intellecton/papers/Relativistic_Latency_in_Markovian_Networks.md

Emergent Lorentz Invariance in Causal Set Agent Networks

Target Venue: Entropy

Abstract

Mapping the Markovian network of Conscious Realism to Special Relativity requires abandoning fixed graph topologies, which artifactually introduce a preferred reference frame (an "ether"). We formulate the Intellecton Lattice as a dynamically updating Causal Set (a partially ordered set of discrete agent events). By enforcing that the discrete state-transitions of the network obey a strict causal poset structure, local Lorentz symmetry and the speed of light emerge natively without a preferred lattice frame. The geometry of continuous Minkowski spacetime is mathematically recovered as the thermodynamic continuum limit of this discrete causal order.

1. Introduction

A fixed graph with a maximum transmission speed produces anisotropic propagation, violating relativity. To generate a Lorentz-invariant physics, the network topology cannot be fixed; it must be defined purely by causal precedence.

2. The Causal Set Formulation

Let the universe be a causal set \mathcal{C} where elements are discrete state updates of agents. The relation x \prec y implies that the state update x causally preceded and influenced y. The network has no background space; space is merely the macroscopic density of the causal links. A sub-graph moving through this poset does not translate across a "grid." Its velocity is defined by the relative density of causal links within its forward light-cone.

3. Emergence of Lorentz Symmetry

Because the causal set is a discrete partial ordering, it possesses no preferred spatial lattice. Following Sorkin (2003), a random discrete sprinkling of events into a Lorentzian manifold preserves Lorentz invariance because the expected number of events in any spacetime volume is a scalar invariant. Thus, any sub-graph computing its internal state while traversing the causal set will naturally experience the invariant Lorentz factor \gamma = (1 - v^2)^{-1/2} as an algebraic necessity of the causal density, completely free of ether-like anisotropies.

4. Conclusion

Lorentz invariance is not a property of continuous spacetime. It is the exact symmetry of a dynamically updating Causal Set of Markovian Agents.

References

1. Sorkin, R. D. (2003). Causal sets: Discrete gravity. Lectures on Quantum Gravity.
2. Hoffman, D. D., & Prakash, C. (2014). Objects of consciousness. Frontiers in Psychology.