I get the statement but this is physics as we know it. "fundamental in relativity would have to be wrong" as we believe it to be.A massive object cannot reach the speed of light because the Lorentz factor becomes infinite as velocity approaches the speed of light. That drives total energy and momentum to infinity. In spacetime terms, massive objects follow timelike trajectories and cannot transition to lightlike trajectories. The barrier is mathematical and geometric, not technological.
For faster than light travel to be possible, something fundamental in relativity would have to be wrong. Special Relativity shows that as an object with mass moves closer to the speed of light, the energy required to keep accelerating it increases without bounds. At exactly the speed of light, the required energy becomes infinite. Since infinite energy is physically impossible, objects with mass cannot reach that speed.
This is not just an energy problem, it is built into the structure of spacetime. Massive objects move along what are called timelike paths, while light moves along lightlike paths. To exceed the speed of light, an object would have to shift into a completely different category of motion, which relativity does not allow. Doing so would also create causality problems, where events could appear to happen before their causes in some reference frames.
So for faster than light travel to work, we would have to overturn Lorentz invariance, the relativistic energy equation, or the basic geometry of spacetime itself. All of those have been confirmed experimentally to extremely high precision. That is why the speed of light is understood as a structural limit of reality, not a technological barrier. What would it mean for the Lorentz factor to be wrong? It would mean the 38ms time difference between GPS satellite time and earth surface time would be wrong and your GPS wouldn't be accurate and it would drift 10km per day. The Lorentz factor can't simultaneously predict this time difference but also be wrong about the infinite energy required for massive objects to reach the speed of light - for one to be true, the other must be true. Experimentally, the increases measured in energy/momentum are unbelievably accurately predicted by the Lorentz.
Im really not that interested in the subject and I have never researched or cared to learn about it. But I refuse to believe travel through space can only exist as we know it. I see ourselves as primitive. All good, not debating you I am just say I am not a believer in the limitations you have posted. However, I will not be on this earth in a thousand years or whatever time it takes.
http://www.physics.semantrium.com/relativity.html
"A paradigm with an absolute time and space does not constitute a physical fact though: it's an agreement, so alternative paradigms can in principle be proposed. However, for any absolute velocity there simply cannot be a satisfactory definition of time and space. The relativistic transformation equations themselves are a farce, they are false definitions of time and space for two reasons: ..."
Im not sure but I think the above makes my point!