Theory · Foundations
What is known, what is debated, what we are guessing
Every entry states what the work establishes and, just as importantly, what it does not. Nothing here is a load-bearing argument for Adjacency Theory.
General relativity
Geometry responds to stress-energy
The Einstein field equations relate spacetime curvature to the stress-energy tensor. Geometry is dynamical and sourced; it is not a fixed backdrop.
- Establishes
- Any proposal that changes effective geometry inherits an energetic bill.
- Does not establish
- That the bill is payable, or that arbitrary geometries are reachable.
Local causal structure
Light cones bound signal propagation locally. No matter how geometry is arranged, the causal structure it defines constrains what can influence what.
- Establishes
- A hard filter every AT proposal must pass at AT-4.
- Does not establish
- That global shortcuts are impossible in principle — only that they must be causally consistent.
Quantum information
Nonclassical correlation without signalling
Entangled systems display correlations no local hidden-variable model reproduces, yet the no-communication theorem forbids using them to transmit information.
- Establishes
- Correlation strength is a real, quantifiable relational resource.
- Does not establish
- Any communication channel. This is the single most common misreading of the field.
Mutual information as a relational measure
I(A:B) = S_A + S_B − S_AB quantifies total correlation between subsystems and is well-defined for any bipartition.
- Establishes
- A candidate, physically motivated replacement for the arbitrary R_ij in AT-0.
- Does not establish
- That any function of I is a distance, let alone a spatial one.
Holography and emergent spacetime
Van Raamsdonk (2010) — building spacetime with entanglement
In holographic settings, reducing entanglement between boundary regions is associated with pinching off the connectedness of the bulk geometry.
- Establishes
- A concrete setting where geometric connectedness tracks a quantum-information quantity.
- Does not establish
- That the same relationship holds in our universe, or at laboratory scales.
Maldacena & Susskind (2013) — ER = EPR
A proposed correspondence between entangled black-hole pairs and Einstein-Rosen bridges: entanglement and geometric connection as two descriptions of one thing.
- Establishes
- A serious conjecture that relation and geometry may be dual descriptions.
- Does not establish
- A traversable shortcut. The bridges in question are non-traversable.
Gao, Jafferis & Wall (2016/17) — traversable wormholes
A double-trace boundary deformation renders a wormhole traversable in a holographic model, using negative average null energy — without violating causality.
- Establishes
- That traversability can be constructed in a controlled model, and that it requires a coupling between the two sides.
- Does not establish
- A faster-than-light shortcut. The traversal is never faster than the boundary channel that enabled it.
Where Adjacency Theory begins
The controllability question
If geometry is emergent from relational degrees of freedom, then there exist controllable variables, a response function, and physical constraints governing a deliberate adjacency change. AT exists to identify all three — or to establish that they cannot exist.
- Establishes
- Nothing. This is the speculation under test.
- Does not establish
- Anything at all until AT-3 through AT-6 produce results.
Standing limitations