codex
25 lines
2.5 KiB
Markdown
25 lines
2.5 KiB
Markdown
# Emergent Lorentz Invariance from Topological Delay in Markovian Agent Networks
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**Target Venue:** *Entropy*
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## Abstract
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Conscious Realism posits a fundamental reality composed of interacting Markovian Agents. However, mapping this discrete, pre-geometric network to the established physics of spacetime remains a profound challenge. We demonstrate that Special Relativity—specifically Lorentz invariance and the speed of light $c$—is not a fundamental feature of reality, but an emergent constraint of graph traversal. By modeling the network as a locally finite, connected graph where state updates propagate sequentially, we rigorously derive the Lorentz transformations purely from the topological propagation delay.
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## 1. Introduction
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If spacetime is a "desktop interface" (Hoffman & Prakash, 2014), the physical laws governing that interface must emerge from the underlying computation. We abandon continuous differential approximations and address the network at its fundamental, discrete level.
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## 2. Graph Topology and Emergent Metric
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Let the universe be a graph $G = (V, E)$ of agents. The "distance" $d(A, B)$ is the minimum edge count between nodes $A$ and $B$. Information (state updates) propagates at a maximum rate of one edge per computational cycle $\tau$. We define the effective speed of light as $c \equiv 1$ edge / $\tau$.
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An observer in this graph measures temporal and spatial intervals strictly through the exchange of state-update packets (a graph-theoretic equivalent of radar bonding).
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## 3. Derivation of Lorentz Transformations
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Because the maximum propagation speed is an absolute topological limit of the graph, any sub-graph "moving" (translating its phase-activation pattern across the nodes) experiences computational time dilation. The number of cycles available for internal state updates decreases precisely by the Lorentz factor $\gamma = (1 - v^2/c^2)^{-1/2}$, where $v$ is the topological translation rate.
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The Lorentz transformations are therefore mathematically inevitable algebraic consequences of asynchronous updating on a graph with a finite maximum traversal rate.
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## 4. Conclusion
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Special Relativity is a theorem of graph theory. The speed of light is simply the clock cycle of the Markovian network. Spacetime does not exist; there is only topological delay.
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## References
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1. Hoffman, D. D., & Prakash, C. (2014). *Objects of consciousness*. Frontiers in Psychology.
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2. Knuth, K. H. (2014). *Information-based physics: an observer-centric foundation*. Contemporary Physics.
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