The Dispersion Interpretation of Inertia
The refractive metric is applied to the momentum four-vector to find the invariant length of that vector,
(34)
which is the invariant rest mass m. This equation is written out in component form in Cartesian coordinates as,
(35)
and the total energy written in terms of the metric components is,
(36)
This is a relativistic energy equation for a probability wave solution on a polarizable space-time manifold. From the above equation Planck's constant can be factored out so that it can be written as a wave dispersion relationship,
(37)
where the effective wavelength
is given as a
function of the wave number 
, 
and,
(38)
These are the equations that govern the dispersion of the probability waves in a polarizable Quantum vacuum such as the Dirac sea [2]. Einstein’s principle of relativity is enforced by these two equations.
For example. Given a real force that acts on
the particle of mass m., such as in a particle
accelerator. We observe that the rest mass remains invariant and
constant, since it is an intrinsic property of the particle.
However the total energy and momentum of the particle change as a
function of the work done to it. They determine the effective
wavelength of the particle. As the total energy and momentum
increase the effective wavelength decreases. This is interpreted
as the contraction of length along the direction of travel caused
by the applied force. It is a direct result of the relativistic
dispersion relationship of the wave function. The relative
contraction corresponds exactly to the amount of energy input by
the work done to accelerate the particle from the momentum p
to p+dp. Thus it accounts precisely for all of the inertia
"felt" as the reaction force, to the applied force. It
is interpreted such that the work done to accelerate an object
physically contracts the wave functions that comprise the object.
Therefore there is resistance to acceleration, which is
then quantified as the rest mass of the object in the
classical sense, 
.