If you look carefully at the analysis in my first quote, by extension this graph, and thus this limit, does not just apply to this engine, it applies to ALL engines. No engine using ANY type of thrust can accelerate at a constant rate beyond a limit where the kinetic energy of the rocket exceeds the total energy of the thrust (delta v) that got the engine to that velocity. Any rocket, any form of thrust that is linearly constant, has a Law of Diminishing Returns on its velocity determined by its kinetic energy. Under constant acceleration, the graph of the instantaneous velocity is not linear.

@JustinThymetheSecond If the rocket exerts a constant force and its mass does not change, it accelerates at a constant rate, which means its kinetic energy does increase more and more rapidly over time. The diminishing returns are instead about designing the rocket. See this post with charts showing velocity and energy over time for a rocket and its exhaust.

In fact, (1) the speed of a rocket with a constant burn rate will curve upwards over time, because it gets lighter as it loses propellant, so the same force applied to a lighter rocket produces higher acceleration. (2) The rate of increase of kinetic energy of the rocket reaches a maximum when the rocket's velocity equals its exhaust velocity, and diminishes at higher speeds because it is decreasing in mass even "faster" than it is accelerating.

I do not consider stack exchange as a legitimate reference. My point is, no rocket engine can increase the rocket velocity beyond the point where the kinetic energy exceeds the total energy input, else at some point all rockets turn into a perpetual motion machine. Accelerate, slam into a heat sink, collect the energy, use it to accelerate the rocket again beyond the intersection of the curves, slam it into a heat sink, repeat ad nauseum, more energy is retrieved than put into the system. Therefore, at some point, the energy of the thrust can not lead to an increase in velocity.

Or the equation for kinetic energy can not be consistent across all velocities, or the equation for kinetic energy has to have some built-in law of Diminishing Returns factor.

@JustinThymetheSecond I'm the one who wrote what I linked, and I stand by it. The reason that "at some point, the energy of the thrust cannot lead to an increase in velocity" is really simple and doesn't require revising Newtonian physics: it's because you run out of propellant, and then your velocity stops increasing. It just so happens to work out, that you're always going to run out of propellant before you break conservation of energy.

Your 'diminishing mass' adjustment only applies to thrust that requires reaction mass. Given a rocket that, for instance, has the reaction mass teleported in, as it is consumed, faces the same limitation as this rocket. Also, the 'laser sail' rockets have this velocity limit. My point is, NO rocket can have a continuous thrust and acceleration beyond the kinetic energy threshold.

Of course, all bets are off if it turns out that inertia can be manipulated somehow. Kinetic energy and inertia are two sides of the same coin. Without inertia, there is no kinetic energy. In some sense, I get the idea that the theory behind this rocket engine alters inertia, and thus the kinetic energy of the system. But then, since your idea requires kinetic energy to produce your 'free energy', it is dead in the water. No inertia, no kinetic energy, no free lunch.

Just repeating the reason why this drive cannot work isn't a frame challenge, it's just missing the point.

My frame challenge is that it just might NOT be a perpetual motion machine, it just might work, but with limitations that restrict it from becoming one.

If it does work, but not as a perpetual motion machine (there are unforeseen restrictions on its operations that prevent the kinetic energy from becoming larger than the applied energy, it could be a very low powered maneuvering thruster but never cross the threshold. Just like all other engines that have restrictions that prevent them from crossing the threshold. The existence of the threshold itself is not sufficient proof to discredit the engine.

@JustinThymetheSecond In the case of a photon rocket, the propellant is the photons themselves. And you do run out of them. For example, if your photons come from a matter-antimatter reaction, you're eventually going to run out of matter and antimatter to react. If you didn't run out then indeed your relativistic kinetic energy would grow without bound and conservation of energy would be violated. But since you do run out it's okay.