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Bubblecar
2004-May-11, 02:35 PM
Max Tegmark's recent publications on the Multiverse (Levels 1 to 4) have attracted some controversy. In my "local" science forum, the following extract from the Level 1 multiverse came in for some criticism (Level 1 is just our "normal" universe, assuming that it's flat & homogeneous, as the CMBR evidence seems to indicate):

If space is infinite and the distribution of matter is sufficiently uniform
on large scales, then even the most unlikely events must
take place somewhere. In particular, there are infinitely
many other inhabited planets, including not just one but
infinitely many with people with the same appearance,
name and memories as you. Indeed, there are infinitely
many other regions the size of our observable universe,
where every possible cosmic history is played out. This
is the Level I multiverse. (From Max Tegmark, Parallel Universes, downloadable here - http://arxiv.org/abs/astro-ph/0302131)

Several critics argued that infinite space & a uniform distribution of matter aren't sufficient to ensure these infinitely many duplicates, or to ensure that "every possible cosmic history is played out". I didn't fully understand these criticisms, but Tegmark now seems to have modified the story somewhat - this scenario is now also dependent on statistical properties derived from quantum fluctuations in the inflation phase -

"...infinite space alone guarantees only that SOME Hubble volume will have a duplicate, not that our own will. However, if (as in the current cosmological standard model) the cosmic density fluctuations originate from quantum fluctuations during inflation, their statistical properties DO guarantee that our (and indeed every) Hubble volume has a duplicate." (From his new Multiverse FAQ, downloadable here - http://www.hep.upenn.edu/~max/multiverse.html)

Since it does appear that the flat, homgeneous universe corresponding to the Level 1 multiverse may well be the REAL universe, how confident can we really be about these infinitely many copies of ourselves, & "every possible cosmic history" being assured of "probability 1" ?

ToSeek
2004-May-11, 05:06 PM
It can be shown mathematically that there are different infinities: even though there are an infinite number of integers and an infinite number of real numbers, the latter infinity is larger than the former. To prove that all of infinite space could hold all of infinite possibilities one would have to demonstrate that the former infinity is equal to or greater than the latter.

Kullat Nunu
2004-May-11, 05:48 PM
It can be shown mathematically that there are different infinities: even though there are an infinite number of integers and an infinite number of real numbers, the latter infinity is larger than the former.

Interestingly, it has been proven that there is no any "mid-sized" infinities between integers and real numbers. On the other hand the opposite has been proved too. Obviously there are areas in mathematics that are yet to be uncovered.


To prove that all of infinite space could hold all of infinite possibilities one would have to demonstrate that the former infinity is equal to or greater than the latter.

Why so?

ToSeek
2004-May-11, 06:26 PM
To prove that all of infinite space could hold all of infinite possibilities one would have to demonstrate that the former infinity is equal to or greater than the latter.

Why so?

Perhaps the infinity of space is aleph-null (integers) while the infinity of possibilities is aleph-one (real numbers). If so, the infinity of space would not encompass all possibilities, and odds would be that you and me and everyone else are unique in the universe.

Chip
2004-May-11, 06:36 PM
If space is infinite and the distribution of matter is sufficiently uniform on large scales, then even the most unlikely events must take place somewhere. - Max Tegmark, Parallel Universes

So that would mean that these guys are real (http://home.swipnet.se/~w-28870/) - somewhere - and "only" a movie, here. :o

Russ
2004-May-11, 06:51 PM
If space is infinite and the distribution of matter is sufficiently uniform on large scales, then even the most unlikely events must take place somewhere. - Max Tegmark, Parallel Universes

So that would mean that these guys are real (http://home.swipnet.se/~w-28870/) - somewhere - and "only" a movie, here. :o
No, they could not be real. The biology of DNA would select against creatures with low an intelect. :wink:

Kullat Nunu
2004-May-11, 06:57 PM
Perhaps the infinity of space is aleph-null (integers) while the infinity of possibilities is aleph-one (real numbers). If so, the infinity of space would not encompass all possibilities, and odds would be that you and me and everyone else are unique in the universe.

I see.

But the article argues that there is "only" 10^(10^115) possibilities to arrange protons in a Hubble volume due to the Pauli exlusion principle.
Realistic, physically possible combinations would be much less common.
Would a Hubble volume (or Milky Way or Earth) where every proton is arranged like in our visible universe still be an identical copy? There are still other particles like photons and such.

Anyway, speculation about multiple universes are extremely interesting. Hopefully their existence will be proven soon.

Intuitively I feel them so realistic. On the other hand, in such multiverse there wouldn't be anything unique (Copernican Principle carried to extremes).

Too bad those Level I universes are totally disconnected from our visible universe due to the accelerating cosmic expansion.

Kaptain K
2004-May-11, 07:01 PM
Then of course there are the Star Trek short stories - Visit to a Weird Planet where, due to a transporter malfunction (like that would ever happen), Kirk, Spock and McCoy wind up on the set in Hollywood and the followup where Shatner, Nimoy, and Kelley wind up on the real Enterprisetm.

Kullat Nunu
2004-May-11, 07:08 PM
Level IV universes have different laws of nature. In such universes just everything would be possible, even Star Trek actors beamed up to real Enterprises...

Maybe everything we imagine really happens somewhere? :o

Bubblecar
2004-May-12, 03:26 AM
Kullat's point about the limited possibilities seems to be the crux of the matter - Tegmark says that the number of possible states for each Hubble volume is finite (though very large indeed), according to quantum theory. Thus, an infinite number of Hubble volumes will ensure that "each possible cosmic history is played out" (although some critics apparently still have misgivings about this conclusion).

I suppose the word "possible" here needs to be interpreted in a very disciplined way, & there might be things that seem to be "possible in principle" (as far as we can tell) which might actually be impossible.

earthman2110
2004-May-12, 03:35 AM
Level IV universes have different laws of nature. In such universes just everything would be possible, even Star Trek actors beamed up to real Enterprises...

Maybe everything we imagine really happens somewhere? :o


Would our imagination cause or be the effect of?
[/quote]

Kaptain K
2004-May-12, 12:18 PM
Would our imagination cause or be the effect of?
Yes! :oops:

earthman2110
2004-May-13, 03:39 AM
AND! if our imagination causes the events in this other place, and we found out about this, we could "play god" with this strange new universe, and we could have all sorts of fun, just using our imaginations! :o yikes

daver
2004-May-13, 04:27 PM
If the dream I had last night is anything to go by, you would NOT want to live in such a universe.

Clifford Simak wrote a book something along those lines.