Energy is Turns per Second (A Geometric Translation of Quantum Mechanics and Relativity)
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2026
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| author | Xu, Lingguang |
| author_facet | Xu, Lingguang |
| contents | <p class="ds-markdown-paragraph"><span class="">This paper translates existing physics — Planck, Einstein, Compton, de Broglie — into a single geometric language: turns per second. Planck’s constant </span><span class="katex"><span class="katex-mathml">h</span><span class="katex-html"><span class="base"><span class="mord mathnormal">h</span></span></span></span><span class=""> is the fixed exchange rate between turns per second and energy. A photon‘s energy is its helical turns per second (</span><span class="katex"><span class="katex-mathml">E=hν</span><span class="katex-html"><span class="base"><span class="mord mathnormal">E</span><span class="mrel">=</span></span><span class="base"><span class="mord mathnormal">h</span><span class="mord mathnormal">ν</span></span></span></span><span class="">). An electron’s rest energy is its intrinsic spin turns per second (the Compton frequency, </span><span class="katex"><span class="katex-mathml">E=mec2=hνC</span><span class="katex-html"><span class="base"><span class="mord mathnormal">E</span><span class="mrel">=</span></span><span class="base"><span class="mord"><span class="mord mathnormal">m</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">e</span></span></span><span class="vlist-s"></span></span></span></span></span><span class="mord"><span class="mord mathnormal">c</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 mathnormal">h</span><span class="mord"><span class="mord mathnormal">ν</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">C</span></span></span><span class="vlist-s"></span></span></span></span></span></span></span></span><span class="">), presented as a geometric analogy, not a literal claim of spinning. A moving electron adds motion turns (de Broglie frequency </span><span class="katex"><span class="katex-mathml">ν=p/h</span><span class="katex-html"><span class="base"><span class="mord mathnormal">ν</span><span class="mrel">=</span></span><span class="base"><span class="mord mathnormal">p</span><span class="mord">/</span><span class="mord mathnormal">h</span></span></span></span><span class="">) to its rest turns, reproducing the relativistic energy-momentum relation. Pair production (</span><span class="katex"><span class="katex-mathml">γ→e−+e+</span><span class="katex-html"><span class="base"><span class="mord mathnormal">γ</span><span class="mrel">→</span></span><span class="base"><span class="mord"><span class="mord mathnormal">e</span><span class="msupsub"><span class="vlist-t"><span class="vlist-r"><span class="vlist"><span class="sizing reset-size6 size3 mtight"><span class="mbin mtight">−</span></span></span></span></span></span></span><span class="mbin">+</span></span><span class="base"><span class="mord"><span class="mord mathnormal">e</span><span class="msupsub"><span class="vlist-t"><span class="vlist-r"><span class="vlist"><span class="sizing reset-size6 size3 mtight"><span class="mbin mtight">+</span></span></span></span></span></span></span></span></span></span><span class="">) is the conversion of a photon‘s helical turns into the intrinsic spins of an electron-positron pair, with threshold </span><span class="katex"><span class="katex-mathml">νγ≥2νC</span><span class="katex-html"><span class="base"><span class="mord"><span class="mord mathnormal">ν</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">γ</span></span></span><span class="vlist-s"></span></span></span></span></span><span class="mrel">≥</span></span><span class="base"><span class="mord">2</span><span class="mord"><span class="mord mathnormal">ν</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">C</span></span></span><span class="vlist-s"></span></span></span></span></span></span></span></span><span class="">. This paper does not propose new physics; it reinterprets existing equations in a unified geometric language. Its value is pedagogical and heuristic.</span></p> <p class="ds-markdown-paragraph"><strong><span class="">Keywords:</span></strong><span class=""> Planck’s constant, photon, electron, turns per second, Compton frequency, de Broglie wave, pair production, geometric translation</span></p> |
| format | Recurso digital |
| id | zenodo_https___doi_org_10_5281_zenodo_20347878 |
| institution | Zenodo |
| language | |
| publishDate | 2026 |
| publisher | Zenodo |
| record_format | zenodo |
| spellingShingle | Energy is Turns per Second (A Geometric Translation of Quantum Mechanics and Relativity) Xu, Lingguang <p class="ds-markdown-paragraph"><span class="">This paper translates existing physics — Planck, Einstein, Compton, de Broglie — into a single geometric language: turns per second. Planck’s constant </span><span class="katex"><span class="katex-mathml">h</span><span class="katex-html"><span class="base"><span class="mord mathnormal">h</span></span></span></span><span class=""> is the fixed exchange rate between turns per second and energy. A photon‘s energy is its helical turns per second (</span><span class="katex"><span class="katex-mathml">E=hν</span><span class="katex-html"><span class="base"><span class="mord mathnormal">E</span><span class="mrel">=</span></span><span class="base"><span class="mord mathnormal">h</span><span class="mord mathnormal">ν</span></span></span></span><span class="">). An electron’s rest energy is its intrinsic spin turns per second (the Compton frequency, </span><span class="katex"><span class="katex-mathml">E=mec2=hνC</span><span class="katex-html"><span class="base"><span class="mord mathnormal">E</span><span class="mrel">=</span></span><span class="base"><span class="mord"><span class="mord mathnormal">m</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">e</span></span></span><span class="vlist-s"></span></span></span></span></span><span class="mord"><span class="mord mathnormal">c</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 mathnormal">h</span><span class="mord"><span class="mord mathnormal">ν</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">C</span></span></span><span class="vlist-s"></span></span></span></span></span></span></span></span><span class="">), presented as a geometric analogy, not a literal claim of spinning. A moving electron adds motion turns (de Broglie frequency </span><span class="katex"><span class="katex-mathml">ν=p/h</span><span class="katex-html"><span class="base"><span class="mord mathnormal">ν</span><span class="mrel">=</span></span><span class="base"><span class="mord mathnormal">p</span><span class="mord">/</span><span class="mord mathnormal">h</span></span></span></span><span class="">) to its rest turns, reproducing the relativistic energy-momentum relation. Pair production (</span><span class="katex"><span class="katex-mathml">γ→e−+e+</span><span class="katex-html"><span class="base"><span class="mord mathnormal">γ</span><span class="mrel">→</span></span><span class="base"><span class="mord"><span class="mord mathnormal">e</span><span class="msupsub"><span class="vlist-t"><span class="vlist-r"><span class="vlist"><span class="sizing reset-size6 size3 mtight"><span class="mbin mtight">−</span></span></span></span></span></span></span><span class="mbin">+</span></span><span class="base"><span class="mord"><span class="mord mathnormal">e</span><span class="msupsub"><span class="vlist-t"><span class="vlist-r"><span class="vlist"><span class="sizing reset-size6 size3 mtight"><span class="mbin mtight">+</span></span></span></span></span></span></span></span></span></span><span class="">) is the conversion of a photon‘s helical turns into the intrinsic spins of an electron-positron pair, with threshold </span><span class="katex"><span class="katex-mathml">νγ≥2νC</span><span class="katex-html"><span class="base"><span class="mord"><span class="mord mathnormal">ν</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">γ</span></span></span><span class="vlist-s"></span></span></span></span></span><span class="mrel">≥</span></span><span class="base"><span class="mord">2</span><span class="mord"><span class="mord mathnormal">ν</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">C</span></span></span><span class="vlist-s"></span></span></span></span></span></span></span></span><span class="">. This paper does not propose new physics; it reinterprets existing equations in a unified geometric language. Its value is pedagogical and heuristic.</span></p> <p class="ds-markdown-paragraph"><strong><span class="">Keywords:</span></strong><span class=""> Planck’s constant, photon, electron, turns per second, Compton frequency, de Broglie wave, pair production, geometric translation</span></p> |
| title | Energy is Turns per Second (A Geometric Translation of Quantum Mechanics and Relativity) |
| url | https://doi.org/10.5281/zenodo.20347878 |