From the wave function to planxel synchronization

For over a century, quantum mechanics was the greatest enigma in physics — not because the equations failed, but because the world they described seemed ontologically alien. Particles behaved like waves, waves collapsed into points, and the very act of measurement seemed to violate the determinism of the universe. Concepts like "wave-particle duality," "wave function collapse," and "irreducible randomness" became almost mystical dogmas — paradoxes that physicists accepted with resignation because the mathematics worked too well to be rejected.

In the Māyā model, all these phenomena cease to be fundamental. They don't disappear — they become mere artifacts of the level of description. Quantum mechanics doesn't describe the strange nature of matter. It describes the way a discrete network of planxels synchronizes and propagates information — beat by beat, phase by phase.

Wave function as a distributed information state of the network

W klasycznym formalizmie funkcja falowa $\psi(\mathbf{x},t)$  jest matematycznym obiektem, którego $|\psi|^2$ daje prawdopodobieństwo znalezienia cząstki w danym punkcie. W ontologii Māyā $\psi$ nie jest „falą materii”, ani fizycznym polem rozciągniętym w przestrzeni. Jest rozproszonym, kolektywnym stanem informacyjnym całej sieci planxeli.

Each planxel stores a local complex information amplitude:

where $\rho$ – lokalna gęstość obciążenia informacyjnego (źródło przyszłej masy), $\theta$ – phase of the local processing cycle (source of time and phase charge).

The evolution of this amplitude in a discrete network with a full neighborhood of 26 neighbors is given by a simple difference rule, which in the continuous limit turns exactly into the Schrödinger equation:

After substituting $\hbar = E_P t_P$ and approximately $m\approx {\rho }_0{m}_P$ (where $\rho_0$​ is the basic load of the pattern in the resting state) we obtain the update rule that each planxel performs in each cycle:

Particle as a synchronized phase defect

A "particle" in Māyā is not an entity that exists and moves somewhere. It is a stable information soliton—a local, self-sustaining phase resonance that maintains its structure as it propagates through the network.

When the pattern is in a dispersed state (a large number of planxels with non-zero amplitude and weak phase correlation), it behaves like a wave: it interferes, diffracts, and travels through multiple paths simultaneously. However, when a strong local interaction with another system (a detector, a screen, another atom) occurs, the network must choose a single coherent synchronization mode – the pattern "condenses" into a single, local, stable defect.

Wave function collapse as the closure of the synchronization cycle

In the classical interpretation, the measurement causes a "wave function collapse" – a sudden, nonlinear collapse of $\psi$ to a single result. In Māyā, there is no additional, mysterious collapse process. There is only the necessity of local closure of the computational cycle.

Let us consider the simplest “measurement” model – the strong interaction of two adjacent planxels:

Niech $\sigma_1$​ i $\sigma_2$ to amplitudy dwóch sąsiadujących planxeli przed interakcją. Reguła synchronizacji w jednym takcie (przy silnym sprzężeniu $\kappa \gg 1$):

After one cycle, both amplitudes immediately become practically equal:

Double slit – the most beautiful proof of phase synchronization

The double-slit experiment is considered the “heart” of quantum mechanics – because in one setting it shows everything at once: waveform, corpuscularity, interference, and collapse.

When we send electrons individually through two slits, an interference pattern is created on the screen — as if each electron passed through both slits simultaneously. However, when we try to determine which slit it passed through, the pattern disappears, and the electrons behave like classical particles.

In Māyā, there is no paradox or observer magic. There is only a phase-locking mechanism in the planxel network.

Step by step – what's happening in the grid

1. Przed szczelinami Wzorzec elektronu jest rozproszony – amplituda fazowa $\sigma =\rho e^{i\theta }$ is non-zero over a large number of planxels. Phases in different regions are weakly correlated → position information is "smeared". 
   $$$$
2. Double Slit Passage Two narrow slits act as two narrow propagation channels. Phase patterns pass through both slits simultaneously – creating two separate "branches" of phase correlation, which begin to diverge and overlap behind the slits. This is classic wave interference: where the phases reinforce → high amplitude, where they weaken → low.
3. Screen without detector (no strong interaction) When an electron reaches the screen without prior detection, its phase pattern is still dispersed over a very large number of planxels. Upon impact, a strong local interaction occurs with a large number of screen atoms. The network must perform a single coherent closure of the synchronization cycle over a large area. The choice of a specific "impact" location depends on the microscopic phase differences across the entire interference region – these differences are maximally mixed by prior golden angle rotations. Therefore, single hits appear random, but after thousands of electrons, a classic, beautiful interference pattern is formed.
4. Detector at the Slit (Strong Early Interaction) When we place a detector at one of the slits, a strong local interaction occurs already at the slit stage. In one cycle, the phases near the detector become rapidly synchronized – one phase branch is amplified, the other is suppressed or completely extinguished. Further propagation occurs only from one slit – the two possibilities can no longer interfere. The pattern on the screen becomes a classic distribution of two Gaussian "hills" – without interference.

The Key Intuition of Māyā

There is no "magic choice" made by the observer. Nor is there any violation of causality or backward action in time.

There is only one thing: at the moment of strong local interaction, the network must perform one consistent phase-synchronization closure – otherwise it cannot continue the calculations in the next clock cycle.

Imagine a simple 2D game in which two objects move across a grid of pixels. One is the "player" and the other is an obstacle.

Most of the time, objects are in a "dispersed" state—their position is determined only with some uncertainty (e.g., the game engine uses probabilistic pathfinding or a fuzzy hitbox). The game doesn't have to decide yet whether they collide—it just keeps both possibilities open in the engine's memory.

But when objects enter into direct, strong interaction (e.g., one enters the other's hitbox), the game engine can no longer maintain two conflicting states. It must make a choice: either a collision occurs or it doesn't. This choice is immediate and irreversible – the old state is overwritten, the new one is saved, and the game advances to the next frame.

From the player's perspective, it looks as if the world has suddenly "decided" what happened. But in reality, there's no magical choice here—only necessity: the engine can't render another frame until it resolves the state conflict.

The planxel network works in exactly the same way.

• Without a detector → synchronization occurs only on the screen → both phase paths have had time to develop and interfere → we see interference bands.
• With the detector → synchronization occurs already at the slit → one phase path is selected and amplified, the other is suppressed → there is nothing left to interfere.

In the game, we don't say "the observer forced the engine to make a choice." We simply say "a collision occurred, so the code had to execute the appropriate procedure."

In Māyā, it's exactly the same: the double slit isn't a paradox. It's the most beautiful proof that reality isn't a collection of objects moving through space—it's a continuous, dynamic synchronization of information in a discrete network.

And that's why, whenever we try to "query" the network too early, we get a classic response. And when we let it run freely until the end, we get a wave-like response.

Not because nature is capricious. Because it must be consistent in every cycle.

Heisenberg's Uncertainty Principle – The Price of Finite-Time Synchronization

Heisenberg's uncertainty principle is:

• Accurate positioning requires strong local phase synchronization in a small region (large ρ, highly coherent phases between neighbors in a narrow region).
• Accurate momentum requires a long, coherent phase wave over a large area (small local
  $\rho$, uniform phase gradient over a large number of planxels).

These two states require opposite types of synchronization in the same measure:

• strong local correlation vs. weak local correlation over a large area.

It's impossible to maximize both simultaneously—because that would mean that the planxel must simultaneously correlate very strongly and very weakly with its surroundings in a single cycle. This is a computational contradiction.

Therefore, there is an inevitable compromise:

Relativistic Mass Increase as a Cost of High-Speed ​​Synchronization

When a soliton propagates at a speed close to $c$, musi być aktualizowany niemal co takt:

Quantum Randomness – Maximum Phase Mixing Through the Golden Angle

Wyniki pomiarów kwantowych wydają się losowe, ponieważ obserwator widzi jedynie końcowy stan synchronizacji, a nie pełną dynamikę fazową sieci. Rotacja fazowa o kąt $\approx 137,5^\circ$ w każdym takcie (związana ze stałą struktury subtelnej $\alpha \approx 1/137$) jest maksymalnie ergodyczna w dyskretnej sieci 3D. Po kilku tysiącach taktów mikroskopowe różnice fazowe zostają wymieszane tak skutecznie, że dla obserwatora, który nie zna pełnego stanu początkowego, wynik wygląda jak czysta losowość – mimo że cały proces jest w pełni deterministyczny na poziomie sieci.

Why does quantum mechanics have to look exactly like this?

When we look at quantum mechanics from the perspective of Māyā, the eternal question that has paralyzed all interpretations for a hundred years disappears:

“Why is nature so strange?”

It is replaced by another one – much simpler, and at the same time much deeper:

“How must a system that is discrete, local, and computationally finite behave if it is to generate a continuous, stable, and isotropic world?”

The answer is: he couldn't have behaved differently.

If reality:

• consists of discrete information processing elements,
• operates in local, indivisible time cycles,
• has limited synchronization bandwidth,
• and does not have access to the "global state" in one step,

its dynamics must take exactly the form described by quantum mechanics.

The distributed wave function is not a quirk of nature — it is the only possible way to encode future pattern configurations in a network that has not yet chosen a single stable mode. Interference is not a paradox — it is a natural consequence of overlapping phase correlations in a network of local connections. Collapse is not a magical act — it is the necessary closure of a synchronization cycle at the moment of strong interaction. Randomness is not fundamental — it is the epistemic shadow of a process that remains fully deterministic at the execution level, but unobservable in its entirety.

If quantum mechanics were:

• fully classical → the world would reveal its graininess and privileged directions,
• fully locally deterministic without state dispersion → the network would block at every interaction,
• fully global → would require non-physical, instantaneous synchronization of the entire universe,

each of these alternatives would lead to contradictions or to an unstable, discontinuous world.

Quantum mechanics is therefore not one of the possible theories, but the only coherent dynamics that can emerge from a discrete, local computational architecture if that architecture is to generate the reality we know: continuous in observation, stable in time, and rich in complex structures.

This is why its formalism is so rigid and yet so universal. This is why it cannot be "simplified" or "replaced" by classical intuition. And this is why it worked perfectly mathematically for a hundred years, yet resisted ontological understanding.

Quantum mechanics is not the foundation of reality. It is an inevitable interface that arises when reality is performed, not given.

Originality and scope of interpretation clause

The approach to quantum mechanics presented in this text does not introduce any new equations, does not modify the existing formalism, and does not undermine any empirically confirmed predictions of quantum theory. The Schrödinger equations, commutation relations, the uncertainty principle, and the probabilistic formalism retain their standard meanings and scope of applicability.

The originality of the proposed approach concerns solely the ontological level of description. Quantum mechanics is interpreted here not as a fundamental description of physical entities, but as the inevitable dynamics of information synchronization in a discrete, local, and clocked processing network (planxels). The wave function is treated neither as a physical field nor as an epistemic tool, but as a distributed information state of the network, and phenomena such as interference, collapse, and uncertainty result directly from the architecture of local closure of synchronization cycles.

Although individual elements – such as discreteness, the informational nature of quantum states, decoherence, and computational models – have appeared before in various contexts of theoretical physics and philosophy of science, their coherent connection in the form of a single, local execution mechanism constitutes the original conceptual contribution of Māyā theory.

In particular, what is new is:

• unambiguous identification of the measurement problem with the need to locally close the synchronization cycle in a finite time,
• interpretation of the uncertainty principle as a computational compromise between conflicting synchronization modes,
• and treating quantum randomness as an effect of maximum phase mixing in deterministic but locally unobservable network dynamics.

The proposed approach is not an alternative quantum theory or a competitor to the existing formalism. It is a mechanical interpretation that aims to reveal what kind of architecture of reality must generate precisely the dynamics described by quantum mechanics.