Physicists routinely use simplifications - ignoring Pluto’s gravity or treating the sun as perfectly round - that make the mathematics easier and bring approximate solutions within reach. In physics, a coupling constant is a number that determines the strength of an interaction. In string theory there is string coupling and it is assumed to be low. If the string coupling is small, these approximate calculations are expected to accurately reflect the physics of string theory. But what if it isn’t? Until '95 there were several version of string theory which came along with different coupling constants. Then in '95 Edward Witten showed the world all these different string theories were the one - with several different approaches to the same thing. Each appeared different when examined in a limited context - small values of its particular coupling constant - but when this restriction is lifted, each string theory transforms into the others. This might not be your cup of tea - first we have different things and then they eventually get fixed by saying they all talk about the same thing? Consider following picture:

You probably have seen this one as I remember being popular few years ago and everyone kept mailing it around trying to figure out what was the secret of illusion. If unfamiliar, when you look at this picture close range you see Albert Einstein. If you take dozen of steps back (or a bit less) it morphs into Marilyn Monroe. But hey, it is the same picture! The morphing from Einstein to Monroe is sort of fun. The morphing of one string theory into another is transformative. It implies that if perturbative calculations in one string theory can't be undertaken because that theory’s coupling is too large, the calculations can be faithfully translated into the language of another formulation of string theory, one in which a perturbative approach succeeds because the coupling is small. Physicists call the transition between naively distinct theories duality. By providing two mathematical descriptions of one and the same physics, duality doubles our calculational arsenal. Calculations that are impossibly difficult from one perspective become perfectly doable from another. Union of these theories was called M theory and it showed there’s much more to string theory than strings.

With the new calculational methods, physicists started analyzing again their equations with much more precision and produced a range of unexpected results. They established that ingredients with various numbers of spatial dimensions do lurk in string theory’s mathematical shadows. The analyses revealed objects, shaped like Frisbees or flying carpets, with two spatial dimensions: membranes (one meaning of the "M" of M theory), also called two-branes. But there was more. The analyses revealed objects with three spatial dimensions, so-called three-branes; objects with four spatial dimensions, four-branes, and so on, all the way up to nine-branes. The mathematics made clear that all of these entities could vibrate and wiggle, much like strings; indeed, in this context, strings are best thought of as one-branes. The more precise methods rectified this failing, revealing a string/M-theory universe with ten dimensions of space and one of time, for a total of eleven spacetime dimensions. For the multiverse story, it is the branes that are central. Using them, researchers have been led by the hand to another variety of parallel universes.

Usually we imagine strings as very very tiny. Indeed, they are, but with enough energy injected you could stretch it and string would become large. We do not have enough energy on Earth to do so, but someone somewhere might just have it enough to do so. If string theory is right, an advanced civilization would be able to pump strings up to whatever size it liked. Natural cosmological phenomena also have the capacity to produce long strings; for example, strings can wrap around a portion of space and get caught up in the cosmological expansion, stretching long in the process (this would cause gravitational waves by the way). Like strings, higher-dimensional branes can be big too. Imagine a long string, as long as an overhead electric cable that runs as far as the eye can see. Next, picture a large two-brane, like an enormous tablecloth, whose surface extends indefinitely. These are both easy to visualize because we can picture them located within the three dimensions of common experience. If a three-brane is enormous, perhaps infinitely big, the situation changes. A three-brane of this sort would fill the space we occupy, like water filling a huge fish tank. Such ubiquity suggests that rather than think of the three-brane as an object that happens to be situated within our three spatial dimensions, we should envision it as the very substrate of space itself. Just as fish inhabit the water, we would inhabit a space-filling three-brane. As we run and walk, as we live and breathe, we move in and through a three-brane. String theorists call this the braneworld scenario.

Braneworld models have attracted a lot of interest in recent years. The central idea of braneworld scenarios is that the visible universe is restricted to a four-dimensional brane (3 space and one time dimension) inside a higher-dimensional space, called the bulk. The additional dimensions are taken to be compact and other branes may be moving through the bulk. Interactions of the visible brane with the bulk and hidden branes introduce effects not seen in standard physics. You may find difficult to picture this. Evolution has prepared us to identify objects, those presenting opportunity as well as danger, that sit squarely within 3D space. Although we can easily picture two ordinary 3D objects inhabiting a region of space, few can picture two coexisting but separate 3D entities, each of which could fully fill 3D space.

Remember two-dimensional life on sheet of paper in previous blog? This is analogous to living on a sheet of paper as a two-dimensional figure. You would have no concept of depth - it is simply not a part of your physical world. This is the concept behind braneworld theory, which says that our four dimensional spacetime is like the sheet of paper, simply a subspace of some bigger, multi-dimensional space that we cannot perceive because all matter and forces (except possibly gravity) we experience are constrained to this subspace (or brane).

The same fundamental laws of physics would apply all across the collection of branes, since they all emerge from a single theory - string (M) theory. Nevertheless, as with bubbles in Inflationary Multiverse, environmental details such as the value of this or that field permeating a brane, or even the number of spatial dimensions defining a brane, can profoundly affect its physical features. Some braneworlds might be much like our own while others might be very different. In the braneworld scenario, our universe is just one of many that populate the Brane Multiverse.
If there are giant branes right next door, why don't we see them? It turns out strings come in two shapes, loops and snippets. Can these strings fly off a brane? A loop ones can. A snippet can’t. String snippets can freely move within and through a brane, gliding from here to there, but they can't leave it. In a braneworld, the strings that make you up and the rest of ordinary matter are snippets. The same is valid for the particles that transmit the three nongravitational forces (EM, strong and weak force). Visible light (stream of photons), can therefore travel freely through the brane, but is also unable to leave brane. |

Two or three branes (as in picture above) or even more might be millimeters away - and light would not travel from one to another. Would there be any hint of presence for neighbor brane then at all? The only remaining force, gravity, is different player.

When objects attract each other gravitationally they exchange streams of gravitons. The more gravitons the objects exchange, the stronger the mutual gravitational pull. When some of these streaming gravitons leak off our brane and flow into the extra dimensions, the gravitational attraction between objects will be diluted. The larger the extra dimensions, the more the dilution, and the weaker gravity appears. If we can establish that we are living on a brane, the mathematics gives us no reason to expect that ours is the only one. If branes float in bulk, can they crash against each other? According to theory - yes. Even more, many theorists speculate such crash would mark beginning where initial state would be very close to what we describe as the Big Bang today. In theory this is known as the Big Splat. Splat here might not be right word as branes actually bounce from each other (they don't merge or split or anything similar). In such setup, we come to the point of cyclic universe. This is because branes can collide and as they bounce of each other they go through universe rebirth process within. Theorists close to this concept calculate life frame (birth, evolution and finally death) to be some trillion years. What is interesting here is that both level I and level II universes exist within single brane (for level II see note about inflation below). Given the cyclic feature, theory gives birth to something called Cyclic Multiverse. Still, Max Tegmark for example, warns it is unclear whether such a world (brane) deserves be be called a parallel universe separate from our own, since we may be able to interact with it gravitationally much as we do with dark matter.

Part of the appeal of a cyclical cosmology is its apparent ability to avoid the knotty issue of how the universe began. If the universe goes through cycle after cycle, and if the cycles have always happened (and perhaps always will), then the problem of an ultimate beginning is sidestepped. Each cycle has its

own beginning, but the theory provides a concrete physical cause: the termination of the previous cycle. And if you ask about the beginning of the entire cycle of universes, the answer is simply that there was no such beginning, because the cycles have been repeating for eternity. This may come as strange statement and first thing to be suspicious about is entropy which is supposed to rise with timeline. That has been brought to attention in Herman Zanstra somewhere in 1950s and he did mathematical model to prove it. Brane theorists were able to address this. The branes themselves continually expand and they do so throughout each and every cycle. Entropy builds from one cycle to the next, but because the branes expand the entropy is spread over everlarger spatial volumes. So, total entropy goes up, but the entropy density goes down. By the end of each cycle, the entropy is so diluted that its density is driven very nearly to zero - a full reset or reboot if you want. The cycles can continue indefinitely toward the future as well as the past and Cyclic Multiverse has no need for a beginning to time.

In inflationary cosmology, expansion in the early universe would have disturbed the spatial fabric that substantial gravitational waves would have been produced. These ripples would have left trace imprints on the CMB and we have missions seeking those out. A brane collision, creates a momentary maelstrom - but without inflationary stretching of space. Still, there is inflation though. A new theory, called brane inflation, suggests that inflation arises from the motion of D-branes in the compactified geometry, usually towards a stack of anti-D-branes. This theory, governed by the Dirac-Born-Infeld action, is very different from ordinary inflation. The dynamics are not completely understood so I won't go into any details (it appears special conditions are necessary since inflation occurs in tunneling between two vacua in the string landscape; process of tunneling between two vacua is a form of old inflation, but new inflation must then occur by some other mechanism).

Any gravitational waves produced would be too weak to create a lasting signal. So evidence of gravitational waves produced in the early universe would be strong evidence against the Cyclic Multiverse. The Cyclic Multiverse is widely known within the physics community but is viewed, almost as widely, with much skepticism. Observations have the capacity to change this. If evidence for braneworlds emerges from LHC testing, and if signs of gravitational waves from the early universe remain elusive, the Cyclic Multiverse will likely gain increased support for sure. Back in 2008, phenomena called Dark Flow has been found and certain views on it made connection to gravity pull by another brane, but model of Dark Flow met criticism as expected and as such it needs additional validation and research (2011 study done by University at Buffalo doesn't validate it for example).

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

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