# Deja vu Universe (nature of repeating)

Posted by Hrvoje Crvelin in Quantum Backuptron on Sep 15, 2011 2:24:48 PMIn previous blog entry we encountered idea of infinite space. Actually, we might claim space is infinite as we do not see the end of it plus there is no indication expansion would stop any time soon (it keeps speeding up). Human notion of matter is such that there is nothing infinite and it is rather hard to cope with concept of infinite. Infinity as per se is rather interesting, but I might more focus on that in some dedicated post one day - not now. If we accept infinite space, does this mean there is infinite number of particles in space too? Surprisingly, discussion on subject will lead us to concepts of multiverse, but we before we hit this theory concept let's check composition of Universe.

Whenever I think of modern view on what is out there I get flashes of history events showing evolution of idea about humans and our position in space. Once upon the time we through Earth was flat. We thought we were in center of Solar system. Even space. We thought world was spinning around us. Since then we learned that we in rather different position; we oribit Sun, Solar system orbits galaxy center, galaxies group in clusters, clusters in super clusters. From what we know, it stops there. Nevertheless, in three polls conducted in 1996 and 1999, 19% of Britons, 18% of Americans, and 16% of Germans said that they believed the Sun orbits the Earth. We, you and me, screen which you use to read this, chair on which you seat, your partner and pet, planets... the whole material world around us - is made of atoms. These atoms are made of nuclei and electrons and nuclei can is made out of quarks. Same particles in different layout as building blocks of everything around us. Once again, it turns out this is not the case when it comes to Universe - this is only a small part of the content of the Universe.

Atoms (matter) today made up for only 4.6%. 4% are free hydrogen and helium atoms. 0.5% are stars. Neutrinos are some 0.4% and heavy elements are are some 0.03% for an example. So, it turns out space is not really space welcoming us at all. We can romantically be described as star dust or nuclear waste to be less romantic (human composition contains traces of elements that may only come from stars during their nuclear processes). While matter should be clear you may wonder what dak matter and dark energy are. For both we can say more is unknown than known (even we do have some progress with dark matter and scientists expect to crack it down within next 20 years).

The mathematics shows that “just the right amount of matter,” the so-called critical density, weighs in today at about 2×10^–29 grams per cubic centimeter, which is about six hydrogen atoms per cubic meter (the equivalent of a single raindrop in every earth-sized volume). Looking around, it would surely seem that the universe exceeds the critical density. The mathematical calculation of the critical density assumes that matter is uniformly spread throughout space. So you need to envision taking the earth, the moon, the sun, and everything else and evenly dispersing the atoms they contain across the cosmos.

Astronomers have been trying for long time to measure the average density of matter in the universe; with powerful telescopes they carefully observe large volumes of space and add up the masses of the stars they can see as well as the mass of other material whose presence they can infer by studying stellar and galactic motion. Until recently, the observations indicated that the average density was on the low side, about 27% of the critical density (equivalent of about two hydrogen atoms in each cubic meter). In the late 1990s, astronomers realized that they had been leaving out an essential component of the tally: a diffuse energy that appears to be spread uniformly throughout space. Even today, a decade after the initial observations, astronomers have yet to establish if the uniform energy is fixed or if the amount of energy in a given region of space varies over time. This energy does not give off light (explaining why it had for so long evaded detection) so we call it dark energy. "Dark" also describes well the many gaps in our understanding. No one can explain the dark energy’s origin, fundamental composition, or detailed properties - issues currently under intense investigation. One explanation for dark energy is that it is a property of space. Albert Einstein was the first person to realize that empty space is not nothing. Space has amazing properties, many of which are just beginning to be understood. The first property that Einstein discovered is that it is possible for more space to come into existence. Then one version of Einstein's gravity theory, the version that contains cosmological constant makes a second prediction: "empty space" can possess its own energy. Because this energy is a property of space itself, it would not be diluted as space expands. As more space comes into existence, more of this energy-of-space would appear. As a result, this form of energy would cause the Universe to expand faster and faster. Unfortunately, no one understands why the cosmological constant should even be there, much less why it would have exactly the right value to cause the observed acceleration of the Universe.

We are much more certain what dark matter is not than we are what it is. First, it is dark, meaning that it is not in the form of stars and planets that we see. Observations show that there is far too little visible matter in the Universe to make up the 23% required by the observations. Second, it is not in the form of dark clouds of normal matter, matter made up of particles called baryons. We know this because we would be able to detect baryonic clouds by their absorption of radiation passing through them. Third, dark matter is not antimatter, because we do not see the unique gamma rays that are produced when antimatter annihilates with matter. Finally, we can rule out large galaxy-sized black holes on the basis of how many gravitational lenses we see. High concentrations of matter bend light passing near them from objects further away, but we do not see enough lensing events to suggest that such objects to make up the required 23-25% dark matter contribution. However, at this point, there are still a few dark matter possibilities that are viable. Baryonic matter could still make up the dark matter if it were all tied up in brown dwarfs or in small, dense chunks of heavy elements. These possibilities are known as massive compact halo objects, or MACHOs. But the most common view is that dark matter is not baryonic at all, but that it is made up of other, more exotic particles like axions or WIMPs.

So if we rule out what we don't know, we are left with some 4% we believe we know enough. Let's assume our universe expands into infinity (flat infinity, no tabletops or similar tricks that would make it finite please). Now, for a moment, imagine large number of decks of cards. You shuffle cards and key questions is can you have paterns repeating? The answer depends on the number of decks. 52 cards can be arranged indifferent ways (52 possibilities for which card will be the first, times 51 remaining possibilities for which will be the second, times 50 remaining possibilities for the next card, and so on). If the number of decks we shuffle exceeds the number of different possible card orderings, then some of the shuffled decks would match. If you were to shuffle an infinite number of decks, the orderings of the cards would necessarily repeat an infinite number of times. An infinite number of occurrences with a finite number of possible configurations ensures that outcomes are infinitely repeated. Can this be applied to Universe?

In an infinite universe, most regions lie beyond our ability to see, even using the most powerful telescopes possible (see previous blog entry on cosmic horizon). Expansion of space increases the distance to objects whose light has long been traveling and has only just been received by us. Same applies for light emitted by us for those who would have us out of their cosmic horizon. Depending on the size of Universe (real one, not bounded by our cosmic horizon), in 2D world we might have as something seen on following picture:

Picture on left shows us in center and ring around is our cosmic horizon. On grand scale, depending on size of Universe, we might have many of those scattered around. Going back to our cosmic horizon on left picture, we have radius of some 40+ billion light years (exact number hardly matters here). We focus on matter and radiation particles. How many different arrangements of the particles are possible?

The more matter and radiation you cram into the region the greater the number of possible arrangements. But you can’t cram pieces in indefinitely as particles carry energy, so more particles means more energy. If a region of space contains too much energy, it will collapse under its own weight and form a black hole. And if after a black hole forms you try to cram yet more matter and energy into the region, the black hole’s event horizon will grow larger. Thus there is a limit to how much matter and energy can exist fully within a region of space of a given size. For a region of space as large as today’s cosmic horizon, the limits involved are huge (about 10^56 grams). Crucial here is not value of limit - it is a fact there is limit. Something finite's in the air.

Finite energy within a cosmic horizon means finite number of particles (known or unknown). This also means each of these particles, lik has a finite number of distinct possible locations and speeds. Collectively, a finite number of particles, each of which can have finitely many distinct positions and velocities, means that within any cosmic horizon (picture right above) only a finite number of different particle arrangements are available (quantum states). Calculations reveals the number of distinct possible particle configurations within a cosmic horizon is around 10^10122 (huge but finite number). The limited number of different card orderings ensures that with enough decks, shuffles will necessarily repeat. By the same reasoning, the limited number of particle arrangements ensures the particle arrangements must also somewhere repeat. What does this mean?

As noted before, matter is pretty much made of same particles. Different particle arrangement, but same particles (at present day there is no proof yet conscious might be coming from something else, but one may keep its mind open). This indicates that out there there is a chance that very same you exists. And both would be real. Your second I would real as much as you (and if mental state comes out of physical properties it means indentical mentally as well). Shocked? There is more. It turns out we can estimate location of next you too. That is, in every region of space that’s roughly 10^10122 meters across, there should be a cosmic patch that replicates ours - you, Earth, Milky Way - everything else that inhabits our cosmic horizon. As there is only one way to duplicate a region exactly, but many ways to almost duplicate it, we find approximate replicates way closed - some 10^10100 meters. This is theory and it is theory which is quite possible.

Approach to such parallel Universe is called Quilted Multiverse by Brian Greene (I like to call it Deja Vu one, but probably there are other names too). Brian wrote very nice book called "The Hidden Reality: Parallel Universes and the Deep Laws of the Cosmos". I highly recommend this book and I plan to spend next few blog posts discussing various Multiverse concepts as described in Brian's book. Nevertheless, it was another author who brought concept of multiple universes to my attention - Max Tegmark. Max is known cosmologist (MIT) and has come up with a mathematical argument for the multiverse. In his view, multiverse as described before is so called Level I Multiverse (IV levels in total). You can find his paper on this subject here. If you wish to visit his site where you can find multiple resources, click here. Highly recommended.

Credits: Brian Greene, Max Tegmark, Stephen Hawking, Wikipedia

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