请问HN:一个愚蠢的维度分析游戏

1作者: egoism2 个月前原帖
几周前,我曾想过电磁学可能存在一个维度阶梯,但我无法将其转化为可用的东西。现在我感到沮丧,分享一些我的Markdown笔记。 <p>从安培的定义开始(N/m, kg/s²)...<p> - V = 电压,以伏特为单位(2019年前等于 m²/s)<p> - Q = 电荷,以库仑为单位(2019年前等于 kg/s)<p> *惯性表面 (J·s²)*<p> <pre><code> ∫V dt × ∫Q dt = m² × kg </code></pre> *作用模式 (J·s)*<p> <pre><code> V × ∫Q dt = (m²/s) × kg ∫V dt × Q = m² × (kg/s) </code></pre> *能量,压力模式 (J)*<p> <pre><code> dV/dt × ∫Q dt = (m²/s²) × kg V × Q = (m²/s) × (kg/s) ∫V dt × dQ/dt = m² × (kg/s²) </code></pre> *功率,压力波 (J/s)*<p> <pre><code> dV/dt × Q = (m²/s²) × (kg/s) V × dQ/dt = (m²/s) × (kg/s²) </code></pre> *冲量,波动转换 (J/s²)*<p> <pre><code> dV/dt × dQ/dt = (m²/s²) × (kg/s²) </code></pre> *空间导数,对“物质”的影响?*<p> - d(表面)/dx ~ 运输<p> - d(作用)/dx ~ 动量<p> - d(能量)/dx ~ 力<p> - d(功率)/dx ~ ??? 传播?<p> - d(冲量)/dx ~ ??? 转换?<p> *空间积分,对“空间”的影响?*<p> - ∫(表面)dx ~ 惯性体积<p> - ∫(作用)dx ~ kg·m³/s<p> - ∫(能量)dx ~ kg·m³/s²<p> - ∫(功率)dx ~ kg·m³/s³<p> - ∫(冲量)dx ~ kg·m³/s⁴<p> 在功率的波动模式中,“相位”= dV/dt,电荷= Q,结合海维赛德的波动方程 `d²(伏特)/dt² + v² * d²(电流)/dx² = d²(电流)/dt² + v² * d²(伏特)/dx²` 那么将会变为.... `d²(相位)/dt² + u² * d²(电荷)/dx² = d²(电荷)/dt² + u² * d²(相位)/dx²` 其中 v² = 1 / LC,u² = 1 / ??
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I thought a few weeks ago, that there might be a dimensional ladder for EM, but I can&#x27;t figure out how turn into something usable. I&#x27;m sharing some of my markdown notes, now frustrated.<p>Starting from how an Ampere used to be defined (N&#x2F;m, kg&#x2F;s2)...<p>- V = Voltage, in Volts, (pre-2019 equal to m2&#x2F;s)<p>- Q = Charge, in Coulombs, (pre-2019 equal to kg&#x2F;s)<p>*Inertial Surfaces (J·s²)*<p><pre><code> ∫V dt × ∫Q dt = m² × kg </code></pre> *Modes of Action (J·s)*<p><pre><code> V × ∫Q dt = (m²&#x2F;s) × kg ∫V dt × Q = m² × (kg&#x2F;s) </code></pre> *Energy, Patterns of Stress (J)*<p><pre><code> dV&#x2F;dt × ∫Q dt = (m²&#x2F;s²) × kg V × Q = (m²&#x2F;s) × (kg&#x2F;s) ∫V dt × dQ&#x2F;dt = m² × (kg&#x2F;s²) </code></pre> *Power, Waves of Stress (J&#x2F;s)*<p><pre><code> dV&#x2F;dt × Q = (m²&#x2F;s²) × (kg&#x2F;s) V × dQ&#x2F;dt = (m²&#x2F;s) × (kg&#x2F;s²) </code></pre> *Impulse, Wave Conversions (J&#x2F;s²)*<p><pre><code> dV&#x2F;dt × dQ&#x2F;dt = (m²&#x2F;s²) × (kg&#x2F;s²) </code></pre> *Spatial Derivatives, Effects on... &#x27;Matter&#x27;?*<p>- d(Surface)&#x2F;dx ~ Transport<p>- d(Action)&#x2F;dx ~ Momentum<p>- d(Energy)&#x2F;dx ~ Force<p>- d(Power)&#x2F;dx ~ ??? Propagation?<p>- d(Impulse)&#x2F;dx ~ ??? Conversion?<p>*Spatial Integrals, Effects on... &#x27;Space&#x27;?*<p>- ∫(Surface)dx ~ Inertial Volume<p>- ∫(Action)dx ~ kgm3&#x2F;s<p>- ∫(Energy)dx ~ kgm3&#x2F;s2<p>- ∫(Power)dx ~ kgm3&#x2F;s3<p>- ∫(Impulse)dx ~ kgm3&#x2F;s4<p>In the wave modes for Power, &#x27;Phase&#x27; = dV&#x2F;dt, Charge = Q, with Heaviside&#x27;s wave equation `d2(Volts)&#x2F;dt2 + v2 * d2(Current)&#x2F;dx2 = d2(Current)&#x2F;dt2 + v2 * d2(Volts)&#x2F;dx2` would then.... `d2(Phase)&#x2F;dt2 + u2 * d2(Charge)&#x2F;dx2 = d2(Charge)&#x2F;dt2 + u2 * d2(Phase)&#x2F;dx2` where v2 = 1 &#x2F; LC, u2 = 1 &#x2F; ??