# No strings attached - dimensions of new reality

Posted by Hrvoje Crvelin in Quantum Backuptron on Sep 20, 2011 12:12:33 PMIn previous two blogs I discussed two models of parallel universes:

- quilted (or deja vu or level I universe)

- inflationary universe (or level II universe)

At this point we continue further, but before we hit the point we need a bit of a introduction to something else - string theory - as quantum wierdness itself generates Multiverse models. Remember when at school you learned about molecules and atoms? Usually you would start of atom as basic unit of matter and you would say it consists of central nucleus and cloud of electrons around it. References to the concept of atoms date back to ancient Greece and India. It took some 3000 years to get from assumption to practice, but atoms become scholar reality. Atoms group into molecules via chemical bonds to form electrically neutral group consisting of least two atoms (same or different ones). Electrons, flying around nucleus, have been discovered in 1897 by J.J. Thomson. They are also believed to be elementary particles as we are not aware of any substructure it consist from. Electrons have negative charge. Proton on the other hands have positive structure and they tend to form nucleus of an atom. They have been theorized since 1815 and finally found in 1919 by Ernest Rutherford. It was Ernest who theorized there might be another, with no electric charge particle making up nucleus. Finally, this has been confirmed by James Chadwick who found neutron in 1932. It took more than 30 years since to suggest and prove there is more if we look at it even smaller scale.

Period of mid 20s to mid 60s of last century was also the time when physicist search of theory of unification. At that time it become apparent our best tooling to describe how things behave at large scale (eg. general relativity) and how they behave at very small scale (eg. quantum mechanical world description) simply didn't match - even though both did excellent job for what they were meant to be. The idea was if we are all made of same particles then one single theory should be out there able to explain everything through laws for this particles itself. Instead, we had this problems where whenever we tried to explain situations involving singularities (like Big Bang or Black Holes) math would just break. At that time, only two forces in nature were known (out of 4 as we know it today); electromagnetism and gravitation (weak theory appeared in theory for the first time somewhere in 30s).

Then in mid 60s things started to happen. In 1964 it has been suggested both neutrons and protons could be split to more elementary particles called quarks. In 1968 this has been confirmed (there are 3 generations of quarks, 6 quarks in total and while first one was found in 1968 it was not before 1995 we found last one). Interesting thing about quarks is they never come along (isolated), but rather in pairs forming what is called hadron (you might get an idea what Large Hadron Collider stands for now). Physicists realized that the methods of quantum field theory, which had been successfully applied to the electromagnetic force, also provided descriptions of the weak and strong nuclear forces. Weak is responsible for, among other things, radioactive decay. Strong one provides a powerful glue that holds together the nuclei of atoms (force carrying particles are called gluon). The word strong is used since the strong interaction is the "strongest" of the four fundamental forces; its strength is 100 times that of the electromagnetic force, some 10^6 times as great as that of the weak force, and about 10^39 times that of gravitation.

While certain structures that would become successful part of string theory were known in 20s, it was only around end of 60s and begin of 70s that string theory started its life. The heart of string theory lied within previous work done under names like S-Matrix and Regge theory and bootstrap models and finally, dual resonance model. In 70s, we find first records of representing nuclear forces as vibrating, one-dimensional strings. As time progressed problems started to count up. Initially this theories were not stable. They included only bosons so fermions need to be included leading to supersymmetry to be invented (supersymmetry is nothing but mathematical relation between bosons and fermions). At the end those string theories including fermionic vibrations were called superstring theories. In 1984 so called first superstring revolution happened. It was realized that string theory was capable of describing all elementary particles as well as the interactions between them. Then in 1994 second revolution happened and M-theory has been born unifying different versions of superstring theory. In 1997 Juan Macadena made some amazing math leading to AdS/CFT correspondence - what would become basis for a holographic principle later on (even though that used to be something Leonard Susskind was after in his continues battle with Stephen Hawking). In 2000s, we further have discovered so called string theory landscape. While this is all nice, can you describe also in sentence or two what really string theory is about? Yes. It is theory which states all objects in our universe are composed of vibrating filaments (strings) and membranes (or branes) of energy. A string is an object with a one-dimensional spatial extent, unlike an elementary particle which is zero-dimensional, or point-like. Quarks and electrons are thought to be made of string(s) for example. An electron is less massive than a quark, which according to string theory means that the electron’s string vibrates less energetically than the quark’s string. The electron also has an electric charge whose magnitude exceeds that of a quark, and this difference translates into other, finer differences between the string vibration patterns associated with each. Much as different vibration patterns of strings on a guitar produce different musical notes, different vibration patterns of the filaments in string theory produce different particle properties.

Strings was are also very very small, on the order of the Planck length - 10^-33 centimeters. The Large Hadron Collidercan probe to scales of about 10^-19 cm; that’s a millionth of a billionth the width of a strand of hair, but still orders of magnitude too large to resolve phenomena at the Planck length. During the summer 2011, just before I was headed for Croatia coast to enjoy some free time with family, ESA announced something unexpected. While Einstein's General Theory of Relativity describes the properties of gravity and assumes that space is a smooth, continuous fabric, yet quantum theory suggests that space should be grainy at the smallest scales, like sand on a beach. According to calculations, the tiny grains would affect the way that gamma rays travel through space. The grains should "twist" the light rays, changing the direction in which they oscillate, a property called polarization. High-energy gamma rays should be twisted more than the lower energy ones, and the difference in the polarization can be used to estimate the size of the grains. Some theories suggest that the quantum nature of space should manifest itself at the Planck scale: the minuscule 10^-33 cm. However, observations are about 10000 times more accurate than any previous and show that any quantum graininess must be at a level of 10^-46 cm or smaller. ESA Integral made a similar observation in 2006, when it detected polarized emission from the Crab Nebula, the remnant of a supernova explosion just 6500 light years from Earth in our own galaxy. This new observation is much more stringent, however, because GRB 041219A was at a distance estimated to be at least 300 million light years. In principle, the tiny twisting effect due to the quantum grains should have accumulated over the very large distance into a detectable signal. Because nothing was seen, the grains must be even smaller than previously suspected.

Another interesting fact coming out of the math of string theory is number of dimensions. We are used to live in 4 dimensions, but string theory requires more dimension than those we are aware of. Additional number of dimensions was first suggested on early days of 20st century. It was Kaluza-Klein duo suggesting there are dimensions that are big and easily seen, and others that are tiny and thus more difficult to reveal - and the same might apply to the fabric of space itself. If you are bird flying over sandy beach you see smooth two dimensional surface... but you fly down suddenly these sand grains start to reveal other dimensions. Within same logic, very very high tower observed from long distance would appear as one dimensional line going to the sky. But there is more then one dimension there, isn't.

Look at the letter S. Its shape is due to a single curved line. A splash of paint on a canvas also has a shape, but this is no longer that of a line but an area. Solid objects have shapes too - cubes, spheres, people, cars all have geometric shapes called volumes. The property that is different in the above three cases (line, surface and volume) is the number of dimensions required to define them. A line is said to be one-dimensional, an area is two-dimensional and volume is three-dimensional. Is there some reason why we should stop here? Well, our brains are hard-coded to three dimensions so we can't imagine worlds with higher number of dimensions very well. Three space dimensions also define 3 arrows of movement we can do (up/down, left/right and forward/backwards). In mathematics these three directions in which we are free to move are called mutually perpendicular, which is the mathematicians’ way of saying "at right angles to each other". n dimensional life exists within n+1 world. If you imagine 1 dimensional world (line, where you can only move within one direction) you would defined as dot or 0 dimensional being. Below is the example:

In both cases our dot is able to move along one dimension (backwards and forwards). The only difference is that space within it lives (1 dimensional line) is flat in one case and in another it is curved. In space, things get even more confusing when dealing with spacetime (which is 3 space dimensions and 1 time dimension) as gravity tends to curve both space and time. To give you an idea of bent space and its influence on dimension consider following example:

What we see on (a) is square (2 dimensions) on flat space. On (b) and (c) we see square being bent within space. On (d) we see space being bent and this reflects shape which as far as we are concern didn't change from (a). In our world, it did of course. But if you imagine to be one dimensional life living and following directions of lines we see as square - you would not be aware of this, would you? To get an idea of life in two dimensional world imagine following picture:

We see 2 creatures living in two dimensional world (space wise). From our point of view, they can move up/down and left/right. That means they can't bypass each other (well, in 2D world you can solve this by one creature to lay down and second one to just walk over it). They do not live on that surface, they live within that surface. They also can't turn around... they can only start walking backwards (in this specific case, for being on left that would be left direction). Now bare in mind, space wise, they live in 2D and you live in 3D. You can see them, but they can't see you. And this is all thanks to just one dimension (in this case we miss backward/forward to make it easier from our perspective). Imagine you went with your hand through their world. What would they see? They would see line appearing from nowhere. If you were to pick up one of the being and placing at somewhere else (for example left one behind right one) then this would be seen again as line appearing from nowhere which does something to left being and it moves us and then behind right without much logical explanation. Exercises in two dimensional world with certain operations we perform daily in our 3D world may sometimes result in strange results.

We already mentioned curved space. We take most of the things for granted and simplified in our everyday life. As a kid, when I heard people used to believe Earth was flat I used to think people of the past were not so smart. But, if nothing, I realize now they just followed sane logic. Look through the window and look at distance. It if flat. If you start walking in one direction soon or later you will get back to the same point, but while doing that there would ne nothing to indicate that surface you walk is not flat. Even the math you learn in school is the one which works for flat surface. Check this out. You are having fun with Polar bears on North Pole, but wish to stretch your legs so you start your journey until equator. Then you turn left (that would 90 degrees) and you walk until let's say some point when you take another 90 degrees and walk back to North Pole. Triangle has sum of 180 degrees for inner angles, but we already made that with two turns. How is that? Illustration helps again:

As we can see, curvature of space makes difference. So, there is number of challenges for scientists when dealing this space as we perceive it - let alone dimensions on top of that. Whole story with dimensions tends to be interesting one, but if you followed carefully you would have noticed it started somewhere earlier... somewhere in '20s of last century. What made those people think about dimensions at that time?

Kaluza revealed that in a universe with an additional dimension of space, gravity and electromagnetism can both be described in terms of spatial ripples. Gravity ripples through the familiar three spatial dimensions, while electromagnetism ripples through the fourth. An outstanding problem with this proposal was to explain why we don't see this fourth spatial dimension. Klein suggested resolution: dimensions beyond those we directly experience can elude our senses and our equipment if they are sufficiently small. Almost half century later and string theory appeared requiring multiple dimensions to make sense.

One of the features of string theory is that particle properties are determined by the size and shape of the extra dimensions. Because strings are so tiny, they don't just vibrate within the three big dimensions of common experience; they also vibrate into the tiny, curled-up dimensions. And much as air streams flowing through a wind instrument have vibration patterns dictated by the instrument’s geometrical form, the strings in string theory have vibration patterns dictated by the geometrical form of the curled-up dimensions. If string vibration patterns determine particle properties such as mass and electrical charge, then these properties are determined by the geometry of the extra dimensions.

So, if you knew exactly what the extra dimensions of string theory looked like, you would be well on your way to predicting the detailed properties of vibrating strings (and so detailed properties of the elementary particles the strings vibrate into existence). The problem is, and has been for some time, that no one has been able to figure out the exact geometrical form of the extra dimensions. The equations of string theory place mathematical restrictions on the geometry of the extra dimensions, requiring them to belong to a particular class called Calabi-Yau shapes (Calabi-Yau manifolds). There’s not a single, unique Calabi-Yau shape. Instead, like musical instruments, the shapes come in a wide variety of sizes and contours. And just as different instruments generate different sounds, extra dimensions that differ in size and shape generate different string vibration patterns and hence different sets of particle properties. An example of Calabi-Yau manifold is shown below.

It is rather unimaginable that shape as this might be behind the shape of reality we see, but this is what modern theory suggests. Even we still fail to figure out right shape, within string theory both general relativity and quantum mechanics finally join together harmoniously. That’s where string theory provides a vital advance. Nevertheless, certain aspects remain to be proved in practice and scientists already have plans and tests ongoing or scheduled. The failure to find supersymmetric particles might mean they don't exist, but it also might mean they are too heavy for even the LHC to produce (that would be current state); the failure to find evidence for extra dimensions might mean they don't exist, but it also might mean they are too small for our technologies to access; the failure to find microscopic black holes might mean that gravity does not get stronger on short scales, but it also might mean that our accelerators are too weak to burrow deeply enough into the microscopic terrain where the increase in strength is substantial; the failure to find stringy signatures in observations of gravitational waves (you may with to join Einstein @ Home as I did if too impatient) or the CMB might mean string theory is wrong, but it might also mean that the signatures are too meager for current equipment to measure. As of today, the most promising positive experimental results would most likely not be able to definitively prove string theory right, while negative results would most likely not be able to prove string theory wrong. The theory will remain speculative until a convincing link to experiment or observation is forged.

In the mid-1990s, string theorists discovered that various mathematical approximations, widely used to analyze string theory, were overlooking some vital physics. As more precise mathematical methods were developed and applied, string theorists could finally step beyond the approximations; when they did, numerous unanticipated features of the theory came into focus. And among these were new types of parallel universes; one variety in particular may be the most experimentally accessible of all. And this is where introduction for next blog entry stops.

Note: Most of illustrations and theory comes from either Brian Greene or Jim Al-Khalili papers. I recommend both authors for anyone who wishes to dive more into the details on this matter.

Credits: Brian Greene, Jim Al-Khalili, Max Tegmark, Stephen Hawking, Wikipedia

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