Foundational Constant #3
The Fundamental Tick (τ₀)
The minimal unit of time
The Plain Truth
Just as space is made of fundamental pixels (the Recognition Length, λ_rec), time itself is not a smooth, continuous flow. At the most fundamental level, reality progresses in tiny, indivisible steps—like the frames of a movie. The duration of one of these "frames" is the **Fundamental Tick (τ₀)**.
This is the shortest possible interval of time that has any physical meaning. Nothing can happen "in between" the ticks, because the ticks *are* the moments when things happen. τ₀ is the clock speed of the universe's processor, the temporal heartbeat that drives all change and all events recorded in the Universal Ledger.
The Logical Derivation: The 8-Beat Cycle
The duration of the Fundamental Tick is not a random value but is a direct consequence of the 8-Beat Cycle (Theorem #4), which is itself a consequence of 3D space.
Derivation from the Universal Rhythm
- A Complete Cycle: The universe operates on a complete cycle of 8 discrete beats or ticks to perform one full recognition of a spatial voxel.
- The Natural Period: The most natural, efficient period for any wave or cycle in the universe is defined by the fundamental mathematical constant `2π`.
- Harmonic Division: To fit 8 discrete steps into this single natural period, the time for each step (each tick) must be the total period divided by the number of steps.
However, there's one more piece: the scaling of this process is governed by the Golden Ratio, φ. Therefore, the denominator is scaled by the natural logarithm of φ, `ln(φ)`, which represents the fundamental rate of self-similar growth.
This uniquely fixes the duration of the Fundamental Tick as:
τ₀ = 2π / (8 * ln(φ))What This Means
The End of Zeno's Paradoxes
Ancient philosophical problems like Zeno's paradox (how can you ever reach a destination if you must first cross half the distance, then half the remaining distance, and so on forever?) are instantly solved. Because both space (λ_rec) and time (τ₀) are discrete, motion is a series of finite steps in a finite number of frames. The infinite divisions are a mathematical fiction.
The Origin of the Speed of Light
The speed of light, `c`, is not the speed of a particle but the processing speed of the spacetime grid. It can now be derived from the fundamental constants of space and time: it is the distance of one "pixel" of space divided by the duration of one "frame" of time.
c = λ_rec / τ₀
The Deeper Truth
Time is not an empty void that events happen in. Time *is* the happening of events. The Fundamental Tick, τ₀, is the duration of a single, irreducible "now"—the moment in which a new entry is written to the Universal Ledger.
The smooth passage of time we experience is the illusion created by an incredibly rapid succession of these discrete, computational moments, much like the smooth motion on a screen is an illusion created by a rapid succession of still frames.