The Equation of Continuity is the four dimensional derivative of
a four dimensional variable set to zero. This is also called the
limit equation and the Boundary equation, and the Homeostasis
Equation. The Continuity Equation is also called the Invariant
Equation or Condition. The most famous equation that is in fact a
continuity Equation is Maxwell's Electromagnetic equations.
(d/dR + Del)(Br + Bv) = (dBr/dR -Del.Bv) + (dBv/dR + DelxBv +
Del Br) = 0
This gives two equations the real Continuity Equation:
0=(dBr/dR - Del.Bv)
and the vector Continuity Equation:
0=(dBv/dR + Del Br)
This Equation will be more familiar when R=ct and dR=cdt and cB
= E then
0=(dBr/dt - Del.Ev) and
0=(dBv/dt + Del Er)
The Continuity Equation says the sum of the derivatives is zero.
The four dimensional variable has two parts a real part Br and a
vector part Bv. The Continuity Equation is the sum of the real
derivatives is zero and the sum of the vector derivatives is
zero.
The term DelxBv is zero at Continuity because this term is
perpendicular to both the other two terms and makes it impossible
geometrically for the vectors to sum to zero unless it is zero.
Only if the DelxBv=0 can the vectors sum to zero. This situation
occurs when the other two terms are parallel or anti-parallel. If
anti-parallel then dBv/Dr is equal and opposite to Del Br and the
vectors sum to zero.
This is Newton's Equal and Opposite statement in his 3rd Law and
is a geometrical necessity for the vectors to sum to zero..
Many Equations of Physics have misrepresented the Continuity
Equation and others have not recognized the continuity Equation as
in Maxwell's Equations.
The Continuity Equation is probably the most important equation
in science!
The Four dimensional space of science is a quaternion
non-commutative (non-parallel) space defined by William Rowan
Hamilton in 1843, (i,j,k and 1), with rules i^2=j^2=k^2=-1.
