The things we’ve been concerned with in the last three articles draws a very good picture for String Theory. It gives us a number of predictions that clearly distinguish it from the Standard Model, and from other theories of quantum gravity, such as Loop-Quantum Gravity and a few others. Not only that, but it unifies the laws of Einstein’s General Relativity with those of Quantum Theory under one overarching framework. But there is a cost. The majority of the predictions made by String Theory deal with such fantastically small numbers that experimental tests for the theory seem to be a long way off, if reachable at all. Nothing would be more pleasant for a string theorist than to present a list of testable predictions achievable in a fairly short time frame – within a decade or so. Clearly, there is no clear way to confirm a theory other than by testing its predictions experimentally. Despite the beauty and elegancy of a theory in question – as long as it fails to provide a way to test it experimentally, it describes our universe no better than Sims 4. String theorists, however, have come up with a few ideas about such a test. In this article we are going to consider these ideas, which I’ve come across – as always – in Brian Greene’s book “The Elegant Universe”.

Edward Witten once said that String Theory has already made an impressive prediction which has been experimentally proven. “String Theory has a remarkable property: it *predicts *gravity.” What Witten meant here was that despite the fact that both Newton and Einstein developed their theories of gravity a long time ago, they did that according to what they and other people observed. The very existence of gravity is predicted by neither of those theories, regardless of how important and beautiful these theories are. Conversely, if string theorists had known nothing about Newton’s and Einstein’s theories, nor about gravity for that matter, they inevitably would have found it while working with String Theory. Because of the existence of a vibrational pattern corresponding to the massless graviton with spin 2, gravity is a necessary part of String Theory. Of course we should not use the word “prediction” here because physicists actually explained gravity long before String Theory; but what’s cool about this is that gravity *naturally emerges* from the mathematical apparatus of String Theory.

As we saw earlier in this series, however, it is not enough for a theory to give such an explanation of an existing phenomenon to be in any way convincing. The majority of physicists would rather accept it if String Theory either makes a testable prediction of a new physical phenomenon or gives an explicit mathematically backed description to some physical characteristics – for example the mass of an electron – that have no such description today. In this chapter we’re going to consider a few possible ways which string theorists are exploring in order to arrive to such a prediction.

Although in the physics community String Theory holds the promise of becoming the best thing since sliced bread, today, after a few decades of work, scientists are still not able to pin down the theory so that it gives clear testable predictions. This is as if you had bought a new air conditioning system for the first time and wanted to set it up yourself, but unfortunately there were no instructions which would explain you how to do that. Similarly, physicists are usually not able to apply the concepts of a new theory to real-world problems unless they write down a complete user manual. Anyway, as we are going to see in this chapter, with some luck string theorists might obtain experimental confirmation of some of the essential components of the theory in the coming years.

### The Controversy Around String Theory

Is String Theory correct? We don’t know. For those who believe that the laws of the microworld should not be separated from the laws describing physical phenomena occurring in the macroworld, and for those who believe that we should not stop our research until we have a theory with unconfined domain of applicability, String Theory continues to be the best bet. Of course it might seem that this widespread concern around String Theory emerged just by chance, and that this place could as easily have been taken by some other theory was it as mathematically adaptable as String Theory is. There are quite a lot of physicists who believe that this is indeed the case. Moreover, they occasionally state that exploring the theory whose domain of applicability is limited to the Planck scale is just a waste of time.

In the mid 1980s, when String Theory gained a high level of attention among theorists, some of the most prominent physicists of that time criticised it severely for its untestability. For example, Nobel laureate Sheldon Glashow said in his speech that physics naturally progresses when theory and experiment both have access to a given question. But instead – he said – string theorists are looking for a kind of harmony which is based on mathematical elegance and uniqueness rather than on testable predictions. The very existence of a theory – he continued – holds on a bunch of magical mathematical coincidences. He argued that this is not in any way enough in order to believe in the actuality of the picture depicted by String Theory, and that such an approach cannot compete with experiment. In his speech he also said that String Theory seems to be so ambitious that it should either be completely right or completely wrong, but the problem is that nobody could even guess how long would it take to finish its development. And Howard Georgi, another astonishingly strong physicist and a famous partner of Glashow in Harvard, was also an outspoken critic of String Theory in the late 1980s.

Richard Feynman shortly before his death indicated that he did not believe that String Theory is the only approach capable of resolving the problem of infinities. He said that in his opinion there could be more than one way to reconcile Quantum Mechanics with General Relativity, and the fact that String Theory helps us to avoid infinities isn’t enough to believe in its special place in physics.

As it usually happens, though, for every sceptic in one camp there is an enthusiast in the other one. Witten once said that when he familiarised himself with the way String Theory unifies quantum theory and gravity, this became the greatest ‘intellectual shock’ in his life. One of the most prominent string theorists, Cumrun Vafa from Harvard, once mentioned that String Theory, without doubt, gives us the deepest understanding of the physical world. And another Nobel laureate Murray Gell-Mann regarded String Theory as a fantastic achievement which will eventually become the theory of everything.

So as we can see, the debates around String Theory were focused on both physical aspects and more philosophical ideas about how physics should progress. People with more ‘traditional’ viewpoints wanted physics to continue following the route which has been so successful in the last centuries: i.e. they wanted theory to be tightly connected with experiment. Others thought that physics had come to a point where theorists could try to push the boundaries with no help from experiment.

Theorist David Gross beautifully expressed his thoughts regarding this matter in 1988. He wrote that it had hitherto always been the case that when scientists started investigating some new areas of physics, the paving of the path was done by experimentalists, and theorists typically followed behind. When experimentalists encountered some unliftable rock, they dropped it on the heads of theorists who then figured out what to do with that rock. The scientists doing experiments were then receiving information about what kind of obstacle they encountered and what to do with it the next time. Even Einstein, who developed an entirely new way of looking at gravity had a lot of experimental data at his disposal to start his work with. Starting from about 1970s, however, the table turned upside down, and, with some exceptions, since that time theorists have had to pave the way for experimentalists.

The theorists working with String Theory do not want to climb the mountain alone. They would rather share their task with their colleagues from the experimental camp, but the technology we have at our disposal today is, most probably, a long way off from being sufficient to achieve the energies required to test String Theory. But even so, as we shall see in this article, string theorists do have some ideas about how to test the theory at least indirectly.

In the 1990s some critics accepted that String Theory actually looks promising. Glashow, for example, connected this with two facts. Firstly, he noticed that in the 1980s the majority of string theorists were over-enthusiastic and often declared that they would find the answers to all questions in physics very soon. However, In the 1990s they became a lot more careful in their statements, so that initial Glashow’s criticism became less applicable. He also pointed out that researchers whose works weren’t connected with String Theory weren’t very successful in the late 1980s and in 1990s, and the Standard Model seemed to be stuck at that time. Which made him accept that String Theory may hold promise to answer the questions which Standard Model seemed to be unable to answer.

Georgi agreed with Glashow and recalled his statements from the mid 1980s in a similar manner. He said that initially String Theory seemed to have bitten off more than it could chew, but a decade later he found that a few ideas from the theory led to some important results which could be relevant for his own works. Thereafter he regarded String Theory as something really useful. This marked a temporary end of criticism in the late 1990s, but later, in the mid 2000s criticism raised again furiously due to the following fact.

In the late 1990s the physics community was shocked to realise that the rate at which the Universe expands is actually speeding up, instead of slowing down as was expected by everybody. This was yet another case when experimentalists observed an unexpected phenomenon, and theorists started to look for an explanation post factum. The found explanation we now call ‘dark energy’ which is driving the expansion of the Universe to accelerate. Some critics of String Theory claimed that it should have predicted dark energy, which would have provided very strong support for the theory. But since it was not the case, string theorists made attempts to incorporate this new fact about the Universe into the theory. And they discovered a way to do that but at a cost.

The new form of the theory with dark energy included resulted in the number of solutions which is beyond imagining. Some estimates have been that this new version of String Theory contained *as many possible solutions as 10 ^{500}*! This number is so absurdly large that it should be regarded as virtually infinite, thus it brought about a second wave of criticism.

As we saw earlier, the critics of String Theory typically strike at the question about whether or not it is scientific in the traditional sense of this word. This is because many believe that a theory in the domain of physics is scientific only if it can provide some means of experimental test in order to either confirm or to falsify it. So the first rise of critics focussed on the idea that String Theory actually *explains nothing* because none of its predictions could be tested. Conversely, this time the critics focussed on another idea, which was that String Theory *explains too much*. Although it might seem to be the opposite to the first one, it still refers to the same problem: whether or not String Theory is scientific.

And the latter of those two might be even worse than the former. If a theory does not have any predictions to be tested, theorists can make an argument that it is due to the fact that further development of the theory is needed in order to eventually arrive at some predictions which will allow experiment to either rule it out or to confirm it. But in the latter case the number of possible versions of String Theory became so enormously huge that there could basically be no way to falsify it. The new model with dark energy incorporated into String Theory was published in 2003, and after that time the discontent that had been present under the surface began to take place at physics conferences and the front pages of some leading science magazines.

This criticism became especially noticeable in 2006 after the publication of the two books written for general public and attacking String Theory. These books are Lee Smolin’s “The Trouble With Physics: The Rise of String Theory, The Fall of a Science, and What Comes Next”, and Peter Woit’s “Not Even Wrong: The Failure of String Theory and the Search for Unity in Physical Law”.

Neither of these authors argue to abandon the study of String Theory entirely, but rather they would like to see scientists pay more attention to alternative theories such as Loop Quantum Gravity and the like. Nevertheless, the majority of string theorists dismiss Smolin’s and Woit’s claims as being just failed attempts to discredit String Theory.

Regardless of the number of attempts to put into question the usefulness of String Theory, however, if it eventually makes some prediction which is going to be confirmed by experiment, critics would have to either accept the theory as it is or to provide a better way to explain those results. To find such a prediction that would allow experimentalists to test the theory at least indirectly has been the main focus of many string theorists in the last couple of decades. In the remaining parts of this article we are going to see what those theorists have been able to accomplish.

### What Can The Shape of Extra-Dimensions Explain?

Without a radical breakthrough in our technology we will, probably, never gain access to the ultramicroscopic scale which is required for the direct observation of strings, if they exist. With the most powerful particle accelerator to date – the Large Hadron Collider – scientists are able to penetrate scales a bit smaller than a billionth of a billionth of a metre. In order to investigate sizes smaller than that we need more energy, and hence more powerful and bigger accelerators which would be capable of focusing more energy on single particles. Planck scale is many orders of magnitude smaller than what is achievable nowadays, and according to some estimates in order to see and measure the properties of a single string we would need an accelerator the size comparable to our galaxy’s. Actually, the above estimate is based on linear extrapolation and is, most probably, *over-optimistic*. As some researchers showed, we would rather need an accelerator *the size of the entire observable Universe!* The required amount of energy is actually not overly large, but the problem is that it’s extraordinarily hard to concentrate that amount of energy in a single particle (or a single string for that matter). Thus we have to find a way to test String Theory at least indirectly. We need to derive some physical consequences that the theory leads to and which would manifest themselves on much larger scales than the Planck size, and which, ideally, would be measurable in the coming decades. In their 1985 paper “Vacuum Configurations for Superstrings” Candelas, Horowitz, Strominger, and Witten made first steps in that direction. Not only did they establish that additional dimensions in String Theory are curled up into Calabi-Yau manifolds, but based on this they also found some consequences for the vibrational patterns of strings. One of the most crucial results of their work even shed light on some old questions in particle physics.

Recall that elementary particles found by physicists in the XX century are being separated into three generations with the corresponding members of each generation having exactly the same characteristics except for different masses. The question in the physics community before String Theory had been: “why are there *three* generations instead of, say, two, or four, or ten? And also, why do particles form these three generations instead of there being just a single list of different particles with no resemblance to one another?” String Theory answers this question as follows. The Calabi-Yau shapes have (quite loosely speaking) openings in them, as shown in the figure 1 below. Such openings may be of many different eccentric kinds, including those associated with multiple dimensions, but the main idea can also be seen in the figure 2 where we show just a simple torus to make things simpler and less abstract. Candelas, Horowitz, Strominger and Witten made careful analysis of the influence these openings exert on vibrating in additional dimensions strings. What they found was pretty intriguing.

Each such opening turns out to be associated with a *generation of vibrational patterns*, each of those generations corresponding to strings with a minimal amount of energy allowed by the mathematical apparatus of the theory. Since the theory demands that the known elementary particles correspond to the vibrational patterns with the lowest amounts of energy, the existence of a few openings in the Calabi-Yau manifolds implies that the vibrational patterns of strings break up into the corresponding number of generations. If a compactified Calabi-Yau shape has three openings, then we are to find three generations of elementary particles! As we can see, according to String Theory the found separation of elementary particles into three families is not inexplicable, but rather is determined by the number of openings in the geometrical shape formed by additional spatial dimensions.

That said, you might think that in 1985 physicists came close to finding the Calabi-Yau shape which would yield the physical properties we observe in the Universe. The number of openings in different Calabi-Yau shapes, though, can vary drastically. Some of those shapes contain three openings, some five, some ten, and up to nearly 500. And the problem lies in the fact that physicists still have no way of discerning which type of the Calabi-Yau manifolds bears investigating more than others.

You might think that since we certainly know that there are three generations of elementary particles, we should pick out those shapes that have three openings and examine them one by one until we find the one that yields the characteristics similar to those our Universe possesses. Unfortunately, this idea has two shortcomings. Firstly, we are not really sure about there being no more than three generations of particles. Three is the number of families we currently know of, but we cannot rule out the possibility that we shall find more in the future. Secondly, as we shall see shortly, this restriction would actually do no good for us since the number of shapes to consider would still be infinite. Thus such a method of arriving at testable predictions is out of the question and we need to find a better way to rule out the majority of candidate shapes. Despite all of this, however, the very fact that String Theory seems to be capable of explaining why there are three generations of elementary particles is fascinating in its own right, and represents a great deal of progress in particle physics.

The number of generations of elementary particles isn’t the only thing which could be explained once the shape of extra-dimensions is determined. Due to the influence of the Calabi-Yau manifolds’ shape on the modes of the strings’ vibration, the extra-dimensions also heavily influence the characteristics of both the matter particles and the force mediators. What Strominger and Witten also showed in their work is that the masses of particles in each of the three generations of matter particles depend on the way the multidimensional openings intersect and coincide with one another. If this doesn’t make much sense to you, do not be afraid, you are not alone. This kind of detail in String Theory is barely visualisable, but to give you a rough idea, this implies that the coordinates of those openings and the way Calabi-Yau shapes wrap around them determine the possible vibrational patterns for the strings vibrating inside those shapes. So as we can see, the question which had no answer whatsoever in the previous theories – namely the underlying mechanism making the masses of electrons, quarks, neutrinos and other matter particles have certain values – possibly obtains an answer in String Theory, albeit we would first need to find the precious Calabi-Yau shape corresponding to the structure of our Universe.

The previous paragraph should have given you an idea about how String Theory might be capable of explaining the characteristics of matter particles such as their mass and charge, but of course string theorists also hope that one day they will be able to explain the characteristics of the force carrier particles in a similar way. When strings vibrate in 10 dimensions, some of their vibrational patterns correspond to the particles having an integer-value spin. These modes are the candidates for the force mediators such as photons and gluons. And, strikingly, regardless of the shape of the extra-dimensions a mode corresponding to the massless particle with spin 2 is always present. As you might guess, we identify this mode as a graviton – the force mediator of gravity. The list of strings corresponding to the particles with spin 1, however, is largely dependent upon the geometric shape of extra-dimensions. The same can be said about their characteristics such as the intensity of the interactions they mediate, their gauge symmetry and others. To summarise this part of the chapter we can say that String Theory might provide us with a scheme explaining all the richness we see in the microworld, which is very exciting, but without knowing which of the huge number of possible Calabi-Yau manifolds the extra-dimensions in our Universe are rolled up into we cannot derive a testable prediction out of the theory.

Why can’t we find out which of the candidate shapes is the one we are looking for? As we mentioned in the earlier chapters, the mathematical apparatus of the theory is so astonishingly complex that we cannot even derive the final set of equations. What physicists do instead is use approximate equations, and in these equations all of the possible candidate shapes are on equal footings; none of them seems to be more promising than others. Thus particular testable predictions still elude physicists.

### Testing Manifolds One by One

We can rephrase our question as follows: even if the mathematical equations of the theory don’t allow us to find out which Calabi-Yau shape the theory chooses, does *any *of those choices conform with the phenomena observed in the Universe? In other words, if we calculated the physical characteristics given by every possible Calabi-Yau manifold, and gather it into a single enormous catalogue, would we be able to find one (or maybe more) that describes our Universe? This is a very serious question but there are a couple of reasons why we cannot answer it exhaustively.

It would be reasonable to start that kind of research by taking only those Calabi-Yau shapes with three openings, thus leading to three generations of elementary particles, right? This would shorten the number of candidate shapes considerably. But the problem here lies in the fact that we can easily deform a torus with three openings (the same, of course, applies to Calabi-Yau shapes) from one form into many others – actually, into an infinite number of forms – without changing the number of openings. One of such transformations of the previously considered torus is shown in the figure 3 below.

Similarly, we can change the form of a Calabi-Yau shape through an infinite number of transformations. And when we were talking about 10^{500} possible Calabi-Yau shapes, we actually grouped all such transformations and considered an infinite group as a single manifold. To add insult to injury, for each 10^{500} shapes there is an infinite number of transformations, and strings’ vibrational patterns depend largely on such transformations. That’s why restricting the possible shapes by three generations of elementary particles would actually not help us to find the solution to this problem at all. Even if all the people in the world were trying to find the answer to this question by simply considering the shapes one by one, with the infinite number of possibilities they would never succeed.

On top of that, the approximate equations used by string theorists are not sufficient for determining precisely which physical characteristics correspond to a manifold under consideration. Those equations allow physicists to make big steps forward and to obtain a rough picture of the characteristics of a vibrating string, but the exact picture – including the mass of a particle, the intensity of interaction and the like – requires equations whose accuracy would surpass the ones from the approximate scheme by far. In earlier articles we mentioned that a typical energy scale for String Theory is comparable to the Planck energy, and the modes of vibration corresponding to the known elementary particles are derived by an extremely precise mechanism of cancellations. Such delicate cancellations require precise calculations because even a small margin of error might influence the obtained result heavily.

So, what to do? After so many solutions to the String Theory equations were derived in the mid 2000s some researchers lost heart concluding that the theory would never make definitive testable predictions. But here the idea of a Multiverse came to the rescue. There are many different versions of the Multiverse theory some of which can be found in our blog, and here we won’t go into details, but what is relevant to us is that in some of those versions the number of universes within the Multiverse might be enormously large, up to infinity. Combining this with the Inflationary model and with the anthropic principle we get the result according to which *each *of those Calabi-Yau shapes *is *actually real, but different shapes are spread out through different universes. As we saw earlier in this chapter, this result led to the major lines of criticism toward String Theory from quite a few physicists, but this fact does not stop the researchers working with the theory to look for new methods in the theoretical framework and to eventually derive some testable predictions.

The description of all the characteristics of elementary particles, and of fundamental interactions would be one of the greatest – if not *the *greatest – accomplishments of theoretical physics. But after all this discussion you might have a completely reasonable question: are there any features in String Theory which would, probably, not confirm but at least favour the theory once found in experimental results, and which could be tested in the near future (or perhaps are being already tested)? Yes, there are such features.

### Looking for Superpartners

Our inability to derive certain testable predictions dictates that we should focus on general rather than specific features of the theory for now. By the word general we refer to such characteristics which are not a subject to the subtle details of the theory such as the shape of extra-dimensions, but rather represent an attribute that would, most probably, be a part of String Theory forever. Such characteristics have high credibility associated with them because the theory relies heavily on them. So even without a fully developed theoretical framework most researchers believe that if String Theory is correct so as these features. In the remaining part of this article we shall focus our attention on such general characteristics starting with supersymmetry.

As we were talking in the seventh chapter of this series, String Theory makes use not only of already established principles of symmetry such as translational and rotational symmetries, but also of seemingly the greatest possible mathematical kind of symmetry which has been called supersymmetry. As was discussed, this implies that in String Theory all the matter particles are tied up to the force mediators making the pairs whose members differ from each other by the value of their spin, the difference being 1/2. (Recall that all the matter particles have half-integer spin, whereas force mediators’ spin is integer valued.) This connection between fermions (matter particles) and bosons (force mediators) allows String Theory to make a prediction: each known particle should have a superpartner. And what’s important here is that none of the known particles is a superpartner to any other. Which implies that according to String Theory (and actually to other theories that rely on supersymmetry) there should be particles that have never been observed before. Some researchers even speculate that these superpartners might represent one of the greatest mysteries of modern cosmology – dark matter. The existence of superpartners is one of the essential components of String Theory, and it does not depend on the subtle characteristics of extra-dimensions and other things.

Superpartners have not been found to date. This might imply that supersymmetry is just wrong, but the other possibility is that superpartners are too heavy to be detected with the modern day accelerators. A lot of String Theory proponents hoped that superpartners would be found at the LHC, but these expectations have not been met yet. Researchers actually made a handful of speculations about the masses of the lightest superpartners, and according to some of those speculations they should have already been found. Unfortunately, this hasn’t been the case yet, but we certainly cannot rule out the possibility that the masses of the lightest superpartners are higher than was expected. There is a great deal of hope that with the upgrade of the LHC in 2016 the accelerator obtained enough power to find superpartners. Time will tell. Another possibility is that superpartners’ masses are not that high, but we need more elaborate methods to detect their presence. So even though the first expectations weren’t met, a lot of researchers continue to believe that supersymmetry will be confirmed pretty soon.

There is one detail, however, that we should bear in mind. Even if superpartners are found, this fact alone would not be sufficient to state that String Theory is correct. As we have seen, there are other theories that rely on supersymmetry, and they will also get credence in case supersymmetry is confirmed. Even though supersymmetry was found by researchers when they were working with String Theory, it can be included in other theories quite easily, and hence isn’t applied uniquely to String Theory. Anyway, if superpartners are going to be found either at the LHC or at some other particle accelerator, this would be a very strong point in favour of the theory.

### Looking for Particles with Fractional Electric Charge

Another possible experimental confirmation of String Theory’s ideas has to do with particles having fractional electric charge. Of course we already know of some elementary particles having fractional electric charge – quarks. But the range of electric charges the known particles have is very limited. Quarks and anti-quarks have charges whose values (taking the electric charge of an electron as a basic unit of measurement) are equal to 1/3 and 2/3. The charges of all the other particles in the Standard Model are 0, +1, and -1. All the matter in the Universe we currently know of is made of the combination of these particles from the Standard Model. String Theory, however, admits of the possibility of there being the modes of vibration corresponding to some exotic electric charges, e.g. 1/5, 1/11, 1/53 and such. These strange charges may occur when the curled up dimensions possess a certain geometric property, which is too technical to be discussed here, and whose description would only over-complicate things, so we won’t go into this kind of detail.

Some Calabi-Yau shapes possess this geometric property, some do not, so this possibility isn’t as fundamental to String Theory as the existence of superpartners. On the other hand, it has some benefit over supersymmetry. As was mentioned above, supersymmetry can be applied to other theories as easily as to String Theory. The prediction about the existence of particles with such exotic electric charges is much more unique to String Theory. Of course, such particles can be included into the models which are based on dimensionless particles, but it would seem very awkward and unsatisfying under those models, whereas in String Theory their existence could easily be explained by the shape of extra-dimensions.

In 1997 physicists observed what’s known as quasiparticles having fractional electric charge. But these are not real elementary particles, but rather an emergent entity which behaves like a particle. A real particle having such a weird electric charge has never been observed to date. So again, we are left with two possibilities: either they don’t exist in our universe, being just a mathematical artefact of String Theory’s equations, or they have such big masses as to not be observed by the operating particle accelerators. However, if someday they are found – this would also be a very strong point in favour of String Theory.

### Considering Some Other Possibilities

There are some other possibilities where either the confirmation of some String Theory’s predictions or finding the explanation to a previously inexplicable phenomena could give quite a bit of credence to the theory. For instance, as Witten once pointed out, it is possible that astronomers might find clear evidence confirming String Theory’s ideas. As we showed in the sixth chapter of the series, strings typically have enormously small size – about Planck length. But strings with huge amounts of energy might grow much larger. As we know, right after the Big Bang all the energy in the Universe was concentrated within a tiny volume, which might have caused a few strings to grow and become macroscopically sized. Those strings would continue to grow with time and today they would have an astronomically large size, albeit remaining one-dimensional (we will come to the strings of greater dimensionality when we start considering M-theory in a few chapters). If this really happened, one day we might be able to find the evidence of the presence of such a string (for example, a little but noticeable effect in the cosmic microwave background radiation). As Witten said, he couldn’t be more happy than to see this kind of confirmation of the theory’s ideas, albeit it now seems like a story from sci-fi movies.

Apart from that, there are several other possibilities which are related to the experimental facilities working with micro-scales rather than with cosmological ones. Below are a few examples.

- The explanation of dark matter. Nowadays, the two greatest mysteries in cosmology are known as Dark Matter and Dark Energy (I believe these names are unfortunate since they can easily be confused by the general public, though they represent two completely different things). The second of those has become the greatest failed possibility for String Theory, since had the existence of dark energy been predicted, its confirmation would have been the greatest success for the theory. Yet, this was not the case, and later, as we’ve seen, its incorporation into the theory yielded an enormous number of solutions to the theory’s equations. The other mystery – dark matter – had already had a great focus for studying before String Theory. The solution, however, is still to be found. String Theory might provide a testable prediction about DM which would be a very serious stake for experimental studies. One of the possible explanations, as we have already seen, is that those dark matter particles might be the superpartners to the known particles or to one another. In the last decade this question became one of the cornerstones of modern cosmology, and a lot of existing theories might get great credence for providing a solution to this puzzle.
- Another possibility is the derivation of definite values for the masses of neutrinos. Initially, the Standard Model predicted that neutrinos should have zero mass, but in 2002 experimentalists found that this is not the case, and all three sorts of neutrino (electron neutrino, muon neutrino and tau neutrino) actually do have very small masses associated with them. The problem is, though, we only have a certain range of masses for neutrinos, and don’t know the exact values. Measuring them experimentally is extremely difficult, but with time better experimental facilities are built and this range is narrowed down. Thus if String Theory could find an explanation for the characteristics of neutrino particles and derive a clear prediction about their masses, this would be a very strong candidate for the experimental proof.
- The third possible way of getting String Theory to experiment is to look for new fundamental interactions, however crazy this might sound. The thing is, some Calabi-Yau manifolds seem to be compatible with such vibrational patterns that correspond to new interactions. The fields for such interactions may be associated with relatively low intensities and a big range of propagation. If new interactions are found in experiments, they might be explained by String Theory, while other theories keep silent about such interactions. Recently a team of physicists even published a paper in which they tried to explain that they might have found footprints of such a new interaction. It is very premature to ring a bell, because as it often happens, that paper is not very convincing, but I just wanted to point to the fact that the idea about new fundamental interactions is actually not as crazy as it might sound.
- Moreover, there are some hypothetical processes which are forbidden by the Standard Model, but are allowed by the String Theory’s framework. One of them is the proton decay, allowed by a few so-called grand unified theories (GUTs) such as Georgi–Glashow model, Pati–Salam model, SO(10), Flipped SO(10), and also by the theories which are close to but not quite GUTs: Technicolor models, Loop quantum gravity, Causal dynamical triangulation, String Theory (M-Theory) and others. The proton is stable under the Standard Model because baryon number is conserved there. GUTs allow for a proton decay by explicitly breaking the baryon number symmetry. A half-life of a proton, however, is around 10
^{31}to 10^{36}years (that is, a typical proton would decay not more often than once in 10 billion billion trillion years), so that should not be very surprising that we have not observed this type of decay if it actually occurs. Experimentalists have been trying to find this type of decay throughout the last decade, but so far with no success. In the following years, however, this might change, which would be a breeding ground for explanation by the aforementioned theories. - And finally, the fifth way where new theories might be very successful is in explaining the observed value of the cosmological constant. As we were discussing in the third article of this series, it was introduced to the field equations by Einstein to make the theory compatible with static universe, which seemed obvious at that time. Later, after Edwin Hubble showed that the Universe does expand and is not static, the value of the cosmological constant was always considered to be zero. This was until 1990s, when two teams of astronomers established that the rate at which the Universe expands is getting higher and higher, which is compatible with the cosmological constant having some positive value. The most natural way of obtaining a positively valued cosmological constant from the current theories is by assuming that it takes its energy from the pairs of virtual particles constantly appearing and annihilating everywhere including empty space. The problem is that when we calculate the value of the cosmological constant in that way we get a result which is 120 orders of magnitude higher than the observed value.
*That is 1 followed by 120 zeroes*! This fact has been called the biggest fail of the current theories at explaining the Universe we live in. That’s why this is one of the most important questions in theoretical physics nowadays. If String Theory was able to explain this huge discrepancy and give a testable prediction about the exact value (again, the observed value lies within a certain range) of the cosmological constant – this would be a major success for the theory.

### Conclusions

The history of physics has a number of examples of ideas which initially seemed completely impossible to put under test. These ideas were later confirmed experimentally, thanks to new experimental facilities and to new methods of testing which had been unexpected when the idea was put forward. A few examples of such ideas are the atomic structure of matter, Pauli’s hypothesis about the existence of neutrinos, and finally the idea about the existence of neutron stars and black holes. Each of these three are now established physics facts.

String Theory has always been in such a position where it was not possible to test it experimentally. However, as we know from Quantum Theory, it might take several decades for a theory to mature. And Quantum Theory had an advantage to String Theory because right from the start it had an access to experiment. In spite of this, however, it took physicists about three decades to fully develop a logical structure to QT, and two more decades to merge it with Einstein’s Special Relativity. String Theory attempts to consolidate QT with General Relativity, which is quite more complicated; and it does not have an access to experiment as yet.

How long will it take physicists to bring String Theory to experiment? Nobody knows. Which means that a big number of specialists play a risky game where it is quite possible that the work of their entire lives will remain unconfirmed or even be proven to be wrong in the future. The progress in theoretical and experimental research will certainly be considerable in the following decades, but will it be sufficient to overcome all the obstacles and eventually put the theory under test? Would the indirect tests described above help us to either prove or disprove the theory? These questions are very important for everybody working on String Theory, but nobody is able to give an explicit answer to them. Only time will tell. The way in which String Theory solves the greatest contradiction of the XX century physics, its potential capability of describing all the matter and fundamental interactions under one overarching framework, and potentially unbounded predictive power make it worth exploring and justify the risks, though.

Thanks everyone.

Previous articles in this series can be found at:

Part 1: Following Einstein’s Dream

Part 2: Special Relativity – the Picture of Space and Time

Part 3: General Relativity – The Heart Of Gravity

Part 4: Quantum Mechanics – the World of Weirdness

Part 5: General Relativity vs Quantum Mechanics

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