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Emergence of the Lorentzian Metric Signature in Temporal Flow Physics John Gavel Abstract: In Temporal Flow Physics (TFP), time is fundamental as a quantized one-dimensional flow, and space emerges from the relational structure of fluctuations in this flow. We rigorously prove that the Lorentzian signature of the emergent spacetime metric arises naturally from the causal and statistical properties of temporal flow fluctuations, rather than being imposed as a postulate. This section formalizes the assumptions, constructs the emergent metric tensor from flow correlations, and demonstrates how causality enforces the Lorentzian signature. 1. Introduction and Setup We consider a fundamental scalar flow field F : M → R , F = F ( x ) , x ∈ M F: \mathcal{M} \to \mathbb{R}, \quad F = F(x), \quad x \in \mathcal{M} where M \mathcal{M}  is an emergent 4-dimensional manifold with coordinates x μ = ( x 0 , x 1 , x 2 , x 3 ) , μ = 0 , 1 , 2 , 3 , x^\mu = (x^0, x^1, x^2, x^3), \quad \mu=0,1...

From Temporal Flow to Emergent Gravity: Why Dimensional Consistency Matters in Temporal Flow Physics By John Gavel Introduction Temporal Flow Physics (TFP) is a new framework where time itself is fundamental , and space emerges as a relational construct from quantized 1D temporal flows F i ( t ) F_i(t) . This is a paradigm shift requires that all derived physics—gravity, matter, fields—fit together dimensionally and conceptually. Today I want to share how the emergent gravitational dynamics , encapsulated by an Einstein-like equation, arise naturally and dimensionally consistently from the dynamics of the flow field F F . This not only validates the theory's internal consistency but links it directly to known physics constants and equations. The Temporal Flow Field and Dimensional Basis The fundamental object in TFP is the scalar flow field : F ( x μ ) F(x^\mu) where x μ x^\mu  are emergent spacetime coordinates constructed relationally from flow comparisons. Dimensional...

Temporal Flow Physics John Gavel     First Principles of Temporal Flow Physics (TFP) Temporal Flow Physics (TFP) proposes that all physical phenomena—space, particles, energy, and forces—emerge from a discrete set of fundamental one-dimensional temporal flows. These flows evolve causally in time, and all familiar structures of physics are secondary to this foundation. The following five first principles define the axiomatic core of TFP and provide the foundation for the formal developments of Unit -1. Principle 1: Time and Flows Are Fundamental Statement: Time is the only fundamental dimension, and reality consists of discrete, one-dimensional temporal flows F_i(t), indexed by node i, each evolving at a local rate: u_i(t) = [F_i(t + Δt) - F_i(t)] / Δt, with Δt approximately equal to the Planck time. Justification: This merges the principles of temporal fundamentality and flow-based ontology. The temporal flow F_i(t) is the primitive ontological entity of the theory, with no pr...