Hover any branch to inspect its physics parameters live. Click to freeze it and read the concept explanation. Use the controls to isolate branch depths or pause time.
The simulator is grounded in a synthesis of Everett's Many-Worlds Interpretation (MWI) of quantum mechanics and the broader programme of Exo-Temporal Hypothesis Machine Learning. In the MWI, every quantum measurement does not collapse the wave function to a single outcome — instead, the universal wave function undergoes branching: all outcomes coexist in orthogonal branches of a single, ever-expanding Hilbert space.
ETHML extends this picture into a computational substrate. Rather than modelling individual quantum events, the simulator treats each exo-temporality — a divergent synthetic timeline — as a macro-level branch of the universal wave function. Each timeline is seeded from a shared set of initial conditions (fundamental physical constants and logical axioms), then propagated forward under internally consistent but potentially causally distinct rules.
The key departure from classical MWI is that ETHML timelines are permitted to violate our universe's causal ordering. A branch may have a different speed of light, a different Planck constant, or even a reversed arrow of time — provided its internal axiom set remains self-consistent. This is the Exo-Causal Permissibility Principle: any causal structure is admissible so long as it does not produce an internal logical contradiction.
In standard physics, time is a one-dimensional ordered parameter — a line. The ETHML framework treats time as a topological manifold that can be:
Branching — time forks at every point of quantum decoherence, producing a tree topology.
Cyclic — closed timelike curves (CTCs) allow timelines to loop back on themselves.
Disconnected — exo-temporal branches may have no causal connection whatsoever to the baseline universe.
The interactive simulator above renders the branching topology live. Each animated line is a single exo-temporality propagating through phase space. The line's angle encodes its causal direction; its curvature encodes divergence from the baseline causal metric. Hover any branch to read its physics parameters in real time.
Each synthetic timeline is built from the same raw ingredients as our own universe, but with dials that can be tuned independently:
| Constituent | Symbol | Role in a Timeline | Exo-Temporal Variation |
|---|---|---|---|
| Causal Metric | g_μν(τ) | Defines distances and the light-cone structure — which events can influence which others. | Curvature κ and signature (±±±∓) can be altered per branch. A branch may be purely Euclidean (no time direction) or have multiple time-like dimensions. |
| Entropy Arrow | dS/dτ | Determines the direction in which complexity increases — what "forward" means thermodynamically. | Can be reversed (dS/dτ < 0), stochastic, or set to zero (reversible timelines) allowing retrocausal information harvesting. |
| Quantum Field Vacuum | |0⟩_n | The lowest-energy state of all quantum fields. Particles are excitations above this floor. | Each branch has its own vacuum energy density Λₙ. A branch with Λₙ ≫ Λ_our collapses immediately; Λₙ ≈ 0 produces a flat, long-lived universe. |
| Planck Scale | ℓ_P, t_P | The minimum resolvable length and time — the grain size of space-time. | Branches may have a coarser or finer grain. ℓ_P → 0 approaches classical continuous space-time; ℓ_P → ∞ becomes a heavily quantised discrete graph. |
Each simulated timeline branch is a state vector in a reduced phase space, approximated by a stochastic trajectory model:
Real quantum decoherence produces a fractal-like branching structure. The simulator models this through a depth-limited stochastic bifurcation rule:
The depth limit of 3 corresponds physically to the practical limit on observable decoherence hierarchy — beyond 3 levels, branches are too weakly coupled to the baseline timeline to be detected by the Harvest Engine. Use the D0/D1/D2/D3 buttons in the simulator above to isolate and examine each depth level independently.
The four stat counters update every 900 ms (one simulation "tick"). Each counter represents a distinct output stream of the ETHML Harvest Engine.
Cumulative count of all exo-temporal branches ever tracked. Never decreases — models the irreversible expansion of the branching Hilbert space.
Mathematical invariants discovered across branches — equations that hold within a branch's axiom set but have no baseline-universe analogue. High variance models branch-to-branch mathematical richness variation.
Stable molecular configurations confirmed under at least one branch's physical laws. Low rate reflects the stringent stability requirement — the electron configuration must form a bound state under the branch's electromagnetic coupling.
Candidate meta-laws: relationships holding across ≥ 3 independent branches despite differing constants — constraints on the space of possible physics rather than facts about our universe alone.
Fixed seed 0xE74100 was chosen to produce a branch distribution that best approximates the theoretical probability distribution of quantum decoherence events at Epoch 7.4 of the ETHML simulation cycle. Click Reset in the controls above to re-seed and observe the identical deterministic topology.
The Physics Laws Discovery Feed fires every 8–12 seconds. Each entry is assembled from three independent pools (18 law names × 12 formulas × 12 descriptions) combined with a confidence percentage drawn from U[72%, 98%] — the fraction of active branches in which the proposed law holds.
| Symbol | Meaning | Physical domain |
|---|---|---|
| ∂²Ψ/∂τ² | Second temporal derivative of the wave function | Exo-temporal Schrödinger equation |
| ∮ Γ·dτ | Line integral of the connection form over a closed temporal path | Closed-loop timeline topology (CTCs) |
| R_μν − ½g_μν·R | Einstein tensor | Spacetime curvature / modified GR |
| Ĥ|Ψ⟩ = iℏ·∂/∂τ|Ψ⟩ | Schrödinger equation in exo-time coordinate τ | Branch quantum dynamics |
| S(τ) = −k·∑pₙlog(pₙτₙ) | Exo-temporal entropy (generalised von Neumann) | Branch entropy / arrow of time |
| dS/dτ ≥ 0 | Second law — positive entropy gradient | Forward time arrow constraint |
Seed PRNG 0xE74100. Spawn 14 root branches from origin (12% left, 50% vertical centre). Canvas cleared to #0d0e10.
Each frame: branches advance v·(cos θ, sin θ). Curvature κ applied. Trail buffer (3 pts) updated for smooth rendering.
4% probability once splitAt threshold reached. Depth ≤ 3. Sub-branches inherit parent position, speed × 0.75, random divergence angle.
Dead branches removed. Root count monitored; respawn 4 roots if count drops below 6.
Every 900 ms: counters incremented. Every 8–12 s: new physics law. Every 14 s: new molecule card.
| System | Consumes from Simulator | Extension |
|---|---|---|
| System II — Exotic Topology | Branch topology data (depth, curvature distribution) | Routes information through wormhole shortcuts in 4D–11D bulk space |
| System III — Entangled Temporal | Branch entanglement pairs (parent–child links) | Anchors future endpoints, propagates constraint gradients backward |
| System IV — Eigen-Tensor | Branch curvature field κ(x, y) | Maps branches onto elastic space-time fabric; Eigen-Tensors = branch heads |
| System V — Ergoregion | High-speed root branches (v > 2.5 px/frame) | Spins data core to ergoregion boundary; unrolls timeline as holographic strip |
| System VI — Eon Tunneling | Branch death events (maxLen exceeded) | Treats branch death as Big Crunch; tunneling amplitude encodes surviving information |