Gauge Emergence in TFP

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How All Gauge Forces Emerge from Discrete Temporal Flows

By John gavel 

I've developed a theoretical framework called Temporal Flow Physics (TFP) that shows how the electromagnetic, weak, and strong forces all emerge from the same underlying discrete structure. Here's what my model does—and why it matters.

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The Core Idea

Standard gauge theory assumes gauge symmetries exist—but it doesn’t explain why. My model starts with something more fundamental: quantized 1D flows evolving in discrete time, defined on a network. These flows are the building blocks of all fields and forces.

Each site on this network supports a complex flow of the form:

F_i(t) = A_i(t) e^{i\theta_i(t)}

The amplitude determines local flow strength, while the phase encodes internal symmetry. The key insight is that gauge connections emerge from local phase misalignments between neighboring flows.

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From Discrete Flows to Gauge Theory

The gauge connection naturally appears as the discrete phase difference between flows at neighboring sites:

A_{ij}(t) = \frac{\theta_j(t) - \theta_i(t)}{\Delta t}

In the continuum limit, this becomes the familiar gauge potential:

A_\mu(x) = \partial_\mu \theta(x)

Under local phase redefinitions , these differences transform as:

A_{ij} \rightarrow A_{ij} + \frac{\Lambda_j - \Lambda_i}{\Delta t}

This is exactly how gauge fields transform under gauge transformations in U(1), SU(2), or SU(3) theories. Hence:

• Gauge invariance is automatic—it emerges from the relative nature of phase comparisons.
• Charge quantization arises topologically—integer winding numbers around closed loops dictate discrete values of charge.
• All gauge groups emerge from the same mechanism—multi-component flows form higher symmetry groups.

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Emergence of the Three Forces

Electromagnetism (U(1))

For single-component flows, local phase misalignments form the U(1) gauge field:

F_i = A_i e^{i\theta_i} \quad \Rightarrow \quad A_\mu = \partial_\mu \theta

Loop integrals of over closed paths yield quantized charge via:

\oint d\theta = 2\pi n

Weak Force (SU(2))

Flows with two components couple to SU(2) link variables . The discrete action includes interactions like:

V(|F_i - U_{ij} F_j|^2)

In the continuum limit, this becomes Yang-Mills SU(2) theory. Spontaneous symmetry breaking occurs when the flows develop a preferred direction in internal space.

Strong Force (SU(3))

Three-component flows form SU(3) triplets—analogous to red, green, blue color charges. The non-Abelian structure leads to confinement: pulling color-charged flows apart stretches the flow field, which breaks by pair creation when enough energy is present.

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Discrete Action and Continuum Limit

The fundamental discrete action is:

S = \sum_i \int dt\, |\partial_t F_i|^2 + \sum_{\langle i, j \rangle} V\left( |F_i - U_{ij} F_j|^2 \right)

Here, are link variables representing parallel transport (i.e., gauge connections), and is a potential minimizing misalignment.

Taking the continuum limit:

F_i(t) \to \psi(x), \quad U_{ij} \to \exp(i A_\mu dx^\mu)

the action becomes:

S \rightarrow \int d^4x \left[ -\frac{1}{4} F_{\mu\nu}F^{\mu\nu} + |D_\mu \psi|^2 \right]

where is the covariant derivative.

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Simulation Results: Coupling Unification with TFP

Using RG evolution extended with TFP corrections, I simulated the gauge coupling flows from the Z boson mass (~91 GeV) to the Planck scale (~ GeV).

Standard Model:
Couplings evolve but fail to unify—this is well-known.

Supersymmetric Model:
Couplings approach a common value near GeV.

TFP-Modified Models:
At high energies, TFP introduces exponential suppression of beta functions:

\frac{d\alpha}{d\log E} = \frac{b\, \alpha^2}{2\pi} + \delta_{\text{TFP}}, \quad \delta_{\text{TFP}} \propto e^{-E / M_\text{Planck}}

This causes all three couplings to converge naturally—even without SUSY—because discrete flow effects dominate above the cutoff scale.

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What This Solves

• UV Divergences: The discrete structure imposes a physical cutoff, making all loop integrals finite while preserving gauge invariance.
• Origin of Gauge Symmetries: Rather than assuming symmetry, it emerges from discrete phase structure.
• Charge Quantization: Follows from winding numbers around flow network loops.
• Force Unification: All gauge forces arise from the same principle: flow misalignment across links.

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Testable Predictions

1. Modified beta functions near due to exponential suppression.
2. Natural gauge coupling unification even without SUSY, due to flow discreteness.
3. Quantized charges from discrete topologies.
4. Enhanced coupling to gravity, since both geometry and gauge fields come from the same flow network.

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The Broader Picture

TFP suggests that all of field theory—including spacetime itself—is emergent. The structure of the Standard Model (gauge groups, three generations, charge quantization) may reflect stable patterns in a deeper flow network.

Ultimately, this framework points toward a unified theory where gravity, gauge fields, and matter arise from discrete temporal flows, with spacetime and symmetries appearing as coarse-grained consequences.

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Why This Matters

Current physics assumes symmetries and continuous fields. TFP derives both from a simpler foundation: quantized temporal flows evolving on a network.

This could lead to:

• A finite, predictive quantum field theory
• A unified origin for gauge and gravitational forces
• A deeper explanation for the Standard Model’s structure

The key idea is simple but profound:
Gauge connections are flow misalignments.
Everything else—photons, gluons, symmetry breaking, confinement—follows from this.

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Next Steps

I'm continuing to analyze:

• Non-perturbative flow interactions
• How entropy and curvature emerge from flow fluctuations
• Black hole analogues and thermal effects in flow networks

And this is testable physics. The modified running of couplings and enhanced unification will leave signatures in future collider experiments or precision coupling measurements.