Tell me more ×
Physics Stack Exchange is a question and answer site for active researchers, academics and students of physics. It's 100% free, no registration required.
up vote 0 down vote favorite
1

Related: 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, Tony Padilla 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 possible number of quantum states that could be represented within each cubic meter of 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. We can easily see that this is not true. The vast majority of our 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 Tony 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 $10^{130}$
    • 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, Tony 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.
share|improve this question
Why do you feel that the premise is 'random bits of matter'? It doesn't look like he assumed that. He only took a worst-case scenario (no organization). Organizing the universe makes this more probable, if anything. – Manishearth♦ Mar 15 '12 at 4:52
I'd be interested to learn how an organized universe makes this more probable, especially in a universe such as ours where the organization calls for most of the universe's volume consisting of little or no mass. – Iszi Mar 15 '12 at 12:22
Oh that's easy. In the worst case scenario, if we have a $l\times l\times l$ 'grid', with $N$ quantum possibilities at every vertex, then the worst case scenario for number of possibilities is simply $N^{l^3}$. Now, if we dictate that there must be some sort of organization in this system, we are applying a constraint (never mind that its not mathematically definable). If there's a constraint, number of cases reduces. – Manishearth♦ Mar 15 '12 at 12:31
@Manishearth I'm still having a hard time understanding how that applies as a general rule. In our universe's case, it would seem the constraint is one that specifically reduces the possibility of this occurrence. If we're looking to find a certain quantum state which is about a cubic meter in volume, and that quantum state contains matter - and, more specifically, a human - and it is known that a very large percentage of the universe does not contain matter, how does this make the likelihood of finding that state more probable? – Iszi Mar 15 '12 at 12:37
2  
I used I used $\TeX$ formatting. To use TeX, enclose the the TeXcode in $...$ or $$...$$. The latter makes the code get its own line. To get you started, superscripts with ^, subscripts with _. These can be combined, eg 1^2_3 gives $1^2_3$. If you want more than one character in a super/subscript, use braces. 10^{100} gives $10^{100}$. For fractions, use \frac{abc}{def} giving $\frac{abc}{def}$. Greek letters like this: \delta \Delta gives $\delta \Delta$. That's all you'll need often, for more complex things, ask me and I'll find a link. – Manishearth♦ Mar 15 '12 at 13:42
show 17 more comments

1 Answer

up vote 1 down vote

Regarding the source of claims such as those, I believe they are due to Max Tegmark, likely from this article. He has curious ideas, though discerning whether they are correct, useful or at least in the realm of possibility is far beyond my capacity. He is a strong proponent of the idea of a mathematical Universe. If I recall correctly, he goes to the point of stating that anything exists at all merely because mathematics/logic exists, and everything we percieve as reality is logical statements playing out in a marvellously complex fashion very far down the line. Why does it happen? Because it can, basically.

Edit: Now I realize this thread is actually quite old, and seems to have been resurrected by a spammer. I apologize if this answer is undue.

share|improve this answer
The answer is not at all undue. Feel free to post an answer any question here, so long as you are answering it (and preferably correctly, with citations if needed), regardless of how old it may be. This is not a "traditional" forum, where old topics are considered generally un-useful. – Iszi Apr 20 at 2:26

Your Answer

 
discard

By posting your answer, you agree to the privacy policy and terms of service.

Not the answer you're looking for? Browse other questions tagged or ask your own question.