Question concerning time travel (somewhat wall of texty)

[Bluntman1138]

There is still not infinite possibilities though, it is still a finite number, every even in the universe could be done every conceivable way then the next done every way in every one of those and it would still be a very large but finite number.

As for the quick calculation, that wasn't really related to this, people have trouble grasping very large numbers(I've been asked why there are so few atoms in a mol before!), it was just to help those who may not realise just how big some numbers are.

True, it wouldn't be infinite. But the number would be so big, we wouldnt even be able to conceive it. So it is labeled as infinite. The number would be that of the number of atoms in the Universe, multiplied by an equal amount of that number. A number we can all agree is inconcievable to the human brain.

But there would never be a Zero chance of the 2 of you meeting up, assuming the 2 are from the same Reality, and assuming the 2 of you dont age and live outside of space time.

As i said, you would most likely die of old age before you reunited. (So on that point it could be Zero chance. But sometimes random isnt all that random as we say in AD&D)

 

[cookyy2k]

Technically, other timelines aren't the same thing as dimensions. It's a really, really small complaint, but I get so tired of seeing dimension used as a generic term for an alternate reality.

Point taken.

But Dimension is still a proper nomenclature for Alternate Timelines, Alternate Realities, Alternate what evers. As they are still different dimensions than the one we currently reside in.

I'd say it'd be more accurate to say that they are points in a different dimension, rather then separate dimensions unto themselves. Just like last week and next week are just two points in the fourth dimension, any given timelines would just be points in, I would assume, the fifth dimension.

The interesting thing about that of course is that it raises the idea of fifth dimensional time travel. Not simply traveling to point in a timeline before it was changed, but traveling back to a version of that timeline before the change ever occurred. In other words, time for time travelers.

If you make that a possibility, it makes the OP question somehow even MORE complicated.

Don't forget in quantum mechanics there is 11 dimensions and in string theory they're upto about 23 so your 5th dimension slot is taken

 

[Whodat]

I would love to answer your question but my mind has been fucked. I need an Asparin :/

 

[So_So_Man]

Now, to complicate things further, think about this:
You know that ridiculously large number of alternate universes there would already be? Your friend jumping into them doubles that number (each universe has 2 possibilities - one where the friend (from your universe) suddenly appears, and one where they don't). Assuming that the universe jumper only jumps to a different universe and doesn't jump to different points in time, the odds of appearing in a universe with your friend are improved to 1/2.

EDIT: re-read part of OP, the machine also jumps in time, so the math gets potentially really weird and complex.

 

[Mike Richards]

The interesting thing about that of course is that it raises the idea of fifth dimensional time travel. Not simply traveling to point in a timeline before it was changed, but traveling back to a version of that timeline before the change ever occurred. In other words, time for time travelers.

If you make that a possibility, it makes the OP question somehow even MORE complicated.

Don't forget in quantum mechanics there is 11 dimensions and in string theory they're upto about 23 so your 5th dimension slot is taken

True, but since I already don't think there are alternate timelines it's not that big a concern. The system is too impractical, and the laws by which other timelines are created and differentiated are too blurry. Classically they are supposed to be created by different outcomes to random events, but the only problem is there are no random events.

Dice rolls aren't random, they are simply the result of too many factors for us to keep track of. The subtle variations in the turn of the hand, air currents, weight distribution, surface properties, probably more. If we could replicate each of those exactly, we could make the die roll the same every time. The seemingly random events of quantum mechanics are probably the same, we just haven't worked out how to keep track of all the factors that make them do what they do.

It makes much more sense to assume there is one fixed timeline, and travel to the past would simply create the history you were already aware of.

 

[FaceFaceFace]

Jesus. I'll just stick with the more common modern-Physics assumption of unalterable time where any time travel you do is part of what has already happened, will later happen, and always has and will, happen(ed). No free will beats having to think so damn much,

 

[Knife]

I think he was referring to the latter i.e. his friend from his time line. In which case IF there is infinite timelines there is 0 chance.

If that is indeed the case, then the safest bet is he will not encounter his friend. He is more likely to win every lottery in the history of time, that is every prize and if he wouldn't even bother buying the ticket.

 

[cookyy2k]

The interesting thing about that of course is that it raises the idea of fifth dimensional time travel. Not simply traveling to point in a timeline before it was changed, but traveling back to a version of that timeline before the change ever occurred. In other words, time for time travelers.

If you make that a possibility, it makes the OP question somehow even MORE complicated.

Don't forget in quantum mechanics there is 11 dimensions and in string theory they're upto about 23 so your 5th dimension slot is taken

True, but since I already don't think there are alternate timelines it's not that big a concern. The system is too impractical, and the laws by which other timelines are created and differentiated are too blurry. Classically they are supposed to be created by different outcomes to random events, but the only problem is there are no random events.

Dice rolls aren't random, they are simply the result of too many factors for us to keep track of. The subtle variations in the turn of the hand, air currents, weight distribution, surface properties, probably more. If we could replicate each of those exactly, we could make the die roll the same every time. The seemingly random events of quantum mechanics are probably the same, we just haven't worked out how to keep track of all the factors that make them do what they do.

It makes much more sense to assume there is one fixed timeline, and travel to the past would simply create the history you were already aware of.

Yeah I'm no fan of the whole multiple timelines stuff. As for quantum mechanics, it works fairly accurately in most cases, there is definitely something we don't understand there though. Also as a side note the big argument between QM and relativity about information speeds (relativity maintaining the cap and QM disputing it) has a decent experimental result on the side of QM now. Pity, I preferred, and did better at, relativity.

 

[Spitfire]

In those circumstances, I think that the chances of entering the same timeline as your friend did are somewhere close to 0.
What I'm wondering is, if there's a time machine that allows you to travel between every existing timeline, meaning it's able to identify them all, then why doesn't it allow you to travel to specific timelines as well? Like, say, the one your friend entered?

 

[The Lugz]

it may well be possible in the future to rewind the energy state of single molecules or small, aged objects to an earlier state that is indistinguishable from the original with some form of energetic field

but i still argue that that's chemistry and not time travel


allot of theory's require multiple universes, space fabric and other nonsense that has yet to be proven by any real scientific method other than educated guesswork

the answer to this thread is we don't know
because if someone did, there would be time travel already


also, infinity is commonly used where indefinite would be the superior idea

i assure you infinity is infinite, indefinite things are simply incalculable or unknown.
time travel certainly falls into indefinite

 

[CplDustov]

Hiya escapists.


Which means the probability of ending up in a world where you can find your friend is zero.

[/b]

I think it's not technically 0... just infinitely small. or as Douglas Adams said... so small as to make no odds.

 

[Jonluw]

What I'm wondering is, if there's a time machine that allows you to travel between every existing timeline, meaning it's able to identify them all, then why doesn't it allow you to travel to specific timelines as well? Like, say, the one your friend entered?

In the original scenario it did have that possibility, but to make the scenario work I cut that bit out.
The official explanation is that it runs on wishful thinking.

Complete and utter hogwash. Consider this - every timeline had at one point 1 of your friend. Whether he left that timeline or not is irrelevant. After the using of the time machine, on average every timeline still has 1 of your friend. You are just as likely to encounter more than 1 of your friend in a given timeline as you are to encounter less than 1 of your friend. That's ofcourse if by "your friend" you mean any possible variation of your friend.
If by "your friend" you mean the one that came from your original timeline, then your chances of ever encountering him again are "0" (not exact 0, but something closer to it than any number you can imagine).

Yeah.
As I said in post #3

Perhaps I should rather define the ratio as lim x→∞ 1/x

I did try to subvert that "Every timeline has 1 of your friend" bit, by saying

...sends the person who presses it to a random point in a random timeline (Except any point in a timeline in which they have been born and have not yet died. Just to simplify the scenario.)

,but I see now that this condition would only apply to worlds wherein you exist; not those where your friend exists, as was my intention. My bad.
In any case, let's just say that by "your friend" I mean the one that came from your original timeline, as it has the same implications.

Aside from that, A machine that lets your traverse parallel universe is not a time machine its a four dimensional vehicle but its not moving through time its simply displacing you to another dimension. You have to break physics to allow yourself to travel between dimensions in such a universe but your not moving through time, just parallel worlds at the same "moment" in time.

The machine does move between timelines; but it also moves in time.
I specified it allows you to travel to any point in any timeline. (Perhaps it wasn't clear that I meant "point in time" not "point in space")

And here's where it get's really fun. There would also be an infinite number of versions of your friend that decided to press the button, and another infinite number of versions of yourself deciding to press the button.

That's an issue.
The scenario I'm trying to construct sort of depends on your timeline being the only one in which you made the machine.
I suppose it's subverted by your trying only to find the friend from your own timeline.

For instance, if you build a time machine and decide to go back to last week, last week will become flooded with an infinite number of versions of yourself from all the other parallels branching off from that point who decided to go back. And that's not even including other versions that decided to visit other points in history.

Keep in mind that there are an infinite number of "last week"s as well though.
You could argue that there is an infinitely greater number of "next week"s, but not every "next-week-you" would decide to travel back to last week.

Spoiler: Also: Hey look, a new dinosaur comic about time travel

 

[Jonluw]

In the many worlds theory, there are an infinite number of timelines.

I'm not sure this is the best way to explain the "many worlds" theory. Basically, what it means is that all alternative timelines are real. How many such alternatives there are isn't strictly covered by the theory itself - our universe (under the final ideal general theory of everything) might be more deterministic than our current model outlines, such that it's only time travel occasions that give rise to new alternative timelines.

It just so happens that you and a friend have invented a time machine of sorts that allows you to jump between timelines. This machine only has a "random" button, that sends the person who presses it to a random point in a random timeline (Except any point in a timeline in which they have been born and have not yet died. Just to simplify the scenario.).

Specified to prevent meeting your world-mate, I suppose. It's worth noting that this isn't a problem for the many worlds theory, because there are no temporal paradoxes in the many worlds theory - you get around any cognitive difficulties by realising that the worlds in which the action is taking place are not the worlds in which the time-traveller originated.

Not specified to prevent you from meeting yourself. I specified it to prevent you from being able to go to all the other worlds in which your friend exists.
When I look at it now though, I see that I completely misphrased it and it doesn't come close to meaning what I intended it to.
See my response to Knife in the last post.

Your friend then goes ahead and presses the "random" button. Furious, you decide to chase after them (they owe you money) by the only means you know: pressing the random button (let's say you can bring the time machine with you when you travel so you can try as many times as you like, but your friend didn't for some reason).

Of course; an infinite number of timelines spring from the point your friend has travelled to. This means that your friend is currently in an ifinite number of timelines. There is also the infinite number of timelines springing from the line in which they didn't press the button in the first place.

Or rather, there exist infinitely many possible events in which your friend spontaneously existed where he hadn't before, as a result of his having travelled from another world. We might suppose this infinity for a given timeline is the cardinality of the time line, in that if it's really totally random, they could quite literally appear at any point whatsoever. Time is often understood to be a continuum, and hence there are not only infinitely many such possible events, but also uncountably infinitely many such events.

This only determines the number of possible events within a timeline. It is a conceptual leap to go from "Possible event" to "genuine alternative timeline" (even though the various modalities of quantum mechanics form some kind of difference in possibility, it's not apparent that this means that all possible differences amount to physically possible alternatives). If the "random" button is based on an actual, metaphysical randomness, then yeah, you guarantee that the mere pressing of the button reveals uncountably many alternative timelines. But this only exponentiates with the number of other such "truly random" events that the universe encounters.

Suppose that we live in an causally deterministic universe with the single exception of the button. What the button does to our physical model is reveal that continuum many other worlds exist. Since these alternative worlds are all physically possible, they too are bound by the physical laws, so are entirely deterministic unless they, too, contain buttons. How many such worlds contain buttons? This is a question for the physics of building the button, rather than the metaphysics of the many-worlds framework.

Problem is, there is also an infinite number of timelines in which your friend is not.

Again, this is a question for the final grand unified physical theory of everything rather than for the metaphysics of time travel. How much does genuine alternative history vary other than in respect to this incident of time travel? Without saying something fairly substantial about the degree of genuine randomness inherent in fundamental physics, you haven't given us enough to go on to presume that there actually are infinitely many such timelines. The consistent suggestion I've made is that the button is the only truly random thing there is, and that only one world (the actual world) contains it. Therefore, the timelines that you can state to be distinct prior to your pressing the button yourself would be limited to "the actual world" and "worlds reached by my friend travelling with the button".

In all of those timelines, some version of your friend exists. You are guaranteed that the world you arrive at has at some point had your friend on it.

Okay, I think I understood that last bit at least...

If I'm interpreting you correctly; you're saying that there aren't in fact an infinite number of timelines.
This is fine and all. The universe might very well be deterministic; but I wasn't really working under the assumption that the many worlds theory was the correct model of the universe. I just recall having heard that this model was the only one wherein time travel didn't cause paradoxes; so I just wanted to know how this particular model would handle the scenario I came up with.
i.e. I'm working from the premise that the many worlds theory is correct. How the world actually works doesn't really factor into it.

The possibility that there aren't actually an infinite number of timelines according to that theory is more problematic though. I and my friend did touch on that, but we set it aside, since it requires that every possible "end" of the universe would also end the branching off of timelines.
Which might very well be the case. I don't know.
But we did conclude that the number of timelines approaches infinite in any case. Which should work just as well, as far as the math is concerned, I think.

I guess it would imply that the probablility of catching your friend approaches zero instead of actually being zero though.
What I'm wondering, then, is if it is actually possible at all to produce an outcome when the probability of said outcome approaches zero.

However, a friend of mine informs me that infinities can have different values. For example, you can prove that one infinity is twice as large as another. Stuff like that.
...
How can it be that when an infinite number of the worlds you can travel to contain your friend, the chance of travelling to the same world as your friend is zero?

It's not so much that infinities have different values but rather that there are different types of infinity. Also, some of what your friend has said may not apply here, because the kinds of infinity we're dealing with are Cardinal Infinities. Because you're looking at probability, what's really going on is we're counting states.

You can distinguish between different infinite cardinal numbers, but not as fine-grained as being able to prove that 2x is bigger than x. In fact, 2x and x are the same cardinal number when x is any infinite cardinal number, because it takes just as many steps to count to x as 2x (you just count in pairs in the latter case!)

What can't be underestimated is just how much bigger one infinite cardinal number needs to be than another to be considered a different infinite cardinal number. For lack of a better turn of phrase, differing limit cardinal numbers are always infinitely bigger than their predecessors.

One of my mentor's examples really comes in to effect here. Probability in this case is like throwing two darts at a line of real numbers and trying to work out the chances to hit the same one twice. It's very difficult for it to be anything other than zero or infinitesimal.

Okay...
I think you completely lost me there.
Except for the last bit. That one I get. And I suppose it embodies my question rather well:
Would the probability of randomly hitting the same number twice on an infinite line of real numbers in fact be zero or would it merely be infinitesimally small?

 

[Tallim]

Heh the problem with infinite probability is that a probability of 0 does not mean the event can't happen. Conversely a probability of 1 is referred to by mathematicians as "almost certain"

Probability = 0 does not mean impossible, is what I am getting at. Even though your brain probably screams at you for trying to think that. So yes you are correct that the chances are 0 that it could happen, but it still could happen.

 

[Knife]

The chance of encountering your friend would never actually be 0, there will always be a chance however small that you will in fact find him. But it would be so small that you would never realistically encounter him (with an emphasis on realistic). You might have a chance to find your friend if you're immortal and have infinte amount of times to use the machine (assuming the amount of timelines is set), unless the amount of timelines grows each time you try (that means exponential growth by the way, while you have a linear amount of times), in which case your chance of finding him would still be "0" (that's what we call an infinitesimal by the way, except we no longer use that term in calculus).

 

[TimeLord]

So you are basically talking about parallel worlds?
To a single observer, the past is history: that which has happened.
The present is the here and now: the events immediately happening.
The future is what is yet to happen.
All this is different when changing the perspective of the observer.

Yet all are illusions of reality. We can apply these terms to an individual's time-stream. Within that context, the illusion becomes real, if ephemeral. Imagine a long winding stream of water, a river, stretching from infinity to infinity. Picture this and one pictures their time-stream. Now imagine a powerful wave of water, travelling along this stream. This is an event wave, a temporal signature, the exo-space-time definition of an event. This wave is an individual. As it sweeps along the stream, the crest of the wave represents the present. The stream behind the wave, which the wave has passed by, is the past. And the parts of the stream which the wave has yet to reach is of course the future.

A clarification is required here. The time-stream is not a history of the universe. It is the history of one space-time event, one individual. That person's past is defined only for them. Someone else's future may be that person's past. Such is the illusion of time.

Within the causal event horizon, every time stream interacts in some small, often insignificant way. The causal event horizon is basically the obersevable universe from the viewpoint of the time traveller. Time streams interacting is in itself not dangerous, nor is it avoidable.

However, there are situations which much be avoided. At all times your own time stream must not loop back on itself. This prevents one from meeting yourself. By travelling simplifying your choice to a point after birth, before death. You risk meeting yourself in the past and/or future. I'm gonna assume that this was not your intention. However, every time stream that can and does, branch off into a new time stream is new, and since you are basically "copying" the universe and changing a tiny part, i.e an event in a single life that while could affect millions, the reality that the time streams run in is still the same size (more or less but than you start talking time loops).

For all intents and purposes the probability of actually following your friend using a random generator is not 0, it's close to 0, close to impossible, but there is always the smallest change of getting lucky. Unless you are (as I think) talking about the moment your friend lands in a point in time, a separate time stream is created due to his actions and every new action he has altered has created more. The chance of finding him gets smaller and smaller still.

That's using Doctor Who logic. Whether it's right or not is a exercise for science!

 

[Mike Richards]

Keep in mind that there are an infinite number of "last week"s as well though.
You could argue that there is an infinitely greater number of "next week"s, but not every "next-week-you" would decide to travel back to last week.

Except that there are an infinite number of branches stemming from each of those infinite parallel 'last week's. Meaning that even if an infinite number you versions of you coming off that point decided not to go back, there would still be an infinite number of versions that did, just as there would be an infinite number of versions where you never existed at all thus rendering the point moot.

And even if it technically wasn't infinite, it would still be far too large a number to be practical or safe.

 

[Indeterminacy]

Okay...
I think you completely lost me there.
Except for the last bit. That one I get. And I suppose it embodies my question rather well:
Would the probability of randomly hitting the same number twice on an infinite line of real numbers in fact be zero or would it merely be infinitesimally small?

Infinities are tricky, but the argument that it's zero is essentially geometric. The dart is an idealised point in the real number line. Points in a continuum have a length of zero. So you're trying to hit a point that has absolutely no spatial dimensions. That's impossible.

If I'm interpreting you correctly; you're saying that there aren't in fact an infinite number of timelines.

Not explicitly (if the button exists and is totally metaphysically random, then there obviously are an infinite number of timelines) - just that this depends on how much of the multiverse is random beyond the conditions specified by the button presses. It is entirely possible that there is almost no randomness other than that introduced by time travellers.

This is fine and all. The universe might very well be deterministic; but I wasn't really working under the assumption that the many worlds theory was the correct model of the universe. I just recall having heard that this model was the only one wherein time travel didn't cause paradoxes; so I just wanted to know how this particular model would handle the scenario I came up with.
i.e. I'm working from the premise that the many worlds theory is correct. How the world actually works doesn't really factor into it.

Except it kinda does - the many worlds theory accounts for the branching of the worlds, not where and how frequently those branches occur. If you want to establish an enumeration of the branches, you need to appeal to the number of physical events that in fact cause branching to happen, and this is a question of physics rather than theories encapsulating time travel.

That is, just how deterministic the world is is still important in deciding how many possibilities there are for your friend to appear in. If the world is completely deterministic then obviously no branching happens. Suppose we have a scenario in which one person ever makes one backwards journey in time, and everything is otherwise completely deterministic. The result could be exactly two worlds where the timeline branches at the arrival point of the time traveller, if the world in which the traveller arrives does not itself subsequently result in more time travel. It would only be more numerous than that if the physical world that results from the timeline that contains the arriving time traveller is one that causes more time travel events.

The possibility that there aren't actually an infinite number of timelines according to that theory is more problematic though. I and my friend did touch on that, but we set it aside, since it requires that every possible "end" of the universe would also end the branching off of timelines.
Which might very well be the case. I don't know.

I guess this is close to what I was getting at, but I think your conclusion is too strict. There's an underlying assumption that all timelines branch. This assumption is too strong as a metaphysical point.

I guess it would imply that the probablility of catching your friend approaches zero instead of actually being zero though.
What I'm wondering, then, is if it is actually possible at all to produce an outcome when the probability of said outcome approaches zero.

I was trying to suggest that it critically depends on just how big the infinity is. The easiest way to think about it is to ask whether there is a way to count through the various branches that will eventually reach an arbitrarily chosen timeline or not, even if the counting procedure itself never finishes with a finite answer for how many there are. If, however, timelines are just that densely packed together such that you must always count an infinite number of them even before you reach one of your choosing, then the darts at the real line intuition kicks in.

 

[Jonluw]

Keep in mind that there are an infinite number of "last week"s as well though.
You could argue that there is an infinitely greater number of "next week"s, but not every "next-week-you" would decide to travel back to last week.

Except that there are an infinite number of branches stemming from each of those infinite parallel 'last week's. Meaning that even if an infinite number you versions of you coming off that point decided not to go back, there would still be an infinite number of versions that did, just as there would be an infinite number of versions where you never existed at all thus rendering the point moot.

And even if it technically wasn't infinite, it would still be far too large a number to be practical or safe.

But the number of "next weeks" that branch from each last week wouldn't be infinite.

As Indeterminacy has been trying to explain to me: it might be very small, it might be very large.
Completely depends on what the theory we're basing the situation on says about the randomness of events.

I was originally sort of going with a "random movements on a quantum level causes a large, but calculable, amount of branches every second" premise. But I'm not so sure now.

Infinities are tricky, but the argument that it's zero is essentially geometric. The dart is an idealised point in the real number line. Points in a continuum have a length of zero. So you're trying to hit a point that has absolutely no spatial dimensions. That's impossible.

Hm. I see: it isn't possible to hit the same point on a line between 1 and 2 twice if you consider the line divided into infinitely many points.
I wasn't thinking of both darts as an idealized point though.

The approach I was going for was rather "Is it possible to hit the same spot twice, when the first dart you throw marks an infinitely large area for you to hit with the next dart - which we may see as an idealized point - when the target outside the area marked by the first dart is infinitely bigger".

I don't know if this produces the same result or what...

Not explicitly (if the button exists and is totally metaphysically random, then there obviously are an infinite number of timelines) - just that this depends on how much of the multiverse is random beyond the conditions specified by the button presses. It is entirely possible that there is almost no randomness other than that introduced by time travellers.

...

Except [how the real world works] kinda does [apply] - the many worlds theory accounts for the branching of the worlds, not where and how frequently those branches occur. If you want to establish an enumeration of the branches, you need to appeal to the number of physical events that in fact cause branching to happen, and this is a question of physics rather than theories encapsulating time travel.

Ah, okay.
See, I was working from a completely baseless assumption that random events on a quantum level produce an exponentially growing number of branches every second.

I did consider the number of parallel worlds at any given time calculable, but the ultimate sum infinite, since I considered time to go on forever (be it in this universe or in other universes)

I was trying to suggest that it critically depends on just how big the infinity is. The easiest way to think about it is to ask whether there is a way to count through the various branches that will eventually reach an arbitrarily chosen timeline or not, even if the counting procedure itself never finishes with a finite answer for how many there are. If, however, timelines are just that densely packed together such that you must always count an infinite number of them even before you reach one of your choosing, then the darts at the real line intuition kicks in.

I was building on the assumption that the density of the timelines approaches infinity.

If we set this as a premise, do we reach the conclusion I was originally considering?

 

[Headdrivehardscrew]

Trying to add something that exludes the use of scary math:

Just as it is highly improbable that you will randomly end up in the random destination (space/time) your friend ended up in, it is just as unlikely that you will ever end up in your space/time point of origin. If we are talking true random, achieving that would be pure coincidence.

Taking it a wee step forward: Imagine all the action of all the various lifeforms we know of on Earth. This yeast colony just pooped out a tiny bit of CO2 while munching on your pizza dough while munching on your sugar-flour mixture. That wolf just had a nightmare and kicked the top wolf in the face. Mr. Rahman just slipped on a banana peel and made 27 people laugh, one of which subsequently died of a heart attack. Mrs. Brown just texted while driving, and Mr. White, who happened to witness this while jaywalking wanted to tell police, but as he dialled 911, he got run over by Mr. Ortiz, who did see Mr. White in time, but was unable to control the large mass of his 18-wheeler plus cargo once he really stepped on those brakes. All the while you read five lines of one book, and someone else snorted two lines of cocaine to feel better.

Recreating all actions of all creatures the way the "happened" once already is just as highly unlikely ("improbable") as your "time-travel" (which is really time-space travel") problem of choice.

Imagine the power and purpose of your "Time Machine" or "System Restore" function of your OS of choice - while they are designed to protect you from yourself and allow you to "go back in time" on your computer, they are not capable of taking you to your future, since they cannot predict what it is you are going to do.

All in all, one possible approach to all this is to synthesize and boil it down to simple questions like

"What if x (z) (...)?"
"What would have been different had I chosen option B over option A?"
(...)

While it is far from scientific, I think Donnie Darko is a wonderful, inspiring piece of art that brings the beauty and a little bit of depth out for our viewing (and thinking) pleasure. I personally do not like "The Butterfly Effect" for various reasons, but it does display some of the tricky bits of trying to manipulate space-time. If you have no allergic responses to being exposed to Walden Schmuck, go for it.

Game titles that bother with the (complicated) subject and do it properly are still very rare, to my knowledge. Only one springs to mind right now: Braid - still, not so much helpful, but an inspiring distraction that is somewhat in the context: Since most creatures and moving bits behave in a pre-programmed fashion, and are so rather easy to understand and their position in space-time (within the confines of the game experience) can be predicted by an average 100%. Seeing as just about nothing that involves the behaviour of lumps of flesh featuring a brain bigger than a pea can be predicted anywhere near 100%, the question and all its possible answers reside heavily in the theoretical field, and you can easily lose yourself in either mathematics or philosophy. Whatever your findings, the cow will still fart according to food/climate/whatever, the yeast will still do its thing and someone will still get run over or fall without anyone forcing them to do so. The randomness of it all is just as mind-boggling as the (theoretical) understanding of the universe itself, and most human ponderings on "time travel" have to be understood as mathematical self-flagellation (or indecent exposure of mathematical asshattery) or sugar-coated brainfarts of a more philosophical nature at best...