Time travel that isn't too loopy and full of holes?

I'll admit, I don't watch anime all that often but when I get into one, I really get into it. And when I heard there is a good anime involving time travel? Well how could I resist?! I started watching this anime at a similar time when I was really into the Big Bang Theory (tv show), so it was like a double-dose of Physics. To add to that, I just read a couple of Hawking's Pop Physics books so I was really primed for some high level thinking on time travel theory.

My Time Travel Theory

I think it was Einstein that first made it theoretically plausible that time travel is possible with this Relativity Theory. Because time is just another dimension being affected by larger powers in physics, Einstein proved that time can be altered. The less gravitational pull on you, the less you experience time. Under new theories in string theory and quantum mechanics, it's theorized that strings do travel back in forth in time. However because we're talking about particles smaller than atoms, it's hard to ascertain this is true. These are boring time-travel theories. Fun ones are like wormholes (the one that swallowed the plane) and the "many worlds" theory (aka parallel universes).

So my take on all this is that time-travel is not possible in the realm of our understanding of physics. Between all the different theories, it doesn't seem possible to transport anything of significant mass in time. However, I do think time travel is possible because time is afterall, just another dimension of experience. I think TV shows and books have made it clear why time travel if used like we fly airplanes presents problems -- simply because affecting the past affects the future. This creates a lot of infinite loops. Time travel would have be possible with parallel universes where you are changing a different timeline. This is what Stein's Gate does so well.

SPOILERS: Stein's Gate and time travel

The essence of why Stein's Gate is great is because of the dilemna that Okabe is put into: he has to choose between two loved ones and even though he can travel through time, there are things he can't change. I think this message is very powerful because there are things that are meant to happen. There are also things that can be altered. Most people seem to either take the deterministic view or the opposing view, but this anime nicely finds a median. The anime did a great job of building up 2 likable female characters in Makise and Mayuri because I really didn't want either of them to die at the end.