Energy To Matter, $i$ Matters

The proposed Breit - Wheeler Process, to create an electron and positron pair.

And how do you collide in space to create two particles driven down the charge time axis in opposing directions?  If matter/anti-matter interaction is collision along the charge time line that results in energy in space-time then by symmetry it should be possible to collide energy in space to move matter again along the charge time line.  Consider the change in energy in space and along the charge time axis if this happens,

$\Delta E_t=0-2m_pc^2=-2m_pc^2$

$\Delta E_{ct}=\cfrac{1}{2}m_e(iv)^2+\cfrac{1}{2}m_e(iv)^2-0=-m_ev^2$

The corresponding decrease in energy along the space axis cannot be equal to the corresponding increase in energy along the charge time axis.  A negative sign gets in the way.

This is not possible; unless the photons are also along the charge time axis.  ie.  $c\rightarrow ic$

$\Delta E_t=0-2m_p(ic)^2=-2m_p(-c^2)=+2m_pc^2$

then

$\Delta E_t=-\Delta E_{ct}$

And thanks to the formulation,

$F=\cfrac{q_1q_2}{4\pi\varepsilon_o r^2}$

where  $\varepsilon_o$  is a measure of the resistance in establishing the electric field.  By symmetry, $\varepsilon_o$  also suggests a resistance in de-establishing a field.  This means space itself can be charged.  So,  it is possible, $c\rightarrow ic$  where  $ic$  is along the charge time line.

In this setup, one photon is on the negative charge time axis and the other in the opposite direction on the charge time axis.  Maybe this will work.  The point is  $i$ and being consistent across time axes.