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Sorry...the explanation is MUCH more simple. Once you exceed the speed of light (if you indeed could, which you can't) what you are REALLY observing is time moving backwards, hence the light's arrival BEFORE it left.
Any theorioes involving infinities are non-renormalizable, and mathematically useless to make predictions or in the assessment of "observations." Negative time IS CERTAINLY permitted and is an integral part of both newtonian and relativistic explanations of forces and fields.