String Theory – part 1: Following Einstein’s Dream

elementary particle hierarchy

The Main Conflict of the XX Century Physics

The tremendous success of physics during the last century is based on two theories put forward in its first quarter. One of them is Einstein’s General Relativity, which describes the Universe on a large scale: from planets to stars, galaxies and galaxy clusters – objects with a large size and huge mass. The other one, called Quantum Mechanics, describes our Universe on its tiniest of scales – from molecules and atoms all the way down to subatomic particles such as electrons and quarks. Both theories work perfectly well on their scales, but they cannot both be correct at the same time.

Physicists have known about this discrepancy for a long time, but it likely requires an overwhelmingly complicated solution. Moreover, it does not stop the progress in physics and allows us to develop new models in both aforementioned fields. You surely do not need to take into account the information about elementary particles inside a large object – such as a star or a galaxy – to calculate its motion. Similarly, the structure of our planet need not be considered in order to obtain the magnitude of a particle’s spin.

However, in some situations the Universe gets extreme and objects with a vanishingly small size have a huge mass. The most famous example of such an object, which is called singularity, is located at the center of each black hole according to our modern understanding of General Relativity. A gigantic mass is squeezed under the force of gravity inside each black hole, and in this case both General Relativity and Quantum Theory (I shall use GR and QT referring to these later on) should be considered in order to make sense of such an object. So far, no one has been able to achieve this. Likewise, a singularity should have been the object where the Big Bang occurred. These two are the examples of objects for the description of which one theory – either GR or QT – is not enough.

For the last three decades of his life Einstein was looking for a theory which, as he thought, would be capable of explaining the whole set of physical laws within a single framework. He never succeeded, but as we now see, he was just ahead of his time as with his prediction of cosmological constant.

For the last several decades many physicists have been working with String Theory, which could do just that – become a theory capable of showing that any events happening in our Universe – from behavior of the elementary constituents of matter and fundamental forces up to the motion of galaxies and the Big Bang explosion – can be described by the same fundamental principles of physics. And not only does String Theory resolve the conflict between GR and QT, it shows that they are indispensable to each other. In this series of articles I shall try to explain the main concepts behind String Theory, some of which are very bizarre and require a dramatic shift to our view, even on some things that seem to be completely unchangeable. If you find any of my explanations unsatisfying, I encourage you to read Brian Greene’s book “The Elegant Universe”, where he explains everything in a great detail and completely understandable form.

Let me start by noting that the conflict between GR and QT is not the first of this kind in physics. At least two more happened in the past. Physicists noticed the first one in the 1800s. According to Newton’s laws if you were to move extremely fast you could in principle surpass a beam of light, whereas according to Maxwell this can never be done. This conflict was resolved by Einstein in his theory of Special Relativity, where he dramatically shifted our view of the very nature of space and time. This theory, however, led to another conflict. It stated that neither material object nor any sort of interaction and perturbation can move faster than the speed of light, while in Newton’s theory some interactions, for example gravitational, propagated infinitely fast. The resolution to this conflict again came from Einstein. In his theory of General Relativity he showed that all interactions do indeed propagate no faster than the speed of light. General Relativity, in turn, led to the third conflict after Quantum Mechanics had been developed. The details of this conflict are not of our concern right now – I shall explain them in later articles – but it will be sufficient for the purposes of this article if I merely say that the smooth picture of space provided by GR is contradicted by the notions of QT which tell us that the Universe behaves extremely fiercely on its tiniest of scales. This conflict has successfully been resolved by String Theory in a very subtle way, which I shall also explain in later articles. The only remaining problem is that we have not confirmed String Theory as being correct, but even though most of its predictions require technologies that would surpass by far our current ones, some of them may be confirmed quite soon.

Atoms and Subatomic Particles

To get an idea of what matter in our Universe consists of at its fundamental level let’s delve a bit into the quantum world. Ancient Greeks proposed the idea that matter can be divided into smaller and smaller parts until the fundamental constituents of it are obtained. They called these constituents atoms. The name has persisted, but it became clear with time that atoms do consist of even smaller constituents. Later, physicists figured out that the smaller components are atomic nuclei, consisting of protons and neutrons, and other particles called electrons which, in a sense, orbit a nucleus. For a long time physicists thought that these three – protons, neutrons and electrons – are those elementary particles that ancient Greeks referred to as atoms. But in 1960s the experiments performed on Stanford Linear Collider confirmed the idea that had been put forward earlier by an American physicist Murray Gell-Mann. According to this idea neither protons nor neutrons are elementary themselves. Instead, they consist of even smaller particles which we now call quarks. Quarks themselves were of two types: u-quarks and d-quarks (up and down). A proton, which has an electric charge of +1, consists of two up–quarks and one down-quark whose electric charges are +2/3 and -1/3 respectively. Thus, they sum up to +1 as required. Likewise, a neutron consists of one u-quark and two d-quarks, and you can easily calculate that they sum up to 0, which is indeed a neutron’s electric charge. And there are neither experimental nor theoretical results suggesting that these three can be divided into smaller elements.

Quarks represent one type of particle, whereas electrons are related to another type which is called leptons. In addition to electrons there are other forms of leptons, one of which is neutrino, whose existence was first proposed by Wolfgang Pauli in 1930s and then confirmed in 1950s. They are extremely hard to detect since they barely interact with matter. If you were to detect one particular neutrino you would need a ‘wall’ several light years long! Fortunately, the number of these particles produced in the core of the Sun is so huge that billions of them pass through your little finger every second! This is why we are able to detect some of them, even though it is a very complicated task. Moreover, in 1930s physicists exploring cosmic rays – streams of particles that bombard Earth’s atmosphere from space – discovered another particle that was called muon. It turned out that it has the exact same properties as electron does, but whose mass is 200 times heavier. The existence of such a particle was so unexpected back then that Nobel laureate Isidor Isaac Rabi greeted its discovery with a phrase “who ordered that?” Nevertheless, muon did exist as well as many other particles which were found in the following decades.

Using powerful technological equipment researchers have found 4 other types of quarks: c, s, t and b (charm, strange, top and bottom), another electron-type lepton – tau lepton, which is even heavier than muon, and two other types of neutrinos – muon neutrino and tau neutrino. All of these particles except for u-quark, d-quark and electron can be born only with high energies and they don’t constitute ordinary matter. However, as we now certainly know, they do exist.

When the number of particles was growing higher and higher, physicists started looking for some patterns for their categorization. And they did find such a pattern so that all of those particles were separated into three generations. The particles of the first generation – up and down quarks, electron and electron neutrino – are the lightest ones. The second generation’s particles – charm and strange quarks, muon and muon neutrino – are somewhat heavier. Finally, top and bottom quarks, tau lepton and tau neutrino – that represent the third generation – are the heaviest. You can see the picture representing these three below.

generations of matter

In addition to these particles, each of them has a corresponding antiparticle that does not differ from its counterpart much but has an opposite electric charge. For example, an electron has an electric charge of -1, so that its antiparticle – which we call positron – has an opposite electric charge, which is +1.

When you see the picture above, it can lead to a greater number of questions than giving answers to. For why is there this number of particles instead of any other? Why is it so large, or, perhaps, so small? Why are there three generations of particles instead of, say, four, or five, or any other number? Did these numbers appear just by chance or is there any scientific explanation to the questions above?

Bosons and Fundamental Forces

Everything gets even more complicated when we take into account the fundamental forces of nature. There are plenty of the types of interactions which we are familiar with in our everyday life. We can interact with things in many ways, e.g. push them, hit, shoot, accelerate them, throw them from an airplane, stretch or compress them, heat or cool them and so on. However, physicists have known for quite a long time that all these interactions can be described by the four fundamental forces of nature. Those are the force of gravity, electromagnetism, weak and strong nuclear forces.

The first of them is the one which we are most familiar with in our everyday life, even though, as Einstein showed, there are some aspects of gravity which might be very counter-intuitive. We need not be concerned with these properties right now, and it will be sufficient for us if I say that gravity is that force which allows our planet to orbit the Sun, the Sun, in turn, to orbit the Galaxy center, and our feet to be kept on the ground, not floating away from the surface.

Electromagnetism is the force which gives us light, because light is nothing but electromagnetic wave. It might be surprising to you, but the electromagnetic force is also responsible for keeping your hands and your monitor on your table, not letting them to, literally, pass through the table. We experience electromagnetic force throughout whole our lives, we just don’t notice that this is it.

The strong and weak nuclear forces are those that propagate to extremely tiny distances becoming completely negligible at a distance greater than the size of atomic nuclei. If you want me to be more precise, the weak interaction has the strength of a similar magnitude to the electromagnetic force at a distance of 10 to the negative 18 meters, but at a distance of around 10 to the negative 17 meters it is 10,000 times weaker than the electromagnetic force. The strong interaction’s strength has the highest magnitude of all at a distance of a femtometre – or 10 to the negative 15 meters, but at a larger distance it quickly dies out. This is why these two forces have been discovered fairly recently, in the mid 1900s.

Weak interaction is often described as ‘something something radioactivity’. Not an explicit description you might say. And this would be true, but since weak interaction only takes place on the quantum level, it has some properties which are really hard to wrap your head around. Thus we often describe it as a force responsible for radioactive decay and also for nuclear fission. I am not going to dig deep into details but will provide you with an example. In nuclear physics, beta decay is a type of radioactive decay wherein a neutron is transformed into a proton or vice versa. We know that both electric charge and energy are conserved; hence when a neutron decays into a proton it produces an electron and an electron antineutrino. Similarly, when a proton decays into a neutron it produces a positron and an electron neutrino. In such a way various chemical elements are converted into others, for example magnesium-23 into sodium-23 or carbon-14 into nitrogen-14. It’s interesting that even some very smart people have no idea of such transmutations.

Strong interaction is responsible for holding quarks inside a proton or neutron (and other composed particles) and for holding protons and neutrons inside an atomic nucleus. Suppose you are examining an element whose atomic nucleus consists of a number of protons and neutrons. Since particles with the same electric charge repel each other, and neutrons have no electric charge, then the protons would push each other apart so strongly that they cannot be held together inside the nucleus. But there is the strong nuclear force – which is stronger than the electromagnetic one on atomic scales – that allows them to be kept inside. The details of the strong interaction are quite involved as with the weak interaction, but the short explanation above should be sufficient for our present discussion.

As we now know, electromagnetism, strong and weak nuclear forces are mediated by the corresponding particles – photons, gluons and weak gauge bosons respectively. If you examine an electromagnetic wave, you can split it until photons are obtained (just as we did with matter in the previous section). Similarly, the strong interaction’s mediators are gluons – the name comes from the word ‘glue’, and it makes sense if we look at the explanation of the strong force above. The weak interaction is mediated by two types of gauge bosons – W- and Z- bosons. You can see a picture showing the matter particles and the force-carriers below.

elementary particles

Physicists also feel that the gravitational interaction should be mediated by the corresponding particles, which are known as gravitons. Yet, their existence is purely hypothetical and has not been confirmed by any experiment at the moment.

The degree of impact for the gravitational interaction depends upon object’s mass and for the electromagnetic interaction upon electric charge. Likewise, the degree of impact for the strong and weak interactions is defined by the corresponding magnitudes of what is called colour charge and weak isospin. But what physicists have been able to define is only the corresponding magnitudes for each particle, leaving the question as to why these magnitudes are what we see behind.

As with the constituents of matter, the difference between the various characteristics of force-carriers leads to a lot of questions. Why are there four fundamental forces instead of three, or five, or, perhaps, one? Why do these forces have such different characteristics? Why do weak and strong interactions propagate to only so tiny distances, whereas gravitational and electromagnetic ones can propagate infinitely far? Finally, why is the strength of these interactions so different?

To get a better idea of the last question, suppose you have a pair of electrons. Then you juxtapose them to see which interaction – gravitational or electromagnetic – is stronger. Gravity would lead to the convergence of these particles, whereas electromagnetism would counteract it. Which force will be stronger? It might be not very surprising to you that gravity will lose, but what’s really surprising is the magnitude. Electromagnetism is tredecillion (10 to the 42nd power) times stronger! Why do we even notice gravity with such a difference? The reason for this is that macroscopic objects consist of roughly the same number of positively and negatively charged particles, such that most of their forces cancel each other out. Experiments have also shown that the strong nuclear force is approximately 1000 times stronger than the electromagnetic one and 100,000 times stronger than the weak force.

But why does our Universe have these properties? This is not a trivial question at all. The Universe would be completely unrecognizable if any of the aforementioned characteristics were different. For example, if the magnitude of the strong interaction were weaker than that of electromagnetism, any elements other than hydrogen would not form. And even a small change in the correlation between the magnitudes of these interactions can lead to the destruction of most atomic nuclei. Then, if electrons were heavier, most of them would coalesce with protons to form neutrons, which would impinge the formation of complex elements. We can provide plenty of examples of this kind, but I hope that the idea is clear: the Universe we see is what it is because the fundamental constituents of matter and particles carrying fundamental forces have the characteristics we measure. But again, is there a scientific explanation as to why do they have these characteristics?

String Theory as a Candidate for Becoming the Theory of Everything

String theory represents a powerful set of notions which can give answers to these questions. Elementary particles such as quarks, electrons and neutrinos are considered to be indivisible. As individual letters constructing various words and sentences cannot be divided into smaller parts, these particles are also, in a sense, a final destination. String theory says otherwise, though. According to it, each particle isn’t point-like but has a tiny vibrating filament of energy, which looks as a point-like object to us because we do not have sufficient energy to detect these filaments. This idea is shown in the picture below.


As we shall see in the following articles of this series, such a shift from point-like particles to vibrating strings takes out the inconsistencies between General Relativity and Quantum Mechanics. Thus, it solves the greatest puzzle of the XX century physics. But this is not the only thing that makes String theory so delightful among many physicists.

In Einstein’s times the strong and weak interactions were unknown, but even the existence of the two other forces was obscure to him. He asked: why there were two interactions and not just one. He was trying to solve this puzzle and was looking for a unified theory which would be capable of explaining the gravitational and electromagnetic interactions as the two sides of one coin. As I’ve mentioned earlier, he was just ahead of his time, and this searching for a unified theory of everything became the Holy Grail of theoretical physics half a century later. Many physicists believe that String theory can take this place.

It shows that the characteristics of all matter particles and force-carriers can be described by a single property – the vibration of strings. It says that all the diversity of particles can be represented by the same physical entity – string, and different modes of vibration lead to various characteristics, hence represent various particles. In this picture one vibrational mode represents electron, another one d-quark and so on. Just as the strings of a violin vibrating with various frequencies produce various musical tones, strings in String theory produce various particles. Force-carriers can also be described by particular vibrational modes. In this sense, everything that we saw in the two previous sections is emanated from one fundamental entity.

vibrational modes

In such a way, for the first time in the history of physics we have a theory which could explain everything about the structure of our Universe at its fundamental level. Therefore, String theory is considered the main candidate for becoming the Theory of Everything (TOE). It does not demand and, moreover, does not admit a more fundamental description. Its confirmation, on the other hand, is unimaginably complicated task and I shall have a look at this question in the later articles.

Some researchers use such terms more cautiously and treat TOE as a theory capable of describing the characteristics of elementary particles and forces with which these particles interact. According to their way of thinking, the term TOE would be too much for such a theory. Reductionists, however, would argue that everything from the Big Bang up to our thoughts and feelings can be described by the means of such a theory since any complex phenomena rise from the fundamental components of a system under consideration. Reductionism is a philosophical principle whose adherents would say that if you know all about components, you know all about everything.

Many would argue that all the richness and beauty of our Universe cannot be described simply by chaotic microscopical processes. How could it be true, after all, that our feelings of love, sorrow and mirth are nothing but physical and chemical reactions taking place in our brain? Steven Weinberg responding to such criticism wrote that the opponents of reductionism feel humiliated by the knowledge that modern physics brings them; and that a reductionist sees the world being frosty and faceless but we must take it as it is not because we like it but because this is written in the book of Nature.

Many people have a different point of view according to which the physical laws of the micro-world are applicable only for micro-objects and you need different laws for explaining behavior of objects on larger scales. For example, you can describe the behavior of an electron or quark but this won’t allow you to explain a storm by the means of what you know about the behavior of individual particles. This seems reasonable but does it actually require new physical laws? A majority of physicists are sure that it does not. The prediction of a storm behavior is certainly overwhelmingly complicated but it seems that this is due to our technological limitations rather than theoretical ones.

However you want to view it, the discovery of a fundamental physical theory will in no way signify the final step for science. The problems of psychology, biology, archeology, chemistry and even physics will in no way be solved right after the discovery of such a theory. Instead, this theory would become a solid foundation upon which later theories can be based and overall scientific understanding can be broadened.

String theory does have its problems, though. The mathematical apparatus of the theory is so complicated that nobody knows its exact equations yet. Consequently, physicists just use its approximate equations but even they are so complicated that we can in no way obtain the exact solutions. This can be summarized by Edward Witten’s – who is one of the leading experts on String theory – phrase “String theory is a part of 21st century physics that fell by chance into the 20th century”.

Regardless of this, the theory has already demonstrated its potential puzzled out the contradiction between GR and QT and making headway on the questions which are considered to require completely mystical explanations otherwise.

Anyway, new physical theories require some testable predictions to be confirmed. This can take years or decades until such predictions will appear, but we already have some that can be confirmed in the next couple of years on LHC. If they do, this will not be a rigorous proof of the String theory’s correctness, but it will certainly boost our confidence. I shall mention these predictions in the later articles.

Just to be clear, nobody is sure that String theory is correct and that it represents the theory of everything, but a lot of its notions and mathematical results are giving hope that it actually does. We do not know, maybe String theory is just a stop-gap, maybe it is a turning point or maybe it will become a final destination.

Next time we shall be talking about the very nature of space and time represented by Einstein’s theory of Special Relativity, which is necessary for the understanding of String theory.

Thank you for your time.


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