请问HN:一个愚蠢的维度分析游戏
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 / ??
查看原文
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 / ??