String Theory – part 7: Supersymmetry


After the expedition of Sir Arthur Eddington had confirmed the prediction of General Relativity about the deviation of starlight’s straight path due to the gravitational pull of the Sun, one of Einstein’s students asked him how he would react if the prediction weren’t confirmed. Einstein answered: “Then I would feel very sorry for the dear Lord since the theory is correct”. What this famous quote tells us is that Einstein believed that his theory was too beautiful to fail.

Such aesthetic arguments, however, do not play the main role when one is considering a scientific question. The success of a physical theory is usually defined by how well is stands against various experiments. There is an important remark to the last statement though. If a theory is in the process of its formulation, the full list of its predictions, which could be experimentally tested, may be inaccessible. Nonetheless, physicists working with the theory should define the direction which the later stages of theory development will take. Sometimes such decisions are dictated by internal consistency, since we certainly don’t want our theory to contain logically absurd notions. Other times, though, physicists do use their aesthetic arguments to make those decisions. This happens because sometimes the physical and mathematical structure at hand is so beautiful and elegant that it strongly attracts physicists’ attention towards itself. We saw in the last article that the first attempt of String Theory to describe the strong nuclear force was unsuccessful, but nevertheless some scientists continued working on it just because of its elegancy. And this has led us to astonishing results. Moreover, because some of the modern day physics theories are extraordinarily complicated to test experimentally, those aesthetic arguments start playing a very important role in the early stages of theory development.

In physics, like in art, one of the major roles in aesthetic principles is played by symmetry. In physics this notion is defined very precisely. As we saw in the third article, Einstein used the notion of symmetry to combine the notions of his Special theory of Relativity with the principles of gravitational interaction in the theory of General Relativity. Nowadays the principles of symmetry used by physicists provided the way to combine the particles representing matter (e.g. quarks, electrons) with those responsible for the fundamental interactions (e.g. photons, gluons). Typically these two types are considered completely different as we saw in the first article of the series. But according to the principle which we are to consider in this article, these types are connected much more closely than we could ever imagine. Basically, this is the largest possible degree of symmetry. Thus this principle is called “supersymmetry”, and String Theory is one of those theories which are based on this principle. The explanation of this principle, given in this article, is taken from Brian Greene’s book “The Elegant Universe”.

Symmetries in Physics

Now I introduce you to the idea of symmetries conceptually, and show you a couple of the most basic, yet extremely important, examples of symmetries in physics. First of all, suppose you live in a universe where the nature of physical laws perpetually changes from one moment to another. Of course we know that even a slight shift of some such parameters – e.g. the Planck constant or the electron’s electric charge – would lead to the demise of any complex creatures, but let’s suppose that the laws of physics remain in the range compatible with life, but they do change each day. Life in such a universe would be not boring at all, since each day you would have to relearn the very basic things. Yet this universe would be a complete nightmare for a physicist living in it, because each day they would have to rediscover the laws of Nature. Your teacher of physics would probably just let you go home each class, because what they prepared for a lesson would make no sense at all when the class takes place. Fortunately, we all know that the Nature doesn’t behave that way. The laws of physics remain unchanged even though sometimes we find out that we need to make slight corrections to the previously derived values, and certainly discover new laws from time to time. Of course this unchangeability does not imply the static Universe, but rather it means that the laws governing our Universe have remained the same throughout its existence. But are we sure that this is indeed the case? The answer is no. There is, for example, an ongoing debate about whether or not the value of the fine-structure constant, and therefore of the speed of light, might change over time. But even though we are not sure about that, all the evidence we have unambiguously show us that even if the laws of physics change over time, they do it extraordinarily slow, so that we can use their current form to figure out what happened in the past up to a fraction of a second after the Big Bang.

Now suppose the laws of Nature change from one place to another and the ones which are applicable and well tested in our part of the Universe aren’t applicable in other parts, where you would find a completely different set of laws. Imagine even that these laws change from one place to another here on Earth, as well as the laws in one country may be completely different from the laws in a bordering country. Such a world would again be a nightmare for a physicist because what they discovered and carefully tested at LHC (located on the border between Switzerland and France) would not apply, for example, in Italy. So in this case physicists would have to derive and test an infinite number of theories to construct a reasonably accurate picture of the entire Universe. Again, we know that this is not the way the Universe behaves. Even though we can’t be 100% sure that the laws we have here are the exact same laws as in a galaxy, say, 50 billion light-years away, we are reasonably confident that this is indeed the case. At least all the evidence we have at our hands shows that the laws of Nature don’t depend upon the location in the Universe. For example, we have tested some aspects of Einstein’s General theory of Relativity by measuring the predicted effects, such as gravitational lensing, in clusters of galaxies located billions of light-years away. And the predictions of Einstein’s theory match the observed data to a very high degree of accuracy.

Again, this does not mean that the Universe is similar at any place. If an astronaut, for example, were to land onto the surface of the comet 67P/Churyumov-Gerasimenko, they would be able to easily jump off of it to space. This fact, of course, does not imply the different laws of physics on Earth and on the surface of that comet. We know that this is due to a very low escape velocity of the comet, which, in turn, comes from its tiny mass compared to Earth’s.

Physicists call these two properties – namely that the laws of physics don’t depend on the spatial location and the moment of time when you conduct your experiment – the symmetries of Nature. This term means that Nature treats any moment of time and any point in space identically, and guarantees that all of them are subjects to one set of fundamental physical laws. These kinds of symmetry evoke a great deal of satisfaction, because they emphasise the elegancy and order in the functioning of the Universe.

When we considered Einstein’s Special and General theories of Relativity we became acquainted with other types of symmetry. For example, we saw that in Special Relativity, according to the principle of relativity, any observer moving with a constant speed is treated identically (symmetrically), which implies that the laws of physics are the same for every observer constantly moving in some direction. Any such observer can treat themselves as being stationary and all the others moving relative to him. Again, this does not mean that a picture would be the same for any observer – those pictures could differ quite dramatically – but rather that all those pictures are governed by one set of physical laws.

Likewise, when Einstein established his equivalence principle, he sufficiently broadened this principle of symmetry by showing that any observer – regardless of their motion, either with a constant speed or with acceleration – can be treated identically, by adding the gravitational field into the picture. Thus Einstein showed that any observer is subjected to one set of the laws of physics.

Another principle of symmetry, which we have not considered yet, is the independency of the laws of physics to the angle at which you’re conducting an experiment. This means that if you carry out an experiment and obtain some result, this result must be the same if you rotate your apparatus by any angle. This is called the rotational symmetry, and it has a similar importance to the ones described above.

Are there any other types of symmetry that we’ve missed? Well, there are actually a lot of them, for example Gauge symmetry which we considered in the fifth chapter, but now we are interested in those symmetries which are related to space and time. In 1967 two physicists, Sidney Coleman and Jeffrey Mandula, proposed a theorem according to which there could be no other symmetries related to the notion of space and time. However, later other theorists found out that this theorem did not take into account one important aspect of quantum theory – spin.

What is Spin?

Elementary particles – like electrons – could revolve around atomic nuclei just as planets orbit their parent stars (of course this analogy isn’t entirely correct, but for our current purpose we can assume it is). It might seem, however, that elementary particles can in no way spin on their axis. After all, every point inside a given rotating body – a billiard ball, a planet, or such as like – moves around the axis of rotation, but the points located exactly on that axis don’t move. So this leads us to the seemingly obvious conclusion that an object which consists of just one such point – a dimensionless elementary particle – cannot spin on its axis since there are no other points that would be located outside of this axis. Many years ago, however, the experimental investigations of this question revealed a new astounding property of the micro-world.

In 1925 Dutch physicists George Uhlenbeck and Samuel Goudsmit found that a number of experimental results related to the characteristics of emitted and absorbed light could be explained if they assumed that electrons have some peculiar magnetic properties. About 100 years before, a French physicist Andre-Marie Ampere had established that magnetism appears due to the motion of electric charges. Investigating this fact Uhlenbeck and Goudsmit established that only one type of electron motion can lead to these magnetic properties – the rotational motion that we now call spin. In contrast to the laws of classical physics, quantum mechanical objects – even if they are point-like particles – do spin on their axes!

But wait a minute. Did these researchers really believe in that seemingly nonsensical conclusion which implied that dimensionless particles somehow magically can spin on their axes? Not quite. Spin represents an inherent characteristic of a particle, akin to the rotational motion but being essentially nothing but a quantum phenomenon. It is one of those strange quantum phenomena having no analogy on macro-scales, and the work of Uhlenbeck and Goudsmit showed just that. Furthermore, their work showed that the magnitude of an electron’s spin never changes and remains the same for indefinitely long. What this shows us is that the spin of electron isn’t a state of its motion, but rather an inherent characteristic like its electric charge or rest mass. If an electron weren’t spinning, it would not be electron!

Although the aforementioned word took into account only electrons, physicists later established that all matter particles share this characteristic. And what’s even more interesting is that any matter particle – including even their antiparticles – has a magnitude of spin similar to that of an electron. Moreover, physicists also showed that the force-carrier particles such as photons, gluons, and elusive gravitons can also be characterised by their spin, which has just a different magnitude. If we are to be a little bit more precise, all the matter particles (known as fermions) have half-integer spin such as 1/2, 3/2, or 5/2, while force-carriers (known as bosons) have integer spins, such as 0, 1, and 2.

What’s particularly interesting about bosons is that the mediators of three fundamental forces – electromagnetic, weak and strong nuclear interactions – all have their spin magnitude being equal to 1, the Higgs boson’s spin magnitude equals zero, and finally, all theoretical considerations related to the elusive mediator of gravitational interaction – graviton – show that the magnitude of its spin should be equal to 2.

In String Theory spin, as well as mass and coupling constants, is determined by the mode of a string’s vibration. Now we can build up a conceptual understanding of how String Theory includes gravity apart from other forces. In their work in 1974 Scherk and Schwarz found that one of the vibrational patterns predicted by the theory corresponded to a massless particle with a spin whose magnitude is equal to 2. As we now see, these characteristics exactly coincide with those of graviton. Hence, gravity is an essential part of the theory.

Now, after we built up a basic concept of spin, let’s return to Coleman’s and Mandula’s theorem and see how the notion of spin can lead us to another symmetry which was missed by that theorem.

Supersymmetry and Superpartners

As we have previously seen, even though the notion of spin has some similarities with the rotational motion of an object on its axis, it quite differs from such a motion at the same time. The discovery of spin in 1925 showed that this new kind of rotational motion just does not have a classical analogy.

This difference leads us to the following question. If the rotation of an object around its axis provides rotational symmetry to the laws of physics, and if spin differs from it, then wouldn’t spin itself lead to another kind of symmetry? By 1971 physicists had established that the answer to this question is indeed positive. Although the proof here is quite involved, the main idea behind it implies that if we are to consider spin from the mathematical perspective, there appears exactly one additional symmetry in the laws of Nature, and it’s been called supersymmetry.

Unlike other types of symmetry, supersymmetry can’t be explained by simple translations of an observer’s frame of reference just because, as shown by the Coleman-Mandula theorem, all kinds of symmetry related to the change of a reference frame are already used up. But because spin is kind of a quantum mechanical analogue of rotational motion, we can think of supersymmetry as based on a reference frame translation in the ‘quantum mechanical extension of space-time’. The mathematical details of the principle of supersymmetry are very subtle (here I should say that I don’t quite understand them myself), so we will not delve into them, but instead will focus our attention on the implications.

In the 1970s scientists found that if the Universe follows the principle of supersymmetry, then its particles – no matter whether they are point-like objects or tiny vibrating filaments of energy – should enter the list of fundamental objects by pairs. Such pairs are now called superpartners, or sparticles. What’s interesting to us here is that the members of one such pair should have different magnitudes of spin, and moreover, these magnitudes should differ by ½. Now remember that matter particles have half-integer spin and mediators have integer spin, which implies that according to the supersymmetry principle these completely different kinds of particles are in fact tightly connected. In other words, matter particles (fermions) and force-carriers (bosons) are superpartners to one another.

After the discovery of the mathematical model of supersymmetry physicists started looking for a way to include supersymmetry into the standard model, but what they found was that none of the known particles could be a superpartner to any other. As later rigorous analysis showed, if the Universe really follows the principle under consideration, then each known particle must have a yet-unknown superpartner with the spin of magnitude ½ less than its known counterpart. For example, the superpartner of an electron – known as a supersymmetric electron, or selectron – would be a bosonic version of the electron with the magnitude of spin being equal to zero. Likewise, for bosons such as photons or gluons, the superpartners would have spin ½ and they are called photino and gluino.

So as we can see, supersymmetry isn’t quite a conservative principle. It requires the existence of quite a few additional particles duplicating those components that we are already familiar with. Furthermore, since this principle was suggested, there has been no single piece of evidence of a superpartner’s existence. So maybe it’s nothing but a wild mathematical idea which many physicists have taken more seriously than they should have? This might seem to be the case, but there are a few points that make physicists seriously consider this possibility. Let us have a look at those.

The Arguments in Favour of Supersymmetry before String Theory

Firstly, physicists just couldn’t put up with the fact that Nature has put into action almost all – but not quite – mathematically consistent types of symmetry. Although such aesthetic arguments don’t always turn out to be correct, we’ve seen before that sometimes they do play an important role in physics. Of course we cannot omit the possibility of not all symmetries being at work in the Universe, but after all, that would be really disturbing.

Secondly, even in the Standard Model – a theory which does not include gravity – some delicate problems related to quantum fluctuations could be solved painlessly with the principle of supersymmetry. These problems in the Standard Model are mainly related to the fact that each type of particles makes its contribution to the quantum chaos. By carefully examining this chaos physicists found out that they could cope with it only through the extraordinarily precise tweaking of some parameters. The precision needed exceeds the value of 10 to the negative 15! Although the Standard Model concedes such precise regulating of its parameters, many physicists find the fact that the theory at hand breaks down after so slight change of one of its parameters quite unsatisfying.

Supersymmetry radically changes this picture. Bosons’ and fermions’ contributions to quantum fluctuations have the tendency to cancel each other out, and as long as bosons and fermions always enter the list of particles in pairs in supersymmetry, that delicate tweaking of the model’s parameters becomes needless. In mathematical analysis those contributions are opposite in sign, meaning that a boson’s contribution is positive while a fermion’s is negative, or vice versa. As a result of this truncation the supersymmetric standard model stops being dependent on that very suspicious tweaking of its input parameters.

The last of the arguments in favour of supersymmetry that we are going to consider here is quite a bit more subtle, so I encourage you to read this part very carefully. This point is related to the notion of grand unification – the unification of 3 out of 4 fundamental interactions. One of the strangest characteristics of fundamental interactions is the huge difference between their strengths. You can see it on the figure 1 below.

stregth of interactions.jpg

If you remember, in the fifth chapter we considered the unification of two of these interactions provided by the work of Sheldon Glashow, Abdus Salam and Steven Weinberg. For their work they were awarded a Nobel Prize in physics, and the unified interaction became known as the electroweak interaction. Later, Glashow with his colleague Howard Georgi suggested that this connection between different forces can be extended to include the strong interaction as well. The work on electroweak interaction showed that electromagnetic and weak interactions merge together under the temperature of one million billion degrees higher than the absolute zero (10 to the 15 Kelvin). Georgi and Glashow showed that the unification with the strong interaction becomes apparent at even much higher temperatures (10 to the 28 Kelvin). Such enormous temperature translated to energy would be only 4 orders of magnitude less than the Planck mass.

Now let us take a step back. We know that the intensity of electromagnetic interaction between two particles with opposite electric charges, as well as the intensity of gravitational interaction, increases when the distance between two interacting bodies decreases. These are simple and very familiar facts from classical physics. Surprises start to emerge when we investigate the influence of quantum physics on the intensity of interactions. Why does quantum mechanics exert any influence on them? This again is due to quantum fluctuations. When we examine the electric field of an electron, in fact we analyse it through the ‘fog’ of virtual particles perpetually appearing and annihilating in the area surrounding the electron. A few decades ago physicists found out that this fog naturally ‘masks’ the actual intensity of the electron’s electric field, just like fog on Earth weakens the intensity of light from a lighthouse. If we keep shortening the distance from the electron in question, we are essentially diffusing the effects of this fog, thus the intensity of the electric field generated by the electron would increase!

This increase isn’t quite the same as the increase of the inherent intensity of the electromagnetic interaction due to the shortening of distance. That’s why physicists differentiate between them. Thus when we are getting closer to an electron, the intensity of its electromagnetic interaction increases not only due to the decrease of distance, but also because the quantum effects around the electron become less apparent. And although we’ve considered electrons in this example, similar conclusions are applicable to any particles carrying electric charge. As we now see, quantum effects increase the intensity of electromagnetic interaction when the distance from a particle decreases.

Conversely, this quantum fog actually increases the strength of the strong interaction. This was discovered in 1973 by David Gross, Frank Wilczek and, independently, David Politzer in their works on asymptotic freedom (they were awarded the Nobel Prize in physics in 2004 for this work). What asymptotic freedom means is that when we examine two quarks being extremely close to one another, the closer they get, the less the strong interaction is between them. When the quarks are in extreme proximity (the distance between them approaches, but not quite gets to, zero) they start behaving as if they were free particles.

Later, Georgi, Weinberg and Helen Quinn used this idea to extend it to a brilliant result. What they showed was that by taking into account all those quantum fluctuations we find that the intensities of the three non-gravitational interactions start to approach each other when we decrease the distance from which we are analysing particles. Although the strengths of these interactions differ tremendously on those scales that are accessible with modern-day instruments, the conclusions made by Georgi, Quinn and Weinberg imply that this difference exists due to the different influence provided by the quantum fog of virtual particles. Their calculations showed that if we were to examine quantum particles from the distance of 10 to the negative 29 centimetre (only 4 orders of magnitude higher than the Planck length), then the intensities of non-gravitational interactions would appear equal to each other.

The energies associated with such fantastically small distances are way beyond what we can expect to achieve in the following decades, but such energies were ubiquitous a fraction of a second after the Big Bang (10 to the negative 39 s) when temperature in the Universe was on the order of 10 to the 28 Kelvin. We can draw a parallel here: just like various types of material such as wood, glass, metals and minerals merge together and form homogeneous and uniform plasma when we heat them to a very high temperature, the three non-gravitational interactions were merged similarly when the temperature was enormous. You can see it on the figure 2 below. Here the force of gravity is also included in the picture, and as you might guess, physicists do hope that eventually even the force of gravity will be included in one unified interaction. However, as long as in this part we are discussing the quantum mechanical picture that does not include gravity, we want to focus our attention on the idea of grand unification of only non-gravitational interactions.

unified force.jpg

Even though we don’t have such instruments that would allow us to test such small sizes or such high temperatures, in the last few decades experimentalists have been able to slightly redefine the values of the intensities of non-gravitational interactions. In 1991 physicists Ugo Amaldi, Wim de Boer, and Hermann Furstenau improved the initial values derived by Georgi, Quinn and Weinberg by using new experimental results, and showed a couple of interesting facts. Firstly, the intensity of the three interactions were actually slightly off (they’ve been almost equal but not quite). Secondly, this slight divergence in the strength of interactions disappears if the principle of supersymmetry is included in the picture! The reason for this is in the additional quantum fluctuations provided by superpartners. With those additional fluctuations the intensities of interactions become exactly equivalent. Physicists are very reluctant to believe that those intensities are so close to each other, but nonetheless are not equivalent. And supersymmetry elegantly resolves this conundrum.

Another important consequence of the result that I’ve mentioned above is that it gives us a possible answer to the question as to why superpartners haven’t been detected yet. The calculations performed by various physicists show us that these superpartners should be much heavier than those particles whose existence is experimentally established. The problem here lies in the fact that we still have too wide a range of possible masses for superpartners. I should also say that based on some calculations the detection of the lightest superpartners was expected even in the first run of the LHC. These expectations weren’t met, and, consequently, some physicists claimed that supersymmetry is most probably not put into action in our Universe. Such claims, however, are premature, and experimentalists continue searching for superpartners. We shall consider the question of possible confirmation of supersymmetry more deeply in the following articles.

Of course the arguments in favour of supersymmetry provided above aren’t unequivocal. We’ve shown how supersymmetry brings the highest possible level of symmetry into the theoretical apparatus of modern physics. You might argue, however, that Nature probably does not press for that level. We’ve also provided the information about how supersymmetry releases us from the necessity of tweaking some of the parameters of quantum theory very precisely, but again, you might not find it to be a compelling argument. After all, a lot of other parameters in our Universe seem to be fine-tuned for any form of complex structures, including living organisms, to exist; so why not add another parameter to this list? We’ve also turned your attention to the fact that on fantastically small scales supersymmetry provides the way for the strengths of non-gravitational interactions to find each other, which would allow these forces to be combined into a single grand interaction. Again, you might say that there is nothing demanding such unification, and those forces might not originate from a single one. Finally, you may have an opinion that superpartners haven’t been found just because the Universe isn’t supersymmetric, and superpartners just don’t exist.

No one can confute any of these objections. However, when we take String Theory into account, the arguments in favour of supersymmetry become largely strengthened.

Supersymmetry in String Theory

As we discussed in the last article, the foundation for the birth of String Theory was laid by the work of Gabriele Veneziano in the late 1960s. This first variant of the theory included all types of symmetry which we discussed at the start of this article, but it didn’t contain supersymmetry (which had not even been proposed at that time). You might remember that the first version was aimed at explaining only the strong nuclear force, hence it contained only the mediators of this force in its spectrum. Because of that, the objects considered by the theory all had the magnitude of spin equal to 1, and hence the theory was called bosonic string theory. That version had a serious issue though.

The spectrum of vibrational modes in bosonic string theory contained a particle known as a tachyon whose mass – or the mass squared to be more precise – was negative. For those of you who remember high-school algebra, this might not be too much of a surprise, since imaginary numbers do have this exact characteristic: squaring such a number would result in a negative number. Anyway, if you do not remember those aspects of algebra, don’t be afraid, we are not going to delve into them, so bear with me.

The possibility of the existence of tachyons has been examined since the time even before String Theory, but so far no one has been able to find a way to derive a consistent theory with tachyons being present. By the time bosonic string theory emerged, some researchers had already shown that it would be extraordinarily hard – if possible at all – to construct a consistent theory with tachyons. Likewise, physicists made all kinds of attempts to find a reason behind this tachyon mode in bosonic string theory, but those attempts weren’t successful either. This problem unambiguously showed that the bosonic version of string theory was certainly missing some important details.

In 1971 Pierre Ramond, a professor of physics from the University of Florida, modified the bosonic version of String Theory by including the fermionic modes of vibration into it. This work along with the later work of John Schwarz laid the foundation of the new version of String Theory. There was a surprising aspect of this new version: bosonic and fermionic modes of vibration entered this new theory in pairs. Each bosonic mode had a corresponding fermionic mode, and vice versa. Later, Joel Scherk, David Olive, and others demonstrated the reason behind this grouping in pairs. New version of String Theory contained the principle of supersymmetry, and this pairing reflected a high degree of symmetry of the new theory. At that time, Superstring Theory emerged. And what’s also important, the works mentioned above showed that the tachyon mode did not appear in this new version of the theory.

Initially, though, the works of Scherk, Olive, and others made contribution mainly to quantum field theory rather than to string theory. By 1973 other physicists had found that supersymmetry, which was discovered in the process of reformulation of String Theory, is also applicable to the theories based on point-like particles. They quickly made all the necessary steps in order to include supersymmetry into quantum field theory. At that stage supersymmetric quantum field theory was born. We saw the consequences in the previous section. Therefore, important results in the development of String Theory even had its impact on Quantum Field Theory.

Even though supersymmetry, as we’ve seen, plays an important role in Quantum Field Theory, in String Theory its role can hardly be overestimated. String Theory is our best bet for reconciling General Relativity with Quantum Mechanics; and only the supersymmetric version of the theory is devoid of a fatal tachyon mode, and also contains the fermionic modes of vibration. Physicists believe that if String Theory is correct, then so is supersymmetry.

The last thing I should mention in this chapter is that from the time when Superstring Theory was discovered, and until the mid-1990s there remained one important problem in the theory.

A Problem of Redundancy

Suppose someone told you that they have a proven explanation of the Bermuda Triangle mystery. Initially you might feel sceptical about their words since you already know that there are a lot of suggested explanations none of which has actually been proven. But being a marine expert you decide to listen to this person because there might be interesting information for your own research. When this person starts explaining their idea elaborately, you find out that they have a number of documentarily proven pieces of evidence to support their idea – let’s say they advocate that the actual reason for aircraft and ship disappearance in the Bermuda Triangle has to do with some particular aspects of the Gulf Stream (this is being one of the actual explanation attempts). In this case most probably you would listen to this explanation entirely, and who knows, maybe this person will even convince you in the correctness of their explanation.

Ok, that’s all well and good, but what if this person, right after that first explanation, tells you that they have another one? You patiently listen to this one as well, and, surprisingly, find out this alternative explanation is supported by evidence as good as the first one. Even though both of these explanations seem very reasonable, this fact makes you feel doubtful, because, being a scientist, you usually look for a single resolution to a conundrum instead of having multiple solutions. But suppose after that you are given the third, fourth, and even the fifth explanation, and each of those 5 are equally reasonable and are equally supported by various pieces of evidence. By the end of this discussion you would certainly have no more insight into the secrets of the Bermuda mystery than you had initially. This example was made up to show you that in solving fundamental questions “more” is sometimes “less”.

By 1985, despite being deservedly respected among physicists, String Theory had been shown to have this exact problem that we touched upon in the previous paragraph. This was due to the fact that supersymmetry – the central part of the theory – could have been included into String Theory by using not one, but five different approaches. All of those five approaches led to the grouping of fermionic and bosonic modes, but the details of this grouping, as well as the results provided by each particular approach, differed quite significantly. Although the names of these 5 theories aren’t really important to us at this point, I’ll mention them for those readers who are eager to look for more information on their own. We shall return to these at a later chapter when we will be considering the unification of those 5 at the start of the second superstring revolution. The names are: type I string theory, type IIA and type IIB string theories, Heterotic string theory SO(32), and Heterotic string theory E8 × E8. All the characteristics which we considered earlier are hold for each of those theories, the differences come about only in details.

Having 5 different versions of the theory which is considered to be a candidate for explaining all the richness around us is quite a bit too much. We live in one universe and therefore are looking for one explanation.

One possible solution to this dilemma could be that four out of five theories are going to be ruled out by experiment, and only one of them will remain. But even if such an approach were led to the expected result, then we would be left with the following question: why are those other four theories even mathematically consistent? Why haven’t they been ruled out at the stage of a theory’s formulation? As Edward Witten once said, “If one of these theories describes our universe, then who lives in other four?” Ideally, the final theory, whether it would be String Theory or anything else, should be the way it is just because there is no other way to derive it. If we were to discover only one logically consistent way to combine the concepts of General Relativity with those of Quantum Mechanics, then many physicists would feel that humankind has achieved the deepest understanding of the laws of Nature.

As we shall see in the later articles, in the mid 1990s string theorists made a giant step in this direction by showing that these 5 theories actually represent 5 different ways of describing one universal theory, which is now called M-theory. We will consider these questions later, but in the next chapter we are going to see that the elegant unification provided by String Theory requires yet another radical reassessment of our beliefs regarding the way the Universe works.


4 thoughts on “String Theory – part 7: Supersymmetry

  1. String theory is not easy and describig so others can follow the thinking behind it is hard so you have done a great job here Aleksei. I personally fing elegance in a theory very compelling and the whole concept of symetires is fundemental to our understanding of how the Universe works.


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