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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.19568278 |
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- <p> </p> <p>Before proceeding with this paper, I highly recommend consulting the following work for foundational context: [https://doi.org/10.5281/zenodo.19477761]</p> <p> </p> <p>We present a rigorous synthesis of Loop Quantum Gravity (LQG) and the Time Wave Field (TWF) theory to resolve the long-standing problem of physical observables and the semiclassical limit in spin foam models. By augmenting the gravitational action with a nonlocal, highly-derivative TWF kernel <span class="math-inline"><span class="katex"><span class="katex-html"><span class="base"><span class="mord mathcal">F</span><span class="mopen">(</span><span class="mord amsrm">□</span><span class="mclose">)</span></span></span></span></span>, we derive the transition amplitudes for augmented W-functions, where the temporal flow emerges from the intrinsic <span class="math-inline"><span class="katex"><span class="katex-html"><span class="base"><span class="mord mathnormal">z</span><span class="mord mathnormal">i</span><span class="mord mathnormal">tt</span><span class="mord mathnormal">er</span><span class="mord mathnormal">b</span><span class="mord mathnormal">e</span><span class="mord mathnormal">w</span><span class="mord mathnormal">e</span><span class="mord mathnormal">gu</span><span class="mord mathnormal">n</span><span class="mord mathnormal">g</span></span></span></span></span> frequency. We demonstrate that in the semiclassical limit, the discrete spin foam structure yields a well-defined graviton propagator with automatic ultraviolet (UV) regularization, effectively recovering the Einstein-Hilbert action in the infrared (IR) regime. Crucially, our framework predicts a frequency-dependent phase deviation in gravitational wave propagation, scaling as <span class="math-inline"><span class="katex"><span class="katex-html"><span class="base"><span class="mord mathnormal">δ</span><span class="mord mathnormal">ϕ</span><span class="mopen">(</span><span class="mord mathnormal">f</span><span class="mclose">)</span><span class="mrel">∼</span></span><span class="base"><span class="mord"><span class="mord mathnormal">f</span><span class="msupsub"><span class="vlist-t"><span class="vlist-r"><span class="vlist"><span class=""><span class="sizing reset-size6 size3 mtight"><span class="mord mtight">3</span></span></span></span></span></span></span></span><span class="mord">/</span><span class="mord">Λ<span class="msupsub"><span class="vlist-t"><span class="vlist-r"><span class="vlist"><span class=""><span class="sizing reset-size6 size3 mtight"><span class="mord mtight">2</span></span></span></span></span></span></span></span></span></span></span></span>. Using Bayesian inference on LIGO strain data, we establish a lower bound for the UV scale at <span class="math-inline"><span class="katex"><span class="katex-html"><span class="base"><span class="mord">Λ</span><span class="mrel amsrm">≳</span></span><span class="base"><span class="mord">1</span><span class="mord">0<span class="msupsub"><span class="vlist-t"><span class="vlist-r"><span class="vlist"><span class=""><span class="sizing reset-size6 size3 mtight"><span class="mord mtight">15</span></span></span></span></span></span></span></span></span></span></span></span> GeV. This work bridges the gap between Planck-scale geometry and interferometric observations, offering a falsifiable signature for quantum gravity at the <span class="math-inline"><span class="katex"><span class="katex-html"><span class="base"><span class="mord">1</span><span class="mord">0<span class="msupsub"><span class="vlist-t"><span class="vlist-r"><span class="vlist"><span class=""><span class="sizing reset-size6 size3 mtight"><span class="mord mtight">−22</span></span></span></span></span></span></span></span></span></span></span></span> strain sensitivity scale.</p>