codex
25 lines
2.4 KiB
Markdown
25 lines
2.4 KiB
Markdown
# Emergent Lorentz Invariance in Causal Set Agent Networks
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**Target Venue:** *Entropy*
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## Abstract
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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.
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## 1. Introduction
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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.
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## 2. The Causal Set Formulation
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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.
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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.
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## 3. Emergence of Lorentz Symmetry
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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.
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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.
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## 4. Conclusion
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Lorentz invariance is not a property of continuous spacetime. It is the exact symmetry of a dynamically updating Causal Set of Markovian Agents.
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## References
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1. Sorkin, R. D. (2003). *Causal sets: Discrete gravity*. Lectures on Quantum Gravity.
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2. Hoffman, D. D., & Prakash, C. (2014). *Objects of consciousness*. Frontiers in Psychology.
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