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| Format: | Recurso digital |
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Zenodo
2026
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| Accès en ligne: | https://doi.org/10.5281/zenodo.19647304 |
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- <p><strong>Revisiting Boltzmann’s Paradox in The Dark Light Theory (TDLT): From Improbable Oscillations to Statistical Admissibility</strong></p> <p>This revised work re-examines Boltzmann’s paradox in light of the mature conceptual structure of The Dark Light Theory (TDLT). An earlier version of the argument interpreted the origin of temporal order and the universe’s low-entropy beginning through the notion of “Nothingness” as a fundamentally improbable structure, characterized by oscillations between limiting states of improbability <span class="katex"><span class="katex-mathml">(P=0)(P=0)</span><span class="katex-html"><span class="base"><span class="mopen">(</span><span class="mord mathnormal">P</span><span class="mrel">=</span></span><span class="base"><span class="mord">0</span><span class="mclose">)</span></span></span></span> and unbounded possibility <span class="katex"><span class="katex-mathml">(P→∞)(P \to \infty)</span><span class="katex-html"><span class="base"><span class="mopen">(</span><span class="mord mathnormal">P</span><span class="mrel">→</span></span><span class="base"><span class="mord">∞</span><span class="mclose">)</span></span></span></span>. In the present formulation, that earlier language is retained only as a philosophical precursor and no longer serves as the primary theoretical basis.</p> <p>Within the mature TDLT framework, the problem is relocated onto a deeper structural level. The central issue is no longer treated primarily as one of improbable fluctuations within an already constituted probabilistic background, but as a question of how a physically legitimate probabilistic regime becomes possible at all. In this reading, the vacuum is not a passive background, but an operationally structured substrate whose action tends to dilute asymmetries and whose correlated reaction tends to contain and coherently process that same dilution.</p> <p>Under this interpretation, three broad operational regimes may be distinguished. In one regime, the available state-space support exceeds the active state content, leading to structural dilution. In another, the active content exceeds the coherent accommodation capacity, leading to compression, instability, or admissibility crisis. Only in the regime where these two tendencies become operationally comparable do states and state-space become mutually coherent enough to constitute a legitimate ensemble in the Boltzmannian sense. It is only there that entropy, probability, and Boltzmannian equations become physically well-defined in a fully admissible way.</p> <p>Accordingly, the Planck regime is not interpreted here as an initial low-entropy state in the ordinary Boltzmannian sense. Rather, it is understood as a pre-metric crisis in the constitution of the very regime in which probabilistic and entropic description could first become legitimate. The low-entropy beginning of the observable universe is then reinterpreted not as a brute statistical anomaly, nor as a mere fluctuation within a pre-given ensemble, but as the retrospective signature of the first post-crisis regime that becomes structurally admissible, physically registrable, and probabilistically measurable.</p> <p>In this way, the present revision moves beyond a purely fluctuation-based account. Boltzmann’s paradox is no longer treated primarily as the rarity of order within an already available ensemble, but as a more fundamental question concerning the emergence of operational coherence, statistical admissibility, and the physical constitution of observability itself.</p>