I've read about tachyons and still can't see how going faster then light relates to going backwards in time.
This effect is due to the dilation of time at relativistic speeds. The speed of light is constant to all observers. If you were traveling parallel to and in the same direction as a particular photon, and you were going 185999 miles per second (one mile per second less than the speed of light), what you would see and what people watching you would see are very different:
People watching you would see the photon slowly out-pacing you by about 1 mile per second. You, on the other hand, would see the photon take off at 186,000 miles per second away from you because the speed of light is constant to all observers.
The reason you would see it going so much "faster" is because time will have slowed down for you to a near stand-still. In fact, right at the speed of light, time stops. A photon experiences no time at all. From a photon's point of view, the entire universe is an instant away. Nay, not even an instant. The whole universe is here. (Another reason I favor an atemporal universe.)
So, if time slows towards a stop as you approach C, what happens if you continue accelerating? Well, for one thing, you would need an infinite amount of energy to do it. For another thing, you'd become infinitely massive in the process. But, assuming you're okay wearing the extra weight and you have all the energy in the cosmos pushing you, you'll still only be able to get TO the speed of light, not beyond it. Accelerating beyond it would take MORE than infinite energy, which obviously cannot exist. It would also make you more than infinitely massive, and Richard Simmons would have to pay you a serious house call.
However, if you did get past that barrier somehow, since time has been slowing down more and more until it stopped, as it continues to slow, it begins going backwards. After all, it cannot speed up and it's dilation must change, so the only way to go is back.
Current theory allows for a whole class of energy that naturally exists at >C speeds - they didn't have to accelerate to get that fast, they are just naturally that fast. Just as a photon doesn't accelerate at the speed of light - it just comes into being at that speed. But, if they are going that fast then they are necessarily traveling backward in time.
This time dilation effect isn't a theory - it's a proven fact. Even in your normal, every day experience you accelerate fast enough to cause time dilation. The guys who maintain atomic clocks have to adjust (believe it or not) for the relativistic effects of accelerating in their van to drive between work sites. (Although the adjustments are incredibly minor.) In a more practical example, the GPS satellite network loses accuracy at the rate of about 20 miles per day unless relativistic effects are taken into account and adjusted for constantly. Those satellites are flying in a circle, and that means that they are constantly experiencing acceleration - and any acceleration causes time dilation.
The detection of tachyons is a tricky thing: If one is headed towards your "detector", it doesn't exist yet and by the time it does exist it's already in the past. They basically exist in "imaginary time" which is a real thing but something that we have no idea how to detect or access. It's like thinking of measuring the volume of a twelve dimension object. It's simply unfathomable to us. But, if they ever are proven to actually exist (not just proven to be absolutely possible, but proven to ACTUALLY exist), the implications would be profound.
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