From Temporal Flow Physics to Quantum Mechanics: How Time Weaves the Quantum World

From Temporal Flow Physics to Quantum Mechanics: How Time Weaves the Quantum World
by John Gavel

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Introduction

What if the mysterious quantum behavior we see in particles isn’t fundamental? What if it emerges naturally from something even more basic — time itself?

Temporal Flow Physics (TFP) proposes just that. Instead of starting with space and particles as the fundamental building blocks, TFP begins with fundamental temporal flows — simple, quantized “lines” of time evolving independently but interacting through internal dynamics. From these flows, the geometry of space and the behavior of matter arise naturally.

Today, we’ll explore how this gives rise to quantum mechanics and the famous Schrödinger equation — the cornerstone of non-relativistic quantum theory.

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Fundamental Temporal Flows

Imagine a network of nodes, each hosting a temporal flow — a vector with three components that changes with time:

$$F_i(t) = \bigl( F_{i,A}(t), \; F_{i,B}(t), \; F_{i,C}(t) \bigr)$$

Each component can be thought of as an abstract internal “direction” of time flow at node $i$.

The dynamics of these flows are governed by an action functional:

$$S_{\text{flow}} = \sum_i \int dt \left[ \frac{1}{2} \left| \partial_t F_i + A_t F_i \right|^2 \right] - \frac{\lambda}{2} \sum_{\langle i,j \rangle} |F_i - F_j|^2 - \sum_i \int dt \, V(F_i)$$

Here:

• The term $\partial_t F_i + A_t F_i$ includes an internal connection $A_t$, encoding causal relations or “twists” in time flow, like a gauge field.

• $\lambda$ controls how strongly neighboring flows influence each other.

• $V(F_i)$ is a potential favoring stable flow configurations — the seeds of structure.

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From Discrete Flows to Continuous Fields

By averaging over many nodes, we define a smooth, coarse-grained field:

$$\bar{F}(x, t) = \langle F_i(t) \rangle$$

This represents an emergent field that varies continuously in space and time — the effective flow.

We can then consider small fluctuations around this average:

$$\delta F(x, t) = F(x, t) - \bar{F}(x, t)$$

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Stable Flow Patterns as “Particles”

Certain stable, localized patterns in the effective flow $\bar{F}(x, t)$ behave like matter. Imagine ripples or knots in the flow that persist and move slowly.

These patterns can be effectively described by a complex scalar field:

$$\psi(x, t)$$

which you can think of as a quantum wavefunction encoding the amplitude of the localized flow configuration at position $x$ and time $t$.

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Deriving the Schrödinger Equation

Expanding the original flow action around these stable states and applying standard approximations (such as ignoring relativistic effects), the effective action for $\psi$ takes the familiar form:

$$S_{\psi} = \int dt \, d^3x \left[ i \hbar \psi^* \partial_t \psi - \frac{\hbar^2}{2m} |\nabla \psi|^2 - V(x) |\psi|^2 \right]$$

where:

• $m$ is an effective mass arising from flow inertia,

• $V(x)$ is a potential landscape determined by the underlying flow potential,

• $\hbar$ (Planck’s constant divided by $2\pi$) emerges naturally from the quantized nature of temporal flows.

By applying the principle of least action (variational principle) to $S_{\psi}$, we obtain the time-dependent Schrödinger equation:

$$i \hbar \frac{\partial \psi}{\partial t} = - \frac{\hbar^2}{2m} \nabla^2 \psi + V(x) \psi$$

This equation governs the evolution of the quantum wavefunction and explains all quantum phenomena in the non-relativistic limit.

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What Does This Mean?

TFP shows that quantum mechanics — with all its strange and counterintuitive features — can emerge naturally from a deeper, more fundamental theory of time.

Time isn’t just a background parameter; it’s the fundamental building block of reality.

Space, particles, and wavefunctions all arise as emergent phenomena from the complex interactions of temporal flows.

The mysterious quantum wavefunction is essentially the shape of a stable pattern in the temporal flow network.

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Conclusion

This perspective offers a new, unified way to understand the quantum world, rooting it firmly in the physics of time itself. By reimagining the universe as a network of interacting temporal flows, Temporal Flow Physics opens the door to unifying quantum mechanics with spacetime geometry and gravity — a major goal of modern physics.

If you want to explore more about how TFP connects to spacetime geometry, gauge theories, and gravity, stay tuned for upcoming posts!