Why String Theory?

by Joseph Conlon

  As we have seen, these axion-like particles originate in an epoch of the universe where it was dominated by moduli, moduli and more moduli. The decay of a modulus to any particle of the Standard Model launches a high-energy Standard Model particle into the hot dense thermal plasma of the early universe. This is analogous to launching a highly energetic particle at the sun and asking what happens to it. It loses its energy. It bumps into other particles, which bump into other particles, which bump into more particles, and rapidly the energy of the original particle is shared out among thousands more. When an axion-like particle is formed, it loses none of its initial energy. It passes through the hot thermal plasma of the early universe like a ghost, giving its energy to none. Unlike particles of the Standard Model, it retains its original energy without loss.

  While far fewer in number than the particles of the Standard Model, the energy of each axion-like particle would be far greater than the energy of the photons that make up the cosmic microwave background. In fact, for the best-guess parameters that one gets from string theory models of the early universe, the energy of each particle is around a million times bigger than the microwave photons that make up the cosmic microwave background. Instead of microwave energies, they have X-ray energies. If they convert to photons, they produce photons with energies at the level of the weakest X-rays.

  We have said that the best place for converting axion-like particles into photons is within large clusters of galaxies. It turns out that there is indeed actually an excess in the number of soft X-ray photons coming from large clusters of galaxies. While clusters of galaxies are suffused with a hot gas that emits copiously in X-rays, at the lowest energies there appears to be more X-ray emission present than can be accounted for by this hot gas: there is a soft excess in the X-ray emission. This was discovered by Richard Lieu of the University of Alabama in the middle of the 1990s. Observations of a number of galaxy clusters, for example the relatively bright and nearby Coma cluster of galaxies, show a pronounced excess in the softest forms of X-ray emission. This excess emission has been sought for in a total of thirty-eight clusters of galaxies, and it is found in around a third of them.

  This excess is at the right energy to come from a cosmic background of axion-like particles. It also occurs precisely from galaxy clusters, objects that have the largest magnetic fields extended over the largest regions. Could it actually be a sign of dark radiation made visible?

  Possibly it is – but while not impossible, the most reasonable answer is probably not’. At this point it is important to state all the caveats on the set of ideas described here. Almost every attempt at finding new physics beyond the Standard Model fails. Most anomalies go away, even the ones produced by excellent and careful experimentalists. A failure to come up with an explanation for a phenomenon is not the same as the absence of an explanation for this phenomenon. Given any choice between an anomaly being explained by either new physics or by incompletely understood aspects of existing physics, the right choice is almost always the latter. Furthermore, the science of hot astronomical gases in astrophysical environments – sometimes known as gastrophysics – is messy, and it is susceptible to both incorrect modelling and incomplete understanding.

  For this reason, astrophysicists are justly nervous of any claims for new physics lying beyond the known laws of nature. For this reason, the evidence for dark matter was dismissed until it became so large and so overwhelming that there was no choice but to accept it. Most anomalies go away. The only way to move forward with anomalies is to take them and batter them with more data until they either grow or vanish.

  For the case of the excess in soft X-rays and a possible relation to a pervasive stream of dark axion-like particles, the method for assault and battery is clear. In this scenario, the strength of the signal depends on the distribution of the magnetic field. The magnetic field is a property of the universe. It can be measured for different galaxy clusters using known techniques, and these techniques are improving. Given these measurements, predictions can be made for the amount of excess X-ray emission that is expected. Through the use of ever more precise X-ray telescopes, the existence and magnitude of the excess emission can be measured and compared to the prediction. Either it will agree or it will not: and on this verdict the correctness of the scenario ultimately stands.

  10.5 EXPERIMENTAL ENNUI

  I have devoted considerable space in this chapter to describing one example of the use of string theory to generate testable ideas for new physics. This idea was born amid the physics of ten dimensions, but it lives in the world of observations. It might be right and it might be wrong. Like all ideas for new physics, it is probably wrong.

  The reasons for devoting so much space to this particular idea are twofold. The first is unashamedly partisan – it involves my own work. I know these ideas, and their internal logic, well. They come from my routine professional life of writing papers, and the research of myself and my collaborators: Michele Cicoli, David Marsh and Fernando Quevedo.

  However, the deeper and more important reason is to put sinewed flesh on the rather abstract bones of the notion that extra-dimensional physics at minuscule scales can leave traces within the majuscule world of physics accessible to observation. I have sought to provide one example of how the abstract concept of extra dimensions can lead to a set of ideas that have observational content and are clearly empirically testable. Furthermore, one would not stumble upon these ideas without thinking about the physics of extra dimensions.

  For some – like myself – this is the principal motivation for working on string theory. It is understanding this universe that makes my heart beat quicker and the hairs on my arms stand up, and gets me eagerly hurrying to the railway station every morning on the way to work. I want to know something new about our world, and I want to understand the parts of it that are not understood. I respect those who seek the quantum-mechanical behaviour of gravity on the smallest scales, but this task does not enthrall me, and I equally feel little passion for the intrinsic mathematics of extra-dimensional geometry topped up with large doses of supersymmetry. My interest in string theory is in what it can offer to physics that can be probed by experiment.

  This view is far from universal. It may seem odd, but most of those who work on string theory are essentially uninterested in any connections with experiment, any public claims they may make to the contrary notwithstanding. This is illustrated through a notion economists call revealed preference’: to see what people really care about, look at what they do and not what they say. The largest annual conference in string theory is the Strings series, which in its heyday would attract up to five hundred participants. While the conference has a notional mandate to cover the whole of the subject, every year there are few if any talks that concern the physics of this world.11 The physics of ideal mathematical worlds is covered in plenty, but the physics of this world gets only minimal attention.

  Along these lines, there are three kinds of objection made concerning connections to experiment. One of these objections deserves a small and limited amount of sympathy, while two deserve none at all.

  The first objection is that there is no unique and unbreakable logical path that runs from string theory and the existence of extra dimensions to any observational proposal. Assumptions have to be made. The path involves qualifiers such as ‘generic’, as well as steps that may be reasonable but are not logically unavoidable. The thrust of this objection is that you end up with a set of ideas that may or may not be interesting, but they do not tell you anything about string theory or extra dimensions as there is no unique logical thread leading from start to finish.

  The reason that this objection deserves some sympathy is that within the scientific ideal as presented in textbooks, ideas have exact consequences. These consequences can be tested experimentally, and a single well-chosen and well-conducted experiment is sufficient to decide whether an idea is correct or not. In the world of Pangloss, the idea ‘there exists extra dimensions
’ would lead to a set of necessary consequences that are directly testable. If these consequences did not manifest themselves experimentally, then the idea would be falsified, and we would know that extra dimensions do not exist. Situations when this occurs – and it sometimes does! – are the scientific ideal: clean ideas cleanly tested. One example involved the Higgs boson at the Large Hadron Collider – there was a guarantee in advance that either the Higgs boson would be discovered, or the Standard Model of particle physics would be wrong.

  The reason that this objection only deserves limited sympathy is that on the whole the world belongs to Candide and not to Pangloss. Science is messy. The mood of the route from theory to experiment is generally the optative rather than the imperative. Life is uncertain. Most of the time, the passage from theory to experiment has to involve qualifiers, hopes, assumptions and ‘if this were also true’ conditionals.

  The second objection, which deserves no sympathy at all, is that most of the time the testable scenarios that are generated by the extra-dimensional muse fail. This deserves zero sympathy because this situation is the default situation when searching for new physical laws beyond those we already know. The search for new phenomena or new laws of physics is a long succession of failures punctuated by occasional and unpredictable success. Anyone contemplating a career looking for deviations from the established laws of physics must be prepared for hard work followed by failure. This is how the subject works; this is normal science; this is where success ultimately comes from.

  This objection of probable failure is like a complaint from the armchair expert to the explorer that there is no point searching for unicorns, as they are bound not to exist. It is indeed correct that unicorns are mythical beasts – but kangaroos are not. The only way to find out what is true is to go and look.

  The final common objection is that it is too early. On this view, we should not start thinking about observational consequences of string theory until we understand what string theory is. According to this objection, before we try and connect string theory to observations we should first wait until we understand the structure of the theory better. It is premature to try and say what the theory predicts until we know what the theory is. We should instead continue to study the theory more, and more, and more, until we finally know exactly what it is. Then, and only then, should we start to think about empirical consequences.

  The problem with this objection is that it is a time-invariant statement. It was made thirty years ago, it was made twenty years ago, it was made a decade ago and it is made now. It is also, by observation, an objection made by those who are uninterested in observation. Muscles that are never used waste away. It is like never commencing a journey because one is always waiting for better modes of transportation, and in the end produces a community of scientists where the language of measurement and experiment is one that may be read but cannot be spoken.

  1As we have seen in chapter 5, in some limits of the theory there are an extra seven spatial dimensions, but this embarrassment of poverties will not modify this discussion.

  2For a wave propagating in the z-direction, the counting in three spatial dimensions is that there is an xx polarisation, an xy polarisation and a yy polarisation: except that there is a further technical condition, called the ‘traceless’ requirement, which enforces a relation between the xx and yy polarisations. This is responsible for the ‘-1’ in the formula and results in two polarisations overall.

  3This paragraph is morally correct, but it comes at the cost of finagling the details. In particular, I have talked about moduli as having interactions of gravitational strength. However, these interactions are not precisely the same as those of the familiar gravitational force. Moduli additionally also interact with the familiar gravitational force, with a strength proportional to the mass. However the gravitational-strength interactions referred to here are different, and are really legacy interactions from the original ten-dimensional gravitational theory. These are comparable in strength, but different in form, to the standard four-dimensional gravitational force.

  4A technical footnote: the production of moduli occurs by a process called ‘misalignment’. The large energy of the early universe drives it far away from the cold and stable state it is in now. This ‘misalignment’ of the state of the early universe compared to its eventual form in the late universe leads to large numbers of moduli being produced as the universe relaxes and settles down into its late-time state.

  5The more technical justification for this is that earlier decaying particles produce relativistic daughter particles, and in an expanding universe the energy in relativistic particles rapidly dissipates due to the Doppler effect. This leaves only the energy in the non-relativistic particles that have yet to decay – the moduli.

  6To be precise, this results in the spectrum of the microwave background, when expanded in spherical harmonics on the sky, having less power on small scales than would otherwise be expected.

  7Historians of science can use the names of scientific concepts as a sociological history of the discipline, by tracing the fluctuating linguistic dominance of Greek, Arabic, Latin, French, German and English. What future historians will make of ‘axion’ is best left to posterity.

  8In more technical language, the strong force generates a potential for theta, and the minimum of that potential is where theta vanishes. Even more technically, this potential arises from non-perturbative ‘instanton’ effects.

  9Which is a shame for Helen Quinn, who would become, if the axion were discovered, the first female Physics Nobel Laureate since Maria Goeppert-Mayer in 1963.

  10Technically, this is a shift symmetry that states that the value of the axion potential is independent of the value of the axion field.

  11Based on the talk titles at the Strings conferences in 2012, 2013 and 2014, my count is that barely one talk in ten, even on a generous interpretation, could be put in this category. The ratio would be even less if talks from ‘external’ speakers brought in as representatives of large high-profile experiments were excluded.

  CHAPTER 11

  Why Strings? Quantum Gravity

  ‘Mummy, when I grow up I want to work out the theory of quantum gravity’. It is unlikely that any child, however precocious or driven, has ever uttered these words. However at a slightly older age this sentiment has been felt by many, many students of physics. Undergraduate physics is a wonderful time: you are hit by one deep insight after another, and over a period of several years you see the entire tapestry of the subject unrolled in front of you. The fusion of quantum mechanics and gravity is known to be missing from this tapestry, and in the full immortal confidence of youth it is easy to visualise yourself as the master weaver casually filling in the absent threads.

  The statement of this problem was reviewed in chapter 4. We have a classical theory of gravity, general relativity, that was constructed by Einstein a century ago. This correctly describes gravity on large scales where we do not expect quantum mechanics to be important. While this is all well and good, we know that the world is in truth described by quantum mechanics. We do have working examples of quantum theories that describe the strong, weak and electromagnetic forces, and we expect that this should extend to gravity. What is needed is a quantum theory of the gravitational force, which will reduce to general relativity at large distances but at short distances will provide a truly quantum theory.

  How short are these distances? The quantum nature of the electromagnetic, strong and weak forces is manifest by the time we reach distances around a billion times smaller than the size of an atom. However the estimate for the length at which quantum mechanics should become important for the gravitational scale is vastly smaller. This length is called the Planck length and is as small compared to these scales as an atom is to the great city of London. It is true that this estimate should be regarded as a worst case scenario, but there are also no known reasons for believing it badly wrong. To guarantee being able to see quantum effects of the
gravitational force, it is necessary to have technology that is able to probe such length scales.

  No such technology exists. There are no known ways to make direct probes, not just of the Planck length but even of any lengths remotely comparable to it. The quantum mechanics of the gravitational force is well quarantined from the reach of direct experiments: even if you had the correct theory, how could you ever know that it was right?

  It should be said that the quarantine of the Planck scale from experiment is not total. The absence of direct probes of quantum gravity does not preclude indirect probes, where physics present at the Planck length can bubble up to produce observable effects in doable experiments. While one very indirect probe was described in the previous chapter, some transmission is possible even for less indirect probes. The reason this can happen despite the smallness of the Planck length is the extraordinary accuracy to which many aspects of standard physics are known.

  Examples are effects that violate special relativity, which is so well tested that even small violations of special relativity at the Planck length can be constrained and excluded. To give a more specific example, one way such effects could manifest themselves is through a dependence of the speed of light on the energy of photons, causing photons of different energies to travel at different speeds. This would be inconsistent with special relativity. If it were true, light from faraway sources in the universe would arrive at different times depending on how energetic the light was. This effect has not however been observed, thereby constraining the structure of physics at the smallest scales.

  While there do then exist some probes of physics at the Planck scale, these probes are both limited and indirect. The field of experimental quantum gravity is, if not entirely barren, not fertile either, and it can only support a small and limited number of workers.

  For all their early dreams, it is these hard facts that divert most of these keen young students away from quantum gravity. Comparison of theory and experiment is not the only aspect to science, but it is enormously fun. It is the opportunity to be either right or wrong, and the ability to know the difference, that gives science its vibrancy and its piquancy. If you want to have a scientific career, you would do well to enjoy it. For many, the paucity of experimental data would render a career thinking about quantum gravity unfulfilling.