Origens of Action-Wave Space

From Light in a Box to Action–Wave Space

For more than a century, physicists have been searching for answers to two closely related questions:

What are particles actually made of?
Where does the probabilistic nature of quantum mechanics really come from?

Rather than taking electrons, photons and spacetime as fundamental ingredients, the AWS framework asks whether they might all be different manifestations of a single underlying structure. A simple thought experiment with light trapped in a box provides a natural route into this idea.

Thought Experiment: Light Trapped in a Box

Imagine a perfectly reflecting, massless box filled with light bouncing around inside.

Light carries energy and momentum. By the famous relation \(E = mc^2\), energy behaves like inertial mass. So when light is trapped in a box:

The box becomes harder to accelerate when there is more light inside.
From the outside, you only feel the total inertia: box plus trapped light.

\(\text{Trapped light behaves as if it has mass.}\)

It is tempting to push this idea to the extreme:

\(\text{Maybe every particle is really a wave trapped in a tiny “box”.}\)

Perhaps electrons, protons and all other particles are not point-like objects, but tiny self-contained wave patterns.

Why “Particle = Light in a Spacetime Box” Fails

If we try to model an electron as light trapped in a small region of ordinary spacetime, serious problems appear:

What is the box made of? Some field or geometry must confine the light. But then we must explain the origin of that confining structure too.
Electromagnetism and gravity do not balance easily. Light spreads out, gravity pulls energy together. In general relativity, it is extremely hard to get a stable, particle-like lump of pure radiation without fine-tuning.
Numbers do not match observations. When you try to reproduce the observed mass, charge and spin of known particles, simple “light-in-a-box” models in spacetime fail quantitatively.

This suggests that the basic idea “particle = trapped wave” might be right, but the usual assumption is wrong:

\(\text{What if the wave is not an electromagnetic wave in spacetime,}\\ \text{but a more fundamental wave living in a deeper space?}\)

Turning the Picture Around: Spacetime as a Shadow

AWS takes a radical but simple step:

Do not assume spacetime is the fundamental arena.
Start instead from a single underlying wave, described by a real scalar phase field \(\Phi\).
Let ordinary spacetime and familiar fields emerge as “shadows” or projections of this deeper structure.

\(\text{It is not light that gets confined in spacetime.}\\ \text{A deeper Action–wave is confined in a deeper space,}\\ \text{and we see its shadows as particles and fields.}\)

In other words, AWS does not put waves inside spacetime. It lets spacetime itself emerge from the behaviour of a more fundamental wave.

The AWS Layer: A Single Fundamental Phase Field

At the deepest level, AWS assumes there is only:

\(\Phi: \text{ a single real scalar phase field on a 4D geometric layer.}\)

This phase field \(\Phi\) assigns a well-defined phase value to every point of the underlying 4D geometry. Only differences of phase matter physically, not the absolute value, so shifting \(\Phi \mapsto \Phi + \text{const}\) changes nothing observable.

On this fundamental AWS layer:

The phase field \(\Phi\) evolves according to a wave equation, so its dynamics are those of a classical wave spreading and focusing on a curved background.
Closed loops in the geometry must return to the same phase, leading to a simple quantization rule:
\(\displaystyle \oint \partial_\mu \Phi\, dS^\mu = 2\pi n\hbar, \quad n \in \mathbb{Z}.\)

This is the AWS version of “only certain standing waves fit in the box”. The “box” is now a compact region of the fundamental geometry, and the allowed standing waves are the quantized, interference-stable patterns of the single phase field \(\Phi\).

Why We Never See Action–Wave Space Directly

A central idea in AWS-Ontology is that we are not outside observers looking at AWS from a distance. We are made of AWS excitations ourselves.

Atoms, electrons, photons, clocks and detectors are all stable, compact patterns of the phase field \(\Phi\) and its flux.
Our measuring devices—rods and clocks—are built from those patterns.
Any experiment we do sends AWS excitations around and reads their effect on other AWS excitations.

That means we never have direct access to the underlying Action–Wave manifold. Instead, what we reconstruct is a coarser, operational layer that we call “spacetime”.

\(\text{Operational spacetime is a bookkeeping layer}\\ \text{built by AWS excitations about AWS excitations.}\)

Mathematically, AWS represents this by a smooth projection

\(\pi : \text{AWS} \longrightarrow \text{spacetime}, \qquad D_x := \pi^{-1}(x).\)

To each spacetime event \(x\), AWS associates a compact internal domain \(D_x\) in Action–Wave Space. The geometry and flux content of \(D_x\) encode what we can observe at \(x\) with our rods, clocks and detectors.

From a Deterministic Action Wave to Quantum Probabilities

On the AWS layer, the phase field \(\Phi\) evolves smoothly and deterministically as a classical wave. Quantum-looking features appear only after projection to spacetime.

Very roughly:

The AWS field \(\Phi(S)\) carries a conserved flux of Action phase.
A spacetime amplitude \(\psi(x)\) is obtained by gathering contributions from the internal domain \(D_x\) using a causal (retarded) kernel:

\(\displaystyle \psi(x) \sim \int_{D_x} G_R(x; S)\, e^{i\Phi(S)/\hbar}\,d^4S.\)
With the right normalization, the conserved flux in AWS projects to the usual Born probabilities \(|\psi(x)|^2\) in spacetime.

In AWS-Measurement terms, “collapse” and outcome selection are not extra rules. They describe how interference-stable patterns in Action–Wave Space survive or are filtered when we condition on a particular measurement outcome in spacetime.

Particles as Trapped Action–Waves

We can now revisit the original light-in-a-box idea with the AWS picture in mind:

Particles are not point-like objects. They are stable, quantized patterns of the scalar field \(\Phi\) confined to compact domains in Action–Wave Space.
These “trapped Action–waves” project into spacetime as massive, inertial particles with definite charges and spins.
The detailed internal topology of the compact domains selects which particle types are allowed and how they interact.

From our spacetime perspective, we see electrons, photons and other fields. From the AWS perspective, these are simply different ways a single underlying wave can organize itself while remaining phase-coherent and flux-conserving.

Self-Induced Curvature: How Action–Waves Confine Themselves

In AWS, waves do not need a pre-built “box” to get trapped. The scalar phase field \(\Phi\) creates its own confining structure: its energy and flux curve the underlying Action–Wave Space, and that curvature bends the wave back onto itself.

Where the phase gradient \(\partial_\mu \Phi\) is large, the associated energy density is high. AWS couples this energy back into the geometry of Action–Wave Space through an Einstein-like relation:

\( G_{\mu\nu}(S) \;\propto\; T_{\mu\nu}[\Phi](S), \)

Here \(G_{\mu\nu}\) measures curvature of the AWS metric and \(T_{\mu\nu}[\Phi]\) is the stress–energy of the phase field. Concentrated Action–flux bends the “rays” of \(\Phi\), much like a dense medium bends light rays.

Regions with strong flux act like self-generated “gravitational lenses” in Action–Wave Space.
The wavefronts are bent into closed loops and compact domains instead of spreading out forever.
Only those loops that satisfy the quantization condition
\(\displaystyle \oint \partial_\mu \Phi\, dS^\mu = 2\pi n\hbar\)
are dynamically stable.

The result is a self-consistent picture:

The wave \(\Phi\) concentrates its own flux.
This concentration curves Action–Wave Space.
The curvature feeds back to trap the wave in compact, quantized domains.

From our emergent spacetime viewpoint, these self-confined Action–waves appear as massive particles with definite quantum numbers. From the AWS viewpoint, they are simply the lowest-energy, interference-stable “vortex” patterns of a single scalar field living on a curved, quantized Action–Wave geometry.

AWS in One Sentence

At the most fundamental level, AWS posits a single real scalar phase field in a 4D Action–Wave Space; particles, fields, spacetime and quantum probabilities are what this one deterministic Action–wave looks like when projected into the coarser world described by our rods, clocks and detectors.