Devil's Advocate #1: Infinite worlds? (Part 1) Wellll...
When most people these days think of multiple universes, they think of the "Many-Worlds Theory." It basically says that every time an event could go in more than one way, it actually goes both ways, each in a different universe. Whether large events like battles and wars going differently, to the submicroscopic, where a particle may or may not change its quantum state, to everything in between like what you decide to have for lunch, it all happens. Somewhere. And people generally say that, because of this, there are (or may be, at least; there's no real proof that the Many Worlds Theory is true) an infinite number of universes out there.
But are there really?
It's time for some numbers.
The universe is estimated to contain 10183 "planck volumes" - cubes a planck length (10-34 m) on a side. This, like all the other numbers here, is approximate, and indeed is believed to be growing as the universe expands. But let's keep it (relatively) simple and static.
The universe is believed to have about 1080 particles in it. Again, give or take a bit.
The number of different quantum states of the particles making up your body - approximately one cubic meter of material - is 101070. This is a huge number, but you must admit it's not infinite.
Putting all these numbers together is actually complicated. You can't just multiply them all; the particles, for instance, are larger than a planck length, and so fit into multiple planck volumes. It's kind of like having a 10 x 10 grid and asking how many ways two 3 x 3 squares can fit in there. And the fact that space isn't chock filled with particles means you can't just take that number of quantum states, compare it to the space in the universe, and scale it up accordingly.
I can't do either of these calculations properly. I simply don't know how. But they can be done. And no matter how you do it, none of the ways you multiply them all together will equal infinity.
So how often do we calculate this? Think of the universe as a reel of film, like a movie; what's the frame rate? It matters; for a movie, it's pointless to calculate faster than 24 frames per second, since that's how fast the frames are going past. You'll be making a lot of calculations where absolutely nothing has changed, so why make them? But if you calculate less than that amount, then you will miss out on some frames, and thus miss some changes.
The "frame rate" of the universe is called planck time, and it's 10-44 seconds long. Nothing can happen in less than that time. And the age of the universe is around 4.34 x 1062 planck seconds. And it is, of course, increasing by the second. So we need to multiply the number we got from the last calculation by 4.34 x 1062 quick!
Of course, it's not that simple. If superstring theory is correct - and, mind you, it may not be - then space consists of not three dimensions, not four (including time), but eleven. The others are scrunched and folded in on themselves until they're too small to be useful. But how they're folded pretty much dictates our physics. And according to calculations, there's more than 10500 ways spacetime can fold. So you have to add that number to the calculations.
Unfortunately, all those different folds would result in different physics. Gravity would be higher or lower, protons would decay at different rates, and so on. It is impossible at this time (and possibly ever) to calculate what the consequences of 10500 alternate physics would be; we're having a hard enough time figuring out the universe we know exists to try calculating others. So for simplicity's sake I'm simply saying they're like ours, mathematically. So you just have to multiply whatever number you got above by 10500. Or leave this out entirely. Up to you.
But wait, there's more! You see, if you simply do the multiplication as I've posed it so far, then probability is useless. If you have something with a 1/2 chance of going one way, and a 1/3 chance of going another way, and a 1/6 chance of going the third way, then if you only create three universes to hold all the possibilities, then from the point of view of the greater multiverse everything had a 1/3 chance of going a certain way. For probability to mean anything, in the example I provided there would have to be six universes, where three were identical, two were identical to each other but different from the first three, and there's one lone universe that's different from any other.
Figuring out the probabilities for each of those 101070 quantum states in a single cubic meter is impossible. It's just too much for our computers. Doing it for everything in the universe probably will always be beyond us.
But the number exists, even if we can't calculate it. It's unbelievably huge, but it's there. But unbelievably huge is still not infinite.
On the other hand, when you're talking numbers this huge, it might as well be.
But are there really?
It's time for some numbers.
The universe is estimated to contain 10183 "planck volumes" - cubes a planck length (10-34 m) on a side. This, like all the other numbers here, is approximate, and indeed is believed to be growing as the universe expands. But let's keep it (relatively) simple and static.
The universe is believed to have about 1080 particles in it. Again, give or take a bit.
The number of different quantum states of the particles making up your body - approximately one cubic meter of material - is 101070. This is a huge number, but you must admit it's not infinite.
Putting all these numbers together is actually complicated. You can't just multiply them all; the particles, for instance, are larger than a planck length, and so fit into multiple planck volumes. It's kind of like having a 10 x 10 grid and asking how many ways two 3 x 3 squares can fit in there. And the fact that space isn't chock filled with particles means you can't just take that number of quantum states, compare it to the space in the universe, and scale it up accordingly.
I can't do either of these calculations properly. I simply don't know how. But they can be done. And no matter how you do it, none of the ways you multiply them all together will equal infinity.
So how often do we calculate this? Think of the universe as a reel of film, like a movie; what's the frame rate? It matters; for a movie, it's pointless to calculate faster than 24 frames per second, since that's how fast the frames are going past. You'll be making a lot of calculations where absolutely nothing has changed, so why make them? But if you calculate less than that amount, then you will miss out on some frames, and thus miss some changes.
The "frame rate" of the universe is called planck time, and it's 10-44 seconds long. Nothing can happen in less than that time. And the age of the universe is around 4.34 x 1062 planck seconds. And it is, of course, increasing by the second. So we need to multiply the number we got from the last calculation by 4.34 x 1062 quick!
Of course, it's not that simple. If superstring theory is correct - and, mind you, it may not be - then space consists of not three dimensions, not four (including time), but eleven. The others are scrunched and folded in on themselves until they're too small to be useful. But how they're folded pretty much dictates our physics. And according to calculations, there's more than 10500 ways spacetime can fold. So you have to add that number to the calculations.
Unfortunately, all those different folds would result in different physics. Gravity would be higher or lower, protons would decay at different rates, and so on. It is impossible at this time (and possibly ever) to calculate what the consequences of 10500 alternate physics would be; we're having a hard enough time figuring out the universe we know exists to try calculating others. So for simplicity's sake I'm simply saying they're like ours, mathematically. So you just have to multiply whatever number you got above by 10500. Or leave this out entirely. Up to you.
But wait, there's more! You see, if you simply do the multiplication as I've posed it so far, then probability is useless. If you have something with a 1/2 chance of going one way, and a 1/3 chance of going another way, and a 1/6 chance of going the third way, then if you only create three universes to hold all the possibilities, then from the point of view of the greater multiverse everything had a 1/3 chance of going a certain way. For probability to mean anything, in the example I provided there would have to be six universes, where three were identical, two were identical to each other but different from the first three, and there's one lone universe that's different from any other.
Figuring out the probabilities for each of those 101070 quantum states in a single cubic meter is impossible. It's just too much for our computers. Doing it for everything in the universe probably will always be beyond us.
But the number exists, even if we can't calculate it. It's unbelievably huge, but it's there. But unbelievably huge is still not infinite.
On the other hand, when you're talking numbers this huge, it might as well be.