On Friday, May 26, 2017 at 2:23:55 AM UTC-5, John Heath wrote:   
   > I am going to make a cannon to test Newtonian physics. The cannon will   
   > consist of gun powder and a cannon ball. The mass of the cannon ball   
   > will be an impressive not 1 not 2 not but 4 electrons... [E = MC^2] ...   
      
   If you're going to put a C^2 into Newtonian theory, you'll have to find   
   a more creative way to do it than to just insert it by hand. So, let's   
   make one grow naturally and organically through the back door. A sort of   
   alternate history in science ("what if Newtonian physics were actually   
   true?")   
      
   Maxwell's equations will then read as follows:   
   On the "kinematic" or "configuration space" side:   
   (A) Field from Potentials: B = curl A, E = -grad phi - dA/dt   
   The d/dt means partial derivative. The derives the magnetic induction B   
   and electric field E from the electric potential phi and magnetic   
   potential A.   
      
   (B) The corresponding "Bianchi identities": div B = 0, curl E + dB/dt = 0.   
      
   On the "dynamic" side:   
   (C) The field equations: div D = rho, curl H - dD/dt = J   
   Here, the dynamic quantities are the electric field induction D, the   
   magnetic field strength H, the current density J and charge density rho.   
      
   (D) The corresponding continuity equation: div J + d(rho)/dt = 0   
      
   These equations hold for both the relativistic and non-relativistic   
   theory and note: no appearance of c yet!   
      
   Now the coup de grace -- the "constitutive" equations. All field   
   theories must have such equations, for they are the equations that link   
   the field kinematics to the field dynamics.   
      
   (E) Constitutive Relations   
   D + alpha G x H = epsilon (E + G x B)   
   B - alpha G x E = mu (H - G x D)   
      
   The quantity G is an indication of the speed associated with a frame of   
   reference in which the constitutive relations become isotropic:   
      
      Isotropic Form: D = epsilon E, B = mu H.   
      
   We will refer to such a frame as a "stationary" frame.   
      
   The relativistic form of this occurs with alpha > 0 (in which case we   
   identify the *invariant* speed as the square root of 1/alpha and call it   
   c).   
      
   The non-relativistic form of this occurs with alpha = 0.   
      
   The EUCLIDEAN form of this occurs with alpha < 0! (Yes, there is a   
   version just a suited for a 4-dimensional Euclidean time-less space as   
   the alpha > 0 version is suited for the 3+1-dimensional Minkowski   
   space-time).   
      
   In all cases, we may take light speed as the square root of   
   1/(epsilon mu), if the product epsilon mu > 0. To avoid confusion, we'll   
   resort to   
   the legacy name for this, which was V.   
      
   V and c need not be the same, not even in Relativity! (Einstein-Laub's   
   1908 papers and Minkowski's 1908 paper where Minkowski geometry was   
   ironically introduced spell out the formalism, albeit with c's all in   
   the wrong and in misleading places!)   
      
   For any of the cases (relativity with alpha > 0, Newtonian theory with   
   alpha = 0 or Euclidean space with alpha < 0), we can always consider V   
   as the speed of light and then proceed to concoct some theory for mass   
   and energy that explains its electromagnetic origin and poses the   
   equation E = mV^2. Basically, that's what Poincare' did back in the   
   early 1900's before Einstein.   
      
   For all the cases of alpha we can consider the "vacuum" as whatever   
   field has a constitutive law that is independent of the speed of the   
   frame of reference; i.e. where the law is isotropic in ALL frames. This   
   may only occur if alpha = epsilon mu.   
      
   In that case, G becomes almost (BUT NOT ENTIRELY!) superfluous. Einstein   
   was wrong in that respect in adopting the thesis that G was totally   
   superfluous. In fact, depending on which of (D,E) and of (B,H) you solve   
   the constitutive relations for and depending on how let alpha go from 0   
   to epsilon mu (assuming epsilon mu > 0) in tandem with how you let G   
   vary, a residue can remain even as alpha -> epsilon mu > 0. Even more,   
   some combinations of (D,E) and (B,H) allow solutions for the   
   constitutive law to be written down that are CONTINUOUS as G exceeds   
   over V (even in the limit as V -> c)!   
      
   --- SoupGate-Win32 v1.05   
    * Origin: you cannot sedate... all the things you hate (1:229/2)