Science Fiction Meets Three Axioms

Could you travel backwards in time, visit the past, or create a causal loop?

The interaction graph is a directed acyclic graph (DAG) — a structural consequence of the axioms, not a dynamical accident. Every edge in the graph advances phase by a positive amount. A closed timelike curve would require returning to the same event with accumulated phase, demanding a single event carry two different phase values simultaneously. This is a contradiction, not a difficulty.

Theorem 3.1 (Time): The interaction graph is acyclic. No closed timelike curves can form regardless of spacetime geometry or matter content.

Could a warp drive, hyperspace jump, or any mechanism allow travel or signaling faster than light?

The speed of light is not an imposed speed limit — it is the universal phase propagation speed, derived from the requirement that observer loops close simultaneously in space and time. The relationship L = cT is a geometric identity, not a law that could be circumvented by clever engineering. A massive observer cannot reach c because its cycle period diverges: loop closure fails before the limit is reached. Any signal between events must propagate along edges of the interaction graph, each bounded by c.

Proposition 4.2 (Speed of Light): No physical process propagates faster than c. Theorem 6.1 (Lorentz Invariance): A massive observer cannot reach v = c.

Could spacetime itself be warped to move a bubble of space faster than light, as in the Alcubierre drive?

Warp drive proposals rely on exotic matter configurations to reshape spacetime geometry. But in this framework, spacetime is emergent from the coherence geometry of the observer network. The metric is not a free field that can be sculpted — it is determined by coherence conservation and loop closure across all observers in the region. Warping it into an Alcubierre configuration would require either violating coherence conservation or breaking the loop closure of every observer the bubble passes through. Both are axiomatically impossible.

Could a wormhole be held open and used as a shortcut between distant points in space?

Wormholes exist in the framework — they are the geometric face of entanglement (ER = EPR). A relational invariant between two spatially separated observers manifests simultaneously as quantum entanglement and as a non-traversable Einstein-Rosen bridge. But the throat area is exactly saturated at the entanglement entropy. Any independent signal through the wormhole would carry additional coherence, requiring a larger throat than the Einstein equations source. The geometry cannot accommodate it. Geometric non-traversability and quantum no-signaling are dual expressions of the same constraint.

Theorem 4.1 (ER-EPR): The wormhole is non-traversable. Corollary 4.2: Non-traversability and no-signaling are dual.

Does the universe split into copies every time a quantum measurement occurs?

The coherence sheaf has a unique global section on the time-ordered nerve of the interaction graph, because the DAG structure makes the geometric realization contractible (vanishing first cohomology). The coherence future is uniquely determined — there is no branching. Quantum indeterminacy is real: the outcome sheaf is multivalued, reflecting Kochen-Specker contextuality. But different outcomes are different ways of realizing the same coherence budget within a single evolving universe, not copies in parallel branches.

Corollary 3.1 (Sheaf Section Uniqueness): The coherence future is uniquely determined. No branching of the coherence sheaf occurs.

Are there other universes with different laws of physics, different constants, or different histories?

The axioms define a single coherence measure on the entire σ-algebra of observer events — a global conservation law, not one that applies per universe. All events lie on a single partially ordered set. Causally disconnected regions (as in eternal inflation) are consistent with the framework, but they are parts of one spacetime governed by one coherence conservation law, not separate universes. The string landscape question (why these constants?) is partially addressed: the observer loop viability conditions severely constrain which solutions can host observer networks, selecting for Λ in a narrow range near zero.

Could a machine run forever, producing energy from nothing?

Coherence is conserved on every Cauchy slice (Axiom 1) and every observer cycle has a minimum coherence cost. You cannot extract more work than you have coherence to sustain, and you cannot create coherence from vacuum. This is not merely the first and second laws of thermodynamics restated — it is their derivation from something deeper. The thermodynamic arrow, energy conservation, and the impossibility of perpetual motion all follow from the same axiom.

Could a conscious observer fluctuate into existence from thermal noise in an empty universe?

Two independent arguments rule out Boltzmann brains. First, a single isolated observer has zero coherence content and is structurally impossible (Multiplicity, Theorem 2.1). At least three mutually defining observers are required for the full axiom set to be non-vacuous. Second, and more fundamentally: complexity does not come for free. The relational invariants that constitute a complex structure like a brain require the entire bootstrap hierarchy to have been traversed — division algebras before gauge groups, gauge groups before particle spectrum, particles before bound states. Each layer depends on the previous one having crystallized. The bootstrap is the only mechanism the framework provides for generating new relational invariants from existing ones. A thermal fluctuation would need to instantiate every layer of this hierarchy simultaneously without the process that creates them. This is not merely improbable — it is structurally impossible, like trying to build the tenth floor of a building without the nine below it.

Theorem 2.1 (Multiplicity): A single observer has C(Σ) = 0. The bootstrap hierarchy has no shortcut: each layer of relational invariant complexity requires the previous layer.