zmatt wrote:*personal opinion*
I don't think time travel back in time is possible with relativity. Relativity allows forward time travel because as the name states we are changing what is experienced "relative" to the observers. In practice it is less actual time travel than it is slowing down time for you and letting the world pass you by. The explanations I have heard and read for possible backwards time travel with relativity is very similar to forwards, it seems as though its a "hack" if you will on our perception of the universe. You travel to a distant place where the light from earth is very old and shows a younger one, then you travel back at relativistic speeds and viola you are with dinosaurs (over simplification). I think that sounds a little silly.
It might sound silly but it's the way it works. The whole "wait-a-minute this implies faster than light travel is equivalent to time-travel" was one of the early criticisms of GR. Turns out that for every experiment we can do, it upholds those laws. We can't go faster than the speed of light, but there exist solutions to the GR metric that allow for such weird time loops. The general expectation is that if we ever get a chance to experiment with one of these, it will explain a lot that we don't know. In short, it may not be possible, but as the theorem stands it is, and nothing has ever suggested that the theory of General Relativity is wrong.
Now, in regards to the op, as far as the question goes no. We can send something back to the wormholes creation from arbitrarily far in the future, but not any further. We also need two wormholes for this skullduggery, but there's no requirement for them to travel through eachother. This is going to be a monster post, so you may want to just go with the pat answer, and the edit at the end noting one possible other restriction,
but if you want an explenation and some interesting results:
What we have created is a simple system. I'm not going to screw around with the dynamics of creating it, and use the far simpler situation of a stable created system. Therefore, we now have a portal from Alpha Centauri to 3-years-in-the-past-Earth, or conversely we have a portal from Earth to 3-years-in-the-future-AC. With this portal alone it is impossible to arrive somewhere before you left. Why? Simple, because to travel between either end NOT using the portal takes four years. Thus, we could do, 4 years Earth-AC, -3years AC-Earth. We could also make it take 7 years if we went +3(portal) years Earth-AC, then the slow classical way 4 years AC-Earth. We could also take 8 years by doing the classical trip without any portals.
Importantly, we could also take almost 0 time, by hopping throught the portal twice, +3 (portal) Earth-AC, -3 (portal) AC-Earth.
In Essence what we've done is allowed any transit time that can be made up of a combination of any two numbers of the set [3,-3, 4, 4], but we can choose each number only ONCE. In fact, what we're actually doing is choosing one of [3,4] for the Earth-AC leg, and one of [-3,4] for the AC-Earth Leg. Thus the choices outlined above can be represented as: (4, -3) = 1, (3, 4) = 7, (4,4) = 8, (3, -3) = 0.
Physically this is a simple scenario, Standing on earth I have two routes to Alpha Centauri, the classical way (4yrs) and the portal (3yrs), represented by our choice of on of the set [3,4]. On AC I have the classical way (4yrs) and the portal (-3yrs), giving a choice of the set [-3, 4]
However, this is reliant on the fact that there is ONLY one portal. With two we can quite easily go back arbitrarily far. By simply constructing a second portal (again not bothering with the dynamics of it's creation) we add to our list of possible ways to move. Let's suppose that we send a second ship with a wormhole in the exact same manner out from earth, with some time dialation the gives us a wormhole whose discrepency is "a" years, much like our first one had a discrepency of 3 years. Again skipping all the dynamics until the wormhole is settled.
So now I'm standing on Earth looking at the three
possible ways to go to AC, I now have the classical route (4yrs), Wormhole 1 (3 yrs) and Wormhole 2: Electric Bugaloo (a yrs). On AC I have the choices of classical route (4yrs), Wormhole 1 (-3yrs) and Wormhole 2 (-a yrs).
So we chose one from each set of [4, 3, a] and [4, -3, -a]. From this we can choose (amoungst others) either (a, -3) = a-3 yrs, or (3, -a) = 3 - a yrs = -(a-3) yrs. As long as (a-3) is not zero (i.e., as long as our second wormhole isn't the exact same as our first wormhole) either (a-3) is negative, or (3-a) is negtive. Since either of those are valid choices I can go back in time with just the two wormholes. Note also that if we sent the wormhole from AC to Earth instead of Earth to AC, a would be negative, that is we could be going backwards (or forwards) on both legs of the trip.
If we allow a third wormhole we can get some very strange effects, for instance, suppose this new third Wormhole has a time difference of "b" years (i.e., travelling from earth you arrive at AC b years into the future). If (3-a) and (3-b) and (a-b) are not factors of eachother (e.g., it isn't a=1 and b=5) We can go back fractions of the time (3-a) rather than ONLY having the choice of incrementing back by (3-a). So if for example the loop between wormhole 1 and wormhole 2 allowed you to travel back 2 years, you could only travel back 2yrs, 4yrs, 6yrs, etc. but if there is another loop with wormhole 2 and 3 that takes 3 years off, you could also go back 3 years (loop 2 and 3) and then forwards 2 years (reverse loop 1 and 2) to arrive one year in the past. If you set your times up right you can reach some pretty arbitrary times in the past, an irrational time backwards would allow you to reach ANY point in the past (after the wormhole loops were setup).
If we allow ourselves to shove one wormhole through another we can of course shove it through a series of these loops, which results in it having the same effect as if we just went through the loops ourselves. Still, if people are commonly wrapping through the same 19 loops or whatever, shortening that will at the least alleviate some congestion (which is going to be a problem, more on that later). The important point though is that this loop shove through a loop is exactly equivalent to if I'd just taken the loops that our "loop in a loop" took.
Alright, now so far I've explained a lot of what it CAN do, which is important to show what it CAN'T do, specifically it CAN'T send us further back than the wormhole creation. Why? Because all the above relied on the idea that the wormholes were already there. If I go through my magical take me to the past loop far enough I will come to a point in the past where, standing on earth, the wormhole has not yet reached AC. At that point there is no loop, and I can't ride it back any further. I must wait for it to be setup, and that's the very first (or last if we're thinking of it in terms of the subjective time of someone travelling backwards) leg I can take. And since each leg is, by the necessity we've already pointed out, less time that it took to setup, that leg won't take you back to before the wormhole existed.
"but aha!" you say "I have a plan! I'll use my loop in a loop!". Sorry, but we've already established that that is exactly the same as just running the loops yourself. the loop in a loop only goes back as far as you. And it you can't set it up to go back further, because to set it up the original loop needs to exist! So the "loop in a loop" has an effective setup time that is always equal or greater (it could be greate if you took some time moving it between loops) than going through it removes, just like the original loops.
"But aha again!" You say, being the annoyingly-eternally-optimistic sort, "I have another, even more fiendish, scheme! I'll bring the portal gun with me!". Alright, so now you have a portal gun with you, great. What can you do with that? Well, you could setup another series of loops, but since this series won't take you back before it's creation, you can't use it to go back further than the new series is created (This new series could also have been created as part of the old series using the loop-in-a-loop method, so it's actually equivalent to the previous ill-thought-up-plan of yours you hypothetical dunce). "Okay, but what I do is setup a portal now, and then wait for the first wormhole to arrive, then I jump into it and arrive on earth one year after the original series (not of Yugioh) was created. Then I fire that end and climb through which gets me...back to the creation of the second series".
Yes. Yes it does. A similar trick (of portalling to the ship as it moves arcross the 4 light-year just from earth to AC setting up the first portal) would allow you to go back even further, to the moment of creation of the first wormhole, back on earth. Which is great, but it relied on that wormhole existing to do it, which was the original problem. You can never go back further than the creation of the first wormhole, so you can never setup a prior wormhole to connect to.
So, in short, you can travel between any two arbitrary spacetime points where the wormhole network exists (note that it has to exist at both those spaces and times), but you can never travel to before the network was setup.
Of course, this is all because the original setup involved a ship that moved slower than the speed of light. Because of that our network can only ever connect to points within the light cone of the creation of the original wormhole. If we could get outside that with some other form of FTL, then we could easily go back arbitrarily in time. Of course, if we have that kind of FTL, what the hell are we using wormholes for?
EDIT: Oh right, forgot to mention the reason congestion could be an issue. Specifically, if I can go through a loop an arbitrary number of times (because I can go back in time, piss around, and then take the loop back again, piss around, and take the loop back again alongside the two previous iterations of me etc.) so can anything. Because, in quantum mechanics, any path and particle that IS possible must be considered (gross oversimplifcation), we get an infinite number of these particles taking these loops an infinite number of times. This is a bad thing, since for one it will have an infinite mass (or mass-energy for photons) which will warp spacetime into a singularity, which will destroy the wormhole. So it's arguably possible that the first wormhole will be fine (since no "going back in time" loops are possible) but any subsequent ones (which, as mentioned before will allow for such messing around) will end up taking out the entire series of wormholes. You could created a series of wormholes that goes outwards, but it would have to be all expanding out radially (or at least mostly radially) from a single hub. Any crossing of two sets of outwardly moving wormholes would screw the entire thing over. Don't cross the streams.