21 lines
2.0 KiB
TeX
21 lines
2.0 KiB
TeX
\section{Related Work and Theoretical Context}
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Analogies between classical and quantum phenomena have a long history in physics. Bohmian mechanics \cite{Bohm1952} attempts to give particles definite trajectories guided by a pilot wave, blending classical-like paths with quantum outcomes. Similarly, prior works have drawn parallels between fundamental forces at different scales \cite{Holdom2017,Panpanich2018}.
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Modified gravity theories like MOND \cite{Milgrom1983} have attempted to explain galactic dynamics without dark matter by modifying Newton's laws at low accelerations ($a_0 \sim 1.2 \times 10^{-10}$ m/s$^2$). Subsequent developments \cite{Bekenstein2004,Famaey2012} have explored relativistic extensions of these ideas. Our approach differs by adding a new force term rather than modifying existing laws, though as we will show, it faces similar challenges in explaining galaxy rotation curves.
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Recent observations have provided unprecedented tests of gravity in extreme regimes. The GRAVITY collaboration's tracking of star S2 orbiting Sagittarius A* \cite{Gravity2018,Gravity2020} has confirmed general relativistic effects with remarkable precision. Similarly, Gaia's astrometric data \cite{GaiaDR3} offers new opportunities to test modified gravity theories at stellar cluster scales.
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\section{Atoms are Balls: Multi-Element Verification}
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\subsection{The Core Insight}
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Current quantum mechanics treats atoms as two-dimensional systems with angular momentum quantum numbers. But what if atoms are actually three-dimensional spinning spheres—balls, not circles? This simple conceptual shift leads to profound mathematical consequences.
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\subsection{Universal Formula for Atomic Binding}
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For any atom treated as a 3D spinning sphere, the binding force emerges from rotational geometry:
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$$F_{\text{spin}} = \frac{\hbar^2 s^2}{mr^3}$$
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where $s = mvr/\hbar$ is calculated from the electron's actual motion. We'll demonstrate this works not just for hydrogen, but across the periodic table. |