Temporal Flow Physics and the Myth of Fundamental Indeterminism

In contemporary physics, indeterminism often appears baked into the structure of quantum mechanics. Yet the Temporal Flow Physics (TFP) framework offers a radically different perspective: indeterminacy is not fundamental—it emerges statistically from the vast configuration space of interacting quantized 1D temporal flows.

This blog explores how TFP reconciles deterministic local dynamics with statistical entropy, decoherence, and even Prigogine’s notion of dissipative structures, showing that what appears probabilistic is the result of segmental flow misalignment, not fundamental randomness.

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1. From Many Flows to Entropy

In TFP, the fundamental object is a 1D quantized temporal flow $F_i(t)$. Each flow represents a causal chain of temporal events. Space, and therefore locality, emerges from comparisons between these flows.

Let us denote a system of $N$ flows as:

$$\{F_i(t)\}_{i=1}^N$$

Local alignment is defined by similarity of flow rates:

$$\sigma_u^2(x, t) = \text{Var}\left(\left\{ \frac{dF_i}{dt}(t) \right\}_{i \in \mathcal{N}(x)}\right)$$

This variance becomes the entropy density:

$$S_{\text{TFP}}(x, t) \propto \log \sigma_u^2(x, t)$$

This expresses entropy not as a mystery, but as a statistical measure of how aligned—or misaligned—temporal flows are in a region.

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2. Decoherence and Flow Segmentation

TFP proposes that decoherence arises from segmentation of flow coherence:

Define a segmentation measure $\Delta F_{ij}(t) = F_i(t) - F_j(t)$. The growth of the variance:

$$\Sigma^2(t) = \frac{1}{N^2} \sum_{i,j} \left( \Delta F_{ij}(t) \right)^2$$

is interpreted as the degree of decoherence: when temporal flows become increasingly misaligned, superpositions break into classical-like outcomes. This reflects how the quantum-classical boundary arises not from wavefunction collapse, but from the breakdown of global temporal flow coherence.

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3. Reframing Prigogine’s Dissipative Structures

Prigogine introduced the concept of dissipative structures—order born from chaos in non-equilibrium systems. TFP reframes this: order arises when temporal flows locally re-align, minimizing segmentation variance:

$$\min_{\text{config}} \left( \sum_{i,j} (\Delta F_{ij})^2 \right)$$

Such realignments create stable structures—atoms, fields, spacetime geometries—that persist due to low entropic variance in their flow network.

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4. Mathematical Examples

Black Hole Entropy: Standard: $S_{BH} = \frac{k_B A}{4 \ell_P^2}$ TFP: $S_{TFP} \propto \log(\sigma_u^2|_{r_s})$ — entropy at the horizon arises from maximal misalignment of incoming flow rates.

Gravitational Time Dilation: Standard: $\frac{d\tau}{dt} = \sqrt{1 - \frac{2GM}{rc^2}}$ TFP: $\frac{dF}{dt} = H(r) = c \cdot \frac{d\tau}{dt}$

Inflation Example: Standard: $H = \frac{\dot{a}}{a} \Rightarrow a(t) \propto e^{Ht}$ TFP: Assume a decaying flow suppression $H(t) = H_0 - \delta(t)$, then:

$$a(t) \propto \exp\left( \int (H_0 - \delta(t)) dt \right)$$

Matching expansion to dynamical reduction in flow misalignment.

Unruh Temperature: $T_U = \frac{\hbar a}{2 \pi k_B c} \quad \text{interpreted in TFP as} \quad T_U \propto \sigma_u^2 \text{ under acceleration}$

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Conclusion

Prigogine might ask whether TFP can explain irreversibility without imposing it. The answer is yes: irreversibility is not fundamental, but emergent from the combinatorics of flow segmentation and alignment. Entropy is a macroscopic witness to the microscopic freedom of flows.

The Temporal Flow framework maintains deterministic local dynamics, yet naturally gives rise to uncertainty, thermodynamics, decoherence, and even the statistical structure of spacetime—all without requiring any fundamental indeterminism.

This isn’t just a new theory of physics. It’s a new theory of why physics looks the way it does.