The math for special relativity predicts that it would take infinite energy to accelerate any amount of matter to light speed and also that the speed of time will approach zero as you get to light speed. Beyond light speed it’s all impossible undefined behavior.
The reason we trust this mathematical model is because it makes a lot of other unlikely but easily testable predictions (about color shifts and about the passage of time at high speeds) which have so far all turned out to be true.
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