Hopefully the title sums it up well, but I'm looking for potential faster than light travel (hoping for real or pseudo-real science here, as much as possible) that doesn't involve a warp drive, which is literally the only theory I know of that defines it as impossible without breaking general relativity - but I'm writing about a civilization so far into the future that calling someone Einstein is an insult, referencing how simple and misguided his theories were/led civilization down the wrong path for centuries due to no one thinking outside his box (I don't actually believe this, I think his work will eventually be "disproved" in some manner, but absolutely fundamental for humanity to get that far in the first place - doesn't mean that can't be lost on a civilization over a 1000 years later with insanely advanced science).
For background, this story begins in 1042, the switch to the new calendar isn't detailed in depth, but occurred around the years 2640-2680 AD. This is a unified, single government Earth with all peoples living in a relative Utopia(or at least believing so, kind of irrelevant to the story, actually). The formation of this new world order is loosely based on western ideologies but focuses on a "healthy" (please don't make me define that!) mix of socialism and capitalism in a true democratic society (technology/AI handles most logistics and enforcement, global votes are held as often as 10% of the population pushes forward any proposal, anyone can propose literally anything, yadda yadda). They have near lightspeed travel after effectively adapting photon cannons developed in war to act as engines in space. They have a firm grasp on what we now describe as anti-matter, describing it instead as "hidden energy", and are able to utilize it in our reality. Our main character was appointed as Director of the Department of Energy in 1026, and has used a bulk of the funding and manpower to achieve faster than light travel, not by a warp drive, but by literally breaking the light barrier (think breaking the sound barrier), and simultaneously clearing the space in front of the ship of all matter by absorbing it and converting it to fuel nearly instantaneously. This does imply an absolute necessity to plot courses carefully, and be extremely careful of traveling through planets and stars, not for the ships safety, but for the gravitational implications of eating a ship sized hole (more so in planets) through something as it travels through. Think a bullet through an apple. Like a wormhole type of travel but literally just ripping through space, matter, and time instead of going around it in another dimension, and the 'wormhole' closes up more or less instantaneously after the ship travels through. However I'm entirely unsatisfied with the "plausible" explanations I've come up with for how this travel actually works. I realize that's because real, modern science doesn't support it as plausible in the first place. Any ideas?
I just want it to be less "hand-wavey"
EDIT: I say faster than light travel without utilizing a warp drive where the term "warp drive" is defined as the ability to achieve faster than light travel by warping space-time around the ship, rather than the ship itself traveling through space-time. I'm very specifically looking for faster than light travel through space-time. "Breaking the light barrier" is a necessary part of the plot.
EDIT 2: To add a couple more details here, this is a brand new development in this society, the main character is presenting his proofs, the opening is an interview with a reporter to describe the new advancements. This is only described in theory until near the end of the story, where they've built out and do the first practical test. To give away the ending, this test is world ending due a miscalculation and hubris preventing it's discovery until too late. They can't actually travel faster than light as they propose. I don't actually need it to be science based and safe - just seem plausible and with a slight equation tweak so it appears safe, but that mistake causes quite a catastrophe when put into practice. The protagonist actually describes in detail his disdain for previous directives disallowing study into warp drives by the department of energy, due to past catastrophes (warp drives at first appeared successful, but no one ever came back, if they did reach a destination), but finds it irrelevant now as he and his department have achieved it without a warp drive, or at least believe they have.