On this approach, the mass of the electron, the value of the fine structure constant, the nature of the observed forces – these are accidental features of the world that belong to the same category of facts as the distance of the earth from the sun or the names of the emperors of Japan. It is unfair to level the charge that such calculations do not make predictions for observations, because that is not their purpose.
In the context of quantum field theory, this style appears in the study of quantum field theories that do not describe nature – but are amenable to exact solutions in the way that realistic quantum field theories are not. These theories have large amounts of symmetry, both super- and otherwise, and this large amount of symmetry can enable exact solutions to be obtained. These solutions are elegant, exact and geometric. They offer beautiful bridges into topics in modern mathematics and conceptual understanding of what makes quantum field theory tick. They are also applicable only to theories that are not applicable to this world.
For obvious reasons, this style of physics is never seen among experimenters. However it has always existed among theorists, with a strength that varies over time. It was certainly the dominant style in string theory throughout the 1980s and 1990s, rewarding with successful careers many people who have written a hundred papers or more, none of which concern either observations or data.
It is the style that was produced by those for whom Edward Witten is the model physicist, and who either consciously or unconsciously attempted to imitate him. Few of these, however, can match his combination of mathematical facility and physical insight, and indeed the work of Witten himself is not restricted to formal topics and has ranged widely though the field.
The style is certainly still common, although less fashionable. This is in part due to the prior harvest of low-lying fruit from the tree of theoretical ideas, and in part due to the coming of the Large Hadron Collider, which revitalised experimental particle physics.
In the late 1990s and early 2000s, following the rush of theoretical breakthroughs described in chapters 5 and 6, this style of approach to string theory was reasonably attractive. Times have changed since then, and it is certainly much harder now for a young person to be hired in a physics department if there is any implicit suspicion that they may regard experimental data as something beneath them.
12.5 IL FAUT CULTIVER NOTRE JARDIN
The English professional football leagues have four divisions.8 At the top, there is the Premier League. This consists of twenty clubs, some of whom also compete in European competitions. The matches between these clubs are televised across the world, with the sale of the television rights bringing in enormous sums of money. The players in the Premier League earn huge salaries, taking home more in a week than an average worker does in a year. For their money, those who watch teams such as Arsenal or Chelsea or Manchester United get to see in the flesh some of the best players in the world competing at the highest level.
However, many of those who pay to watch live football do so outside the top division. Many people pay good money to watch not Liverpool FC but their near neighbours Tranmere Rovers. On a typical weekend, something like a quarter of a million people in England spend an afternoon watching football at a match outside the Premier League.
Why is this? The answer is not that the lower league clubs are merely affordable alternatives for when seats are unavailable for the big match. The same fans also went to Prenton Park rather than Anfield in the olden days of huge, cheap terraced stands, when even the biggest clubs rarely filled their grounds.
Nor is the answer the freefall of once great clubs down through the leagues. It is true that it is an unwritten rule of football supporting that an allegiance to a club, once given, can never be retracted. In this context there are few sins more heinous than changing club simply because the original choice now loses miserably and continuously, and one fancies watching graceful tiki-taka passing rather than up-and-under hoofball. Most lower league clubs have been so throughout their history, drifting like flotsam between second, third and fourth tiers via the occasional promotion or relegation. The choice to support Colchester United or Doncaster Rovers is not attended by any expectations of glory.
What are the positive reasons to watch lower league football? There are attractions among the lower divisions that are absent at the highest levels. As a supporter, you want your team to win every match, and you are disappointed when they lose. However many fans do not really at heart want their team competing at the top end of the top division. They prefer things the way they are. They are pleased that the club is part of the local community and does not arrange its preseason fixtures with an eye to the Shanghai fanbase. They like the fact that they know Bill on the turnstiles and Jenny who sells the programmes by the main stand. They feel a connection with players who are local lads on a good wage, but who do not get to date pop stars. They enjoy recognising other supporters rather than being one of a gigantic horde. They like the fact that their club is a club and not a brand. They can feel that the club is theirs.
There are many benefits to life outside the headlights. There are also many scientists who genuinely prefer working in topics away from centre stage. They are happier when they know personally everyone else who works on a similar topic, and they enjoy getting together with them at small meetings to discuss progress. They like the ability to take a problem, think about it, turn it over in their minds, and make progress, away from the danger of being bulldozed by a stampede of hungry postdocs hunting the next big thing. Their work may not feature in press releases or in the plenary sessions of major conferences, but they also get to avoid the frustration of seeing others take over ‘their’ problem. They thrive best within a smaller ecosystem rather than seeking dominance.
The areas these scientists work on are not fashionable. Sometimes, areas are unfashionable for good reasons. The problems involved are difficult, and when solved confer no broader illumination. Questions that were once provocative become irrelevant as the subject advances – no one cares anymore about the fine details of the steady-state model of the universe. Those who continue working in such areas do fade away into gentle obscurity, accompanied by ever decreasing levels of interest in their research and ever increasing teaching requests from their head of department.
However, topics can also be unpopular for no better reason than that they are unpopular. Fashions are fickle. If an area is out of favour due to prejudice or misjudgement, those who are prepared to invest time in it will do well – and occasionally extraordinarily well. Both quantum field theory and string theory were once marginal areas ignored by the majority and populated by small numbers of scientists.
Some scientists enjoy hunting for such undeservedly unloved areas and cherishing them. The future for those in such areas is bright. Even so, once success comes there are different responses to it. The most natural attitude is to continue working on the same topic, and as a founder of the field be carried upwards on a rising tide of interest. For some though, part of the pleasure of working on an unfashionable area is the opportunity to think deep, foundational thoughts and thereby shape its development. As the topic becomes part of the mainstream, and so enters the province of the many, their job is done – and they head off to search for another neglected patch in order to make it bloom.
This pattern is seen in many of the very best scientists, whose skills are not fully tested by repetitive calculations. They are possessed of originality of approach, the technical ability to change topics, and the confidence that having done so they can find insights that others have missed. These skills allow them to contribute in many different areas. As one example, as a graduate student Frank Wilczek did work on the strong force that would win him the Nobel Prize. However rather than simply refine predictions for the behaviour of the strong force, over the next decade he also made central contributions to the theory of axions – the type of particle we met in chapter 10 – and also discovered a novel form of quantum statistics, called anyonic s
tatistics, which applies in two spatial dimensions and is relevant to many problems in condensed matter physics.
This chapter has described some of the many different ways to be a theorist. There are even more ways to be a scientist in general. While all types are needed for the subject to flourish, I now turn instead to arguments that string theory is not a flourishing subject, but is rather a pestilent weed in the garden of science.
1The most truly batshit crazy of these ‘theories’ double down on their ideas by merging revolutionary accounts of physics with political conspiracy theories. The results have to be read to be believed; I will forward examples of these theories to anyone interested.
2It always is a he. While most physicists are male, there are many outstanding women in the subject. Crackpots are however universally men – I have yet to encounter even a single female crackpot.
3This fact has led to one of the worst possible pieces of advice provided for giving seminars – assume the audience has zero knowledge but infinite intelligence.
4The year 1983 was a triumphal year for Rubbia’s collaboration: they discovered not only the W+, the W–, the Z0 and the top quark, but also supersymmetry. The following year was however less good as the last two had to be undiscovered.
5The details of the trigger are one of the terrors of the night for CERN experimentalists: what if there was a major fundamental discovery accessible to the Large Hadron Collider, but it was missed because the trigger caused all the necessary data to be placed in an electronic garbage can?
6While the Nobel Prize committee insists on experimental confirmation of ideas, Silicon Valley billionaires do not. The largest monetary prize in physics is the three-million-dollar Fundamental Physics Prize founded by the technology investor Yuri Milner. One of the inaugural awards was for ‘original approaches to outstanding problems in particle physics’, even though the predictions of these original approaches have failed all experimental tests.
7Funding councils that focus on metrics to evaluate quality may find amusing one aspect of the citation records of the two Randall-Sundrum papers. The arXiv numbering of these papers are hep-ph/9905221 and hep-th/9906064, referring to ‘(h)igh (e)nergy (p)hysics’, and then either (th)eory or (ph)enomenology, followed by year, month and paper number. However, with referencing people sometimes get confused. There is a paper by different authors on a relatively minor and obscure topic, but with the numbering hep-th/9905221. This paper now has almost two hundred citations – but examining these it is clear they almost entirely come from people mistyping ‘t’ for ‘p’ when attempting to reference the first Randall-Sundrum paper.
8As the name suggests, football is a game in which the feet and not the hands are used to propel the ball.
CHAPTER 13
#EpicFail? Criticisms of String Theory
Toddlers and Taleban alike know that it is always easier to knock down than to build up. Criticism is cheap and criticism – of anything – is easy. The critic gets to pick his point and time of attack. The critic does not have to be fair, and the critic does not have to provide either a solution to the issues he raises or any alternative proposal to deal with them.
For a topic whose subject matter is at almost maximal remove from daily concerns, string theory attracts a surprising amount of emotion. At the time of writing, the first three options on the google autocomplete of ‘String theory is’ are ‘dead’, ‘wrong’ and ‘bullshit’. It is a topic on which people have real and polarised opinions. Having last encountered any science or mathematics amidst the fraught years of adolescence is no obstacle at all to holding strong opinions on string theory’s relative merits compared to other ideas for quantum gravity.1
Of course, criticism has many positive features. The concept of the loyal opposition is a glorious feature of parliamentary democracy. The good faith exchange of contradictory views can sharpen vague ideas into blades that cut. False pretensions and claims are blown away by a need to provide clear answers to clear questions. Critical debate can bring the point of disagreement into focus, thereby showing where hidden assumptions are entering in. Every scientist grumbles about the referee reports they get back on the papers they submit for publication, but few would deny that on the whole these reports lead to improvements in the quality and readability of the papers.
There are many criticisms that have been levelled at string theory, and the aim of this chapter is to provide responses to these criticisms. In doing so I have tried to be fair and to do my best by arguments even when I disagree with them. In my formulations, I have attempted to capture the spirit of these criticisms and to put them in their most convincing form. Sometimes they involve unspoken assumptions. Whenever possible I have sought to allow these assumptions and to meet the criticisms on their own ground.
However, I also want to make clear that what I address in this chapter are criticisms of string theory, and not the promotion of any individual alternative theory. This chapter deals with the arguments made that string theory is wrong or misguided, and not with arguments that some other theory is right. This is a case to be made by those who believe in it, and I have provided some references in the bibliography for those who want to pursue their arguments. For this reason this chapter will not deal with any criticisms of the form But string theory is so much worse at frying burgers than my theory’.
I will give partial consideration to such arguments in the next chapter, which is the counterpoint to this one. The next chapter deals not with why string theory is wrong, but with why string theory is right. It gives the positive case for why string theory has been so much more successful than any other proposed theory of quantum gravity. In doing so, it will in part address these unfavourable comparisons of string theory to other theories, as well as including some brief comments on these proposals. These comments will be brief – this book is not primarily about quantum gravity and it is certainly not about all theories of quantum gravity ever proposed.
So, what are the reasons put forward that string theory is ex operibus diaboli?
CRITICISM: The attractiveness of string theory comes from its claim to solve the high-energy (sometimes called ultraviolet) problems of supergravity by making the divergences finite. However, there is no actual proof that string theory is finite. The calculations only hold at the lowest orders in perturbation theory and have not been extended further. Beyond these, finiteness is simply a conjecture, but not one that has actually been proven. As such, the finiteness of string theory might be an interesting idea, but one should not place too more store by it.
The strength and weakness of this point lies entirely in the word ‘proof’. ‘Proof’ is a heavily loaded word. It is also a word that has more in common with mathematics than physics. The interesting structures of physics are too complicated to be described at the level of mathematical detail that can happily accommodate the mathematicians’ notion of proof.
In 1984, one of the main selling points of string theory was that it offered a possible answer to apparently insuperable problems with the supergravity theories. This answer was partly conceptual and partly calculational. There were indeed calculations that gave finite answers where supergravity gave infinite answers. However, and at least as importantly, there were also conceptual arguments, through which the extended nature of the string provided a reason why these problems should be absent in string theory.
One aspect of this argument was that strings are extended objects and so tend to smear out infinities associated to point particles with no spatial extent. Another more technical point was that the structure of string theory offered a way to reinterpret any high energy problems of supergravity as low energy questions. On this way of thinking, the short-distance infinities of supergravity could be re-understood as long-distance effects. However, divergences associated to long-distance effects were already well understood through studies of quantum field theory and were known to be harmless. These arguments made string theory attractive in 1984: it proposed a new way to solve a
n old problem, and wherever the new ideas could be tested, they worked.
At that time, the question of whether all these ideas really did work as they appeared was a good and interesting question. Were the cancellations that had been found in the superstring merely a lucky coincidence? The arguments for finiteness worked neatly in the simplest settings – at the lowest orders in perturbation theory. However, even if they were saying something, there could still be something more that had been missed. Was superstring theory really consistent? This is ultimately what the criticism above asks – is string theory actually a theory that makes sense?
Superstring theory in 1984 was a relatively new and poorly understood structure focussed on the particular problem of quantum gravity. In this context, any proof of finiteness would have been very welcome. Such a proof would have, by necessity, automatically greatly extended the technical tools available in string theory. The techniques then used for describing fermions became prohibitively complicated beyond the lowest orders of perturbation theory, and of necessity any proof would have had to include methods for working at all orders in perturbation theory. Any general proof would have greatly extended the relatively few calculations that existed and would have offered clues to how the theory should be developed.
However, by the time we reach 2015 string theory has produced so much more of interest that this question of proof’ is far less interesting. The number of positive, surprising and correct results produced by string theory is now so large that there can be no reasonable doubt that string theory as known today does represent a consistent mathematical something, even if it is not possible to define exactly what that something is. As one example, we saw in chapter 8 one of the highly intricate formulae that string theory reproduces in the AdS/CFT duality. It is beyond reasonable doubt that these agreements are not simply a fluke.
Why String Theory? Page 32