One of the most fundamental, yet least contested, assumptions of modern physics is the treatment of time as a continuous, universal coordinate—a kind of background in which all events are "embedded." Classical physics, and later the theory of relativity, treated time as a smooth and infinitely divisible quantity. Even in general relativity, where time loses its absolute character and intertwines with space into four-dimensional spacetime, it remains a continuous entity: curved and relative, but devoid of intervals or graininess.

Quantum mechanics has revolutionized almost all fundamental concepts of physics. Energy, momentum, angular momentum, and even position have lost their classical status and been subordinated to the principles of quantization and uncertainty. Time, however, remained an exception. In the formalism of quantum mechanics, it is neither an observable nor an operator, but an external parameter—classical, continuous, and untouched by quantum fluctuations. This is not because its quantization has been ruled out, but because no coherent language or mechanism has been found to allow for its meaningful implementation. The very question "is time discrete?" proves difficult to formulate unambiguously within the current theoretical framework.

Physics, paradoxically, therefore does not know what time is in its essence. It describes its manifestations and consequences — time dilation, the entropy arrow, causal relations — but does not provide an ontological explanation of its nature. Time appears as input to the theory: a coordinate relative to which processes occur, not an entity requiring its own explanation.

It is significant that physics has established a fundamental time scale below which the classical concept of time loses its meaning – Planck time

$t_P \approx 5{,}391 \times 10^{-44}\ \mathrm{s}$

Yet, this scale has not been incorporated into any coherent, mechanistic description of time as a process or structure. It is most often interpreted as a limit to the applicability of known theories or a cognitive barrier, rather than as a trace of a deeper dynamic from which time might emerge.

Equally intriguing is the problem of the arrows of time – why does time flow in one direction, from the past to the future? Physics has a statistical explanation (increase in entropy in closed systems), but there is no consensus on the fundamental cause. Why did the universe begin in a state of low entropy? Why are processes irreversible at the microscopic level, even though fundamental laws (e.g., Schrödinger's equations) are time-reversible? This is one of the greatest unresolved questions—physics describes the arrow of time but does not explain its origin.

In Māyā, time ceases to be an assumption. It becomes emergent effect of the simple calculation mechanism.

Time as a counter for local update cycles

In the planxel model, time is not a primordial entity or a continuous continuum. It is a counter of completed update cycles in planxels. Each tick of Planck time $t_P$ is one complete Eulerian cycle in the planxel—a closed operation of state processing and synchronization. The sequence of these closed cycles creates what we perceive as the passage of time. A single local Planck cycle alone does not "last" time – is a basic, indivisible operation. Only next completed cycles create time – like successive frames of a film creating the impression of movement.

An analogy for simplicity (in a vacuum): Let us assume, figuratively, that each individual Planck tick corresponds to a step of 1 cm "length" - this is not a literal spatial length, but a convenient way of visualizing the local updating rhythm.

Near a massive star – due to the higher information load – the same update cycle requires more processing, so its effective “step” becomes longer, e.g. to 5 cm.

If 10 such ticks occur in a second in a vacuum (10 × 1 cm), then for an observer in a vacuum, after one second on the star only 2 ticks have passed (2 × 5 cm = 10 cm of "processed reality").

This is what physicists call time dilation – only they didn't know it was extension of the local beat caused by processing load. This same analogy also beautifully explains gravitational geodesic effects: particle paths through space must take the same "elongated" steps, which manifests as curvature of the paths—exactly as predicted by general relativity!

The arrow of time stems from the irreversibility of the process itself: each cycle records a new state and overwrites the old one – there is no going back. It is not the statistical fluctuation of entropy that is primary – it is structural irreversibility of the record in a discrete computational process.

The key thing is that time is local. The rhythm of the cycles is not universal – it depends on the local information load of the planxel:

• In low-load areas (space vacuum) – cycles run quickly and evenly – time flows “normally”.
• In areas of high load (near mass, in a gravitational field or at relativistic speeds) – the planxel must process more information in synchronization with its neighbors. The load regulator slows down the state correction, which increases the local Planck time clock (${P,\mathrm{e}\mathrm{f}\mathrm{f}}_{}>t_{\mathrm{P<span\; style="font-family:\; Georgia,\; \text{'}Times\; New\; Roman\text{'},\; \text{'}Bitstream\; Charter\text{'},\; Times,\; serif;font-size:\; 16px"> </span>}}$$t_{P,\mathrm{eff}} > t_P$

This slowing down of the synchronization rhythm manifests itself as local time dilation – exactly as described by the general theory of relativity in the Schwarzschild metric:

$d\tau = dt \sqrt{1 – \frac{2GM}{rc^2}}$

Physics has known about this effect for over a century, but did not know its mechanism. Einstein described it geometrically (curvature of space-time), but he did not explain why time can flow differently in different places and why in this mathematical form.

In Māyā, the mechanism is simple: time is not an abstract coordinate, but a local processing clock. Where there is more data to synchronize, the clock ticks slower.

When we rewrite the Schwarzschild metric in Planck units (G and c as ℓ_P/t_P relations):

$d\tau = dt \sqrt{1 – \frac{2 m \ell_P^2}{m_P r t_P^2}}$

The constants "disappear" – the mechanism remains: more load → longer local clock speed → slower time.$d\tau / dt = \sqrt{1 – 2 \frac{M}{m_P} \frac{\ell_P}{r}}$

A precise example: time dilation on the Earth's surface

Fundamental constants (exact values):

• Planck length: ${\mathrm{\ell }}_P\approx 1,616\times 10^{-35}$ m${\mathrm{}}_{}$
• ${\mathrm{<span\; style="font-family:\; Georgia,\; \text{'}Times\; New\; Roman\text{'},\; \text{'}Bitstream\; Charter\text{'},\; Times,\; serif">s</span>}}_{}$
• Planck mass: $m_P\approx 2,176\times 10^{-8}$ kg
  ${}_{}$

Earth parameters:

• Earth's mass: $M_{\oplus }\approx 5,972\times 10^{24}$ kg
• Mean radius of the Earth: $r_{\oplus }\approx 6,371\times 10^6$ m${}_{}$

Key calculations in Planck units:

1. Ratio of Earth mass to Planck mass: $M_{\oplus }\mathrm{/}{m}_P\approx 2,74\times 10^{32}$
2.  Stosunek długości Plancka do promienia Ziemi:
   $\ell_P / r_\oplus \approx 2,54 \times 10^{-42}$
3. Key dimensionless load factor:
   $2 \times (M_\oplus / m_P) \times (\ell_P / r_\oplus) \approx 1,39 \times 10^{-9}$

Effect on the local Planck time cycle:

In GTR: $d\tau \mathrm{/}dt=\sqrt{1-x}$​, gdzie $x = 1,39 \times 10^{-9}$

Approximation for small x:

$\sqrt{1 – x} \approx 1 – \frac{x}{2} \approx 1 – 6{,}95 \times 10^{-10}$

Interpretation in Māyā:

• Time flows slower by a factor of ≈ 6.95 × 10⁻¹⁰ (approx. 0.695 parts per billion).
• Local Effective Tact: 
  $t_{P,\mathrm{eff}} \approx t_P \times (1 + 6.95 \times 10^{-10})$ ${}_{}$

This is exactly the same as the gravitational time dilation on the Earth's surface according to GTR – a value known and measured, among others, in the GPS system.

Why didn't physics see the discreteness of time?

Quantum mechanics quantized everything—energy, momentum, angular momentum—but not time. Why? Not because time "resists" quantization, but because throughout the development of physics, it was treated as a classical background: a coordinate at which quantization occurs, not an object requiring its own explanation. In the prevailing formalism, time is neither an observable nor an operator, but an external parameter relative to which the evolution of states is defined. In such language, the very question "is time discrete?" loses meaning before it is even posed.

The lack of time quantization was therefore not a data gap or a theoretical oversight. It was a consequence of the accepted ontology. For over a hundred years, physics had assumed that something happens in time, instead of asking, what is time itself if anything can happenYou don't quantize coordinates — you quantize processes. As long as time remains background, it can have no structure or elementary step.

In Māyā, the starting point is reversed. Time is not the arena of events, but their effect. It is the number of completed cycles of local processing in planxels. Here, Planck time does not serve as a limit of cognition or a conventional unit, but rather as a physically significant tick of a computational clock — the smallest possible operation. There is no shorter time step, because it is impossible to execute a fraction of a synchronization cycle.

This approach naturally explains why time always appears continuous in quantum experiments. The resolution of 10⁻⁴⁴ s is so extreme that any real measurement encompasses not a single tick, but an astronomical number of cycles. An observer never measures a single elementary time step—they always average billions of billions of operations. Time continuity is therefore not an ontological fact, but a statistical property of the rendering.

In this sense, discrete time could not be detected directly, because it is not a feature of observable phenomena, but a feature of the mechanism that generates them. Physics saw the effects of rhythm, but not the clock itself. The lack of a "time quantum" was not a failure of the theory, but a signal that the question was posed from the wrong level of description.

Time appears continuous not because it is, but because we only experience a rendering resulting from an incomparably faster, discrete rhythm of execution.

Consequences for the physics of time

The acceptance of time as an emergent counter of local update cycles leads to a profound reorganization of concepts that physics has so far used in a fragmented and often paradoxical way.

The arrow of time is no longer derived from entropy itself. Its primary source is not the statistical asymmetry of macrostates, but the structural irreversibility of the process: each cycle of updating records a new state and overwrites the previous one. Entropy remains a valid macroscopic description, but it becomes a secondary phenomenon – a statistical shadow of the fundamental, unidirectional dynamics of cycles.

Time dilation no longer requires an ontological curvature of spacetime. The geometry of general relativity retains full formal correctness, but reveals itself as an efficient description of consequences. The mechanism is a slowing down of the local processing clock: where the planxel must process more information as part of synchronization, a single tick takes longer, and the number of completed cycles per reference unit decreases.

Unification with quantum mechanics occurs at the level of ontology, not formalism. The problem of "classical time in quantum theory" disappears because time is no longer an external parameter. It is a discrete, physically significant execution time, common to both quantum and gravitational dynamics. Quantum evolution does not occur w czasie – zachodzi in subsequent cycles.

The problem of time travel and the related causal paradoxes also disappears., such as the grandfather paradox. In Māyā, going back in time is physically impossible because there is no mechanism for undoing update cycles. Each tick overwrites the previous state of the network and leaves no access to earlier configurations. The past is not a region of space-time to which one can "return," but a set of states that have ceased to exist as an active rendering configuration.

In this light, solutions of the General Theory of Relativity that admit closed timelike curves appear not as real physical possibilities, but as artifacts of a geometric formalism that ignores the discrete, irreversible nature of execution. Time travel paradoxes therefore require no additional protective rules or "chronological censorship"—they disappear ontologically along with the assumption of continuous time.

From this perspective, it becomes clear that physics has long operated with correct formulas describing time, but their significance has not been recognized. These equations do not provide a smooth operation of an abstract quantity, but rather the relationships between cycle counters in a discrete, locally clocked processing network.

This is Māyā: time does not “flow”.
Time is counted – beat by beat, planxel by planxel

Originality Clause (Time as a Mechanism)

Māyā theory does not claim primacy in the very idea that time can be emergent, local, or connected to microscopic dynamics. These concepts have appeared previously in various strands of theoretical physics and the philosophy of time, but usually in the form of an ontological interpretation or postulate.

The originality of Māyā's approach lies in the first consistent treatment of time as counter of completed local execution cycles and on the identification of Planck time not as the limit of knowledge, but as a physically meaningful tick of an elementary processing operation. Time here is not a coordinate or parameter of evolution, but the result of a discrete, irreversible process of state updating in planxels.

In this sense, the known equations of general relativity and quantum mechanics are not modified but read mechanically: time dilation, the arrow of time, and the locality of rhythm cease to be geometric or statistical facts, but are revealed as direct consequences of constraints and synchronizations in the computational architecture of reality.