"Observable universe" vs actual universe

[m1omg]

Why do so many people think observable universe is the whole universe? I see people making claims like "A googol is SO LARGE that it is even larger than the number of elementary particles in the universe" and they always cite the "observable universe" figures to make it seem "universe is really small in fact". There is a very real possibility that the universe might be in fact be infinite (meaning an infinite number of elementary particles so not even Graham's number might actually approach the actual number of particles in the universe anymore than a googol or the number 1 does) and even the accepted cosmology finite universe models generally predict an universe larger than any human idea of infinity - http://en.wikipedia.org/wiki/Orders_...9#Astronomical - the lowest boundary for the size of the universe is 250 billion years and the figure predicted by inflational models is more than 10 to the power of a googolplex - in fact that means that the universe is large enough to have a near-infinite number of cosmological horizons that are exactly the same as ours!

If the latter number is correct, the size of the entire universe is much, much, much higher compared to the observable universe than the size of the observable universe compared to a planck volume.

So no, our universe is not just 93 billion light years big (or 14 billion as some people not understanding comoving distance or the expansion of the universe believe). Our universe is probably so big that it contains a near infinite number of your identical twin, doing the exact same thing as you are doing right now. Now that is humbling.

[primummobile]

Just to nitpick... there is no such thing as "near infinite". Either it is infinite or it is not.

[m1omg]

I know that, I used the word near-infinite in the layman context, because the actual possible size of the universe mentioned on Wikipedia and in this paper http://arxiv.org/abs/hep-th/0610199 is larger than any human beings idea of infinity. In short, if this is true, and if you said that the actual universe is as large compared to the observable universe as the observable universe is compared to a single Planck volume, you'd be underestimating the size of the universe by more than a factor of googolplex.

What is even more humbling is that if the resolution proposed in the paper is true, the number mentioned is a lower bound. The universe might just as well be still finite, but unimaginably larger than that or infinite.

[grapes]

Although I don't have a problem with "near-infinite" (it's just any number that's a million times bigger than any number in the current discussion :) ), I have another nit. Just because there are an infinite number of things, it's not necessarily even true that two have to be identical, or even nearly identical. Just saying.

[m1omg]

I'm not saying the entire universe is observable universe repeated infinitely, just that laws of probability say that after a mind bogglingly huge distance (mentioned on that wikipedia page), you are certain to encounter an exact copy of our observable universe. Considering how small any observable universe is compared to the probable size of the actual universe it is like having many identical-color sand grains at the bottom of the Mariana Trench - most of the universe will be very different to our observable universe (in terms of exact structures, there will obviously be stars, galaxies... just like in ours and the same physical laws), but some tiny areas will happen to be exactly like our observable universe because the universe is so big that it can happen out of random chance.

There is an exact number of how far would you have to go before encountering a twin of our observable universe on that Wiki page, with references. It is mind bogglingly big, but much smaller than the "predicted size of the actual universe after inflation" number.

Btw for me "near infinite" is pretty much any number that is so big that it stops mattering in which unit you give it. 10 to the power of 10 to the power of 10 to the power of 122 (sorry, not sure how to insert superscripts) is such a big number that you could say that the predicted size of the universe is 10 to the power of 10 to the power of 10 to the power of 122 Planck lenghts and it wouldn't matter. Plack lenghts, light years, gigaparsecs, lenghts of the observable universe ... any unit stops being meaningful at this scale.

[Selfsim]

I have another nit. Just because there are an infinite number of things, it's not necessarily even true that two have to be identical, or even nearly identical. Just saying.

In an infinite universe which has existed for an infinite amount of time, there will be an exact doppelganger (duplicate) of oneself .. as everything that is possible, will happen (like an exact duplicate) ... and has already happened an infinite number of times !
I believe Max Tegmark, (theoretical physicist), produced these, and several other remarkable theoretical ramifications, in a paper several years ago .. (Mind you, there's a very long trail of deep theoretical thinkers who have trodden this same path before him ...)

Interestingly also, its the only theoretical paradigm, (I'm aware of), in which 'other' life can be legitimately predicted to exist with 100% certainty ...

Pity its not practically possible to show that such an infinite universe actually exists beyond our observable one, however ...


Neat thread ! .. Thanks m1omg !

Cheers

[Strange]

In an infinite universe which has existed for an infinite amount of time, there will be an exact doppelganger (duplicate) of oneself .. as everything that is possible, will happen (like an exact duplicate) ... and has already happened an infinite number of times !

I just can't buy that. There are an infinite number of integers. None of them are the same. This is like the often repeated claim that (all versions of) the complete works of Shakespeare must appear in the decimal expansion of Pi. It ain't necessarily so.

Incidentally, looking up some data for a similar discussion elsewhere, I came across this:

If the universe is finite but unbounded, it is also possible that the universe is smaller than the observable universe. In this case, what we take to be very distant galaxies may actually be duplicate images of nearby galaxies, formed by light that has circumnavigated the universe.

http://en.wikipedia.org/wiki/Observable_universe

[primummobile]

I just can't buy that. There are an infinite number of integers. None of them are the same. This is like the often repeated claim that (all versions of) the complete works of Shakespeare must appear in the decimal expansion of Pi. It ain't necessarily so.

Incidentally, looking up some data for a similar discussion elsewhere, I came across this:

http://en.wikipedia.org/wiki/Observable_universe

I disagree with that. What do you mean that there are an infinite number of integers? The infinite set contains every finite set. You are a finite set of quantum states. To be otherwise your body would need to be made up of an infinte number of particles, which is obviously nonsense.

If you have infinitely repeating series of finite states you must have infinite copies of those states. In a random system they are likely to be pretty far removed from one another spatially, especially when you increase the number of variables. If our solar system started as one of a gazillion possible quantum states that are available with a gajillion elementary particles then that state will be repeated somewhere in an infinite sequence.

[Strange]

I disagree with that. What do you mean that there are an infinite number of integers?

The cardinality (size) of the set of natural numbers (or integers) is infinity. No two integers in that set are the same.

If you have infinitely repeating series of finite states you must have infinite copies of those states.

But you can have an infinite non-repeating series (made up of finite states) as well. Just because it is infinite doesn't mean it has to be repeating.

[Moose]

The cardinality (size) of the set of natural numbers (or integers) is infinity. No two integers in that set are the same.

He's right. {1, 2, 2, 2, 5} is a valid subset of integers.

Your statement "no two integers in that set are the same" would be accurately written as "no two unique integers in that set are the same". Tautological, yes. Listing them in numerical order, and uniquely, is just a convention. Not a property of integers. Otherwise, the concept of identity would fail utterly.

Any identity that equals 1, (2/2, for example), is a representation of an integer, and falls within the integer set.

That said, the properties of the set of integers says absolutely nothing about the properties of the universe. While such a metaphor can be useful to explain an assertion, it does nothing whatsoever to support it. The only answer we really have to the size and shape of the actual universe is "we don't know; we may never know; and that won't stop us from guessing".

[Edit: Actually, you know what? Never mind. I don't think I can let myself get involved in this discussion. This is going to wind me up far too much, and it's just not important enough to offset the hassle of setting off my OCD today. Enjoy.]

[primummobile]

The cardinality (size) of the set of natural numbers (or integers) is infinity. No two integers in that set are the same.

Ok, that was a really stupid question for me to ask. For some reason, and I have no idea why now, I was thinking that you were referring to digits and not numbers. Please forget I ever asked that.

But you can have an infinite non-repeating series (made up of finite states) as well. Just because it is infinite doesn't mean it has to be repeating.

I'm not so sure about that. Just to keep it simple and not make my calculator crap out on me, let's just consider a sequence of ten digits where you can only use each digit one time. There are 3,628,000 (10!) possible ways for those digits to be arranged. Somewhere in the value of pi you should expect to see each of those possible arrangements, and you should be able to find each arrangement an infinite number of times. But, that's not a realistic comparison to the universe because the digits can be repeated in each sequence. In that case, the number of possible ten digit combinations is 10^10, which is 10,000,000,000. That is significantly larger, but in an infinite sequence every grouping of ten digits must be one of those 10 billion combinations. That means you should expect to find each of those sequences an infinite number of times. Of course there are further complications, especially when you consider that the 10 digit sequence can begin and end in random places. I don't know how that would change the possibilities, but it would make it much, much larger. But if you try it an infinite number of times you will find the same patterns repeating in there somewhere.

Have you ever read anything about those people who attempt to make predictions based on the Bible or other large books? They are able to find all kinds of names and almost anything else just by selecting random characters from the text and looking for a pattern. The results are hokum, but imagine if the book were infinite. You'd be able to find anything in there.

[Strange]

Ok, that was a really stupid question for me to ask.

I did wonder

Please forget I ever asked that.

Asked what?

I'm not so sure about that. Just to keep it simple and not make my calculator crap out on me, let's just consider a sequence of ten digits where you can only use each digit one time. There are 3,628,000 (10!) possible ways for those digits to be arranged.

But your "each digit one time" introduces a constraint that may not always be valid. Take the first 10 digits of the decimal expansion of pi and it doesn't apply (1415926535), although it gets closer to being true over longer sequences. But Pi is only guaranteed to contain every possible sequence (an infinite number of times) if it is normal. Which it almost certainly is but it isn't known. It is possible that at some point in the decimal expansion the digit 3, say, no longer occurs.

[Strange]

While such a metaphor can be useful to explain an assertion, it does nothing whatsoever to support it. The only answer we really have to the size and shape of the actual universe is "we don't know; we may never know; and that won't stop us from guessing".

Agreed. And, just to be clear, I am not asserting that the universe is or is not infinite, or that if it is infinite that it does or doesn't repeat itself. I'm only saying that it might or might not. We don't (can't?) know.

[Edit: Actually, you know what? Never mind. I don't think I can let myself get involved in this discussion. This is going to wind me up far too much, and it's just not important enough to offset the hassle of setting off my OCD today. Enjoy.]

I feel similarly!

[primummobile]

But your "each digit one time" introduces a constraint that may not always be valid. Take the first 10 digits of the decimal expansion of pi and it doesn't apply (1415926535), although it gets closer to being true over longer sequences. But Pi is only guaranteed to contain every possible sequence (an infinite number of times) if it is normal. Which it almost certainly is but it isn't known. It is possible that at some point in the decimal expansion the digit 3, say, no longer occurs.

I don't argue that. I was just showing a progression from 'each digit once' to random.

I just personally believe that if the possible conditions are finite and you have infinite iterations you will stumble across infinite copies of each possible condition. But I argued this in another thread for too long, and not very long ago. I'm content to let it be as well.

[m1omg]

It is technically possible that universe is smaller than the observable universe, but extremely unlikely. A flat universe suggests an infinite universe and so far WMAP indicates that the universe is flat or near-flat, meaning that it is either infinite or finite but extremely big. Furthermore the 250 billion light year limit is, quoting Wikipedia "lower bound of the (possibly infinite) radius of the universe, if it is a 3-sphere, according to one estimate using the WMAP data at 95% confidence[23]. It equivalently implies that there are at minimum 21 particle horizon-sized volumes in the universe.".

In short, it is very unlikely that our universe is a small one, and most likely, it is either an unthinkably large one or infinite one.

About numbers being an infinite set yet not repeating... true, but structures in the universe are not numbers. Numbers follow after each other, subatomic particles, planets, people, aliens... do not. The laws of probability and quantum mechanics don't apply to integers but they apply to the physical universe. You can have a mathematical construct where nothing ever repeats, but not physical things.

[m1omg]

In an infinite universe which has existed for an infinite amount of time, there will be an exact doppelganger (duplicate) of oneself .. as everything that is possible, will happen (like an exact duplicate) ... and has already happened an infinite number of times !
I believe Max Tegmark, (theoretical physicist), produced these, and several other remarkable theoretical ramifications, in a paper several years ago .. (Mind you, there's a very long trail of deep theoretical thinkers who have trodden this same path before him ...)

Interestingly also, its the only theoretical paradigm, (I'm aware of), in which 'other' life can be legitimately predicted to exist with 100% certainty ...

Pity its not practically possible to show that such an infinite universe actually exists beyond our observable one, however ...


Neat thread ! .. Thanks m1omg !

Cheers

Thanks for all the responses folks, it is a very interesting topic to think about

The neat thing is, the universe does not even have to be infinite for that (the predicted distance between dopplergangers is mind bogglingly huge, but much, much lower than the size of the universe according to cosmological inflation). And it can be proven by the geometry of the universe - if universe is curved inwards, it is finite, if it is flat or saddle shaped, it is infinite http://en.wikipedia.org/wiki/Shape_of_the_universe .

[Strange]

You can have a mathematical construct where nothing ever repeats, but not physical things.

Penrose tiles?

[primummobile]

Thanks for all the responses folks, it is a very interesting topic to think about

The neat thing is, the universe does not even have to be infinite for that (the predicted distance between dopplergangers is mind bogglingly huge, but much, much lower than the size of the universe according to cosmological inflation). And it can be proven by the geometry of the universe - if universe is curved inwards, it is finite, if it is flat or saddle shaped, it is infinite http://en.wikipedia.org/wiki/Shape_of_the_universe .

The number I've heard, and remembered, is 10^43,000,000,000,000 LY between duplicates on average.

[m1omg]

The number I've heard, and remembered, is 10^43,000,000,000,000 LY between duplicates on average.

Indeed, and the lenght between dopplergangers of our exact observable universe is predicted to be 10^10^115 light years. This is a number large enough that if you said the lenght is 10^10^115 Planck lenghts it would not be a big mistake. It pales however to the lower limit on the size of the universe predicted by some inflational models which is 10^10^10^122 light years. In short, the distance predicted between dopplergangers of both single people and entire observable universes is huge enough to surpass any number human mind can imagine, but there is probably enough space in the universe for more than a googolplex "observable universe dopplergangers".

That is, if the universe is really big, but finite. If it is infinite, then the number of dopplergangers will be infinity.

[primummobile]

That is, if the universe is really big, but finite. If it is infinite, then the number of dopplergangers will be infinity.

Yup. I agree with that.

[primummobile]

Penrose tiles?

My wife wants to put Penrose tiling in the basement and I am resisting vigorously.

[m1omg]

Penrose tiles are interesting, but then, they are specifically designed to not repeat, unlike the universe.

[primummobile]

Penrose tiles are interesting, but then, they are specifically designed to not repeat, unlike the universe.

The way I understand Penrose tiles is that they are non-symmetrical but any finite pattern in the tiles will eventually repeat itself as you add to it. I may be wrong about that. If I am, then it's not Penrose tiling that my wife wants to put into the basement.

[m1omg]

The way I understand Penrose tiles is that they are non-symmetrical but any finite pattern in the tiles will eventually repeat itself as you add to it. I may be wrong about that. If I am, then it's not Penrose tiling that my wife wants to put into the basement.

That is the way I understood it too. I suspect that whatever "non repeating" qualities Penrose tiling has it probably doesn't apply to a group of Penrose tilings a googolplex meters wide.

[Selfsim]

The neat thing is, the universe does not even have to be infinite for that (the predicted distance between dopplergangers is mind bogglingly huge, but much, much lower than the size of the universe according to cosmological inflation). And it can be proven by the geometry of the universe - if universe is curved inwards, it is finite, if it is flat or saddle shaped, it is infinite http://en.wikipedia.org/wiki/Shape_of_the_universe .

Hi m1omg;

I'm intrigued …

When you say: "the universe does not even have to be infinite for that" I'm left with some ambiguity about exactly what you mean. Could you, perhaps, clarify a little for me ?

At the moment, I think I'm still justified in sticking with the concept that in the practical universe we live in, our measurements will always be bounded by practical observational horizons (eg: the cosmological horizon), and our measurements will always have uncertainties, which become an issue when making estimates of such huge distances/timescales and geometries … so, we will always be bounded by these 'practicality horizons'. In theory however, such horizons might be irrelevant, so at least in theory, I get that doppelgangers are certain. But in practice they, (and inevitability, other lifeforms) are not.

I think the distinction of: 'in theory' and 'in practice' are very important in preserving clarity in these kinds of discussions, and in this particular case, the theory is constantly under test … and the tests are asymptotically limited by measurement resolutions, and uncertainties.

Regards

[m1omg]

The only real rule that must be met is that the universe has the same physical laws everywhere as here. This is supported by both the Big Bang theory and the inflation theories, plus it was confirmed that the structure of the universe is homongenous at any scale beyond http://en.wikipedia.org/wiki/Observa...d_of_Greatness http://en.wikipedia.org/wiki/Cosmological_Principle . In short, universe produces galaxies, planets, superclusters everywhere and there is no magical "life giving" property of this exact region of space. The existence of dopplergangers is reality in any universe large enough, not just theory. And the universe does not have to be infinite simply because the odds of multiple exact Jonases or Earths or Hubble volumes are not infinitely small, just very very low so the distance between dopplergangers can be accurately calculated.

I don't think this really has anything to do with the "other life" issue, as the probability for alien life within this Hubble volume is unimaginably larger than the probability of a dopplerganger appearing, which is why the distance between dopplerganger is extremely large.

So either universe is smaller than 10^43000000000000 light years, or each of us has a dopplerganger. It all sounds very silly until you learn to appreciate the magnitude of numbers like this. You live in a ridiculously huge universe, you get ridiculously improbable things happening.

It is the same as with winning a lottery million years in a row, normally it is impossible, but if you played the lottery for a let's say 10^100 years, it starts not just being possible but a necessary logical result of playing the lottery that long. The only difference is that playing the lottery for 10^100 years is impossible while the universe being roomy enough for dopplergangers is a very serious possibility because of cosmic inflation and the geometry of the universe.

[Cougar]

It all sounds very silly until you learn to appreciate the magnitude of numbers like this.

This reminds me of a story Murray Gell-Mann told in The Quark and the Jaguar. As a student, he was assigned to calculate the probability that a human on Earth would suddenly appear on the moon, due to quantum tunneling. The result is also an extremely low probability. IIRC, he took that as so ridiculously small, it might as well be zero, and was so for all practical purposes.

I abhor infinity.

[DoggerDan]

Our universe is probably so big that it contains a near infinite number of your identical twin, doing the exact same thing as you are doing right now. Now that is humbling.

I just did something fairly unpredictable. I slapped myself. You're saying that if the universe is indeed infinite that there's a duplicate me out there somewhere with precisely the same molecules including those in my hand which just slapped my face?

Isn't it equally likely, statistically speaking, that there is infinite variation such that no two people would ever be exactly alike?

[HenrikOlsen]

In an infinite universe which has existed for an infinite amount of time, there will be an exact doppelganger (duplicate) of oneself .. as everything that is possible, will happen (like an exact duplicate) ... and has already happened an infinite number of times !

I just can't buy that. There are an infinite number of integers. None of them are the same.

The chance of any specific integer being picked by random out of all integers is infinitesimally small, the chance of an integer less than a given integer being picked is also infinitesimally small, individual integers don't have a finite non-zero chance of happening so the argument doesn't apply to them.

This is like the often repeated claim that (all versions of) the complete works of Shakespeare must appear in the decimal expansion of Pi. It ain't necessarily so.

Pi isn't random, arguments about random numbers doesn't apply to its digits.

[primummobile]

This reminds me of a story Murray Gell-Mann told in The Quark and the Jaguar. As a student, he was assigned to calculate the probability that a human on Earth would suddenly appear on the moon, due to quantum tunneling. The result is also an extremely low probability. IIRC, he took that as so ridiculously small, it might as well be zero, and was so for all practical purposes.

I abhor infinity.

I know what you mean about infinity. It seems to create more problems than it solves.

When I was in college, there was always a little bit of a competition between the math professors and the engineering professors. The engineers thought the mathematicians had their heads in the clouds, and the mathematicians thought the engineers were too grounded.

Anyway, I remember being in one of my introductory electrical theory classes and there being a student arguing with the instructor about how capacitor theory has to be wrong because a capacitor never really fully charges or discharges, although we usually consider them to be after five or six time constants. So the professor illustrated his point with a story...

Two men, a mathematician and an engineer, were placed against the wall on one side of a room. A bucket of gold was placed on the far wall. They were told that they could have the gold if they followed one simple rule. In walking to the gold, they were only allowed to cover half the distance to the far wall with each step. The mathematician threw up his hands and walked out of the room because he knew that no matter what he did he could never cover that distance to the far wall. The engineer, on the other hand, just walked across the room until he was close enough to reach out and grab the gold with his hand.

I don't know why, but I've always gotten a little bit of a kick out of that story. I think it's a good illustration of the difference between theory and reality.