# Can the Universe repeat itself?

by gravenewworld
Tags: repeat, universe
 P: 1,385 I remember my philosophy professor asking us this question- Take all the matter in the universe, it is an ungodly number, however it is finite. Given that there is a finite number of matter in the universe, there is only a finite number of ways that all the matter can arrange itself. So is it possible that the universe can repeat itself given an INFINITE amount of time? Would it be possible for all the matter that composes your body right now to arrange itself again later on trillions upon trillions of years from now in the same exact order so that you would exist again?
 P: 15,325 Actually, there was an article a year or so back in Sci Am that pointed out that it doesn't need to take any time at all, let alone an infinite amount of time. It could be existing right now. All it requires is that the universe be infinite in size. If you go in any direction for a certain distance (and they calculate the distance) you will HAVE to encounter a (subset of the) universe that is identical to this one. They start quite simple. Imagine a universe in which there are only four atoms: A,B,C,D and only four locations for those atoms to exist: 1,2,3,4. There are only a certain number of ways you could lay out this grid before you had to start repeating a pattern. This would happen in any direction you chose to go. You can derive a formula that says "with X atoms and Y spaces you can go only Z distance in any direction before you are forced to repeat the pattern of 4 atoms in 4 spaces". (I'm not sure how they get around the obvious flaw in the argument: Who says the rest of that infinite universe has to have any atoms in it at all? Then you could repeat hard vacuum indefinitely without ever duplicating a pattern of atoms. I think there's some condition about large-scale homogeniety.) Anyway, when you scale it up to universe size, the numbers (while very large) are not infinite. I think the number was something like 10^120 metres. This means that, given the premise of a universe of infinite size, you could travel (let's say) 10^120 metres in any direction of your choosing, and land your spaceship next to an identical copy of yourself.
 P: 34 Nothing as elaborate as an infinite universe is required to substantiate an affirmative answer. Suppose (correctly!) that there are only finitely many particles in the universe. Then Poincare's Recurrence Theorem shows that, after a really really long time, the state of the universe at that time will be a state that is arbitrarily close to the current state of the universe. The time for this to happen is called the Poincare Recurrence time -- it is not an infinite amount of time, but it is a much longer period of time than the time given for our best guess about the age of the universe.
P: 244

## Can the Universe repeat itself?

 Quote by NickJ Nothing as elaborate as an infinite universe is required to substantiate an affirmative answer. Suppose (correctly!) that there are only finitely many particles in the universe. Then Poincare's Recurrence Theorem shows that, after a really really long time, the state of the universe at that time will be a state that is arbitrarily close to the current state of the universe. The time for this to happen is called the Poincare Recurrence time -- it is not an infinite amount of time, but it is a much longer period of time than the time given for our best guess about the age of the universe.
Suppose that we do not really have any idea of what the 'universe' actually is, why it is, what was before the big bang and are there more than one big bangs now in existence. Now suppose with all this less than sure knowledge, we might not know what will happen given enough time.
 P: 160 If you have "finite complexity" then the universe has a finite number of possible configurations. Given enough time to exhaust all possible configurations then I don't see that there is a choice: a previous configuration must be repeated. If so then this must also repeat forever since the universe didn't end the first time around so it has no reason to end this time around either: endless loop! Given this scenario then we may have all lived this before and may do it again later. Funny that I don't remember it though... But "finite complexity" is not trivial. It requires truly atomic building blocks otherwise you can always come up with new configurations by splitting particles differently and do so infinitely. You also need atomic positions in both space and time otherwise you can create infinitely many new configurations just by nudging one particle in any new position where it never was before, or at a different relative time compared to other particular motion. And of course you also need to have a finite number of laws of nature, complete determinism in other words. This is a whole topic in itself. For instance: a universe created out of nothing (without any cause) implies at least some degree of non-determinism. Also an infinite set of natural laws (and how do we know there are not an infinite number of them?) pretty much guarantees infinite complexity as well. But to make a long story short: given finite complexity and infinite time then we probably are in an endless loop. Conversely, given infinite complexity or finite time then we probably aren't.
P: 1,603
 Quote by NickJ Nothing as elaborate as an infinite universe is required to substantiate an affirmative answer. Suppose (correctly!) that there are only finitely many particles in the universe. Then Poincare's Recurrence Theorem shows that, after a really really long time, the state of the universe at that time will be a state that is arbitrarily close to the current state of the universe. The time for this to happen is called the Poincare Recurrence time -- it is not an infinite amount of time, but it is a much longer period of time than the time given for our best guess about the age of the universe.
How does one account for entropy in this scenario?
We seem to observe a universe in which the entropy was much lower in the past and which appears to be marching inexorably to higher and higher entropies in the future.
Poincare's simple recurrence model only applies to mechanically reversible processes.
The prevailing source of low entropy is the gravitational field, it is what drives the nuclear powerhouses of the stars. Eventually the universe will end up as a collection of burned out stars and debris, in an apparently ever-expanding space. To "repeat" the universe one would then need to somehow recreate the conditions of the big bang.

How does Poincare's model apply in such a scenario?

Best Regards

MF
 P: 34 MF- I think you're on to an interesting puzzle. Boltzmann, one of the original people to think about how to account for entropy, encountered what is known as the recurrence objection to his attempt to derive something like the second law of thermodynamics from classical microscopic dynamics: Boltzmann wanted entropy to always increase; but if Poincare recurrence happens, at some point it must decrease. So some people think that entropy increase is periodic or something like that (with the period determined by the Poincare recurrence time). But other people make the following observation: Poincare's recurrence theorem fails for systems with infinitely many particles (because the phase space for such a system is not compact). So, somehow, the idealization of an infinite number of particles is needed to account for why there is genuine entropic increase. Weird. Still other people think that our microscopic dynamical laws, which happen to be time-reversal invariant, are incorrect -- that we need to build an asymmetry into our laws in order to account for genuine entropic increase. It's a very puzzling issue, I think.
 Emeritus PF Gold P: 8,147 The question of entropy in a cyclical physical system goes to what is called ergodic behavior. Basically the Poicare worldline in the phase space passes through every small neighborhood of phase space eventually, and the combination of all these microstates, on the average, gives you entropy. (Much oversimplified!). But not all systems behave ergodically! Famously the Fermi-Pasta-Ulam (FPM) model of linked anharmonic oscillators does not; its states even at arbitrarily late times are linear combinations of large amplitude solitons.
P: 1,603
 Quote by selfAdjoint The question of entropy in a cyclical physical system goes to what is called ergodic behavior. Basically the Poicare worldline in the phase space passes through every small neighborhood of phase space eventually, and the combination of all these microstates, on the average, gives you entropy. (Much oversimplified!). But not all systems behave ergodically! Famously the Fermi-Pasta-Ulam (FPM) model of linked anharmonic oscillators does not; its states even at arbitrarily late times are linear combinations of large amplitude solitons.
For the benefit of forum members who do not understand the FPM model etc, what does all this mean in plain English?

The main drivers of increasing entropy in our universe are the universal attraction of gravity plus the expansion of space, combined with the fact that the Big Bang (for some reason) seems to have been a very low-entropy state to begin with. In addition, the universe appears (on the latest evidence) to be expanding at an accelerating rate. This will eventually lead to an ever-widening universe of burned-out stars. In simple plain English, how does one get from that kind of high-entropy "heat death" back to the concentrated but spatially very uniform mass-energy of the Big Bang?

In other words : Gravity plus universal expansion are the dominating mechanisms which take us from low entropy "Big Bang" to high entropy "Heat Death". What underlying physical mechanism(s) do you think would be at play to convert us back again from "Heat Death" to "Big Bang"?

Best Regards

MF
P: 1,011
 Quote by moving finger In other words : Gravity plus universal expansion are the dominating mechanisms which take us from low entropy "Big Bang" to high entropy "Heat Death". What underlying physical mechanism(s) do you think would be at play to convert us back again from "Heat Death" to "Big Bang"? Best Regards MF
If there was no gravity, but the same expansion, heat death would happen more quickly. Greater dynamical friction will decrease entropy (the SI unit of entropy is J/K (Joules per Kelvin)). For example, as a nebula contracts, K in the nebula increases relative to coldness of outspace, meaning more work can be done at the nebula.

The reason why entropy in the universe increases is because the universe is radiating faster than it is absorbing. If the expanding universe did not have gravity and consisted of diffuse gas and dust only, we would have the same problem of heat death (emission > absorption).

Very roughly (http://en.wikipedia.org/wiki/Kinetic_theory) - I'm new to this:

$v_{rms}^2 = \frac{3kT}{molecular\ mass}$

Given that average molecular mass and k are constants, it would follow that temperature is proportional to the square of the velocity (if I am doing this right). Since velocity squared in force relationship of 1/r^2 is inversely proportional to distance (where potential is proportional to 1/r and v^2), it would follow that temperature is inversely proportional to radius for a given energy content, and thus entropy of the universe would be proportional to radius. That the radius of the universe is increasing is directly related to the increasing seperation of matter in the universe, which is has a similar effect on the trend of entropy as does radiation that is not being reabsorbed.

All you need to get rid of the heat death is for someway to decrease the radius of the universe, and that requires a strong field of attraction.
P: 1,603
 Quote by kmarinas86 All you need to get rid of the heat death is for someway to decrease the radius of the universe, and that requires a strong field of attraction.
"All you need....." - my point exactly.

Poincare recurrence is fine for a reversible mechanical system in absence of gravity and universal expansion, but given that gravity exists, and that the universe is expanding, Poincare recurrence alone will not result in a cycling of the universe. Something else (you have suggested a "strong field of attraction" to "decrease the radius of the universe") is needed.....

In absence of this "something else" there is (as far as I can see) no underlying mechanism enabling cyclic recurrence....

MF
P: 11
 Quote by NickJ Suppose (correctly!) that there are only finitely many particles in the universe. Then Poincare's Recurrence Theorem shows that, after a really really long time, the state of the universe at that time will be a state that is arbitrarily close to the current state of the universe.

A finite number of particles may not be enough to invoke Poincare Recurrence. In infinite space, although there may be finite matter, it may not be clear how to model the universe to fit his requirement for a measure-preserving dynamical system with finite measure. Or is it?
P: 15,325
 Quote by FlowerPUA 1. The “heat death” hypothesis of the universe appears to be flawed. With no kinetic energy in the universe it would be a “frozen wasteland”. However a finite mass, separated by a finite distance would still feel a small force of gravity over the immense distances. This force, however small, on an infinite timeline would lead to collisions, and ultimately all the mass converging again onto one point, perhaps for another “big bang”.
You are assuming the particles have stopped expanding and have come to rest.

 Quote by FlowerPUA 3. It was mentioned above that we would be separated a distance of 1x10^120 metres from a repetition. I don’t really understand this concept at all. It is to my understanding that the universe has a finite (1x10^70) number of atoms spread out over a finite distance which is expanding into an infinite amount of space. Are you suggesting that there could be more mass, from yet more “big bangs” in the same universe?
Yes, that is the idea.
 P: 31 Can Cyclic Universe mean Eternal Return?
PF Gold
P: 3,273
 Quote by gorgos Can Cyclic Universe mean Eternal Return?
Also called Eternal Recurrence.

Yes! All you need is an infinite universe, an eternal universe or an eternally cyclical universe. No matter how unlikely something is, such as the probability that this exact world and moment will be copied somewhere, then in one of these infinities it will repeat itself, an infinite number of times.

That's infinity for you!

Garth
P: 166
 Quote by NickJ Nothing as elaborate as an infinite universe is required to substantiate an affirmative answer. Suppose (correctly!) that there are only finitely many particles in the universe. Then Poincare's Recurrence Theorem shows that, after a really really long time, the state of the universe at that time will be a state that is arbitrarily close to the current state of the universe. The time for this to happen is called the Poincare Recurrence time -- it is not an infinite amount of time, but it is a much longer period of time than the time given for our best guess about the age of the universe.
http://en.wikipedia.org/wiki/Poincar...rrence_theorem
P: 622
 Quote by Garth Also called Eternal Recurrence. Yes! ....... ......That's infinity for you! Garth
Perhaps not quite! It seems to me that your post betrays a somewhat B.C. (Before Cantor, that is!) understanding of infinity. In fact some infinities are much more infinite than others, as George Orwell might have put it.

Consider a small universe made of a finite number of elements (whatever these are, and if the universe can be said to consist of "elements" in this anthro'centric way). These elements may be distinguishably arranged in a number of ways that is, general speaking, factorially greater than the actual number of elements, say, as 120 (5!) is greater than 5

Now imagine the number of elements to be increased, towards infinity. Their distinguishable arrangements remain factorially more numerous-- i.e. enormously so-- than the element number, all the way up to infinity. No matter how big the universe is, there are always vastly more ways it can be arranged than there are elements in it.

Specifically, there is no need for an infinite universe to include more than one Garth --- I suspect that you may be quite unique in the larger factorial infinity of the universe, even if it is itself infinite!

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