Introduction / Handwaving
The Continuity Wars takes place in a universe whose laws are much like our own. They are not entirely identical, however. In the 'verse where and when the Continuity Wars are fought (hereafter referred to as the CWV), time travel is not only possible, it is practically inevitable.
This has farther reaching consequences than it appears at first glance. Causality, the idea that effects must have causes, and that those causes must precede those effects, is a basic assumptions of physics in our universe. Though it is generally not easily apparent to non-physicists, the small level, nanoscopic universe of electrons and quarks and configurations builds up to the level of humans and eventually up to planets and stars and whatnot.
I am not a physicist. (At least, not yet. Give me another six to seven years). I don't think anyone here is. This is one of the few major handwaves I'm going to throw in here. That rule is that the universe works, consequences be damned. I don't know enough to right a plausible universe down to the quantum level, so where the CWV's rules make a mockery of the quantum stuff, the quantum stuff loses. The big stuff, though is all the same, except for the part where time travel works.
That said, this here is science, no magic. Magic – the supernatural in general – is any system where there are mental phenomenon that don't reduce to non-mental material parts. In the CWV, this is not the case. Everything is material, everything works because it is made of smaller pieces following simple rules. It just isn't necessarily the same rules.
This is where the second major hand wave comes in – the actual part of what makes something go back in time. I can't think of a plausible structure that would do it other than some sort of relativistic effect, but those are unsatisfactory for other reasons, relating to what we do know about how they work and the material costs implicit in them. So in this case what exactly the time machines do get their stuff going backward in time is undetermined. The “rules” I have are focused around the effects of time travel, with the exact how being “undermined, but known in universe”.
The Basics
The CWV operates on the principle of weak causality, where our universe operates on rules of strong causality. Under strong causality, it is impossible to have an event that has no actual cause. Under weak causality, events must have a possible cause, but doesn't necessarily need an actual cause. The best way to think about it is that the time travel events are not caused by something that happens in the future, but rather something that happens in the present. If, at 8:00 there is a 100% chance of you going on to send something back to 8:00 from 9:00, then you can expect that object to show up at 8:00. At 8:00, you can conclude not that the object was caused to appear by something that happened at 9:00, but rather that the configuration of the universe being such that an object would be send back in time to 8:00 was certain. If at 8:00 there is only a 10% chance of you sending the object back in time, you would expect to find the object a correspondingly lower percentage of the time.
That said, once an object has actually arrived, there are no strings attached. Nothing has to happen. However, if the actual chances are altered by a person's decisions, those decisions are part of the probabilities at any given time. If, for example, you would spend money send back in time and not send it back in time when it was time to do so, the money would simply never appear.
Weaker causality means that the impossible becomes the merely improbable. This is the closes way I can keep time travel stories and keep the universe from degenerating into nonsense in a heartbeat.
Note that in this universe probability - what you can and cannot know - are considered properties of events, not properties of minds. The probably of any given event includes the proababilty of time travel, but more weakly than things that currently exist. For example, when calculating the probablitity that someone will go back in time, the fact that another time traveler might come back and kill his younger self is only weakly considered, and so only results in a small reduction in probability.
What Actually Happens To The Stuff
When an object travels backward in time, it simply “pops” and disappears. Conservation of energy and matter don't work exactly when dealing with time travel. The matter is simply no longer there, and has (probably) reappeared in the past. In some cases it won't, and that matter is gone. In an equal number of cases, objects will appear without being sent back. Over any sufficiently large stretch of time, mass/energy is conserved.
The same applies to showing up. If there's something in the way, things get...unpleasant. Both the teleport-ee and the unlucky object he landed on will probably explode – as if they had been compressed together with unimaginable force, and then let go.
Other Consequences
For starters, this time machine business makes for a practical teleporter, and no, there is nothing you can do to stop it. It makes defense planning...interesting to say the least. Of course, the ability to go back in time and blow up your opponent before they can attack you evens things out a little bit.
I don't know what happens when you try to time travel while going close to the speed of light. The only possible answer to that is that God kills a catgirl every time someone tries it.
I'd like this thread to be for general discussion/questions regarding time travel, so the chronolab can be for specific thought experiments that these rules don't cover.