问 HN：一个关于量纲分析的无聊游戏
1 分•作者: egoism•7 个月前
几周前，我曾设想过可能存在一个电磁场的维度阶梯，但一直无法将其转化为可用的东西。现在我分享一些我感到沮丧的 Markdown 笔记。<p>从安培的定义开始（N/m，kg/s²）...<p>- V = 电压，单位为伏特，（2019 年前等于 m²/s）<p>- Q = 电荷，单位为库仑，（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，应力模式（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，应力波（J/s）*<p><pre><code> dV/dt × Q = (m²/s²) × (kg/s)
V × dQ/dt = (m²/s) × (kg/s²)
</code></pre>
*冲量，波的转换（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 ~ 传输<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 ~ kgm³/s<p>- ∫(能量)dx ~ kgm³/s²<p>- ∫(功率)dx ~ kgm³/s³<p>- ∫(冲量)dx ~ kgm³/s⁴<p>在功率的波模式中，“相位”= dV/dt，电荷 = Q，使用 Heaviside 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...
`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't figure out how turn into something usable. I'm sharing some of my markdown notes, now frustrated.<p>Starting from how an Ampere used to be defined (N/m, kg/s2)...<p>- V = Voltage, in Volts, (pre-2019 equal to m2/s)<p>- Q = Charge, in Coulombs, (pre-2019 equal to kg/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/s) × kg
∫V dt × Q = m² × (kg/s)
</code></pre>
*Energy, Patterns of Stress (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>
*Power, Waves of Stress (J/s)*<p><pre><code> dV/dt × Q = (m²/s²) × (kg/s)
V × dQ/dt = (m²/s) × (kg/s²)
</code></pre>
*Impulse, Wave Conversions (J/s²)*<p><pre><code> dV/dt × dQ/dt = (m²/s²) × (kg/s²)
</code></pre>
*Spatial Derivatives, Effects on... 'Matter'?*<p>- d(Surface)/dx ~ Transport<p>- d(Action)/dx ~ Momentum<p>- d(Energy)/dx ~ Force<p>- d(Power)/dx ~ ??? Propagation?<p>- d(Impulse)/dx ~ ??? Conversion?<p>*Spatial Integrals, Effects on... 'Space'?*<p>- ∫(Surface)dx ~ Inertial Volume<p>- ∫(Action)dx ~ kgm3/s<p>- ∫(Energy)dx ~ kgm3/s2<p>- ∫(Power)dx ~ kgm3/s3<p>- ∫(Impulse)dx ~ kgm3/s4<p>In the wave modes for Power, 'Phase' = dV/dt, Charge = Q, with Heaviside's wave equation
`d2(Volts)/dt2 + v2 * d2(Current)/dx2 = d2(Current)/dt2 + v2 * d2(Volts)/dx2`
would then....
`d2(Phase)/dt2 + u2 * d2(Charge)/dx2 = d2(Charge)/dt2 + u2 * d2(Phase)/dx2`
where v2 = 1 / LC, u2 = 1 / ??