Yeah, I don't know if the EM Drive works. Last I saw, once they accounted for the lorentz effect, a number of labs drastically cut their reported thrust findings. And the warp effect that Dr. White saw was explained by the fact that EM fields (like the microwaves in the EM Drive) affects the speed of photons.
But it's kinda interesting how you stated this part:
It implies that the equations of physics have some terms in them which work for macroscopic (not astronomical), moderate speed (non relativistic), macroscopic energy (i.e. not high energies) which mysteriously cancel out perfectly in almost all macroscopic circumstances.
Because we DO have special equations for our understanding of astronomical physics. Dark energy is causing galaxies to accelerate away from each other. We think the universe is expanding. We only really observe it at inter-galactic distances.
Because we DO have special equations at relativistic speeds. Time slows down.
Because we DO have special equations at high energies. Crazy stuff I really don't understand where atoms break down and it's all quark-soup or something.
Because we DO have special equations for microscopic (and smaller) things when they get so small that they run into quantum physics.
We also have special equations for how the empty void of space "wobbles" and splits into matter and anti-matter, but recombine and cancel each other out most of the time. Look up the casimir effect.
All of these laws of physics are in full effect and take place inside that chamber of the EM Drive. It's not like quantum physics goes away for macroscopic things. We just expect all the random aspects to balance each other out and give things a mostly definite position and momentum. And for the expansion of space to be ludicrously small. And for it to remain in our time-scale reference frame as we're going the same speed and we're next to similar masses.
If the EM Drive works, and yeah, that's STILL a big "if", then it'll probably generate some more equations like all of the above have done.
Or, it implies that space has absolute position and speed
... Hey lemme run this one by you. I haven't gotten a good answer to this one yet:
Consider 3 bodies in space. Earth, a mothership, and a babyship. Earth isn't at a stand-still, but we can take it a frame of reference. The mother ship launches from Earth at .99c to the right. That's 1:7 time dilation. A day on the mothership is a week on Earth. Now the mothership isn't at rest, but from it's frame of reference it launches a babyship going 0.99c to the right. That stacks with Earth. So a day on the babyship is a week on the mothership is 49 days on Earth.
And yes we can compare all those timepieces. We know the planned course of these things and know where they plan on being. We know the speed of light, their proximity to mass. We have really good telescopes and they have their atomic clocks hanging out a window we can look at. We can't know these values in real-time, but in hindsight with calculation, we can know their exact location and clock reading at any given point.
Alright. All that is simply setup. Here's the meat.
What if we launch the babyship to the left? Towards Earth. 0.99c - 0.99c = 0 and it's going the same velocity as Earth. So what do the clocks all show on these three bodies? The mothership is not standing still, but we can use it as a frame of reference. If she launches the baby one way, does she see it's clock speed up but if she launches it the other way she sees it's clock slow down? That means there's absolute velocity.
If it doesn't matter which direction she chooses, then how the hell do her observations of earth and the baby jive?
How about we slap an atomic clock on a resurrected SR-71 and have it fly along the 3 axis somewhere on Earth with some really good ground-based position tracking to see if we can see a difference in the time dilation depending on the direction it's heading?