 Quote by granpa
it would just mean that there would be one simultaneous 'now' for everyone .a preferred frame. nothing else would change.
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Quote by RandallB
Correct - no time paradox created.
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Why do you guys think so? I'm pretty sure you're wrong. (See #3).
Edit: OK, I think I get it. You interpreted the question as "What would happen if we let the invariant speed of special relativity go to infinity?" while I interpreted it as "What would be the consequences if we could send messages at speeds much higher than the invariant speed of special relativity?".
Maybe the OP can explain what the question was about.