Would one actually find their doppleganger in a "Googolplex Universe"?
Related: http://physics.stackexchange.com/questions/22187/infinite-universe-jumping-to-pointless-conclusions
I've recently become a fan of Numberphile, and today I happened to watch their video regarding Googol and Googolplex. In the video, I found a rather confusing claim that I'm hoping someone here can help me sort out.
It's first stated in the introduction, and then explained in more detail at around 4:10. The claim can be summed up as this:
In a universe which is "a Googolplex meters across", if you would travel far enough, you would expect to eventually begin finding duplicates of yourself.
Getting deeper into the detail of this, <PERSON> explains that this is because there is a finite number of possible quantum states which can represent the volume of space in which your body resides. That volume is given as roughly one cubic meter, and the number of possible states for that volume is estimated at $10^{10^{70}}$. This is obviously much less than the number of cubic meters within a "Googolplex Universe", and so the idea does make some sense.
But I believe the idea relies on a false premise. That premise would be that the universe as a whole is entirely comprised of random bits of matter. 275
We can easily see that this is not true. The vast majority of our observed universe is occupied by the near-vacuum of space, and those volumes which are not empty are occupied by some fairly organized objects which all interact according to certain laws and patterns.
So, I'm curious to know two things:
1. Who originally proposed this idea? Is it something that perhaps <PERSON> just came up with to include in the video, or is there a noted physicist or mathematician who actually wrote about this at some point?
2. Given the possibility that a universe similar to ours could exist and be one Googolplex across, would this actually be probable? Or, would the natural order and organization of the universe prevent this from being as likely as it might be in a more random universe?
EDIT (To resolve some comments)
A note regarding the size of the universe, in respect to this question. In the linked video, the following constraints are mentioned:
* The number of particles in the universe is $10^{80}$
* Stated at 1:38 in the video.
* The number of the grains of sand that could fit within the universe is $10^{90}$.
* Stated at 1:55 in the video.
* The number of Planck volumes in the universe is $10^{183}$
* Stated at 2:22 in the video.
* The size of the universe is $(10^{26}m.)^{3}$
* Stated at 6:36 in the video.
A few times in the video, <PERSON> does qualify his statements by referring specifically to the observable universe. However, sometimes it's not quite so clear.
So, to simplify the problem for the purposes of this question, let's assume:
* Our universe is finite, and much less than a Googolplex in diameter.
* The "Googolplex Universe" suggested in the video, and in question here, is also finite. 710