Infinite space and identical worlds

Great Debates
1

Infinite Parallel Universes

This Scientific American article is claiming that the Universe is so big that it is sufficiently large to be called infinite. It then goes on to argue that “In infinite space, even the most unlikely events must take place somewhere,” therefore there must be an infinite other worlds out there exactly like our earth, with identical histories.

http://www.sciam.com/article.cfm?articleID=000F1EDD-B48A-1E90-8EA5809EC5880000

I just wanted to throw my 2 cents into this argument.

This reasoning is total complete crap.

Incredibly huge is not the same as infinite. There is no “sufficiently large”.

There is an incredibly huge number of oxygen atoms making the rounds on Earth. Does this mean there are lots of oxygen atoms that have lead exactly the same existence in identical circumstances? No. There may be two oxygen atoms that have done very similar things, but they remain in completely different contexts.

The reason “infinity” is such a powerful mechanism is because its power is INFINITE and sufficiently large doesn’t cut it.

Ok argue with me if you want. Thanks.

2

Well if any given volume of space has only a finite number of possible states, then you don’t need an infinite universe to get a repeated state.
The numbers in the article though look far too small.

3

To give a back of postcard Gadanken experiment, if the universe only consisted of boxes. Each box containing balls marked 1 to 100 randomly positioned in 100 possible spaces. It would take 100! boxes before there was likely to be a repeat.
If each box was 1 meter cubed then such a number of boxes would fill a cube of sides 10[sup]35[/sup] meters. So even a universe as incredably simple as the one I imagined here would repeats on a m[sup]3[/sup] scale only every 10[sup]35[/sup] meters or so.

4

One thing that tripped me up until I re-read the article, is that they aren’t claiming a doppelganger 10[sup]28[/sup] meters from here, but 10[sup]10[sup]28[/sup][/sup] (that’s 10^10^28 if the double superscript doesn’t display right). That seems a sufficiently brain-wrenchingly huge distance. I liked how on the second page they state that a volume identical to our entire observable universe is “only” a bit more than a googleplex (10[sup]10[sup]100[/sup][/sup] ) meters away (they gave 10[sup]10[sup]118[/sup][/sup]).

I think that “sufficiently large” is acceptable in this context, since as Bippy said, you’re dealing with a finite number of particles that can only have a finite number of states. Take as large a group of particles as you want (say planet sized), determine the states available for each particle (or particle type, if that’s allowed), do some combinatorics, and voila: you have a measure of how unique that area is: it’s in only one particular choice of x possible states. Given greater than x repetitions of that size volume, you’d expect a repeat.

One catch I wasn’t able to resolve (I got a little lost midway through the Level II multiverse) is what about the relative frequency of the states your concerned with? For example, 10 protons, 8 neutrons, and 10 electrons in a particular bound state is awfully common in the glass of water I’m sipping, but much more rare if you’re sitting halfway between Sol and Alpha Centauri.

5

Darn I missed the 10 to the 10[sup]28[/sup]. That puts the number much more in the ball park of reasonablity.
I don’t know that are necessarily a finite number of states within any given finite area. It would require that everything is quantised and limited. Also the relative likelyhood of different states would be of immence importance as well.
Anyway if there are no multiverses, wouldn’t the size of the universe be constrained to its age times the speed of light ? That would be a lot less than 10[sup]10[sup]28[/sup][/sup]m.

Cheers, Bippy

6

I thought Quantum Mechanics had quantized everything (with the exception of gravity), and that these states had definite upper and lower boundaries. And after reading through the article again, it looks like they took the different probabilities into account by setting an upper limit of particles/energy (based on the universes size and temperature), then counting the combinations that could occur with whether or not something is there. So with your box, that’s 2[sup]100[/sup] different combinations: from no balls to all 100 balls. If there are red balls and green balls, that’d be 3[sup]100[/sup]. Then you start adding in all the possible states each could have, and work your way from there.

Absolutely, but it looks like this article is saying that based on cosmological findings, space-time seems to be bigger than that. This could have two causes:

  1. At one point in its lifecycle, the universe was actually expanding “faster” than the speed of light. Since we’re talking about the actual fabric of space, not matter, this shouldn’t conflict with relativity. This would obviously lead to a situation where the radius of the universe is greater than cage. Of course, observing anything past cage is impossible, since the space out there would be “blocked” by the big bang radiation, as we’re looking both out into space and backwards in time. That marks the edge of our observable universe.

  2. Our “universe” came into being embedded in an existing space-time. I think this is what the article is discussing with the Type II multiverse. The “Big Bang” didn’t create the whole universe, just our little pocket of it.

After finally making it through the whole thing, I had to chuckle at the fact that Type III (the standard quantum branching universe that I’ve come across in so many sci-fi stories) is considered the “boring” one.

And going back to the OP, since this is basically an exercise in combinations, “sufficiently large” is good enough, because we’re talking about numbers that are just friggin’ huge (though still finite). I mean, the ratio of the diameter of the universe (10[sup]26[/sup] m) to the smallest length with meaning ( planck length, 10[sup]-35[/sup] m) is only 10[sup]61[/sup]. So if you like the analogy of our universe as a sub-atomic particle in a larger one, you’d have to do that nesting, uh

<quick scribbling to calculate, let’s see, one nesting would be 10[sup]61[/sup], two would be 10[sup]61[sup]2[/sup][/sup]… no, wait, 10[sup]61[/sup] is about 10[sup]10[sup]1.8[/sup][/sup], so two would be, um…>

a whole lot of times to get the distance between you and your doppleganger to show up at the opposite end of the universe of the outer one.

And this’ll teach me to get into a weird cosmological debate, as I’ve been working on this for far too long, and I should be in bed.

7

Well, no, that’s only the size of the visible universe. If the universe has “open” geometry, then it is literally infinite in extent, not merely huge. As time goes on, more and more of the universe becomes visible. If there is no re-collapse then we would eventually be able to “see” our doppelgaengers. This is the assumption of the article.

What cosmological discussions always seem to miss is that, even if our local bit of universe looks geometrically open, and looks like it’s going to go on expanding forever, we are only seeing a tiny portion of the whole universe. What’s going on elsewhere may look very different, and lead to different conclusions.

At any rate, the claim on the cover of SA that “Parallel Universes Really Exist!” is complete crap. None of the parallelism “levels” have any logical necessity, and all of them are completely untestable (contrary to the author’s claim). This is an article about religion, not science.

8

I actually got lost at a few places. For some odd reason my brain can’t hold onto the difference between the Plato world view and the Aristitian world view. IIRC Plato’s was there is a set bunch of rules that everything follows and we have misinterpreted them sometimes and Aristotles view was…well I didn’t exactly follow except for our reality is basically what it appears to be from us (sort of solipsistic).

I’m also a bit curious-all of these parallel universi (the plural?) assume that the universe is infinite. Is this a given now, or is it still up in the air?

9

The current evidence suggests that the universe is spatially flat and the expansion is accelerating. This suggests that it is infinite in extent and will go on expanding forever. As I said above, it doesn’t prove either one. A torus, for instance, is a space that is spatially flat but finite in extent. Again, just cause it looks like we’ll go on expanding forever, we have a very limited view of the universe and we can’t know what’s going on elsewhere.

10

I read this article last night, and I’m still a bit foggy, but didn’t they make a case for multiple universes and occum’s razor? I wish I could remember off-hand, what it was.

11

How can anything be said to have a finite number of states. If I am 5 feet from a doorway there are an infinite number alternate distances I could move to get closer to that doorway. For instance I could cut my current distance in half an infinite number of times.

If I am spinning at 1 rpm I could double my rpm’s an infinite number of times, there is no finite number of possible rpm’s.

I don’t care how big a number is. If it is not infinity, then it doesn’t hold the power of infinity over the flippin Earth. Yes, you will get duplicates if we are talking boxes of white balls each of which have 100 possible states.

But the earth and life do not have a finite number of states. Particles don’t have a finite number of locations, there are infinite possible locations within any given space.

Particles do not have a finite number of possible velocities, the range is infinite

Particles do not have a finite number of possible rates of spin, the possibilities are infinite.

The only reason infinity has the infinite power to theoretically do anything, is because it is infinite, not mind boggling huge. So what if it is mind boggling huge, we have little pathetic 4lb brains. Very big is not infinity.

12

>>didn’t they make a case for multiple universes and occum’s razor?<<

The bit about Occam’s razor can be found on pages 8 and 9 of the online article. Here is part of what it says:

13

But this is exactly what quantum mechanics tells us is not the case. For every thing you mentioned here there is not a continuum of possible values, instead each one has only a limited number of possible values. You come to a point where you cannot cut your distance by half again, you can be a planks distance away or at the point there is no inbetween state. As you know c the speed of light puts an upper limit on all that involves motion, and distance being quantised makes speed both quantised and limited. So there are a finite number of possible relative speeds.

Now direction is something I am not sure about the quantisation of, for that reason I spoke of speeds above, not velocities. Does anyone have info (link best) on the quantisation of 3D angular direction?

Cheers, Bippy

14

hmm…i will digest that…thanks bippy

15

I loved the Plato/Aristotle comparison.

IANA Philosopher, but basically Aristotle was more of an empiricist, focusing on physical reality. Plato, to the contrary, was concerned with ideal forms as reality. (Refer to the Allegory of the Cave in Plato’s Republic.) In terms of universes, the article would have us think of Aristotle as the mechanical engineer who thinks in terms of physical stuff and how it relates and interacts with other stuff, while Plato is the theoretical physicist who thinks in terms of formulas and numbers.

For me the real debate is infinite vs. finite. Once you establish infinity smirks then you can easily posit parallel universes in one or another form as an absolute certainty. Currently I have to admit I am not sufficiently versed in theoretical physics to come to a conclusion either way. Intuitively, I would not expect the universe (or multiverse) to be infinitely large, but as the article points out at its conclusion, we speak of things that are outside the realm of intuition. If sufficient evidence were presented, I would certainly be willing to pick a side.

16

Any bets on whether or not this article was done up by a bunch of physicists/cosmologists out drinking?

Regarding the infinite vs. finite-but-large distinction, the basic premise seems to be that unless there is some state/property of a particle/wave that is a true continuum (can have any real value), a duplication must occur given a sufficiently large finite universe with random variation. Of course, it’s possible that in the multiverse, some state combinations (like empty space) take up the vast majority, so you’d have to have an even larger space to search in to discover a duplicate of yourself. So it’s not so much as to whether or not you have a duplicate, but how large of a finite universe is required for that to happen. In an infinite universe, duplication of any finite state combination is a given.

Um, wait. The set of integers are infinite, but there’s only one “1”, does that have any bearing? I guess not, since the set is of infinite size, but so is the domain (the size of unique items the set contains). So if the combination of quantum states is infinite (the domain), wouldn’t that mean that a “just” infinitely sized universe wouldn’t necessarily have duplication? Or would we need one of those “bigger” infinities?

After mulling over the angular orientation question, I think that would also be bounded by the Planck length. For a given object, the smallest angle it can rotate is where a point on its perimeter moves one planck length. So while there may be no “Planck angle”, there is a limit to how little a given object can rotate, giving a finite number of orientations. Now whether or not this holds for all possible reference frames in a whole other ball of wax.

17

Can someone dumb down the article for me? Because it seems to be at odds with everything else I’ve ever read about physics. I don’t know if they’re saying they discovered something new, or if I just don’t understand it, or if it’s just bullshit.

First of all, what is meant by the universe being “flat”? I thought the universe exanded in all 3 dimensions - does it just expand more in 2 of the 3 dimensions?

How do fluctuations in the microwave background suggest an infinite universe? I have always understood that space-time is thought to be finite and expanding. One of the first questions a student asks is “What is beyond the edge of the universe?”, and the answer usually given is “nothing”, i.e. space-time is contained within the universe. I thought the universe was not a structure within a pre-existing geometry, but rather is the geometry itself. The article would seem to directly contradict this. They seem to be saying that our universe is a structure that exists within an infinite geometry. What gives?

Also, they seem to be conflating the idea of parallel universes with the idea of identical structures within one infinite universe. I thought the theory of parallel universes described seperate, finite universes, where you could never contact your “double”, since there is a disconnect between alternate universes. To me, this seems a completely different proposition than a universe which is so vast that identical structures develop within the one universe.

And can the anthropic principle really be used to demonstrate that parallel universes exist?

The example they give is that the conditions for us to be here had to be of a very exact nature, and are so coincidental as to necessitate parallel universes. Isn’t this the same sort of nonsense that Creationists use to claim proof of God? It sounds like a re-vamped “Wind blowing through junkyard builds 747” argument. It just seems like so much mental masturbation to me. Am I missing something?

Finally, how are they calculating the probability of my “double” existing? Even if another Earth exists which is remarkably similar to ours, the exact same conditions that led to the inception of life on Earth would have to be duplicated. Since we don’t know what those conditions were, how can we calculate the probability of them occuring?

18

I haven’t read the article yet, but I will do so. My first impression is that the authors (like Nietzsche and many others who philosophize about infinite recurrence) have failed to account for the possibility of a static repetition. In other words, a universe large enough (in either time or duration) guarantees that at least one state repeats. There is no guarantee, however, that any particular state repeats.

For instance, a Universe that lasts forever might approach entropic stasis. That state would “repeat” forever, but you would never get to another “Earth like we know now”. The same applies for “close enough to infinite” space in a fully quantized reality. Yes, if the Universe is sufficiently large some state must repeat. There is no guarantee, however, that all of the repetition is not of one very boring state.

19

Would the distance numbers be raised to another level when you consider that for there to be an identical Bippy there not only needs to be all the Bippy quanta in one place at one time, but also that there needs to be consistency over time. The other Bippy would have needed to have evolved (devolved?) out of priumates that evolved out of mamals … So it would not just require the quantum state at one point to be equal but over an extremely long time span to have been significantly similar?
After all a momentary virtual particle Bippy would not be a real Bippy :wink:

20

But if all the Bippy quanta popped into place, wouldn’t that include all the Bippy memories? So how do you know you didn’t just now pop into existence? And you could pop out any secon