Assume each and every time traveler (traveling "into the past") decides to meet up at a universally agreed-upon destination (specified to the plank time).

Also assume that each and every time traveler is assigned a unique prime number of plank units to go back in time.

It it guaranteed that every possible combination of time travelers will meet together in some alternate universe or another.

... This is not going to end well.

Honestly I didn't find it too difficult to follow, but I guess that's how my mind works. I do a lot of these thought experiments too, maybe that's why.
I do like this idea, but I guess I'd have to agree that it makes things a bit difficult for a story. This evolved beyond hard sci-fi and expecting the reader to follow becomes a bit of a rash assumption lol.

I can't really guess at any way of using this further, except as a fun puzzle. Make scenarios and see how well they can be plotted out. Make a game with any of your other brainy friends. It's a good concept to make people re think over and over as they try to visualize.

Sam, I think the best way to look at this would be using elementary physics.

in normal time, the position of a particle is given by x = velocity * time
if hypertime acts the way you suggest, it implies x = velocity * (time + hypertime)

as such, this is really like modeling time travel with an infinite number of IDENTICAL timelines out of phase with one another. I think this is a wasted use of hypertime, because you can model it with one timeline and traditional 'back to the future' style time jumps.

a more interesting scenario would be using x = velocity * time + hypervelocity * hypertime

where hypertime would be carrying the universe to a different future at a hypervelocity???

Somewhere in the past I read a paper whose premise was: "Assuming string theory is true, which combinations of spatial dimensions + temporal dimensions could harbor intelligent life forms?" Unfortunately I can not see to Google it up. However, IIRC one of the points the author makes is that for intelligent life to exist in any sense we mean the term, it must be possible to look out in the world, make observations, make predictions, and act on those predictions meaningfully. Two time dimensions were mentioned as being right out, because string theory predicts it to be a chaotic maelstrom from which no useful information could emerge.

Interestingly, he writes off two spatial dimensions for much the same reason. Where we only have to worry about our past light cone when making decisions, and further only our very local past light cone, apparently in two spatial dimensions the entire universe is continuously interacting with the entire universe, so despite the fact the universe is notionally much smaller it is actually much "bigger" in the sense that an intelligent lifeform must worry about. (If I am recalling correctly.)

I didn't come up with that paper, but I did find this while looking for it: http://www.phy.duke.edu/~muller/Talks/Columbia_100412.pdf

Of course in those cases, the physicists are talking about "real" two temporal dimensions that could exist in string or other real theories, and yours are less "physical" than that, but still, the principle seems to hold almost no matter how you slice it. Two time dimensions is just gibberish. (Arguably, it's why you can't fully harmonize Back to the Future in the end, no matter how hard you try. Though you've had some fun trying.)

The way I envisioned this was as a sheet of chain mail, being pulled off the edge of a table at an angle. The point at which the chain mail slides off the edge is the present, the mail still on the table is the future, and the tangled heap on the floor is the past.

Each link is an arbitrarily small amount of time. Assuming that the edge of the table is on the left, and the mail is in front of us, then each vertical column of links is a certain point in time in different timelines, and each horizontal row is comprised of different points in time inside a single timeline.

Since the mail is angled relative to the edge of the table, in some [columns/timelines], a given [row/moment] is in the [heap/past], and in others it's [on the table/in the future]. There is exactly one [column/timeline] per sheet in which a given [row/moment] is [on the edge/in the present].

Now imagine that there are multiple sheets on the same table, and replace "sheet" with "hypertimeline". Hope that helps.

This reminds me of the fan theories of how temporal mechanics in Chrono Trigger work. If we apply principles from there to more coherent physical models, I wonder how they would hold up. For example, time traveling events are subject to time travelers' immunity. What this more or less amounts to is that if Alice travels to January 1, she will arrive on January 1 in all subsequent timelines, regardless of any causality.

I also suspect that problems have a tendency to arise if we assume that instantaneous spacetime travel is allowed.

If this works how I imagine it works, though, the whole "infinite stack of derailed timelines" can't happen.

If you travel back in time ten years, it implies that 10 years "up" from yours, there existed a timeline where that version of you did the same thing, and your timeline must still be present for you to make the jump or else you'd have no story, so this model must be inherently self-consistent. In terms of TV Tropes, "You Already Changed The Past" comes to mind.

Wow, my head exploded but I *think* I got what you're saying. Could be interesting, but mega hard to explain in the confines of fiction, where you have to keep the reader entertained too.

Do you still maintain that list of types of time travel? May want to put a link to here from that.

I'd just like to point out that this sort of time travel produces effective "waves" in hypertime. Think of one of the classic simplified time travel cases, where someone looks at the setting of a circular dial, goes back in time, and then sets that dial to whatever they recorded, plus some extra turning (ignoring whatever setting they find the dial in). If they turn it 0 radians (or exactly 2 pi, 4 pi, etc.) from what they saw, then a single timeline is consistent; the dial is always at one setting. If they turn it some other number, there is a grandfather paradox within a single timeline, but it can be resolved consistently either by invoking multiple timelines or some sort of "forcing" that prevents such paradoxes. That is, a dial that was turned to face up, would then turn face down, and vice versa. You'd need multiple universes or for some other mechanism to turn the dial (or prevent this sort of time travel in the first place).

Along your proposed "hypertime", there is a trivial continuous solution, which is that the dial turns steadily as you go through the different timelines (along a line of constant "clock" time, say, 1/1/2000). The rate of turning of the dial depends on how far back in time you go and how far you turn the dial. Each version of you gets a dial setting from some previous version of you, and gives a new one to the next person. There are actually infinitely many continuous solutions (because the "wave" of dial settings has a maximum wavelength based on the degree to which you turn the dial and the amount of time you travel through, but no minimum, since arbitrarily close universes could have arbitrarily different starting dials). With a discretized spacetime, there are still very large numbers of consistent solutions; the system is underdetermined unless there is some extra interaction between the universes that couples them. However, with coupling, and after specifying a mechanism for travel along hypertime, this sort of hyperuniverse can have deterministic outcomes to time travel experiments (aside from the usual difficulties with quantum measurement).

Not sure I'm being clear here, but the kicker is this. A case of going back in time ten years and killing yourself sets up a sort of "square wave", where ten hypertime-years worth of universe have you showing up and killing yourself, and the next ten have you never having arrived, living, and leaving to kill yourself, and the next ten have you killing yourself... However, if there's an interaction between universes that causes them to align, then high-frequency components get damped out. That is, it's energetically unfavorable to have sharp boundaries between "you live" and "you die" universes. If this factor is very weak, it doesn't matter, and you can do what you want, like go back and straightforwardly kill yourself. If it is very strong, nearly all universes are nearly identical and all time travel that would change the future is impossible. But in the middle, you have cases where there's near-continuous variation between universes. So in between the "you live" and "you die" states, you might have intermediate cases where you almost kill yourself but fail, or where you never arrive from the future but some other murderer does, or something kills you other than yourself, or some other bizarre case. The universes may not end up with identical events, but nearby universes could line up in ways that seem bizarrely coincidental or fated. Because the time travel process would require a certain amount of work (to get out of the lowest energy, all-universes-are-identical state), that work could result in events that look like a decrease in global entropy (waste heat being released either through the time travel mechanism or via random "noise" bouncing through the interaction between universes).

I guess that what I'm saying is, I'm having an otherwise slow day and find this idea interesting.

Suddenly relitivistic FTL time travel paradoxes seem trivial...

Wow, I actually thought of this same theory a little while back. (Didn't make a blog entry about it though, so I guess credit goes to you as first publisher ;). By the way, I'm a bit uncertain, does yours go infinitely far in both the forwards and backwards directions? (In mine I would start at the most 'future' time and try to work work it back from there).
I came to the same conclusion you did: That such a time-travel model is too complex to be feasible for any sort of story, or even more than very basic thought experiments. However, in my opinion it is the way parallel universes would probably work in reality. For this reason I decided that the following modified model would work better. It is similar to those used in certain sci-fi stories:

Okay, for simplicity, firstly assuming only backwards time-travel: Whenever you 'time-travel' a new parallel universe is 'created' (or perhaps 'activated'?), identical to how the first was. Both the universe you come from and the universe you arrive in then continue to run forwards as normal. Anyone in this new universe is now free to travel back to the original universe (back to the future), but cannot change its true past at all (that's water under the bridge so to speak). And the people in the old universe are free to travel to the other universe. (Provided anyone traveling actually has a 'time-machine'). And people in both universes are free to bring into being completely new universes at different (in this model, past) points in time. I haven't quite considered what would happen if you allowed forwards time travel as of yet.

In any case, you would probably then want to make time-travel prohibitively expensive to prevent a whole array of new universes popping into being. Perhaps just something to consider...

HT seems like a very complicated space. There could be some interesting mathematical puzzles to solve in HT.

I would like to point out that what Sean said sounds awfully familiar to how the time-traveling RTS game Achron works (you can time travel within a certain period around you, of which it gets too expensive to go further, but it causes propagating 'waves' to go through time and change battles, even while in the midst of such a battle or whatever). Fascinating game and quite familiar to this conversion.

I read so much crap from the physicists, that you'd not worry to be 'plausible' or to make sense in you SF stories.

Brian Green's "The elegant universe" make people believe that strings and superstrings are part of a theory. And this is not true. Maybe it is in the wish-list of 'stringers' but Smolin, a former stringer :-), five years ago published "The Trouble With Physics" The rise and fall of String theory, where he pointed out that if youn don't play strings, you are out of theoretical physics researches. Besides Smolin, Peter Woit, a matematician, wrote "Not Even Wrong". This one made me understand a little better, maybe because I have a Math degree, that strings don't make sense. They even aren't wrong.

And then? Who cares to be believable or to make sense in fiction?
My 9 y.o. daughter and me often talk about the two dimensions of time.
And I think: why only two? Why not three?

When you travel in space, you also travel in time. The first dimension of time.
An ordinary trip is nothing less going from A to B.
Coordinates are A(xA,yA,zA,t1) and B(xB,yB,zB,t2) and t2 >= t1

An hypertrip could consider the other two dimensions of time and you don't need to explain in a fictional paper, just like Greene didn't explain anything in his (scientific?) works.

Just imagine what should happen if...
Flatland people could not imagine so many space beyond the second dimension

I'd suggest also fractal time, with non integer dimensions, like (log 6)/(log 2)
but time is gone, the post is over though I've something more to say

I'm going to elaborate on the video game OvermindDL mentioned http://achrongame.com/

It's an RTS with freeform time travel, and the system it uses is very much like what you've described. Due to engine limitations, the timewaves are usually several minutes apart, and time travel is only possible inside a narrow band of realtime/hypertime. But otherwise, it's very much like what you've described. ("Timewave" is the game's term for individual universes which it is not possible to exit without a time machine; "timeline" is reserved for the current moment in hypertime.)

The net results are usually very rapid divergence of the different timewaves, even if you're only sending information into the past and not soldiers. The game engine tries to mitigate this by merging timewaves together once they fall too far into the past, which results in a single almost-consistent timeline. It is also possible to abuse the slight temporal inconsistencies to duplicate units, but this takes time and energy, is easily subject to outside distruption (you're in a war zone, after all), and it is usually easier to build new units from scratch.

We did wonder about how Special Relativity affected all this. Some people hypothesised that, in much the same way as FTL travel can be abused for time travel, realtime-travel can be abused for hypertime-travel. I'll see if I can find my notes on the subject. As you can imagine, if you want to remove this possibility it gets complicated.

The basic idea (a 2D time sheet) is simple and is something a lot of people have thought of. Not hard to visualise. The consequences of 'time travel' in this model do seem convoluted, though.

Sean's wave model sounds coherent, but I may indeed have to draw diagrams to understand it fully.

Jeremy, are you talking about http://en.wikipedia.org/wiki/Spacetime#Privileged_character_of_3.2B1_spacetime ?

The Aether - Part Deux.
Your theory is plausible. It's consistent. It shows that, as we know, causality cannot be violated, because if it is, things break. Your theory could accurately describe the universe. We can't test whether it does, though, so it can be safely discarded if it doesn't benefit science. It sure is fun to speculate on, though.

No fair. I came up with this first after watching Doctor Who.

This makes perfect sense to me. A very simple framework through which very complex situations are possible. And on top of this: A fundamental limit (the beginning of time) which allows timelines to be isolated from one-another, avoiding the "wouldn't have one person done X and ruined it for everybody by now?" dilemma which often springs up in time travel frameworks.
This is not convoluted at all. It can lead to convoluted situations, but that's not a sign of a bad framework.

The situations which this allows the possibility of are indeed complex enough that I think that software used to model them could be interesting. At the very least, a theoretical object model for such a system could be interesting.

Piers Anthony used the very bare tip of this idea -- parallel universes separated by instants of time -- in his books ORN and OX (See http://en.wikipedia.org/wiki/Of_Man_and_Manta). He didn't use the idea to explore time travel, however -- just alternate universes.

http://goo.gl/LoF5g shows a snippet view in Google Books search with this text:
"... an instant of time instead of by physical distance. Our connection happened to be to this particular alternate, Paleo -- a purely random selection. We could as easily have landed on a world removed by a single year, or by five billion years."

I don't see what benefit there is to using this system of time travel. From your own perspective, it behaves the same as an "alternate timeline" model, like the one you used in Ed Stories and Be Here Now. You travel back in time, and you derail that new timeline however you see fit, and if you prevent your past self from traveling back in time, there's no paradox, because you just changed timelines. The fact that an alternate copy of you that you never met and never can meet is also traveling back in time (or not) doesn't change a thing. Since you can't distinguish it from a standard alternate history model, what's the point of this?

What's stopping you from claiming that this hypertime universe is a single timeline which is part of another whole set of timelines. Meaning, the time travel done by your traveler is an event taking place in a timeline, albeit a much larger one which is a composite of many others. This timeline could be a single line of an even larger 2D timeline.

This is not so disconcerting, as it soon becomes clear that all of the "yous" that make jumps from a given moment all do so along a vertical line. Essentially all of the time travelers in parallel timelines shift up or down simultaneously but maintain their temporal displacement from one another. This is not unlike a sort of "time wave" that propogates along this "time medium," if you will.

What would interest me is to observe many time travelers jumping around and observing how these "time waves" interact with one another. If the behavior is similar to waves observed in our universe, then it should be possible to view interference. If one time traveler hops back and forth between two times, one might suggest that there are points along the direction of travel where the time traveler gets his existence temporarily canceled out by destructive intereference from himself or herself or yet other travelers. It is also conceivable that his or her existence can in some way be "enhanced" through constructive interferece, although I have no idea how to characterize what that would actually translate to physically.

Many apologies for the double post, but I'd just like to add that, from a first person perspective, the game Chrono Trigger is indistinguishible from your description of 2D time.


Alex.

Paul: Yes! Funny that all my searches missed out on a Wikipedia page :-/

At least we aren't being asked to imagine four balls at the edge of a cliff. ;)

JeremyBowers: you are almost certainly referring to http://space.mit.edu/home/tegmark/multiverse.pdf

This reminds me of the way they use time travel in The Red Wing (http://www.comicbookresources.com/?page=article&id=31554 first link I found - all four issues are out now). I'm not entirely certain it isn't the same concept largely because they don't go to great lengths to clarify their concept of how space time is structured and quite a bit seems to be left up to the reader to puzzle out on their own. It's a fun read if you like that sort of thing.

This is useless for time travel, because it's incredibly destructive. Consider: any time travel event that takes place creates a pattern over all the infinity of universes (which are specified as identical). Multiple jumps (which won't have the same length) set up interference, as previously stated. Consequentially, time travel is practical for a brief period and then becomes completely unpredictable, as the place you jump to stops bearing any resemblance to a past you would recognize.

Unless..

You stated that the universes are all the same because they're being "dragged along". Would using time travel break this mechanism? In that case, the first timejump would degenerate the universe into a "traditional" multiverse, where universes would evolve unaffected by the ones "above" them. Maybe that adds a probabilistic component, where the universe below your time travel interference starts out the same but quickly deteriorates without the guiding influence of universe above it. Actually, using time travel creates a discontinuity - the universe being time travelled to would try to exert drag on a universe that is of a vastly different configuration. Could this effect be measured? Or would it add up to noise?

Anyway, this is not as elegant as it looks at first glance.

So what you do lower in hyper-time doesn't affect what happens higher in hyper-time?

Surely if all universes are identical to each other your decision to go back in time would already have happened in all universes above you in hypertime? i.e. say you decide in 2020 to travel back to 2010, 10 years 'up' in hypertime there is a timeline where the present time is 2030. 10 years in the past in this timeline a version of you made the decision to travel back in time 10 years, arriving in 2010 in the original timeline. Since it is given that you make the decision to travel back in time despite the presence of another version of you in your own timeline, the 'course of history' has not changed, in fact any decision you make to go back in time will have already happened upwards in hypertime and so it is actually impossible to change history, and there aren't waves of timelines playing out different events. All timelines follow the same series of events.

Allow free will, then it becomes simple because only a few you's will travel back.