Infinite Universe, All Combinations of Matter Exist

[Nickerbocker]

Hello,

I heard a scientist on the radio claiming that, if the universe is infinite, that all possible combinations of matter/energy exist somewhere in that infinite-ness. So, for example, as I sit typing, I am wearing a gray sweater. As I understand it, somewhere in the infinite universe I exist doing the same typing but wearing a red sweater.

But, what I don't understand is, this scientist said there was a finite amount of possible combinations for matter/energy. Is that really true?

As I understand it, the possible combinations of distance between, say, two atoms would also be infinite. So, if both space and matter/energy-combinations are infinite, doesn't that mean that the existence of every possible combination of matter/energy is an impossibility?

 

[phinds]

I can't give you a supportable, factual, answer but my own point of view is that all these many-worlds interpretations are more like magic than physics and need to be treated with the fact in mind that ALL conclusions follow logically from a false premise.

SO ... to my mind it is a logically true statement to say

Infinite universes exist and therefore <put in any statement you like>

 

[Whovian]

It look like the OP was talking about a single, infinitely large Universe instead of infinitely many (finite or infinite) Universes.

 

[phinds]

It look like the OP was talking about a single, infinitely large Universe instead of infinitely many (finite or infinite) Universes.

Ah, now that I reread it, I think you are right. If that's the case then I don't think

if the universe is infinite, that all possible combinations of matter/energy exist

makes sense, but again, this is just my opinion and I have no evidence.

 

[Whovian]

Yea, we'd need someone skilled in combinatorics w/ infinity to see if, in an infinite Universe, we can expect the expected value of the number of times an arbitrary arrangement of atoms and such shows up to be >0. And even that relies on a few assumptions.

 

[haael]

Information capacity of any finite region of space is finite. This is a consequence of quantum mechanics. That means, for any given size, there exist only finite number of energy/matter states that can fill a box of the size.

Now if you take the infinite universe and divide it into regions of finite size (no matter how big), they will always be repeating. There is finite number of building blocks you can compose your universe of.

The same goes for infinite time. If the universe was eternal, then every event sequence did happen before and will happen in future. If you are interested, then for medieval philosophers this was one of the proofs that God exists :). The eternal universe with repeating events seemed for them like a paradox, so they deduced that if can not be eternal. That means, it must have been created at some point, therefore God exists. These discussions go back to the ancient Greece if I am not mistaken.

As I understand it, the possible combinations of distance between, say, two atoms would also be infinite.

No, the distance between two atoms can not be measured with infinite precision.

 

[Nickerbocker]

Yes, I looked it up, and it was Zeno of Elea, whom predated Socrates and Plato. He had a cool theory on the infinite universe ... http://everythingforever.com/parmzeno.htm

Are you saying that the distance between two atoms cannot be measured with "infinite" precision because of the "strange" behavior of sub-atomic particles?

And, if the distance between two atoms cannot be measured with infinite precision, then how can you deduce that in a finite space there is a limited number of energy/matter positions? Doesn't the fact that you cannot properly measure the position of subatomic particles, or measure the distance between two atoms with infinite precision make your very concrete conclusion an impossibility?

Finally, does it matter whether I am talking about one infinite universe or an infinite number of finite universes?

 

[Vorde]

My understanding of this was that as the size of the universe went to infinity the probability of anything appearing went to 1 in an asymptotic style. I always interpreted this as meaning that statistically, in an infinite universe anything should happen, not that anything does happen.

 

[Nickerbocker]

I think that is right. But my concern is that there is no finite number of terms to truncate. That is, the terms themselves are infinite, if that makes any sense.

 

[dbmorpher]

If I am eating a chip, there are infinite ways I could eat it, it doesn't mean I will eat it in infinite numbers of ways as it is only one chip. There are other chips though and for each of them another infinity, though it is more common for me to eat the chip some ways than maybe with my pinkie toe.
These chips are good. :)

 

[Zmunkz]

Everything would be repeated an infinite number of times and with an infinite number of variations. Brian Greene explores this particular infinite universe in his book, "the hidden reality", starting on page 27. The crux of the point is, in any finite region, there are a finite number of quantum states in which it could be. In a region the size of our visible universe, the number of states is about 10^10^122. This means, once you had examined that many expanses of space the size of our visible universe, you would necessarily start seeing repeats.

And of course, in any infinite region, there are an infinite number of "finite regions". So, you would see each variation an infinite amount of times.

 

[Curious_Dude]

I know that this comment is probably not going to follow the logical flow of comment here, but here are my thoughts:

1. According to one of the main laws of physics, energy can not be created or destroyed. This suggests that the amount of energy is actually finite, since it cannot keep getting created (therefore cannot be infinite).

2. Thanks to Einstein, we know that basically everything is energy.

3. If everything is energy, and there is a finite amount of it, Therefore, every "different" universe will only have to have some sort of a difference of displacement of energy.

4. To make each different universe truly different, requires there to be at least one infinitely small piece of energy in a very slightly different (infinitely small different) spot.

5. According to this logic, there is indeed a Finite amount of universes. A huge amount of them, but nonetheless, finite.

6. HOWEVER, We forgot about time! If that piece of energy is in a different spot, at a very slightly different (infinitely small different) time, then that is also the sign of a completely different universe! And, if time is infinite, then that suggests that the amount of universes is infinite!

7. However once again, there are theories which state that time is also finite, due to the fact, that if it were infinite, then we would be seeing constant strange fluctuations occurring very frequently, and yet we do not see them occurring. This would suggest again, even more universes exist, yet are still finite.

8. To add some controversy, It is very possible that other universes, parallel universes or ones in different dimensions, may not abide by the same laws that we have in this universe. In a different universe, there might not be a law of conservation of energy, and time there might truly be infinite. Therefore, that would suggest, that maybe there are an infinite amount of universes after-all.

9. Going back to points 4-6, if there is an infinitely small difference in time, distance, or amount of energy, then its a different universe right? However, how can we or anyone tell you how many infinitely small portions of time, distance, or energy are in a certain universe? There is an infinite amount of infinitely small portions. Therefore, there is in fact, an infinite amount of universes. and also, in this case, an infinite amount of terms to truncate.

10. However, point 9 is a bit like the mandelbrot set. You can split ANYTHING into equally infinitely small portions. Does that make the object truly have an infinite amount of size? No. In reality, you are just measuring something with basically a zero unit stick. Sure, the amount of times that stick will be used to measure something is infinite, however, it is still nonetheless, a measurement of some sort. And if it is a measurement, then no matter how small it is, this suggests a FINITE size (be it time, distance, amount of energy). So this again, would suggest, that in fact, there are only a FINITE amount of terms to truncate, and also a FINITE amount of universes.

The truth is: WE JUST DON'T KNOW! We might never know. Maybe the point of life is to experience all of the universes... forever. (That would suck, lol). Really... no one knows. Best thing to do is just live in one reality. When people from a different reality visit us, then we can start talking.

So to answer your question: In my own opinion, weighing all these things, especially points 8 and 10, I would say that there are a finite amount of possible combinations for matter/energy in THIS UNIVERSE. As for other universes... ask God.

 

[SteveL27]

Everything would be repeated an infinite number of times and with an infinite number of variations. Brian Greene explores this particular infinite universe in his book, "the hidden reality", starting on page 27. The crux of the point is, in any finite region, there are a finite number of quantum states in which it could be. In a region the size of our visible universe, the number of states is about 10^10^122. This means, once you had examined that many expanses of space the size of our visible universe, you would necessarily start seeing repeats.

And of course, in any infinite region, there are an infinite number of "finite regions". So, you would see each variation an infinite amount of times.

But this does not follow logically. Label the regions 1, 2, 3, ... Now there are only finitely many possible states. Each of our numbered regions must be in one of those states. For simplicity let's say there are only 5 possible states, call them S1, S2, S3, S4, and S5.

Now it's possible that the assignment of states to regions is: S1, S2, S3, S4, S5, S5, S5, S5, ...

In other words: If there are finitely many possible states and infinitely many regions; then the best you can say is that some state is repeated infinitely many times. But any particular state might well only appear once, or even not at all. Maybe the distribution of states is S5, S5, S5, ... and no other state even happens once.

In other words in an infinite universe, it's certain that some state appears infinitely many times; but as far as anyone particular state, there's no reason it has to appear even once.

So in an infinite universe, some person has infinitely many instantiations; but you or I, probably only one. And some potential people don't ever show up at all.

If Brian Greene missed this point, that just shows that even smart people are not infallible.

By the way this logic applies even if the total number of regions is uncountably infinite. If you label the regions using real numbers, it's still the case that at best only one state has infinitely many instantiations; and all other states may appear zero or once or 47 times or infinitely many times.

Finally, "region" might be a person-sized region or a solar system or a galaxy. So in an infinite universe in which each bounded region of spacetime may only take one of finitely many states; then there is some person with infinitely many instantiations; one planet with infinitely many instantiations; one galaxy with infinitely many instantiations. But it's possible that for any given state of a person, planet, or galaxy, that state appears zero, once, or infinitely many times.

 

[Zmunkz]

I am not sure I agree with your analysis 100%. If we are dealing with an infinite expanse, then any arrangement that has a non-zero probability of occurring will occur infinitely.

infinity * X = infinity, for all X > 0

On the other hand, I do yield to your implied point that not every "possible" arrangement is really possible given the laws of physics as we know them (and assuming they permeate the infinite expanse unchanged), thus we do have to exclude states that have a truly 0% chance of occurring.

I don't see any physical reasons why the exact same quantum states as currently exist, save a change to the colors of a sweater (per the OP's question), should be impossible. As long as P(state) > 0, we can conclude that yes, that combination exists an infinite number of times in the infinite universe hypothesis.

 

[bohm2]

I don't follow the argument. The set of integers is an infinite set but that set does not exhaust the set of rational numbers. So I'm not sure what an infinite universe would imply?

 

[SteveL27]

I am not sure I agree with your analysis 100%. If we are dealing with an infinite expanse, then any arrangement that has a non-zero probability of occurring will occur infinitely.

Was this in response to what I wrote? There are a lot of interesting posts up there so before going into any kind of detail I wanted to make sure you were talking about my argument.

Actually I am making a purely mathematical point. States into bins. An infinitary version of the pigeonhole principle. I think that's a pretty good model for the idea of a universe composed of an infinite collection of finite (shall we say bounded? I think that's what people mean) regions.

But I am not referring to anything that might or might not happen in "reality," whatever that means. This is purely a math exercise; but one that I think illustrates the essence of the situation.