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Sound Propagation in the Structured Vacuum Network V23: Zero in Vacuum, Bounded in Matter

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1. Verfasser:	ACOSTA PADILLA, ALFREDO LUIS
Format:	Recurso digital
Veröffentlicht:	Zenodo 2026
Schlagworte:	structured vacuum, sound velocity, acoustic propagation, vacuum network, torsional waves, adiabatic index, Pell equation, plastic constant, dodecahedral geometry, zero sound vacuum, upper bound, TVS23, beyond standard model, elastic solids, diamond General Physics (physics.gen-ph) Condensed Matter — Mechanics of Solids (cond-mat.mtrl-sci) Mathematical Physics (math-ph)
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_version_	1866901885003235328
author	ACOSTA PADILLA, ALFREDO LUIS
author_facet	ACOSTA PADILLA, ALFREDO LUIS
contents	<p class="font-claude-response-body break-words whitespace-normal leading-[1.7]">We derive the propagation of mechanical waves (sound) within the Structured Vacuum Theory with 23 channels (TVS23). Three results follow from the geometry of the V23 network with zero free parameters. First, sound velocity is identically zero in the vacuum: the V23 network contains no topological knots, and mechanical transmission requires knots. Second, sound velocity in any material is bounded above by the torsional wave speed <span class="katex"><span class="katex-mathml">c/23≈13,043c/23 \approx 13{,}043 </span><span class="katex-html"><span class="base"><span class="mord mathnormal">c</span><span class="mord">/23</span><span class="mrel">≈</span></span><span class="base"><span class="mord">13</span><span class="mord"><span class="mpunct">,</span></span><span class="mord">043</span></span></span></span> km/s. Third, in gases the adiabatic index <span class="katex"><span class="katex-mathml">γ=(N+2)/N\gamma = (N+2)/N </span><span class="katex-html"><span class="base"><span class="mord mathnormal">γ</span><span class="mrel">=</span></span><span class="base"><span class="mopen">(</span><span class="mord mathnormal">N</span><span class="mbin">+</span></span><span class="base"><span class="mord">2</span><span class="mclose">)</span><span class="mord">/</span><span class="mord mathnormal">N</span></span></span></span> is derived from the number of active V23 modes per molecular knot, reproducing experimental sound speeds for monatomic, diatomic, and polyatomic gases with errors below 0.5%. For elastic solids, a geometric estimate gives <span class="katex"><span class="katex-mathml">vs&sim;(c/23)4/23≈5,440v_s \sim (c/23)\sqrt{4/23} \approx 5{,}440 </span><span class="katex-html"><span class="base"><span class="mord"><span class="mord mathnormal">v</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist"><span class="sizing reset-size6 size3 mtight"><span class="mord mathnormal mtight">s</span></span></span><span class="vlist-s"></span></span></span></span></span><span class="mrel">&sim;</span></span><span class="base"><span class="mopen">(</span><span class="mord mathnormal">c</span><span class="mord">/23</span><span class="mclose">)</span><span class="mord sqrt"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist"><span class="svg-align"><span class="mord">4/23</span></span></span><span class="vlist-s"></span></span></span></span><span class="mrel">≈</span></span><span class="base"><span class="mord">5</span><span class="mord"><span class="mpunct">,</span></span><span class="mord">440</span></span></span></span> m/s consistent with observed metal values; for the hardest solid (diamond), the Pell solution <span class="katex"><span class="katex-mathml">(x,y)=(24,5)(x,y)=(24,5) </span><span class="katex-html"><span class="base"><span class="mopen">(</span><span class="mord mathnormal">x</span><span class="mpunct">,</span><span class="mord mathnormal">y</span><span class="mclose">)</span><span class="mrel">=</span></span><span class="base"><span class="mopen">(</span><span class="mord">24</span><span class="mpunct">,</span><span class="mord">5</span><span class="mclose">)</span></span></span></span> of <span class="katex"><span class="katex-mathml">x2−23y2=1x^2-23y^2=1 </span><span class="katex-html"><span class="base"><span class="mord"><span class="mord mathnormal">x</span><span class="msupsub"><span class="vlist-t"><span class="vlist-r"><span class="vlist"><span class="sizing reset-size6 size3 mtight"><span class="mord mtight">2</span></span></span></span></span></span></span><span class="mbin">−</span></span><span class="base"><span class="mord">23</span><span class="mord"><span class="mord mathnormal">y</span><span class="msupsub"><span class="vlist-t"><span class="vlist-r"><span class="vlist"><span class="sizing reset-size6 size3 mtight"><span class="mord mtight">2</span></span></span></span></span></span></span><span class="mrel">=</span></span><span class="base"><span class="mord">1</span></span></span></span> gives <span class="katex"><span class="katex-mathml">vs=c/24≈12,491v_s = c/24 \approx 12{,}491 </span><span class="katex-html"><span class="base"><span class="mord"><span class="mord mathnormal">v</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist"><span class="sizing reset-size6 size3 mtight"><span class="mord mathnormal mtight">s</span></span></span><span class="vlist-s"></span></span></span></span></span><span class="mrel">=</span></span><span class="base"><span class="mord mathnormal">c</span><span class="mord">/24</span><span class="mrel">≈</span></span><span class="base"><span class="mord">12</span><span class="mord"><span class="mpunct">,</span></span><span class="mord">491</span></span></span></span> m/s (observed: 12,000 m/s, error 4.1%), with equilibrium distance <span class="katex"><span class="katex-mathml">req=λ0⋅ρ≈1.40r_{\rm eq} = \lambda_0 \cdot \rho \approx 1.40 </span><span class="katex-html"><span class="base"><span class="mord"><span class="mord mathnormal">r</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist"><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mathrm mtight">eq</span></span></span></span><span class="vlist-s"></span></span></span></span></span><span class="mrel">=</span></span><span class="base"><span class="mord"><span class="mord mathnormal">λ</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist"><span class="sizing reset-size6 size3 mtight"><span class="mord mtight">0</span></span></span><span class="vlist-s"></span></span></span></span></span><span class="mbin">⋅</span></span><span class="base"><span class="mord mathnormal">ρ</span><span class="mrel">≈</span></span><span class="base"><span class="mord">1.40</span></span></span></span> Å (observed: 1.54 Å, error 9%), where <span class="katex"><span class="katex-mathml">ρ=1.3247…\rho = 1.3247\ldots </span><span class="katex-html"><span class="base"><span class="mord mathnormal">ρ</span><span class="mrel">=</span></span><span class="base"><span class="mord">1.3247</span><span class="minner">…</span></span></span></span> is the plastic constant — the real root of <span class="katex"><span class="katex-mathml">x3−x−1=0x^3-x-1=0 </span><span class="katex-html"><span class="base"><span class="mord"><span class="mord mathnormal">x</span><span class="msupsub"><span class="vlist-t"><span class="vlist-r"><span class="vlist"><span class="sizing reset-size6 size3 mtight"><span class="mord mtight">3</span></span></span></span></span></span></span><span class="mbin">−</span></span><span class="base"><span class="mord mathnormal">x</span><span class="mbin">−</span></span><span class="base"><span class="mord">1</span><span class="mrel">=</span></span><span class="base"><span class="mord">0</span></span></span></span>.</p>
format	Recurso digital
id	zenodo_https___doi_org_10_5281_zenodo_19712686
institution	Zenodo
language
publishDate	2026
publisher	Zenodo
record_format	zenodo
spellingShingle	Sound Propagation in the Structured Vacuum Network V23: Zero in Vacuum, Bounded in Matter ACOSTA PADILLA, ALFREDO LUIS structured vacuum, sound velocity, acoustic propagation, vacuum network, torsional waves, adiabatic index, Pell equation, plastic constant, dodecahedral geometry, zero sound vacuum, upper bound, TVS23, beyond standard model, elastic solids, diamond General Physics (physics.gen-ph) Condensed Matter — Mechanics of Solids (cond-mat.mtrl-sci) Mathematical Physics (math-ph) <p class="font-claude-response-body break-words whitespace-normal leading-[1.7]">We derive the propagation of mechanical waves (sound) within the Structured Vacuum Theory with 23 channels (TVS23). Three results follow from the geometry of the V23 network with zero free parameters. First, sound velocity is identically zero in the vacuum: the V23 network contains no topological knots, and mechanical transmission requires knots. Second, sound velocity in any material is bounded above by the torsional wave speed <span class="katex"><span class="katex-mathml">c/23≈13,043c/23 \approx 13{,}043 </span><span class="katex-html"><span class="base"><span class="mord mathnormal">c</span><span class="mord">/23</span><span class="mrel">≈</span></span><span class="base"><span class="mord">13</span><span class="mord"><span class="mpunct">,</span></span><span class="mord">043</span></span></span></span> km/s. Third, in gases the adiabatic index <span class="katex"><span class="katex-mathml">γ=(N+2)/N\gamma = (N+2)/N </span><span class="katex-html"><span class="base"><span class="mord mathnormal">γ</span><span class="mrel">=</span></span><span class="base"><span class="mopen">(</span><span class="mord mathnormal">N</span><span class="mbin">+</span></span><span class="base"><span class="mord">2</span><span class="mclose">)</span><span class="mord">/</span><span class="mord mathnormal">N</span></span></span></span> is derived from the number of active V23 modes per molecular knot, reproducing experimental sound speeds for monatomic, diatomic, and polyatomic gases with errors below 0.5%. For elastic solids, a geometric estimate gives <span class="katex"><span class="katex-mathml">vs&sim;(c/23)4/23≈5,440v_s \sim (c/23)\sqrt{4/23} \approx 5{,}440 </span><span class="katex-html"><span class="base"><span class="mord"><span class="mord mathnormal">v</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist"><span class="sizing reset-size6 size3 mtight"><span class="mord mathnormal mtight">s</span></span></span><span class="vlist-s"></span></span></span></span></span><span class="mrel">&sim;</span></span><span class="base"><span class="mopen">(</span><span class="mord mathnormal">c</span><span class="mord">/23</span><span class="mclose">)</span><span class="mord sqrt"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist"><span class="svg-align"><span class="mord">4/23</span></span></span><span class="vlist-s"></span></span></span></span><span class="mrel">≈</span></span><span class="base"><span class="mord">5</span><span class="mord"><span class="mpunct">,</span></span><span class="mord">440</span></span></span></span> m/s consistent with observed metal values; for the hardest solid (diamond), the Pell solution <span class="katex"><span class="katex-mathml">(x,y)=(24,5)(x,y)=(24,5) </span><span class="katex-html"><span class="base"><span class="mopen">(</span><span class="mord mathnormal">x</span><span class="mpunct">,</span><span class="mord mathnormal">y</span><span class="mclose">)</span><span class="mrel">=</span></span><span class="base"><span class="mopen">(</span><span class="mord">24</span><span class="mpunct">,</span><span class="mord">5</span><span class="mclose">)</span></span></span></span> of <span class="katex"><span class="katex-mathml">x2−23y2=1x^2-23y^2=1 </span><span class="katex-html"><span class="base"><span class="mord"><span class="mord mathnormal">x</span><span class="msupsub"><span class="vlist-t"><span class="vlist-r"><span class="vlist"><span class="sizing reset-size6 size3 mtight"><span class="mord mtight">2</span></span></span></span></span></span></span><span class="mbin">−</span></span><span class="base"><span class="mord">23</span><span class="mord"><span class="mord mathnormal">y</span><span class="msupsub"><span class="vlist-t"><span class="vlist-r"><span class="vlist"><span class="sizing reset-size6 size3 mtight"><span class="mord mtight">2</span></span></span></span></span></span></span><span class="mrel">=</span></span><span class="base"><span class="mord">1</span></span></span></span> gives <span class="katex"><span class="katex-mathml">vs=c/24≈12,491v_s = c/24 \approx 12{,}491 </span><span class="katex-html"><span class="base"><span class="mord"><span class="mord mathnormal">v</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist"><span class="sizing reset-size6 size3 mtight"><span class="mord mathnormal mtight">s</span></span></span><span class="vlist-s"></span></span></span></span></span><span class="mrel">=</span></span><span class="base"><span class="mord mathnormal">c</span><span class="mord">/24</span><span class="mrel">≈</span></span><span class="base"><span class="mord">12</span><span class="mord"><span class="mpunct">,</span></span><span class="mord">491</span></span></span></span> m/s (observed: 12,000 m/s, error 4.1%), with equilibrium distance <span class="katex"><span class="katex-mathml">req=λ0⋅ρ≈1.40r_{\rm eq} = \lambda_0 \cdot \rho \approx 1.40 </span><span class="katex-html"><span class="base"><span class="mord"><span class="mord mathnormal">r</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist"><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mathrm mtight">eq</span></span></span></span><span class="vlist-s"></span></span></span></span></span><span class="mrel">=</span></span><span class="base"><span class="mord"><span class="mord mathnormal">λ</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist"><span class="sizing reset-size6 size3 mtight"><span class="mord mtight">0</span></span></span><span class="vlist-s"></span></span></span></span></span><span class="mbin">⋅</span></span><span class="base"><span class="mord mathnormal">ρ</span><span class="mrel">≈</span></span><span class="base"><span class="mord">1.40</span></span></span></span> Å (observed: 1.54 Å, error 9%), where <span class="katex"><span class="katex-mathml">ρ=1.3247…\rho = 1.3247\ldots </span><span class="katex-html"><span class="base"><span class="mord mathnormal">ρ</span><span class="mrel">=</span></span><span class="base"><span class="mord">1.3247</span><span class="minner">…</span></span></span></span> is the plastic constant — the real root of <span class="katex"><span class="katex-mathml">x3−x−1=0x^3-x-1=0 </span><span class="katex-html"><span class="base"><span class="mord"><span class="mord mathnormal">x</span><span class="msupsub"><span class="vlist-t"><span class="vlist-r"><span class="vlist"><span class="sizing reset-size6 size3 mtight"><span class="mord mtight">3</span></span></span></span></span></span></span><span class="mbin">−</span></span><span class="base"><span class="mord mathnormal">x</span><span class="mbin">−</span></span><span class="base"><span class="mord">1</span><span class="mrel">=</span></span><span class="base"><span class="mord">0</span></span></span></span>.</p>
title	Sound Propagation in the Structured Vacuum Network V23: Zero in Vacuum, Bounded in Matter
topic	structured vacuum, sound velocity, acoustic propagation, vacuum network, torsional waves, adiabatic index, Pell equation, plastic constant, dodecahedral geometry, zero sound vacuum, upper bound, TVS23, beyond standard model, elastic solids, diamond General Physics (physics.gen-ph) Condensed Matter — Mechanics of Solids (cond-mat.mtrl-sci) Mathematical Physics (math-ph)
url	https://doi.org/10.5281/zenodo.19712686