It’s only a problem if you are mistakenly under the impression that something is somehow prohibited from undergoing constant acceleration for an arbitrary length of time. Which would put you at odds with long established theory from some great scientific minds, but you’d be far from the first person to plant a flag on that hill just to die on it.
I'm unsure as to why you think that I am mistaken. You have made a statement but failed to provide any evidence. What theory, what scientists? I'm honestly unsure as to whether this is authentic or a joke. The speed of light in a certain medium is a speed barrier that cannot be surpassed, numerous experiments have proved this. One such example is the phenomenon of Cherenkov radiation, which is the blue glow observed in nuclear coolant pools. Light travels much slower underwater than in a vacuum, so nuclear material can emit radiation that would be traveling faster than light in water. This cannot happen, and so the particles emit photons to release energy.
If you are referring to linear acceleration, then I am right. An object is prohibited from undergoing linear acceleration for an arbitrary length of time. Acceleration is change of velocity. For a linearly accelerated flat earth to match empirical observations of gravity, the world would have to constantly increase it's velocity. At some point, in this case just under a year as I previously mentioned, the world would reach the speed of light. The idea of the speed of light then has to either be dispelled with, which contrasts with observations, or has to be somehow overcome. The acceleration cannot be changed, because that would result in a perceived change of gravity. The speed of the earth cannot be changed, because then everyone would smack into the ceiling at the speed of light (which would be quite a sight).
I'm quite certain you can't demonstrate that you are right, because doing so would violate General Relativity, which I strongly suspect is the very theoretical framework you are referring to when you say nothing can travel faster than "the speed of light" (which you probably meant to call simply c, or the vacuum speed of light, but whatever it doesn't matter). The issue is that you are defining the speed of something either against some sort of a preferred FoR (which doesn't exist) or from some independent observer's FoR, which is necessarily going to be different than that of an observer standing on the surface of a constantly accelerating disc.
So. The ball is in your court. If you'd like to disprove Relativity, have at it, but you own the burden of proof if that's the path you want to go down. I'll pick Einstein in this particular battle of wits though. At least he knew his own model.
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