IF the universe is infinite, how far do you have to travel to meet a copy of yourself

[mrsmtih]

IF the universe is infinite, how far do you have to travel to meet a copy of yourself?

To clarify. I understand that the universe as we think of it today is not considered to be infinite. Yes it might be finite but unbound, but this is a hypothetical situation. I recently read a book called "The infinite Book" by John Barrows and he talks about the concept of infinity and how Cantor brought about the modern theory of sets.

One question that was posed in the book is the study of the universe before we knew the general shape before the discovery of the cosmic background radiation. He stated a figure of some order of magnitude that you would have to travel 100^100^100 billion light-years (or something like that) IF the universe was infinite before you met a copy of yourself. I was wondering where the author got the figure from(no source was stated). How was the math calculated?

[Durakken]

It sounds like a completely random number...

If the universe is infinite and repeats itself then every piece of the universe would have to be symetrical... you'd just have to go the distance it is to get to where the universe begins to repeat itself...

In a truly infinite universe, which is what you are talking about, You have to account for an opposite for everything that has happened...Think about this. We can measure time down to some billionth of a second (and that means at each of those intervals of time something can happen differently and thereofr a new set would have to be created)...and we know the universe doesn't repeat for roughly 13.5 billion light years which is also 13.5 billion years, but we don't need to calculate for that as it is too high for us to comprehend really. Instead let's lower the the number to make it more easily comprehendable...

Let's imagine a universe 1 minute old and we can only measure in seconds. The initial reaction to this is 60 seconds in a minute thus 60 seperations and 1 light minute to get to a copy, but this is a bit more tricky than that... First it's exponential increase. So it's not 60 its doubled every second
1, 2, 4, 8, 16, 32, 64, 128, 256, 512, 1024, 2048, 4096, 8192, 16384, 32668, 65336, 130672, 261344, 522688...

we can keeping going, but i don't want to type and do more of the math and that's only 20 seconds of the 60.

Anyways once you calculate that you then have to realize that at least 1/2 of those repeats will not have you in it and 1/2 of those left will have no care to go look for you, and then half of those left from that last group will have left to find you. we're now down to 12.5% that have a chance to meet of trillions of repetitions...now...

Half will meet before they leave...
>of these half will destroy each other
>the other half will meet
half will go on to the journey to find their copy...
>1/3 will meet and destroy each other
>1/3 will meet
>1/3 of these left they will not meet.

your the 2nd 1/3 which is 2.08% chance of this happening at the very beginning of the universe... So what is the distance you must travel to meet yourself from all this...let's take 20light seconds which we have the number for... The number is something like... 522688 * 20(10,453,760)* 2.08% = 2,174,382.08ls or 25.17light days to meet a copy of yourself...

Oh and did i mention you would have to travel this distance practically instantaneously as not doing that would cause even more copies and more space to be generated...which means it becomes an exponentially greater distance...regardlessly you still have less than 2.08% chance of meeting yourself even without 13.5billion years of generating an incomprehensible number of copies.

[mrsmtih]

Wow finally a satisfactory answer. Thanks for you help!

[dcl]

In a truly infinite Universe, you could in principle travel as far as you wished without necessarily ever finding a copy of yourself, finding a second copy of anything you had already encountered, or finding yourself back at your starting point. On the other hand, none of those possibilities could be ruled out. However, I feel compelled to reject the idea that the Universe is infinite. It is believed that the superfast expansion of the Universe during the inflation era was always finite. That rules out the possibility of the extent of the Universe being infinite. It seems to me that the only plausible geometry for the Universe is that of an expanding four-dimensional hypersphere with its three-dimensional "surface" the Universe we know its center and its center the point where the Universe first came into existence. I cannot take seriously the idea that the Universe has the shape of a dodecahedron or a cube with opposite faces "glued" in the topological sense or Dr. Gay's doughnut.

[DrRocket]

IF the universe is infinite, how far do you have to travel to meet a copy of yourself?

To clarify. I understand that the universe as we think of it today is not considered to be infinite. Yes it might be finite but unbound, but this is a hypothetical situation. I recently read a book called "The infinite Book" by John Barrows and he talks about the concept of infinity and how Cantor brought about the modern theory of sets.

One question that was posed in the book is the study of the universe before we knew the general shape before the discovery of the cosmic background radiation. He stated a figure of some order of magnitude that you would have to travel 100^100^100 billion light-years (or something like that) IF the universe was infinite before you met a copy of yourself. I was wondering where the author got the figure from(no source was stated). How was the math calculated?

It sounds as though this book has created some confusion with regard to the notion of infinity.

When you discuss the notion of the infinite in the context of sets, you are in the realm of what are called cardinal and ordinal numbers. In that setting there are different magnitudes of infinity. For instance there are infinitely manny integers. There are also infinitely many real numbers. But in a very real sense there are more real numbers than there are integers. The cardinal number of the real numbers is larger than the cardinal number of integers. If you really want to explore this notion, the book Naive Set Theory by Paul Halmos is pretty good.

The notion of infinity wth respect to the universe, is more one of what is called compactness than of cardinality. An easy example is that a circle is compact, while the real line is not, and the line extends "infinitely" in both directions. Yet locally both the circle and the real line "look like" line segments. Similarly a sphere and the plane look alike locally, while the sphere is compact and the plane is not.

[eburacum45]

Max Tegmark has calculated how far you have to travel to meet a copy of yourself, assuming that the universe continues infinitely beyond the Hubble Volume. You would have to travel outside the visible universe, and far beyond, until you met an exact copy of yourself; travel a bit further (quite a bit, actually) and you would find an entire visible universe (a Hubble Volume) identical to our own in every respect.

Tegmark laid all this out in a Scientific American article a few years ago, which is no longer available for free on the net; but his webpage is here, http://space.mit.edu/home/tegmark/multiverse.html
with the information that the nearest exact copy of you is 10^{10^29} meters away. Much further than the edge of the universe. Of course there is no way of knowing what lies beyond the edge of the observable universe, by definition, so we will never know if he is correct..

[grant hutchison]

He stated a figure of some order of magnitude that you would have to travel 100^100^100 billion light-years (or something like that) IF the universe was infinite before you met a copy of yourself. I was wondering where the author got the figure from(no source was stated). How was the math calculated?

The calculation Barrow used comes from cosmologist Max Tegmark, and it's based on the number of different ways a volume of space of some given size can be filled with fundamental particles.

To borrow Tegmark's worked example in the May 2003 edition of Scientific American:
First imagine a toy two-dimensional universe which has space for just four particles: each location in this universe can be empty or it can contain a particle. There are therefore 2⁴ = 16 different possible universes of this sort. If we have a volume containing more than 16 of these universes, at least one of the universes must be a perfect copy of one of the others. In the two-dimensional example, this means that the mean distance between duplicate universes is sqrt(16) = 4 times the characteristic diameter of the toy universes.

Tegmark then assumes that our observable Universe (the Hubble volume) has a diameter of 8x10²⁶m, and that a nucleon measures 2x10^-13m across, which gives the Universe a capacity of around 10¹¹⁸ nucleons, and therefore allows for 2¹⁰¹¹⁸ possible ways of filling a Universe-sized space with nucleons. Small matters of cube roots and the diameter of the Universe are insignificant in the face of such a huge number, so he comes out with a final distance between identical copies of our Universe of (about!) 10¹⁰¹¹⁸m.

Similar reasoning leads him to suggest that identical copies of human beings are separated by about 10¹⁰²⁸m, and that within 10¹⁰⁹²m there is a volume of space 100 light-years in diameter which is identical to our own local space.

Grant Hutchison

Edit: I see I was typing while eburacum45 posted, above.

[trinitree88]

[QUOTE=mrsmtih;1261768]IF the universe is infinite, how far do you have to travel to meet a copy of yourself?

mrsmith. Hmmm. To infinity & beyond....... If you're Buzz Light-year, the phonies will have copies out before the movie hits the theatres..

[Ken G]

One can certainly ask if there is actually any meaning whatsoever to a calculation such as Tegmark's, but he can always simply state that his calculation is only intended to be valid if there is such a meaning. Personally, I simply dispense with it by asserting that I see no evidence for the validity of any of the assumptions involved, including if there is even a real physical meaning to numbers of that magnitude, and including if there is any scientific content in a calculation that cannot be tested.

[grant hutchison]

One can certainly ask if there is actually any meaning whatsoever to a calculation such as Tegmark's, but he can always simply state that his calculation is only intended to be valid if there is such a meaning. Personally, I simply dispense with it by asserting that I see no evidence for the validity of any of the assumptions involved, including if there is even a real physical meaning to numbers of that magnitude, and including if there is any scientific content in a calculation that cannot be tested.

The standard disclaimer that comes with newspaper horoscopes might have been useful: "For entertainment purposes only".

Grant Hutchison

[John Mendenhall]

Personally, I simply dispense with it by asserting that I see no evidence for the validity of any of the assumptions involved, including if there is even a real physical meaning to numbers of that magnitude, and including if there is any scientific content in a calculation that cannot be tested.

Yes, agreed, assumption #1 being that any volume can be identical to any other volume at any scale - the photon background alone negates the idea.

[mrsmtih]

In a truly infinite Universe, you could in principle travel as far as you wished without necessarily ever finding a copy of yourself, finding a second copy of anything you had already encountered, or finding yourself back at your starting point. On the other hand, none of those possibilities could be ruled out. However, I feel compelled to reject the idea that the Universe is infinite. It is believed that the superfast expansion of the Universe during the inflation era was always finite. That rules out the possibility of the extent of the Universe being infinite. It seems to me that the only plausible geometry for the Universe is that of an expanding four-dimensional hypersphere with its three-dimensional "surface" the Universe we know its center and its center the point where the Universe first came into existence. I cannot take seriously the idea that the Universe has the shape of a dodecahedron or a cube with opposite faces "glued" in the topological sense or Dr. Gay's doughnut.

dcl the point is that this is all speculative and asking about where Barrow's got the figures from. Other members have answered the question and I thank them.

Regardless I appreciate your input.

[mrsmtih]

The standard disclaimer that comes with newspaper horoscopes might have been useful: "For entertainment purposes only".

Grant Hutchison

yes very entertaining... why else read about it? =O

[Ari Jokimaki]

I don't think you can have exact copies in infinite universe, and here's one of my earlier posts that explains why.

[astromark]

I may or may not agree with with this idea that there could or might not be a duplicate of me or anything at all any where at all. If i were to except infinite as an description of the universe then yes there could most likely be a infinite number of perfect duplicates of me... Utter nonsense! The probability of such a duplicate is also infinitely remote. No. Yes.
So the answer can only ever be no. Just one planet Earth. Just one humanity. Just the one of me. Infinite possible also includes infinite improbability in an infinitely random possibility. Face it. We might just be the only life form in the whole of the universe that has reached this point. Or there are billions of us.... we just do not know.
Finite probability in an finite universe or infinite in infinaty..? I think no duplicate exists of me or us.
Humanities abilaty to search the cosmos is at best pathetic. We have not even learned how to look. How can we know what we can not see.

[cosmocrazy]

I may or may not agree with with this idea that there could or might not be a duplicate of me or anything at all any where at all. If i were to except infinite as an description of the universe then yes there could most likely be a infinite number of perfect duplicates of me... Utter nonsense! The probability of such a duplicate is also infinitely remote. No. Yes.

There would certainly be some entertaining reading Astro! All them "you's" in the universe!

[Exposed]

To meet a perfect copy of yourself, you're better off staying here on earth and waiting for your perfect copy to be born (assuming you can live a very long time).

To put this the other way around, the probability of there being two humans, excluding identical siblings, with the same genotype is less than 1 - P(N,m) < 10 - 271. In fact we can see from the above calculation that we would require a human population size of approximately 10^150, a number larger than current estimates for the number of elementary particles in the universe, in order to have a non-negligible probability of two humans having the same genotype.
http://ase.tufts.edu/cogstud/papers/hirsch.fin.html

Still, those odds seem better than travelling out the edge of the visible universe to find your unique copy

[Jetlack]

Why would one necessarily have to travel great distances in order to meet repeat instances? If the universe is genuinely infinite then time is the great repeater. Given infinite time then everything happens an infinite number of times, including the evolution of humans and each and every individual. I dont see how travelling/distance adresses the issue.

[Jetlack]

Just to add one more thought:

Considering how well nature appears to conserve energy; then surely staying still and using infinite time and waiting for it to happen is more energy efficient than trying to use infinite space to chase a copy of oneself. If one has all the time in an infinite universe why bother going anywhere. It will all come to you given enough time.

If that makes any sense...

[mugaliens]

IF the universe is infinite, how far do you have to travel to meet a copy of yourself?

Approximately 23 feet. That's the distance between my bed and my bathroom mirror.

Seriously, if it's infinate, that's a difficult question to answer, but we can see a simple example in math:

f1=x/x²

and

f2=x²/x

As x--> (approaches) infinity, f1-->0 while f2-->infinity

Thus, the question becomes, what's more likely? Covering more distance? Or running into an exact duplicate of yourself where the position, type, spin and charge of every quark is identical?

The odds of meeting an exact copy are infinately small.

Now, if by "copy" you don't mean an "exact copy," but a reasonable replica (same, the same DNA in both the sperm and the egg). An identical twin.

Then the odds are very much improved, but still, in our current stage of science, not at all calculable, as we still do not have any proof of how prevalent life is on other planets, or even if there is life on other planets. It may be that life is all but a given on any Earth-like world, but it may also be that it's exceedingly rare.

We just don't know.

[Drunk Vegan]

It seems to me as though the idea is complete nonsense if we're talking about a single universe. In a multiverse it's entirely possible there are other versions of yourself, even ones with very similar life histories, but in a single universe there's no reason why there'd be two of you just because the universe is inifinite.

Think about it, a series of numbers can reach infinity, but never repeat:

1, 2, 3, 4, 5, 6, .... Infinity ... each number is unique.

[cosmocrazy]

It seems to me as though the idea is complete nonsense if we're talking about a single universe. In a multiverse it's entirely possible there are other versions of yourself, even ones with very similar life histories, but in a single universe there's no reason why there'd be two of you just because the universe is infinite.

Think about it, a series of numbers can reach infinity, but never repeat:

1, 2, 3, 4, 5, 6, .... Infinity ... each number is unique.

I agree i don't see why anything has to repeat in an infinite universe. There could be just infinitely unique no of things. Just as plausible!

[grant hutchison]

I agree i don't see why anything has to repeat in an infinite universe. There could be just infinitely unique no of things. Just as plausible!

This would be fine if we could keep on making an infinite number of new "things". But we seem to have a limited variety of different building blocks (that is, a relatively small number of different kinds of subatomic particle), combined with a strict set of rules by which they can be assembled. Therefore, the number of ways we can fill a finite volume with these building blocks is finite. Therefore, there is a finite number of "things" of a given size that can be assembled from those building blocks. Therefore, if we have enough "things" of a given size, we'll have duplicates.

Grant Hutchison

[cosmocrazy]

This would be fine if we could keep on making an infinite number of new "things". But we seem to have a limited variety of different building blocks (that is, a relatively small number of different kinds of subatomic particle), combined with a strict set of rules by which they can be assembled. Therefore, the number of ways we can fill a finite volume with these building blocks is finite. Therefore, there is a finite number of "things" of a given size that can be assembled from those building blocks. Therefore, if we have enough "things" of a given size, we'll have duplicates.

Grant Hutchison

Yes i see your point.

ok, we could also say that our duplicate self is infinitely distant away from us, therefore it would take an infinite time & distance traveled to reach our duplicate self, therefore never able to meet our duplicate self, so never proving the existence of such, and so on... it makes absolutely no sense

[grant hutchison]

ok, we could also say that our duplicate self is infinitely distant away from us ...

But what is going to fill that infinite space between you and your duplicate? Each human-sized chunk of that intervening space has to contain some permutation of subatomic particles and voids, and we know that within a finite distance we'll exhaust all possible new ways of filling human-sized bits of space in this way. So permutations will have to start repeating.

You're therefore claiming that Nature will fill infinity with duplicates of other types of human-sized region, but will never ever duplicate your particular human-sized region. Why would that happen?

Grant Hutchison

[Durakken]

If you mean a 100% exact copy of every atom of your being that has experienced 100% the exact same thing it is impossible...Why? You both choose the same direction to travel in and thus will always be the same distance apart :P

[cosmocrazy]

But what is going to fill that infinite space between you and your duplicate? Each human-sized chunk of that intervening space has to contain some permutation of subatomic particles and voids, and we know that within a finite distance we'll exhaust all possible new ways of filling human-sized bits of space in this way. So permutations will have to start repeating.

You're therefore claiming that Nature will fill infinity with duplicates of other types of human-sized region, but will never ever duplicate your particular human-sized region. Why would that happen?

Grant Hutchison

No I'm not claiming anything i am just suggesting one possible consequence of infinite space. There could be billions or more copies of ourselves in infinite space that we bump into on our travels as the universe repeats itself. on the other hand there could be only one copy infinitely distant away with nothing in between, or there could be just 1 unique you. I don't see "infinity" as a physical possibility, in physical reality infinity is the same as zero. Also i don't see why infinite space would have to mean infinite universe? The OP asks how long it would take to meet one's copy if you continued to travel through the universe. My answer to this would be. Until you reach the end of this universe and start again in a copy of it, or travel between parallel universes, or never at all.

[Ilya]

The calculation Barrow used comes from cosmologist Max Tegmark, and it's based on the number of different ways a volume of space of some given size can be filled with fundamental particles.

To borrow Tegmark's worked example in the May 2003 edition of Scientific American:
First imagine a toy two-dimensional universe which has space for just four particles: each location in this universe can be empty or it can contain a particle. There are therefore 2⁴ = 16 different possible universes of this sort. If we have a volume containing more than 16 of these universes, at least one of the universes must be a perfect copy of one of the others. In the two-dimensional example, this means that the mean distance between duplicate universes is sqrt(16) = 4 times the characteristic diameter of the toy universes.

The unstated assumption here is that all possible configurations are equivalent, and anything that CAN happen, DOES happen. Which is not at all a safe assumption.

Let's rephrase the original question in terms of this four-particle universe:

How far do you have to travel to meet a copy of universe 0101?

Answer: no way to tell. Yes, any volume of 16 or more four-particle universes will have at least two which are identical, but not necessarily ANY 0101 universes. For all you know, 0101 universe is the only one in existence, all others are 0000, and remaining 14 combinations do not exist at all.

Tegmark then assumes that our observable Universe (the Hubble volume) has a diameter of 8x10²⁶m, and that a nucleon measures 2x10^-13m across, which gives the Universe a capacity of around 10¹¹⁸ nucleons, and therefore allows for 2¹⁰¹¹⁸ possible ways of filling a Universe-sized space with nucleons. Small matters of cube roots and the diameter of the Universe are insignificant in the face of such a huge number, so he comes out with a final distance between identical copies of our Universe of (about!) 10¹⁰¹¹⁸m.

Similar reasoning leads him to suggest that identical copies of human beings are separated by about 10¹⁰²⁸m, and that within 10¹⁰⁹²m there is a volume of space 100 light-years in diameter which is identical to our own local space.

It is blatantly obvious that human-sized (roughly 70 liters) volumes are NOT all equivalent. Vast majority of such volumes throughout Hubble volume consist of vacuum, and very very few have even slight resemblance to a human being, let alone a particular human being. By far more likely, a volume of space 10¹⁰²⁸m in radius contains mostly identical 70-liter vacuum-volumes, and not a single volume outside Earth which could be described as "human". And exact equivalent of "you" may not exist anywhere else in the infinite universe.

[astromark]

Under the rules of infinity then yes, we may find a life form that has had a history that has shaped it as has ours....No way is that possible. Ever. The completely random run of events is not ever the same, even in the infinite universe.
Remembering that the current held best guess is that this universe is in fact finite. Is it possible that a duplicate of this could be found? I say NO. The fact that it has happened once is astonishing enough.

[Ivan Viehoff]

Max Tegmark has calculated how far you have to travel to meet a copy of yourself, assuming that the universe continues infinitely beyond the Hubble Volume.

He assumes a bit more than that. He assumes "If space is infinite and the distribution of matter is sufficiently uniform on large scales." The latter part of that, at least, is a very big "if".

It is entirely possible to have an infinite extent without repetition, even in very simple situations. Infinite aperiodic tilings http://en.wikipedia.org/wiki/Aperiodic_tiling (often associated with Roger Penrose) are well known. In fact rather than it being merely possible, it is in fact overwhelmingly likely. The range of possibilities for objects and their arrangement in the universe is so "large" (in the sense of cardinality) that the possibility of repetition in an infinite space of merely the cardinality of the continuum is exceedingly implausible.

When he says:

"If there are indeed many copies of "you" with identical past lives and
memories, you would not be able to compute your own future even if you had complete knowledge of the entire state of the cosmos! The reason is that there is no way
for you to determine which of these copies is "you" (they all feel that they are). Yet their lives will typically begin to differ eventually, so the best you can do is predict probabilities for what you will experience from now on. This kills the traditional notion of determinism."

I think he has killed his own argument. He acknowledges that matter does not evolve deterministically from a starting point. So how is it possible that any two identical starting positions would in fact evolve identically for any extended period at all? Even in an infinite universe with sufficient uniform starting conditions, there can only be a countably infinite number of copies of any large-scale ensemble. Surely the size of the number of possibilities for its chaotic evolution is so large that all of them (almost surely) diverge. Absence of determinism is not merely the consequence of quantum effects such as random decay, it is also a consequence of Planck uncertainty in a universe where differences smaller than Planck uncertainty, through chaos, soon result in large differences. Consider a game of snooker/pool. This is a machine for magnifying small errors. You don't have to play the game for very many shots for the gravitational effect of the planet Jupiter to start making a perceptible difference.