Quadratic form of energy and momentum are well proven in accelerator experiments.
E2 =(mc2)2 +(pc)2
Also energy is the sum pf potential and kinetic where gravity is part of the potential.
E = T + K
E2 = T2 + 2TK + K2
Comparing the two quadratics at high speed it appears that (mc2)2 and (pc)2 must be related to each other, for a quadratic equation to be necessary.
Taking (mc2) as T, K is calculated
K = - (mc2) + SQRT( (mc2)2 + (pc)2 )
Implication is that momentum increases faster than expected from applied thrust field, from conversion of mass to kinetic energy caused by acceleration.
A graph of my creation is attached. The top line slope is the total energy gain including conversion of mass to kinetic energy in this representation. The maximum point is a critical condition that occurs inside a kinetic wormhole. Farther right shows mass conversion continuing without need of engine power.
The vehicle and contents may convert to gamma rays at the point where three lines meet if acceleration continues to the extent that reverse engine power is not able to stop it.
This is the alternative representation to infinite energy needed to reach light speed in the well accepted equation.
E2(1-v2/c2) = (mc2)2
Mass decreases as speed increases, going to zero at light speed in agreement with observation that massless objects travel at light speed.
The bottom line is momentum.
Why is Energy A Quadratic equation?