From One First Principle to the Physics We Observe
Modern physics is powerful, but it begins from several different “starting points.” Quantum mechanics opens with Hilbert spaces and operators. Quantum field theory adds fields, gauge symmetry, and renormalization. General relativity starts with spacetime geometry and curvature. These layers fit together operationally, yet conceptually they look like a toolkit assembled from multiple foundations.
Action–Wave Space (AWS) asks whether that patchwork is inevitable. What if we insist on a single first principle, and treat everything else—quantization, probability, spacetime, forces, and matter—as consequences of that one principle plus consistency (causality, conservation, and global coherence)? The goal is not to “reinterpret” known physics, but to explain why the familiar structures show up at all.
The core idea is simple to state: Action is primary. Instead of starting with particles, operators, or even spacetime, AWS starts with a single phase-like quantity whose job is to keep track of accumulated action.
1) If Action is Primary, Phase is the Natural Primitive
In standard quantum theory, phase is already doing the heavy lifting. In the path-integral viewpoint, every possible history contributes with a phase weight of the form \(e^{iS/\hbar}\). Interference—constructive and destructive—comes from how these phases add up. So action is not just a classical bookkeeping device; it directly controls what becomes observable.
AWS takes that seriously and reverses the usual order of explanation. Instead of “choose dynamics → compute an action → get a phase,” AWS treats a single scalar phase field \(\Phi\) as the starting object, with physical meaning tied to accumulated action. Once you commit to that, the central question becomes: what structure must the world have so that a globally coherent phase field can exist and evolve causally? For the conceptual entry point, see AWS-Phase.
2) Quantization as Global Coherence (Why Integers Appear)
“Quantization” often sounds like an extra rule imposed on nature: operators don’t commute, eigenvalues come in discrete sets, and probabilities are postulated. AWS tries to push quantization deeper—into a requirement of global consistency.
If the physically meaningful quantity is the phase factor \(e^{i\Phi/\hbar}\), then that factor must be single-valued. When you go around a closed loop and return to the same point, the phase factor must return to itself. That forces the net phase change around the loop to be an integer multiple of \(2\pi\hbar\). In plain terms: coherent interference around loops turns phase into counting.
Once this “loop consistency” is taken seriously, two big things follow. First, topological winding becomes a real physical resource (not a mathematical decoration). Second, the propagation of phase naturally picks out characteristic directions—lightcone-like directions—because causal phase transport can’t spread arbitrarily. This is how AWS motivates a Lorentzian causal structure and a compatible flux geometry from a single phase field, rather than assuming spacetime geometry first. For the detailed geometric construction and the quantization logic in this setting, see AWS-Geometry-I.
3) What “Spacetime” Means in AWS: An Operational Shadow
In everyday physics, we speak as if spacetime is the primary arena: events happen “at” points \(x^\mu\). But experimentally, what we actually have are records—detector clicks, pointer readings, interference fringes, correlated outcomes. Those records are already the result of a filtering process: only certain features of the underlying dynamics become accessible as stable, communicable, repeatable facts.
AWS makes this explicit. “Spacetime events” are treated as labels for equivalence classes of deeper configurations—coarse-grained descriptors of what a measurement setup can reliably distinguish. That shifts the conceptual burden: instead of postulating spacetime as the stage, AWS treats spacetime as an emergent bookkeeping layer for operationally stable outcomes. This ontological reading—what is real, what is emergent, and what “events” actually refer to in this framework—is developed in AWS-Ontology.
4) Why Compact “Internal Rooms” Appear: Stability Forces Topology
Once phase coherence and conserved flux are central, you naturally run into a stability question: where can coherent phase patterns live without dispersing or becoming inconsistent? AWS answers by introducing compact internal domains associated to operational events—small “rooms” where quantized flux and interference stability can lock in. The intuition is similar to how vortices or flux tubes become stable objects in other coherent media: conservation plus global coherence encourages localized, structured configurations.
But AWS goes further: it argues that not every compact topology is viable. A scale-invariant stability/variational principle strongly restricts which internal geometries can support quantized flux without pathological curvature behavior. The upshot is a narrow, stable topology class that becomes a structural backbone for what appears in the low-energy projection. This topology-selection mechanism is developed in AWS-Fiber.
5) Projection: How AWS Produces Observable Amplitudes
If operational spacetime is an emergent label space, then you need a precise way to map fundamental configurations into observable amplitudes. AWS implements this with a causal projector: a retarded kernel that ensures nothing propagates backward in time in the operational description.
At the level of intuition, this kernel plays the role of a “rendering engine.” The underlying phase geometry contains far more information than any detector can access; the projector filters out what cannot appear as a stable spacetime record, and it does so in a way that respects causality and locality. Schematically, the observed amplitude is built as a fiber integral, e.g. \(\psi(x)=\int_{D_x} G_R(x,S)\,A(S)\,e^{i\Phi(S)/\hbar}\,d\mu(S)\). The microlocal/analytic backbone for treating this projector rigorously is developed in AWS-Kernel.
6) Why Probabilities Look Like |ψ|² (Born Rule Without a Postulate)
Textbook quantum mechanics tells us to compute probabilities using \(|\psi|^2\). AWS aims to explain why that rule is the natural output of a causal projection, rather than an independent axiom.
The key idea is that a good projection should preserve “norm” information: it should not arbitrarily create or destroy total weight when mapping from the fundamental configuration space into operational spacetime. When the projection behaves (approximately) like an isometry, the squared magnitude of the projected amplitude becomes the natural pushed-forward measure on spacetime. In the same language, the measurement calculus (POVMs and instruments) emerges from how regions and readouts act through the projector. This operational measurement structure and its testable dynamical consequences are developed in AWS-Measurement.
7) The Big Picture: One Non-Circular Derivation Chain
At this stage the storyline has a clear spine: a single phase field supplies global coherence; global coherence enforces quantized flux; stable flux sectors force compact internal structure; compact structure enables a causal projection; causal projection produces operational amplitudes; near-isometric projection yields Born-like probabilities and modern measurement objects.
The important point is that this is meant to be non-circular. Probability is not assumed to get quantization; quantization is not assumed to get geometry; geometry is not assumed to get spacetime. Instead, these are presented as successive constraints that become unavoidable once you take a globally coherent action-phase seriously. The unified “framework theorem” style synthesis of this chain—what is assumed, what is derived, and how the modules lock together—is stated in AWS-Framework.
8) Gravity Returns as an Infrared Interface
Once you have an operational spacetime description, you can ask what effective dynamics governs it in the long-distance (infrared) limit. AWS’s claim is not that it replaces relativity with something unrelated; it is that classical general relativity reappears as the natural coarse-grained description of the projected sector, with additional structure controlling high-curvature regimes through phase coherence and flux constraints.
In other words, the familiar Einsteinian picture is treated as the correct macroscopic language for the operational layer, while the underlying phase geometry provides a UV completion and a principled origin for curvature bounds, projection observables, and high-curvature phenomenology. This gravity sector is developed in AWS-QG.
9) From Fixed Internal Structure to the Standard Model
The Standard Model is usually presented as a list of ingredients: gauge group, fermion representations, three families, a Higgs sector, and a set of couplings. AWS aims to turn that list into an output: once the internal compact domain has a fixed, stable topology and supports quantized flux sectors with nontrivial holonomy, the space of admissible low-energy fields becomes highly constrained.
The AWS claim is that gauge structure and matter content can be read as the projection of internal holonomy/flux organization, and that Yukawa-like structures arise as geometric overlap data rather than arbitrary inputs. The full sector-level construction is presented in AWS-SM.
10) Benchmarks: Atoms and Black Holes as Stress Tests
A framework that claims to derive quantum structure needs hard benchmarks. AWS emphasizes two extremes: precision microscopic spectra and deep gravitational thermodynamics. On the atomic side, the hydrogen spectrum is treated as a “must-pass” test because it probes quantization, relativistic structure, and radiative-scale corrections in one compact package; this benchmark is developed in AWS-H. On the gravitational side, black-hole entropy is used as a test of whether the same phase/flux structure can reproduce area-law thermodynamics and its corrections without importing extra UV regulators; this benchmark is developed in AWS-Entropy.
The Whole AWS Story in One Derivation Chain
- Start: treat a single scalar phase as accumulated action, so interference is fundamental rather than appended. (See AWS-Phase.)
- Meaning: interpret “events,” “objects,” and “spacetime labels” as operationally stable descriptors of deeper phase configurations. (See AWS-Ontology.)
- Geometry: require causal, globally coherent phase transport, which forces a Lorentzian (lightcone) structure plus a compatible flux geometry and quantization-by-coherence. (See AWS-Geometry-I.)
- Topology: demand stable, finite-energy flux sectors, which strongly restricts admissible compact internal domains and fixes the structural “room” where coherence can lock in. (See AWS-Fiber.)
- Projection: map internal configurations to operational spacetime amplitudes through a retarded (causal) kernel, acting as a physical “rendering” operator. (See AWS-Kernel.)
- Probability & measurement: obtain Born-like weights and POVM/instrument structure as push-forwards of a near-isometric projector, with testable dynamical scaling laws. (See AWS-Measurement.)
- Synthesis: state the full non-circular dependency chain explicitly—what is assumed, what is derived, and how the modules lock together. (See AWS-Framework.)
- Gravity: recover classical GR as the infrared interface of the operational layer, with high-curvature behavior controlled by phase/flux consistency. (See AWS-QG.)
- Standard Model: read gauge structure and matter content as low-energy projections of fixed internal holonomy/flux organization, with couplings and mixings tied to geometry. (See AWS-SM.)
- Benchmark (gravity/thermo): reproduce black-hole entropy and its corrections from the same phase/flux backbone. (See AWS-Entropy.)
- Benchmark (atomic/precision): derive hydrogen spectral structure as interference-stable modes selected by phase coherence and projection. (See AWS-H.)