# If the universe really is infinite, then...

There would be another Earth, exactly like this one. On that planet there would be a duplicate of you doing the exact same thing that you are doing.

In fact, there would be an infinite number of Earths just like this one.
Is that idea plausible to you? it is to me.

I don’t see how the conclusion of an exact duplicate follows from the premise of an infinite universe. Please explain how one follows the other.

It’s the mere idea of infinity - it boggles the mind.

No the universe is not infinite according to all accepted models.

For a start, in a universe of an infinite size and infinite age the sky would literally be filled with radiation from the infinite number of stars.

A universe oinfinite size but finite age, wouldn’t have that problem, but it would have the problem of how something infinite can be formed in a finite time.

Aside from the problems of an infinite universe, there is no guarantee that there would be an exact duplicate of this planet. It’s very likely, but that’s all you can say.

I’ve wondered something similar to this. What would be the odds of the existence of another planet that is almost indistinguishable from Earth in the universe? It must be quite high, but I’m pretty sure that the number of stars in the universe is a far greater number. Therefore, couldn’t it be at least theoretically possible?

I have no exact numbers, so if anyone has estimates on the number of stars in the universe, it would be greatly appreciated.

Remember, infinity can be different ‘sizes’ There are an infinite amount of integers. That is, numbers, starting count at … darn, does integer count zero? I think so. 0, 1, 2, 3, and so on. However, there are also an infinite amount of even integers; 2, 4, 6, 8, and so on. There will never be an odd number in the second set of numbers, but both are infinite.

Both of the sets listed by E-Sabbath are the same size. But that’s a different sense of “infinite” than that put forth in the OP.

The idea of the OP is not only plausible, but it is one of the many theories bandied about by cosmologists. The one I’m familiar with is called, I believe, the multiple universe theory, and goes something like this: As time flows, an infinite number of universes are formed in which all the inifite possibilities unfold. For example, you had a decaf coffee this morning, but in one of the other universes, you had a latte with extra whipped cream on top. In another universe, someone slipped poison into your coffee and you died. Etc. I probably mangled this a bit, but I think I got it about 95% correct. Of course, there must be one universe where I got it 100% right…

Sounds like you’ve been watching Sliders

I think you are thinking of the common sci-fi perception of “dimensions”.

Uh… Just because something is infinite, doesn’t mean there are duplicates.

Numbers are infinite. The number 2, is always number 2. There is no such thing as “another 2”.

I do believe there are other planets like earth out there. But not exactly like earth. I could see other planets looking like Jupiter but with a blue sky and with normal weather paterns. With massive continents and large body’s of water, just a different shape ya know?

Infinite space is not sufficient to derive duplicates of everything we know (as an aside, the OP might want to read Nietzsche for some similar ideas on “eternal recursion”). Infinite space could be filled with nothing but dispersed hydrogen. Infinite time doesn’t get you there; the Universe might degrade to heat death and a single particle, flying forever without interaction. Infinite time and infinite influx of energy/matter to cause reactions (steady state, wormholes, accordion big bangs, whatever). That does get you to duplicates of every man, woman, and child. Infinite duplicates, in fact.

Again, not necessarily. It’s possible for things to be off by a very little each time.

After doing a bit of a throught experiment I don’t think you’re as far off track as some say but first a few disclaimers.

Most folks are in agreement that the universe is not infinite. Not the space contained or the stuff in it. Your statments rests on a couple of big assumptions, that the space in the universe is infinite and that it contains an infinite number of stars with orbinting bodies. That gives you a bit of a basis but it’s still pretty weak. It’s basically saying that any subset of infinity (planets just like the earth where I just made myself a cup of cocoa [Swiss Miss? brand] before typing this message) is also infinite. That’s weak but there is more logic than people have given you credit for.

I would agree with Padeye, and go you one further in saying that if there were an infinitely large universe, with an infinite number of star systems, and that the formation of such star systems was truly random (ie, if event Y has a probability of X in one section of the universe, it has that probability everywhere), then it seems perfectly rational to conclude that each event would have an infinite number of dupilicates. (Here I’m defining “event” to be pretty much anything: a person existing; a planet existing; Bob Dole sipping a latte and spilling some on his shirt at 11:26AM; and so on.)

Using the notion of the set of whole numbers or some such is a false analogy. The set of whole numbers isn’t random - it’s well ordered. It was designed that way. But imagine, say, an infinite series of coin flips. And consider the odds of seeing a given finite sequence of coin flips twice. If the sequence is small - eg, heads-tails-tails (HTT), then you won’t have to go far to see it again. You’ll probably see it two or three times given only 20 flips or so. If the sequence is long - HTTHTHHHHTHTT - you’ll probably have to go quite a ways before you see it repeated. Nevertheless, given an infinitie number of tosses, you’ll see it again. And you’ll see it an infinite number of times, because as the length of the series heads off towards infinity, the probability of seeing sequence X appear Y times is 1, regardless of what X and Y are.

Assuming the universe is truly random, it can basically be modelled as a really complex series of coin tosses. And you’ll have to fly pretty darn far before you find Earth’, or You’, or even Seven-Continents-That-Vaguely-Resemble-Those-On-Earth’. But that doesn’t mean they’re not out there.

So I would say that the OP’s logic is spot on, even if the underlying assumptions are, to but it not-too-delicately, fatally flawed.
Jeff

There’s a flaw in your logic. It is possible that in an infinite number of flips, you have no heads whatsoever. There are repeats, but a particular sequence is not repeated. Earth may never be duplicated.

And probability 1 doesn’t mean “guaranteed to happen” given an uncountable sample space, like the set of all infinite sequences of coin flips. This was covered in GQ sometime in the past year; do a search there.

I believe to answer this we need to know whether any given area of the universe can contain a finite number of states, or an uncountable infinity of states. Where a state is any arrangement of particles/waves within the given area.
An uncountable-infinite number of states would occur if any thing within the area can have a continuum of possible values each distinguishable from one-another (example if colour was a continuum, then between red and violet there would be an uncountable-infinite number of differing colours). If such continuums exist then an infinite universe would not necessarily contain any two areas that are identical to each other. If however any given area of the universe has only a finite number of states, then given a non-uniform universe we can be sure that such an area will repeat an infinite number of times within that universe. If such an area contained the Planet Earth for example, then we can be sure of an infinite number of Planet Earths.

Cheers, Keithy

Yes, they are both the same size, but one is missing half the elements of the other.

actually, the general consensus now is that the universe is finite.

let’s make this a bit clearer. the universe might expand infinitely, there might be an infinite amount of “space” outside the universe. but the universe is made up of a finite amount of mass/energy, the density of which scientists are now working very hard to determine (it will tell us the fate of the universe).

a few other things: if there are infinitely many possibilities, there may be no duplicates of anything, even when infinitely many occurrences are considered. consider the two infinite sets, all integers, and all integers greater than two. one set has 2, the other doesn’t.

and a bit of a nitpick…you cannot flip a coin infinitely many times and not get a heads. you can flip any finite number of times and not get a heads. there is a difference. it’s hard to explain what that is, though.

There might even be one where Spock has a…beard.:eek: