Because of quantum effects, for any given volume of space there is a finite (albeit very large) number of ways that matter and energy can be arranged within it.

Therefore, using the pigeonhole principle we can prove that for any particular volume of space there must be SOME configurations that repeat.

(For example, it’s not too surprising to think that if we look at spheres of space one centimeter in diameter, there are probably a large number of them that contain only one hydrogen atom in their exact center. That’s probably a pretty common configuration.)

My question is: In an infinite universe must ALL possible configurations of matter occur? We know that some must repeat, but is it possible that some configurations don’t exist anywhere, even in an infinite universe?

Is there a version of Earth where everyone looks like Spongebob Squarepants and flies to the moon on weekends in boats pulled by zombie swans to eat moon cheese?

What I just described is a VERY UNLIKELY configuraton of matter. It couldn’t exist as the result of natural processes. It could only occur through countless random quantum effects all accidentally combining to create a very, very unstable combination of matter and energy.

How about an Earth were everyone flickers back and forth between a male and female version of themselves 10 times a second?

Are there, in fact, some things that are so unlikely that they can’t exist even in an infinite universe?

I do not believe this is true. If you take an volume comprised that immediately encloses a hydrogen atom, what is it that’s repeating in it? Or go smaller, go the the electron level, or plank length level. There is repetition in that space?

I think you’re misunderstand my use of “volume”. I don’t mean a specific, unique location in space. I mean a particular size of space under consideration. For example, we can imagine the entire universe broken down into overlapping one-centimeter spheres and compare the contents of the different spheres.

I will be very interested in the feedback of those who, unlike me, know what they are talking about. My instinct is to say that in an infinite universe, everything is infinitely likely (which is subtly, but possibly inconsequentially, different from the statement that everything “must” be true somewhere).

Isn’t the state of the art in cosmology that the universe is not infinite? (Not to imply that we’re not entitled to hypothesize, but only to defuse the disturbing notion that I should be on the lookout for my squarepants-wearing doppelganger.) Even if the universe, however, is not infinite, there could be an infinite number of universes. Last time I checked, which was several years ago, that was one interpretation of quantum physics proposed in order to resolve Schrodinger’s Cat-type uncertainties.

Assuming an infinite universe has some physical laws consistent across all of it, then some configurations of matter are impossible. Does physics itself preclude the idea of someone flicking genders 10 times a second?.. probably.

And are you speaking of a universe that’s randomly “seeded” with matter? If there’s only so much matter, then there are only so many configurations that will exist. Otherwise, you run out of stuff to put in the piegonholes.

But conceptually, it seems to me that anything allowable by physics would indeed occur in an infinite universe, along the lines you’re thinking of.

I’m specifically thinking of combinations of matter that could only occur through random atomic- or molecular-level effects all lining up in exactly the right way.

For example, at any given time some molecules in a bowling ball are headed down and some are headed up. Gravity introduces a bias that means at any given time more are headed down than up, giving the bowling ball weight. However, it’s possible (but very, very unlikely) that all the molecules in a bowling ball could just happen to move up at the same time, allowing it to levitate.

In an infinite universe, is there a planet where bowling balls all hover an inch off the ground … ?

Everything possible occurs with probability 1, but that doesn’t mean that everything possible must occur. Those two statements are only equivalent when dealing with finite or countably infinite sample spaces, and the possible set of states for an infinite universe is uncountable.

Then I’m on your side. I think there is a planet of the floating bowling balls. In fact, there’s an infinite number of them. And there’s an infinite number of planets where Pochacco is asking this question, and Muttrox is giving this answer, and Ultrafilter is about to come along and explain a little better why I’m way off base.

(I do seem to remember a point dealing with Occam’s paradox about the night sky, whereby having an infinite number of stars doesn’t neccessarily mean that there must be a star wherever you look, if the distribution wasn’t random…)

I’m just thinking about summations from my calc 2 class, where you have things approaching a limit (in this case, 100% chance of occuring), but that don’t actually reach that point, ever. So, as the size of the universe increases towards infinite, you have an increasingly likely chance that configuration x exists. This doesn’t mean that when you reach infinite that the chance hits 100%, even if it approaches 100% as the size of the universe increases.

Maybe someone who has actually done any calculus in the last 9 years can say that more clearly than I.

Actually, if I have a “side” it’s the opposite. I suspect there are some configurations of matter that I can imagine that NEVER occur anywhere in even an infinite universe. However I lack the mathematical and scientific training to formulate a solid argument in support of this position.

Nope.
Give every particle in the universe a unique identifying number 1,2,3…infinity.
Each particle has a closest neighbor particle.
If particle 3 has particle 257 as its closest neighbor, then the configuration in which particle 3 has (say) particle 867 as its closest neighbor does not exist.

For the purposes of this discussion all particles of a particular type (with particular spin, energy level, etc.) should be considered equivalent. Obviously one atom of hydrogen can’t be in two places at once. But there can be two atoms of hydrogen in different locations that are in exactly the same state.

Given the infinite and eternal, is it possible that this exact configuration of matter will be repeated at some point, perhaps repeated infinite times, and that I have an infinite number of future existences to look forward to?

The possibility, if it is one, is both comforting and disturbing.

If the number of atoms, electrons, quarks, etc. in the universe is countable (That is equivalent in size to the number of integers), but space-time is continuous (That is equivalent in size to the set of real numbers which is “larger” than the set of integers), then the answer would have to be ‘no’ as the number of arrangements of just two particles would have to be at least the size of the set of real numbers based simply on their distance from each other an dignoring any other descriptors.

Now it’s possible that the number of particles in an infinite universe is equivalent in size to the set of real numbers, or that space time is discrete (at the Planck length or something) and so its size is only that of the integers, but I still don’t think the answer is yes. It would seem to me (but it’s been too long since set theory) that the set of all arrangements of an infinite number of partices would be at least one higher cardinality.

I’m assuming that the number of particles is countable and that space-time is quantized. Otherwise we can’t assume anything repeats.

The tricky bit is that since we’re talking about a bounded volume the number of particles isn’t infinite. However I do suspect the answer lies with comparing different levels of cardinality.