation in the causal DAG.

Predictions & Tests

1. GW ringdown envelopes (null-preserving): Post-Kerr residual PSD follows a one-parameter envelope \( \mathcal F(2\pi f\,\ell)\) without shifting geodesic arrival times. Test: stack events; collapse vs \( \kappa=2\pi f\,\ell\).
2. Photon-ring contrast vs frequency: Slight frequency-dependent smoothing of sharp features in EHT images, ring location fixed by GR. Test: multi-band contrast scaling.
3. Pulsar timing through deep potentials: Phase variance with curvature along null paths: \( \langle\delta\varphi^2\rangle \sim (\omega\ell)^2 \int R_{abcd}k^a k^b k^c k^d\,d\lambda.\)
4. Strong-lensing micro-speckle: Same images/paths as GR, tiny chromatic contrast ripples set by \(\ell\).
5. Lab analogs: Optical cavities with null-preserving partial reflectors emulating \( \mathcal F(\omega\ell) \) without path shifts.

Falsifiability

• Any observation of residuals that imply path/arrival shifts inconsistent with GR geodesics falsifies the null-preserving mirror.
• Failure to find a consistent \(\ell\) across events/data classes when analysis systematics are controlled weighs against universality.
• Evidence that internal reflections modify \(T_{\mu\nu}\) at resolution events (beyond small radiative backreaction) falsifies geometry preservation.

Roadmap

1. Phase 1: Derive/fit \( \mathcal F(\omega\ell)\) on real GW ringdowns; cross-validate \(\ell\) across detectors/events.
2. Phase 2: Photon-ring contrast vs frequency; pulsar-timing curvature variance; lensing micro-speckle statistics.
3. Phase 3: Kernel-level link to field theory (BRST-safe), mapping \(\ell\) to a derived micro-scale; cosmology fits (null tails).

Data & Code Availability

Minimal scripts (NumPy/SciPy/matplotlib) suffice to reproduce ringdown residual envelopes and \(\ell\) estimates on public LOSC/LVK datasets. We keep a one-file demo in the repository; no external GW libraries are required.