Time travel would likely be instantaneous from your perspective, since you're not actually moving in any dimension except time. Speaking of which, I've seen a lot of comparisons of time to space. IE, if we can move both forward and backward in space, why can't we do the same in time? It's been explained to me on
another thread that time is not a spatial dimension.
In regards to going 'around' time, I believe the reference is similar to the standard two-points-on-a-piece-of-paper example for describing how a wormhole might work. If you haven't heard of it before, it goes like this:
Consider two dots on a piece of paper. What is the shortest possible distance between these two points? The answer seems simple, a straight line, right? Wrong. The shortest distance is to fold the piece of paper so that the two points touch. The distance is now zero, and you can travel there without moving! The question is, how to bend spacetime such that two desired points connect. Stephen Hawking seems to have a lot to say on this subject... I suggest finding some of his literature if you're really interested in the wormhole idea.
In regards to:
There is one more method I know of: Closed timelike curves. Apparently when you got in a circle, you'll end up where you were a little while later. If you went fast enough, you'd be back at where you started before you went, so you would achieve a fraction of a step into the past. If you kept on doing so, you could apparently go thousands of years or more back to earlier events. Unfortunately, you would need cosmic string, and other exotic materials to achieve such a Back-to-the-Future-esque flight.
In order to go fast enough that you arrive just as you depart, you would have to be traveling at an infinite velocity. In other words, you don't travel you just
are. As if that doesn't seem difficult enough, in order to arrive
before you depart, you'd have to go faster. In other words, this theory assumes it's possible to go faster than infinite velocity.
Finally, one last note. In regards to:
I cannot believe for one moment that if time travel was possible, that there would not be some indication of it. That it would be so restricted or policed to never let idiots leave things behind.
Hmm... hope I don't offend anyone but... how about that Bible? Or perhaps... Stonehenge? Similar such features may turn out to be exactly those kind of 'traces,' but we'd never suspect it because we're so used to hearing about them.