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Light travels in photon packets, So if we get to travel at that speed or faster, we go up in flames. What's the word again... auto-combustion?
It's spontaneous combustion. And no, you won't burst into flames because A: space is a vacuum mostly sans oxygen and B: the molecular bonds whch bind your corporeal atoms would disintigrate first. In other words, you'd vanish before getting a chance to burst into flames.
Quite a few accurate explanations in this thread but also several misunderstandings, which unfortunately, I've no time to clarify. Suffice to say...
You can travel faster than light, assuming space itself is travelling with you. The answer lies within matter itself and more importantly, dark matter.