Why Traditional Physics Runs into Infinities — and How Temporal Flow Physics Avoids Them
By John Gavel
In one-dimensional physics, divergences are not just a technical nuisance — they are a symptom of a deeper structural problem. Traditional models assume that points along a line are complete, independent, and infinitely compressible. Flux does not spread, point sources become singular, and internal closure is absent. Integrals blow up, fields diverge, and infinities appear. This is not because nature is infinite, but because the model allows differences to exist without closure.
TFP’s Core Principle
Temporal Flow Physics (TFP) takes a different approach. A dimension is not a container — it is a serialized causal resolution step. Interactions exist only as part of a completed causal cycle:
\[ t_n \rightarrow X, \quad t_{n+1} \rightarrow Y, \quad t_{n+2} \rightarrow Z \]
A physical volume is defined by the composition of these steps:
\[ V = \mathcal{R}_Z \circ \mathcal{R}_Y \circ \mathcal{R}_X \]
If a cycle does not complete, the structure is not physically real. Traditional “1D” physics is, in TFP terms, one-third of an unfinished computation. Unfinished computations cannot diverge: they are rejected before any continuum mathematics is applied.
Finite Capacity and the Folding Tax
Moving from conceptual to causal mechanics, TFP introduces the idea of finite site capacity. Each site in a network has a finite capacity, \(K\), meaning it can only handle a limited number of interactions per tick:
\[ H = K(K-1) \]
Every relational “signal” — a difference, reflection, or increment — consumes part of this capacity. When multiple signals overlap, or neighboring sites are busy, the effective contribution of any single path is diluted. We call this the folding tax, \(\delta\).
Summing these contributions across all sites naturally yields a finite cumulative magnitude, even in networks that are infinite in principle. Analogous to summing \(\displaystyle \frac{1}{n^p}\) over an infinite 1D array, TFP weights each step by the site’s effective capacity (dividing by \(n\), \(n/2\), or applying the \(\delta\)-tax). This enforces finite propagation and prevents divergence.
From Divergence to Latency
In traditional theories, interactions can compress without cost, producing infinities. In TFP, every interaction consumes causal budget. As a system attempts to collapse into lower-dimensional behavior:
- Internal recursion cost increases
- Available handshake capacity decreases
- Propagation slows instead of diverging
Where traditional physics predicts infinity, TFP predicts latency. Differences accumulate only as far as the causal budget allows, and no unclosed structure ever propagates.
Why This Matters
TFP enforces:
- Finite causal cycles
- Mandatory closure
- Budgeted interactions
By combining conceptual axioms with explicit site-level mechanics, TFP explains why traditional 1D physics diverges and how a finite, well-defined physical structure emerges naturally. The infinities are not canceled after the fact — they are never generated in the first place.
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