Question concerning time travel (somewhat wall of texty)

[Jonluw]

Hiya escapists.

So I just happened to be thinking of time travel in a "many worlds"-setting (I was watching Steins; gate), and a question that I thought was interesting arose:

Please note that I don't really know much about the many worlds theory. Feel free to point out mistakes I make concerning how such a world would work.

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

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.

Problem is, there is also an infinite number of timelines in which your friend is not.
To me, this makes it appear that the probability of you ending up in a timeline your friend is in is ∞/∞ which presents some logical problems.
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.

Assuming, then, that every timeline branches off at the same rate, the ratio between the ∞ in the numerator and the ∞ in the denominator should stay constant.
Since the point your friend has jumped to and the timeline in which he didnt travel both have an infinite number of parallell worlds, the number of timelines without your friend in them should be ∞ times larger.
This sets the ratio of worlds with your friend vs. worlds without your friend to 2/2*∞ = 1/∞

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

So I turn to you, escapists, and ask: Is this correct, or am I talking complete nonsense?
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?

 

[Amphoteric]

If 1/Infinty = 0

Then 1=0 by multiplying both sides by infinity.

infinity is a weird concept.

 

[Jonluw]

If 1/Infinty = 0

Then 1=0 by multiplying both sides by infinity.

infinity is a weird concept.

Hm, yes.
Seems you can't really treat infinity that way.
Perhaps I should rather define the ratio as lim x→∞ 1/x

I can't really say I know how this all works.

 

[Indeterminacy]

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.

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.

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.

 

[JoesshittyOs]

Math scares me.

I'm gonna go lay in a fetal position and cry in the shower.

 

[cookyy2k]

If 1/Infinty = 0

Then 1=0 by multiplying both sides by infinity.

infinity is a weird concept.

incorrect. infinity multiplied by 0 is undefined.

 

[Amphoteric]

If 1/Infinty = 0

Then 1=0 by multiplying both sides by infinity.

infinity is a weird concept.

incorrect. infinity multiplied by 0 is undefined.

I know, I just couldn't be bothered editing my post after I posted it.

 

[Bluntman1138]

Sounds to me the OP and his friend was watching Sliders while high, and thus this arguement arose from that.

It wouldnt be an impossible feat to travel to the same dimension. It would be VERY improbable. The odds wouldnt even be able to be calculated, as per the definition of infinite. Most likely, you would spend your entire lives trying to find on another, or the Device you are using to jump runs out of power.

Of course, why would you keep following him? You may hit a dimension where you are a King or something. Then all you have to do is kill yourself, and take over. Forget the 50 bucks owed to you, you own the world.

 

[cookyy2k]

As for the probability of randomly picking the same timeline out of an infinite array of possibilities the chance is effectively 0.

However it should be pointed out that since the universe has begun there is not enough decisions been made to give infinite unique timelines. The number will be huge but not near infinite.

For a quick calculation on just how big some big numbers are;

Say their is 10[sup]10[/sup] people on earth (over estimate)

Now lets say that each speaks 30 words a minute (again overestimate)

So assuming humans don't sleep, that gives 3x10[sup]11[/sup] words a minute world wide, that's 1.8x10[sup]14[/sup] an hour, 4.32x10[sup]15[/sup] a day.

Giving us a total estimate of 1.58x10[sup]18[/sup] a year!

Every figure is an overestimate and it only gives 10[sup]18[/sup] words spoken world wide per year. The number seems small in standard form but it is in reality huge.

 

[Mike Richards]

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.

Even if the button destination is truly random, an infinite number of alternate versions spread across an infinite number of versions means that each individual timeline would be overrun by an infinite number of visitors from other timelines, even if the device never existed in that world.

Problems like this are just part of the reason why I think the whole many worlds concept is too impractical to really work.

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.

 

[Mike Richards]

Sounds to me the OP and his friend was watching Sliders while high, and thus this arguement arose from that.

It wouldnt be an impossible feat to travel to the same dimension. It would be VERY improbable. The odds wouldnt even be able to be calculated, as per the definition of infinite. Most likely, you would spend your entire lives trying to find on another, or the Device you are using to jump runs out of power.

Of course, why would you keep following him? You may hit a dimension where you are a King or something. Then all you have to do is kill yourself, and take over. Forget the 50 bucks owed to you, you own the world.

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.

 

[Twilight_guy]

I think you misunderstand what different infinities mean. In a many world scenario there is a continuum of timelines. That means uncountably many. If you take an infinite number of continuums they are still be equivalent in "size" to the original. (You can prove that mathematically). The "number" of "timelines" doesn't change if you create more of them in this way. Anyways it doesn't really matter since if there is an infinite number of timeline your chance of finding him is 0. Its one in a non-finite number which is equivalent to 0. 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.

 

[Bluntman1138]

Say their is 10[sup]10[/sup] people on earth (over estimate)

Now lets say that each speaks 30 words a minute (again overestimate)

So assuming humans don't sleep, that gives 3x10[sup]11[/sup] words a minute world wide, that's 1.8x10[sup]14[/sup] an hour, 4.32x10[sup]15[/sup] a day.

Giving us a total estimate of 1.58x10[sup]18[/sup] a year!

Every figure is an overestimate and it only gives 10[sup]18[/sup] words spoken world wide per year. The number seems small in standard form but it is in reality huge.

This of course all assume that our planet is the ONLY planet in the universe with Life. And it assumes that ONLY the decisions of humans matter (and only speech as well) .

There was 3 billion years of life before humans came along. In one time line a T-rex took a crap at a specific spot, in another that T-rex took a dump 2 minutes later at a different spot.

The Infinite Earth Dimensions would be affected by everything, all the way back to the Big Bang. Not just Earth, not just humans, and not just by speech. So your math would be way off, as you would not be able to even estimate the number of "decisions" made throughout the History of the universe.

 

[Bluntman1138]

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.

 

[cookyy2k]

Say their is 10[sup]10[/sup] people on earth (over estimate)

Now lets say that each speaks 30 words a minute (again overestimate)

So assuming humans don't sleep, that gives 3x10[sup]11[/sup] words a minute world wide, that's 1.8x10[sup]14[/sup] an hour, 4.32x10[sup]15[/sup] a day.

Giving us a total estimate of 1.58x10[sup]18[/sup] a year!

Every figure is an overestimate and it only gives 10[sup]18[/sup] words spoken world wide per year. The number seems small in standard form but it is in reality huge.

This of course all assume that our planet is the ONLY planet in the universe with Life. And it assumes that ONLY the decisions of humans matter (and only speech as well) .

There was 3 billion years of life before humans came along. In one time line a T-rex took a crap at a specific spot, in another that T-rex took a dump 2 minutes later at a different spot.

The Infinite Earth Dimensions would be affected by everything, all the way back to the Big Bang. Not just Earth, not just humans, and not just by speech. So your math would be way off, as you would not be able to even estimate the number of "decisions" made throughout the History of the universe.

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.

 

[Knife]

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. On average for every timeline you encounter you will meet 1 of your friend. Whether or not you'll see 50 on your first try and 0 on your next 49 tries or 1 every time for 50 tries, depends on the exact nature of the time machine. All in all however you have more than 50% (or exactly 50%) chance to encounter atleast 1 of your friend - if we assume that the amount of timelines where your friend didn't use the machine is equal to the amount of timelines where your friend did use the machine then you have 50% to get to either one, if you get to one where he did not use the machine then he'll be there (which guarantees at least 50%), if you get to one where he did use the machine then there is still chance bigger or equal to 0 that your friend from the other 50% timelines that did use the macine jumped in this particular timeline. 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).

 

[cookyy2k]

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. On average for every timeline you encounter you will meet 1 of your friend. Whether or not you'll see 50 on your first try and 0 on your next 49 tries or 1 every time for 50 tries, depends on the exact nature of the time machine. All in all however you have more than 50% (or exactly 50%) chance to encounter atleast 1 of your friend - if we assume that the amount of timelines where your friend didn't use the machine is equal to the amount of timelines where your friend did use the machine then you have 50% to get to either one, if you get to one where he did not use the machine then he'll be there (which guarantees at least 50%), if you get to one where he did use the machine then there is still chance bigger or equal to 0 that your friend from the other 50% timelines that did use the macine jumped in this particular timeline. 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).

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.

 

[Mike Richards]

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.