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Of Strings and ToEs

There are many non-standard theories about how the universe could have formed; they are often very imaginative and highly mathematical. Some revolve around the idea that there is a ‘Theory of Everything’, a ToE. The most well developed ToE is string theory, the idea that part icles are made up of tiny, wriggling strings of energy. ToE theories aim to combine the four fundamental forces into one unified theory: gravity, the electromagnetic force (that creates electricity and magnetism), the weak nuclear force (that causes radioactivity), and the strong nuclear force (that holds the nuclei of atoms together). Such a theory could have profound implications for our understanding of the universe but it has eluded scientists for over 100 years, so getting a ToE would be a truly amazing achievement. There are also GUT theories (grand unification theories) that aim to combine three of the four fundamental forces (excluding gravity). There are less ambitious theories, but equally important, that are looking to combine the large scale of gravity with the microscopic scale of the quantum particle world, these ideas are called ‘quantum gravity’. They are investigating the possibility of making gravity behave in chunks, we call that being quantised. One possibility is that there is a gravity particle. We even have a name for it, a graviton. We have never seen a graviton, but if we ever did then that could confirm some of our theories of quantum gravity and could be revolutionary. From these ideas we also get the concept of multiverses; that there is not just one universe but many that exist and can even interact with each other.

Our theories of how matter behaves at the microscopic quantum level are well establish and fit the evidence extremely well. We also have the theory of relativity that fits how matter behaves on a large scale. These two theories are not compatible, mathematically and conceptually they are quite different. We would like to have one theory that explained the very small and the very large and everything in between. This is a ToE, a Theory of Everything. String theory is the main ToE that we have today.

Not long after Einstein came up with the idea that gravity is the effect of space being curved, German physicist, Theodor Kaluza [72], started to wonder whether the electromagnetic force could also be described by curved space. He developed the mathematics but he needed to add another curved dimension for electromagnetism to exist in. Amazingly, the equations worked and he had a theory where gravity and electromagnetism could exist in a four-dimensional curved space. What could this other dimension be? Swedish physicist, Oskar Klein [73], came up with a proposal; the other dimension is curled up on an extremely small scale so we cannot see it. These ideas and equations became known as the Kaluza-Klein Theory.

By the 1990s, the Kaluza-Klein theory had been developed into a theory that combined all four fundamental forces into one theory, called string theory. String theory says that all particles, even the smallest sub-atomic particles, are made up of tiny vibrating strings of energy. These strings can vibrate in different patterns to create the different particles that we can detect. There are only certain resonant vibrations that are allowed that are determined by the shape that the strings can form (similar to vibrations of musical instruments being determined by their shape and size). These vibrations are quantised energy. One of the successes of string theory is that it creates a universal force that acts on all particles that looks much like gravity and it does that by using quantised energy. It can explain gravity and all the particles and forces in the universe. It seemed to be the Theory of Everything that is being searched for.

An artists interpretat ion of a multi-dimensional space

Figure 4.5: An artists interpretat ion of a multi-dimensional space. The six small dimensions are curled up into Calabi-Yau space which sit on the three large-scale dimensions of space that is familiar to us, represented by the grid structure in the diagram. Credit: Shutterstock.

There are a few problems with the theory. Similar to Kaluza, in order for the mathematics to create extra forces then extra dimensions are needed. String theory requires six extra dimensions of space that are tiny curled up dimensions that we cannot see. There is a mathematical six-dimensional shape called a Calabi-Yau space that could possibly be the shape of these extra dimensions (see Figure 4.5). The vibrations of the Calabi-Yau space could be creating all the particles and forces that we see in our three-dimensional world. A string theory called М-Theory adds another large space dimension so it has ten space dimensions and the one time dimension which all theories have making it an 11-dimensional theory. Unfortunately, we have never seen any evidence for these extra dimensions.

For string theory to work it also needs something else. It needs to add in supersymmetry to become what is called superstring theory. Supersymmetry is where each fundament al particle has a symmetrical partner particle. This is not that helpful because no such particles have been detected but the maths works. To explain why none have been seen maybe these particles are very heavy, meaning that we need very high energies in particle accelerators to be able to see them. Even the energy produced in the Large Hadron Collider at CERN is not high enough which could be why we haven’t seen them. The problem with making the partner particles heavy is that supersymmetry is now broken. In addition, supersymmetry creates additional interactions between particles that are known not to exist. To get round this problem another symmetry was added called R-parity.

Another major problem with string theory is that it requires a universe that has a negative cosmological constant. This is the same cosmological constant that we know as dark energy. From our measurements of the universe we know that the value of the cosmological constant is positive.

String theory remains the main ToE in physics. It can be used to describe many different universes but it cannot be used to predict how our unique universe works. Despite being a promising and well developed theory, there is no evidence for string theory and increasing amounts of effort are now being put into other ideas.

Some theories are not trying to provide a solution to everything in physics. Quantum gravity is a class of theories that are looking to make gravity quantised but not looking to unify all the forces. It is hoped that these quantum gravity theories could help improve our cosmological models, for example, to explain what caused the fluctuations that seed matter formation in the early universe or what happens in a black hole. One of the main quantum gravity theories is called ‘Loop Quantum Gravity’.

In loop quantum gravity, space is made up of a network of extremely small loops (similar to the small extra dimensions of string theory). Curved space gives us gravity so now gravity can be defined by quanta of curved, looped space. The loops represent the volume of space and links between the loops represent the surfaces where the volumes meet. The mathematics combines general relativity and quantum theory into one theory, but it does not provide us with a solution where we can get back to how gravity works in our universe. Like string theory it is a very mathematical solution and so far loop quantum gravity has solved some problems but also created others.

Producing a theory where gravity is quantised is proving to be difficult. To get round this problem there is another class of theory called ‘emergent gravity’. These use the concept that gravity is an emergent property. What do I mean by this? Gravity could be created by the effect of a collection of objects behaving in a coordinated way. An example of this is a crowd in a football stadium producing a wave that goes round the stadium by individuals standing up at different times. One person on their own can’t produce the wave, it is an emergent property of many people moving. Gravity could be the same thing. If this is the case then we don’t need to know what the properties of the individual objects are so we don’t need to quantise gravity. Whether this, or any of the other unifying theories, will gain any evidence for them is something we are waiting for.


The idea that our universe may not be the only universe in existence is called ‘multiverses’. A universe that is at the limit of what we will ever be able to see, called the observable universe, could be said to define other universes. The spacetime continuum surrounding our observable universe could be considered as another universe, or other universes, that live next to each other.

There are other more interesting ways that multiverses have been proposed. One of these is related to inflation. An idea developed by Paul Stein- hardt, Alexander Vilenkin and Andrei Linde [74, 75] says that during inflation not all regions of space expanded together, some regions stopped inflating resulting in bubble universes each possibly having a different set of laws of physics and fundamental constants. Our universe would be a bubble living within a sea of bubble universes. This multiverse idea is called ‘eternal inflation’. There are many quantum fluctuations that could have happened during inflation producing many different bubbles with each one producing more bubble universes, going on eternally. Maybe the bubble universes could have been created by multiple big bangs in the universe, after-all why should our Big Bang have been the only one to happen.

Another way of producing multiverses is using string theory. It can predict many different types of universes each one having different values for the fundamental constants. This is one of the problems with string theory, it can create too many different universes and is not able to predict just one. By coupling string theory to the eternal inflation idea it is possible to produce many different, very strange universes that exist alongside our universe.

Another version of multiverses from string theory comes from ‘branes’ (by Paul Steinhardt and Neil Turok [76]). Branes are structures from string theory that form in higher dimensional space (more than three dimensions). Our universe exists on a three-dimensional brane floating in four (or more) dimensional space. Other three dimensional branes exist with other universes on them and they float around in the multi-dimensional space. When they collide there is a big bang and the universes reset themselves producing universes that could evolve and expand like our own.

An alternative idea for multiverses is that black holes could produce new universes. A black hole is where matter has become so dense and the gravity so strong that not even light can escape from it. Lee Smolin [77] proposed that microscopic quantum effects in a black hole could lead to it exploding resulting in a big bang and this would start a new universe. Each new universe would have slightly different fundamental constants depending on the small variations of the quantum fluctuations at the time of the explosion and so would behave in very different ways.

The last multiverse idea that I will mention comes from quantum mechanics. This is called the many-worlds interpretation of quantum theory. This is to do with how, on a microscopic quantum scale, matter changes when we measure it. We do not understand the process that causes the change, but we do know that the mathematics we use describes it very well. One interpretation of this measurement problem is that when a measurement is made then all possible outcomes of that measurement come into existence but we only see one of those outcomes, the rest are in many different worlds.

The Holographic Universe

Can the universe really be a hologram? Well there is a theory that says that it could act like one. This may sound strange, almost fanciful, but there are reasons for it which are backed up mathematically. The idea is called the 'holographic principle’ and was proposed by Dutch physicist and Nobel prize winner Gerard ‘t Hooft [78] and put within a framework of string theory by American physicist Leonard Susskind [79].

The idea came from work on black holes. There is a problem with theories of black holes that is called the ‘black hole information paradox’. As the black hole swallows up matter, then the information that was contained in the matter is lost. This information is called entropy and one of the fundamental laws of physics, the second law of thermodynamics, states that entropy should always increase (or at least stay the same). A black hole appears to be removing entropy from the universe. This is a problem. Jacob Bekenstein in 1981 [80] proposed that the information from matter falling into a black hole is contained within fluctuations at the surface of the hole.

The holographic principle states that we can know what happens inside a volume of space by encoding it on the surface at the same resolution. What does this mean? It means that whatever we can know about a volume of space we can also know by looking at the surface of the same piece of space. Consider it as information flowing through a surface and we can see only what is at that surface, but from that information we can tell what particles are in there, their temperature, how fast they are moving and all that defines what is inside. Recently, a possible test of the holographic principle was proposed by Erik Verlinde and Kathryn Zurek [81] using gravitational waves. The effect has yet to be detected.

I include the holographic principle because it is one of the few ideas that links gravity, thermodynamics and entropy. Although, so far there is no evidence, I can’t help but wonder whether somewhere in the idea is a fundamental concept to do with surfaces and gravity and entropy that could help us understand reality.

The ideas that I have outlined in this section are some of the ideas that are around in physics. The thing to remember about them is that they are ideas. They may have a lot of complicated maths supporting them but the observational evidence is not there. So why do scientists still work on them? In the 1980s, some of the ideas did show promise, string theory was one of them, and the hope was that they could be developed into the full theory of everything. Since then that promise has waned. As the ideas haven’t agreed with how our universe behaves then more elaborate and complex ideas have been added to make them fit. Despite much work and many scientists working on these ideas it is still the case that there is no evidence. We should remember though that these are the many ideas that happen before a scientific revolution. So maybe one of these ideas will break through, or maybe something totally different will be found. We wait and see. What we do know is that we do not have a complete theory of the universe yet. There are a couple of upsides to having many new ideas. They do make good science fiction and many films and novels have used multiverses in them. More importantly, they have also captured the public’s imagination and maybe they bring people into science that wouldn’t have otherwise.

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