No, you can't travel back in time. If you were to go faster than the speed of light I guess you might be able to see yourself coming, if that makes sense, so that you are technically seeing things that already happened, but you wouldn't fall into some weird time warp and end up in 1000 BC or something.
If you go the speed of light (300,000 km/s or 186,000 miles/s), time would stop, including your biological clock. Thus you would not age. Ever.
Maybe that's how Heaven works (eternal life).
Cheers.