| 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. Starting from how an Ampere used to be defined (N/m, kg/s2)... - V = Voltage, in Volts, (pre-2019 equal to m2/s) - Q = Charge, in Coulombs, (pre-2019 equal to kg/s) *Inertial Surfaces (J·s²)* ∫V dt × ∫Q dt = m² × kg
*Modes of Action (J·s)* V × ∫Q dt = (m²/s) × kg
∫V dt × Q = m² × (kg/s)
*Energy, Patterns of Stress (J)* dV/dt × ∫Q dt = (m²/s²) × kg
V × Q = (m²/s) × (kg/s)
∫V dt × dQ/dt = m² × (kg/s²)
*Power, Waves of Stress (J/s)* dV/dt × Q = (m²/s²) × (kg/s)
V × dQ/dt = (m²/s) × (kg/s²)
*Impulse, Wave Conversions (J/s²)* dV/dt × dQ/dt = (m²/s²) × (kg/s²)
*Spatial Derivatives, Effects on... 'Matter'?*- d(Surface)/dx ~ Transport - d(Action)/dx ~ Momentum - d(Energy)/dx ~ Force - d(Power)/dx ~ ??? Propagation? - d(Impulse)/dx ~ ??? Conversion? *Spatial Integrals, Effects on... 'Space'?* - ∫(Surface)dx ~ Inertial Volume - ∫(Action)dx ~ kgm3/s - ∫(Energy)dx ~ kgm3/s2 - ∫(Power)dx ~ kgm3/s3 - ∫(Impulse)dx ~ kgm3/s4 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 / ?? |