(I originally posted this in a sci-fi forum. I was trying to illustrate how writers on these shows play fast and loose with concepts in physics. How'd I do?)
Well, let me just ramble for a moment...
If I were writing some fiction, and convinced myself that I wanted to throw in chaos theory in relation to n-dimensional planes, I'd have to imagine some kind of force that crosses between those dimensions. Otherwise the gauge aspect of chaos theory wouldn't hold at all (if the planes were not connected by *something*, then the idea of local vs. global is meaningless between dimensions). So, let's further imagine this force is some kind of field, and we know (heh) that fields typically have some particle counterpart.
We now have a transdimensional field, and we have particles which are generally considered a physical manifestation of energy (E=mc^2 takes care of that for us). Ok, good. Now we need a name that gathers that together. For sake of my own ego, I'll call them lokkions (bigger heh).
These so-called (by me) lokkions exist, because we say they do, and so we can detect them in some way. Perhaps it's indirectly, but nonetheless if we can detect, we can influence. Now we're getting somewhere! Since we presume the gauge part of chaos theory holds true, and if we suppose that lokkions interact chaotically (they are sensitive to initial conditions), and finally that we can somehow manipulate them, we have a tool for doing *something* across the dimensions.
Stick with me, 'cause it gets really hairy right here...
It's not enough to do *something*, because if the system is non-linear and exquisitely sensitive to the start of some event, we can leverage the localization of chaos theory in our dimension to also do *something* in another dimension. Let's assume for the moment that we get to choose which dimension, and not think too hard about it. Let's further assume it's a dimension that allows us to survive, and is conveniently aligned in such a way that we don't pop out into the middle of a sun. A nice dimension with bikinis and piña colladas.
Mmm... coconut. Where was I?
Oh, dimensions. We have a tool now, and we can change the very fabric of time-space (locally, remember) to allow us to travel without using a worm hole. And (bonus points), it works both ways! Again, the gauge aspect of chaos theory allows us symmetry - if we can get there, we can get back. Of course, we'll need the same tools there as here.
But wouldn't you know it? The specific flavor of energy relies on some exotic combination of field interactions that can be detected but not manipulated by our current technology (see the paradox? I already said if we could detect, we could manipulate. but we're writing fiction, so we just shrug and say "except in this case"). Moreover, that exotic combination must occur here and there at the same moment in time. Then we need to figure out a way not to control the fields, but to redefine time between the dimensions. It's relative, right? We push into hyperspace, thus changing our time relative to the time in Piña Collada Prime (I just made that up), and set our sensors to look for a confluence of fields.
We find it, pop through, sniff the air, and check our clock against star charts (worry about those details later). We see that while it took us 3 days to find the confluence, barely an hour passed in PCP (remember our other dimension?). See, we can now say there's an inversion in relativity due to symmetry that isn't realized until you hop the border. And bonus points because it works going both ways - when we get back, we only left two hours plus how ever much time passed in PCP. Presuming we can find another confluence in the same 3-day window.
And guess what? Some of you are thinking we just found a new way to cover huge distances but gain back the time. Well, I'm afraid it doesn't work that way, Sir. Because we are the ones traveling, we still age normally in our own plane of reference. We get back in 2 hours, but aged 6 days.
See there? I've built my own limitations and plot twists, setting up for hard decisions in the future.
I need a beer.