Tag: string theory

25 years of Maldacena’s bridge

Twenty-five years go, in 1997, an Argentine physicist named Juan Martin Maldacena published what would become the most highly cited physics paper in history (more than 20,000 to date). In the paper, Maldacena described a ‘bridge’ between two theories that describe how our world works, but separately, without meeting each other. These are the field theories that describe the behaviour of energy fields (like the electromagnetic fields) and subatomic particles, and the theory of general relativity, which deals with gravity and the universe at the largest scales.

Field theories have many types and properties. One of them is a conformal field theory: a field theory that doesn’t change when it undergoes a conformal transformation – i.e. one which preserves angles but not lengths pertaining to the field. As such, conformal field theories are said to be “mathematically well-behaved”.

In relativity, space and time are unified into the spacetime continuum. This continuum can broadly exist in one of three possible spaces (roughly, universes of certain ‘shapes’): de Sitter space, Minkowski space and anti-de Sitter space. de Sitter space has positive curvature everywhere – like a sphere (but is empty of any matter). Minkowski space has zero curvature everywhere – i.e. a flat surface. Anti-de Sitter space has negative curvature everywhere – like a hyperbola.

A sphere, a hyperbolic surface and a flat surface. Credit: NASA

Because these shapes are related to the way our universe looks and works, cosmologists have their own way to understand these spaces. If the spacetime continuum exists in de Sitter space, the universe is said to have a positive cosmological constant. Similarly, Minkowski space implies a zero cosmological constant and anti-de Sitter space a negative cosmological constant. Studies by various space telescopes have found that our universe has a positive cosmological constant, meaning ‘our’ spacetime continuum occupies a de Sitter space (sort of, since our universe does have matter).

In 1997, Maldacena found that a description of quantum gravity in anti-de Sitter space in N dimensions is the same as a conformal field theory in N – 1 dimensions. This – called the AdS/CFT correspondence – was an unexpected but monumental discovery that connected two kinds of theories that had thus far refused to cooperate. (The Wire Science had a chance to interview Maldacena about his past and current work in 2018, in which he provided more insights on AdS/CFT as well.)

In his paper, Maldacena demonstrated his finding by using the example of string theory as a theory of quantum gravity in anti-de Sitter space – so the finding was also hailed as a major victory for string theory. String theory is a leading contender for a theory that can unify quantum mechanics and general relativity. However, we have found no experimental evidence of its many claims. This is why the AdS/CFT correspondence is also called the AdS/CFT conjecture.

Nonetheless, thanks to the correspondence, (mathematical) physicists have found that some problems that are hard on the ‘AdS’ side are much easier to crack on the ‘CFT’ side, and vice versa – all they had to do was cross Maldacena’s ‘bridge’! This was another sign that the AdS/CFT correspondence wasn’t just a mathematical trick but could be a legitimate description of reality.

So how could it be real?

The holographic principle

In 1997, Maldacena proved that a string theory in five dimensions was the same as a conformal field theory in four dimensions. However, gravity in our universe exists in four dimensions – not five. So the correspondence came close to providing a unified description of gravity and quantum mechanics, but not close enough. Nonetheless, it gave rise to the possibility that an entity that existed in some number of dimensions could be described by another entity that existed in one fewer dimensions.

Actually, in fact, the AdS/CFT correspondence didn’t give rise to this possibility but proved it, at least mathematically; the awareness of the possibility had existed for many years until then, as the holographic principle. The Dutch physicist Gerardus ‘t Hooft first proposed it and the American physicist Leonard Susskind in the 1990s brought it firmly into the realm of string theory. One way to state the holographic principle, in the words of physicist Matthew Headrick, is thus:

“The universe around us, which we are used to thinking of as being three dimensional, is actually at a more fundamental level two-dimensional and that everything we see that’s going on around us in three dimensions is actually happening in a two-dimensional space.”

This “two-dimensional space” is the ‘surface’ of the universe, located at an infinite distance from us, where information is encoded that describes everything happening within the universe. It’s a mind-boggling idea. ‘Information’ here refers to physical information, such as, to use one of Headrick’s examples, “the positions and velocities of physical objects”. In beholding this information from the infinitely faraway surface, we apparently behold a three-dimensional reality.

It bears repeating that this is a mind-boggling idea. We have no proof so far that the holographic principle is a real description of our universe – we only know that it could describe our reality, thanks to the AdS/CFT correspondence. This said, physicists have used the holographic principle to study and understand black holes as well.

In 1915, Albert Einstein’s general theory of relativity provided a set of complicated equations to understand how mass, the spacetime continuum and the gravitational force are related. Within a few months, physicists Karl Swarzschild and Johannes Droste, followed in subsequent years by Georges Lemaitre, Subrahmanyan Chandrasekhar, Robert Oppenheimer and David Finkelstein, among others, began to realise that one of the equations’ exact solutions (i.e. non-approximate) indicated the existence of a point mass around which space was wrapped completely, preventing even light from escaping from inside this space to outside. This was the black hole.

Because black holes were exact solutions, physicists assumed that they didn’t have any entropy – i.e. that its insides didn’t have any disorder. If there had been such disorder, it should have appeared in Einstein’s equations. It didn’t, so QED. But in the early 1970s, the Israeli-American physicist Jacob Bekenstein noticed a problem: if a system with entropy, like a container of hot gas, was thrown into the black hole, and the black hole doesn’t have entropy, where does the entropy go? It had to go somewhere; otherwise, the black hole would violate the second law of thermodynamics – that the entropy of an isolated system, like our universe, can’t decrease.

Bekenstein postulated that black holes must also have entropy, and that the amount of entropy is proportional to the black hole’s surface area, i.e. the area of the event horizon. Bekenstein also worked out that there is a limit to the amount of entropy a given volume of space can contain, as well as that all black holes could be described by just three observable attributes: their mass, electric charge and angular momentum. So if a black hole’s entropy increases because it has swallowed some hot gas, this change ought to manifest as a change in one, some or all of these three attributes.

Taken together: when some hot gas is tossed into a black hole, the gas would fall into the event horizon but the information about its entropy might appear to be encoded on the black hole’s surface, from the point of view of an observer located outside and away from the event horizon. Note here that the black hole, a sphere, is a three-dimensional object whereas its surface is a flat, curved sheet and therefore two-dimensional. That is, all the information required to describe a 3D black hole could in fact be encoded on its 2D surface – which evokes the AdS/CFT correspondence!

However, that the event horizon of a black hole preserves information about objects falling into the black hole gives rise to another problem. Quantum mechanics requires all physical information (like “the positions and velocities of physical objects”, in Headrick’s example) to be conserved. That is, such information can’t ever be destroyed. And there’s no reason to expect it will be destroyed if black holes lived forever – but they don’t.

Stephen Hawking found in the 1970s that black holes should slowly evaporate by emitting radiation, called Hawking radiation, and there is nothing in the theories of quantum mechanics to suggest that this radiation will be encoded with the information preserved on the event horizon. This, fundamentally, is the black hole information loss problem: either the black hole must shed the information in some way or quantum mechanics must be wrong about the preservation of physical information. Which one is it? This is a major unsolved problem in physics, and it’s just one part of the wider context that the AdS/CFT correspondence inhabits.

For more insights into this discovery, do read The Wire Science‘s interview of Maldacena.

I’m grateful to Nirmalya Kajuri for his feedback on this article.

Sources:

Getting ahead of theory, experiment, ourselves

Science journalist Laura Spinney wrote an article in The Guardian on January 9, 2022, entitled ‘Are we witnessing the dawn of post-theory science?’. This excerpt from the article captures its points well, I thought:

Or take protein structures. A protein’s function is largely determined by its structure, so if you want to design a drug that blocks or enhances a given protein’s action, you need to know its structure. AlphaFold was trained on structures that were derived experimentally, using techniques such as X-ray crystallography and at the moment its predictions are considered more reliable for proteins where there is some experimental data available than for those where there is none. But its reliability is improving all the time, says Janet Thornton, former director of the EMBL European Bioinformatics Institute (EMBL-EBI) near Cambridge, and it isn’t the lack of a theory that will stop drug designers using it. “What AlphaFold does is also discovery,” she says, “and it will only improve our understanding of life and therapeutics.”

Essentially, the article is concerned with machine-learning’s ability to parse large amounts of data, find patterns in them and use them to generate theories – taking over an important realm of human endeavour. In keeping with tradition, it doesn’t answer the question in its headline with a definitive ‘yes’ but with a hard ‘maybe’ to a soft ‘no’. Spinney herself ends by quoting Picasso: “Computers are useless. They can only give you answers” – although the para right before belies the painter’s confidence with a prayer that the human way to think about theories is still meaningful and useful:

The final objection to post-theory science is that there is likely to be useful old-style theory – that is, generalisations extracted from discrete examples – that remains to be discovered and only humans can do that because it requires intuition. In other words, it requires a kind of instinctive homing in on those properties of the examples that are relevant to the general rule. One reason we consider Newton brilliant is that in order to come up with his second law he had to ignore some data. He had to imagine, for example, that things were falling in a vacuum, free of the interfering effects of air resistance.

I’m personally cynical about such claims. If we think we are going to be obsolete, there must be a part of the picture we’re missing.

There was an idea partly similar to this ‘post-theory hypothesis’ a few years ago, and pointing the other way. In 2013, philosopher Richard Dawid wrote a 190-page essay attempting to make the case that string theory shouldn’t be held back by the lack of experimental evidence, i.e. that it was post-empirical. Of course, Spinney is writing about machines taking over the responsibility of, but not precluding the need for, theorising – whereas Dawid and others have argued that string theory doesn’t need experimental data to stay true.

The idea of falsifiability is important here. If a theory is flawed and if you can design an experiment that would reveal that flaw, the theory is said to be falsifiable. A theory can be flawless but still falsifiable: for example, Newton’s theory of gravity is complete and useful in a limited context but, for example, can’t explain the precession of the perihelion of Mercury’s orbit. An example of an unfalsifiable theory is the one underlying astrology. In science, falsifiable theories are said to be better than unfalsifiable ones.

I don’t know what impact Dawid’s book-length effort had, although others before and after him have supported the view that scientific theories should no longer be falsifiable in order to be legitimate. Sean Carroll for one. While I’m not familiar enough with criticisms of the philosophy of falsifiability, I found a better reason to consider the case to trust the validity of string theory sans experimental evidence in a June 2017 preprint paper written by Eva Silverstein:

It is sometimes said that theory has strayed too far from experiment/observation. Historically, there are classic cases with long time delays between theory and experiment – Maxwell’s and Einstein’s waves being prime examples, at 25 and 100 years respectively. These are also good examples of how theory is constrained by serious mathematical and thought-experimental con- sistency conditions.

Of course electromagnetism and general relativity are not representative of most theoretical ideas, but the point remains valid. When it comes to the vast theory space being explored now, most testable ideas will be constrained or falsified. Even there I believe there is substantial scientific value to this: we learn something significant by ruling out a valid theoretical possibility, as long as it is internally consistent and interesting. We also learn important lessons in excluding potential alternative theories based on theoretical consistency criteria.

This said, Dawid’s book, entitled String Theory and the Scientific Method, was perhaps the most popular prouncement of his views in recent years (at least in terms of coverage in the non-technical press), even if by then he’d’ been propounding them for nine years and if his supporters included a bevy of influential physicists. Very simply put, an important part of Dawid’s arguments was that string theory, as a theory, has certain characteristics that make it the only possible theory for all the epistemic niches that it fills, so as long as we expect all those niches to filled by a single theory, string theory may be true by virtue of being the sole possible option.

It’s not hard to see the holes in this line of reasoning, but again, I’ve considerably simplified his idea. But this said, physicist Peter Woit has been (from what little I’ve seen) the most vocal critic of string theorists’ appeals to ‘post-empirical realism’ and has often directed his ire against the uniqueness hypothesis, significantly because accepting it would endanger, for the sake of just one theory’s survival, the foundation upon which almost every other valid scientific theory stands. You must admit this is a powerful argument, and to my mind more persuasive than Silverstein’s argument.

In the words of another physicist, Carlo Rovelli, from September 2016:

String theory is a proof of the dangers of relying excessively on non-empirical arguments. It raised great expectations thirty years ago, when it promised to [solve a bunch of difficult problems in physics]. Nothing of this has come true. String theorists, instead, have [made a bunch of other predictions to explain why it couldn’t solve what it set out to solve]. All this was false.

From a Popperian point of view, these failures do not falsify the theory, because the theory is so flexible that it can be adjusted to escape failed predictions. But from a Bayesian point of view, each of these failures decreases the credibility in the theory, because a positive result would have increased it. The recent failure of the prediction of supersymmetric particles at LHC is the most fragrant example. By Bayesian standards, it lowers the degree of belief in string theory dramatically. This is an empirical argument. Still, Joe Polchinski, prominent string theorist, writes in that he evaluates the probability of string to be correct at 98.5% (!).

Scientists that devoted their life to a theory have difficulty to let it go, hanging on non-empirical arguments to save their beliefs, in the face of empirical results that Bayes confirmation theory counts as negative. This is human. A philosophy that takes this as an exemplar scientific attitude is a bad philosophy of science.

All the science in ‘The Cloverfield Paradox’

I watched The Cloverfield Paradox last night, the horror film that Paramount pictures had dumped with Netflix and which was then released by Netflix on February 4. It’s a dumb production: unlike H.R. Giger’s existential, visceral horrors that I so admire, The Cloverfield Paradox is all about things going bump in the dark. But what sets these things off in the film is quite interesting: a particle accelerator. However, given how bad the film was, the screenwriter seems to have used this device simply as a plot device, nothing else.

The particle accelerator is called Shepard. We don’t know what particles it’s accelerating or up to what centre-of-mass collision energy. However, the film’s premise rests on the possibility that a particle accelerator can open up windows into other dimensions. The Cloverfield Paradox needs this because, according to its story, Earth has run out of energy sources in 2028 and countries are threatening ground invasions for the last of the oil, so scientists assemble a giant particle accelerator in space to tap into energy sources in other dimensions.

Considering 2028 is only a decade from now – when the Sun will still be shining bright as ever in the sky – and renewable sources of energy aren’t even being discussed, the movie segues from sci-fi into fantasy right there.

Anyway, the idea that a particle accelerator can open up ‘portals’ into other dimensions isn’t new nor entirely silly. Broadly, an accelerator’s purpose is founded on three concepts: the special theory of relativity (SR), particle decay and the wavefunction of quantum mechanics.

According to SR, mass and energy can transform into each other as well as that objects moving closer to the speed of light will become more massive, thus more energetic. Particle decay is what happens when a heavier subatomic particle decomposes into groups of lighter particles because it’s unstable. Put these two ideas together and you have a part of the answer: accelerators accelerate particles to extremely high velocities, the particles become more massive, ergo more energetic, and the excess energy condenses out at some point as other particles.

Next, in quantum mechanics, the wavefunction is a mathematical function: when you solve it based on what information you have available, the answer spit out by one kind of the function gives the probability that a particular particle exists at some point in the spacetime continuum. It’s called a wavefunction because the function describes a wave, and like all waves, this one also has a wavelength and an amplitude. However, the wavelength here describes the distance across which the particle will manifest. Because energy is directly proportional to frequency (E = h × ν; h is Planck’s constant) and frequency is inversely proportional to the wavelength, energy is inversely proportional to wavelength. So the more the energy a particle accelerator achieves, the smaller the part of spacetime the particles will have a chance of probing.

Spoilers ahead

SR, particle decay and the properties of the wavefunction together imply that if the Shepard is able to achieve a suitably high energy of acceleration, it will be able to touch upon an exceedingly small part of spacetime. But why, as it happens in The Cloverfield Paradox, would this open a window into another universe?

Spoilers end

Instead of directly offering a peek into alternate universes, a very-high-energy particle accelerator could offer a peek into higher dimensions. According to some theories of physics, there are many higher dimensions even though humankind may have access only to four (three of space and one of time). The reason they should even exist is to be able to solve some conundrums that have evaded explanation. For example, according to Kaluza-Klein theory (one of the precursors of string theory), the force of gravity is so much weaker than the other three fundamental forces (strong nuclear, weak nuclear and electromagnetic) because it exists in five dimensions. So when you experience it in just four dimensions, its effects are subdued.

Where are these dimensions? Per string theory, for example, they are extremely compactified, i.e. accessible only over incredibly short distances, because they are thought to be curled up on themselves. According to Oskar Klein (one half of ‘Kaluza-Klein’, the other half being Theodore Kaluza), this region of space could be a circle of radius 10-32 m. That’s 0.00000000000000000000000000000001 m – over five quadrillion times smaller than a proton. According to CERN, which hosts the Large Hadron Collider (LHC), a particle accelerated to 10 TeV can probe a distance of 10-19 m. That’s still one trillion times larger than where the Kaluza-Klein fifth dimension is supposed to be curled up. The LHC has been able to accelerate particles to 8 TeV.

The likelihood of a particle accelerator tossing us into an alternate universe entirely is a different kind of problem. For one, we have no clue where the connections between alternate universes are nor how they can be accessed. In Nolan’s Interstellar (2014), a wormhole is discovered by the protagonist to exist inside a blackhole – a hypothesis we currently don’t have any way of verifying. Moreover, though the LHC is supposed to be able to create microscopic blackholes, they have a 0% chance of growing to possess the size or potential of Interstellar‘s Gargantua.

In all, The Cloverfield Paradox is a waste of time. In the 2016 film Spectral – also released by Netflix – the science is overwrought, stretched beyond its possibilities, but still stays close to the basic principles. For example, the antagonists in Spectral are creatures made entirely as Bose-Einstein condensates. How this was even achieved boggles the mind, but the creatures have the same physical properties that the condensates do. In The Cloverfield Paradox, however, the accelerator is a convenient insertion into a bland story, an abuse of the opportunities that physics of this complexity offers. The writers might as well have said all the characters blinked and found themselves in a different universe.

Some notes on empiricism, etc.

The Wire published a story about the ‘atoms of Acharya Kanad‘ (background here; tl;dr: Folks at a university in Gujarat claimed an ancient Indian sage had put forth the theory of atoms centuries before John Dalton showed up). The story in question was by a professor of philosophy at IISER, Mohali, and he makes a solid case (not unfamiliar to many of us) as to why Kanad, the sage, didn’t talk about atoms specifically because he was making a speculative statement under the Vaisheshika school of Hindu philosophy that he founded. What got me thinking were the last few lines of his piece, where he insists that empiricism is the foundation of modern science, and that something that doesn’t cater to it can’t be scientific. And you probably know what I’m going to say next. “String theory”, right?

No. Well, maybe. While string theory has become something of a fashionable example of non-empirical science, it isn’t the only example. It’s in fact a subset of a larger group of systems that don’t rely on empirical evidence to progress. These systems are called formal systems, or formal sciences, and they include logic, mathematics, information theory and linguistics. (String theory’s reliance on advanced mathematics makes it more formal than natural – as in the natural sciences.) And the dichotomous characterisation of formal and natural sciences (the latter including the social sciences) is superseded by a larger, more authoritative dichotomy*: between rationalism and empiricism. Rationalism prefers knowledge that has been deduced through logic and reasoning; empiricism prioritises knowledge that has been experienced. As a result, it shouldn’t be a surprise at all that debates about which side is right (insofar as it’s possible to be absolutely right – which I don’t think everwill happen) play out in the realm of science. And squarely within the realm of science, I’d like to use a recent example to provide some perspective.

Last week, scientists discovered that time crystals exist. I wrote a longish piece here tracing the origins and evolution of this exotic form of matter, and what it is that scientists have really discovered. Again, a tl;dr version: in 2012, Frank Wilczek and Alfred Shapere posited that a certain arrangement of atoms (a so-called ‘time crystal’) in their ground state could be in motion. This could sound pithy to you if you were unfamiliar with what ground state meant: absolute zero, the thermodynamic condition wherein an object has no energy whatsoever to do anything else but simply exist. So how could such a thing be in motion? The interesting thing here is that though Shapere-Wilczek’s original paper did not identify a natural scenario in which this could be made to happen, they were able to prove that it could happen formally. That is, they found that the mathematics of the physics underlying the phenomenon did not disallow the existence of time crystals (as they’d posited it).

It’s pertinent that Shapere and Wilczek turned out to be wrong. By late 2013, rigorous proofs had showed up in the scientific literature demonstrating that ground-state, or equilibrium, time crystals could not exist – but that non-equilibrium time crystals with their own unique properties could. The discovery made last week was of the latter kind. Shapere and Wilczek have both acknowledged that their math was wrong. But what I’m pointing at here is the conviction behind the claim that forms of matter called time crystals could exist, motivated by the fact that mathematics did not prohibit it. Yes, Shapere and Wilczek did have to modify their theory based on empirical evidence (indirectly, as it contributed to the rise of the first counter-arguments), but it’s undeniable that the original idea was born, and persisted with, simply through a process of discovery that did not involve sense-experience.

In the same vein, much of the disappointment experienced by many particle physicists today is because of a grating mismatch between formalism – in the form of theories of physics that predict as-yet undiscovered particles – and empiricism – the inability of the LHC to find these particles despite looking repeatedly and hard in the areas where the math says they should be. The physicists wouldn’t be disappointed if they thought empiricism was the be-all of modern science; they’d in fact have been rebuffed much earlier. For another example, this also applies to the idea of naturalness, an aesthetically (and more formally) enshrined idea that the forces of nature should have certain values, whereas in reality they don’t. As a result, physicists think something about their reality is broken instead of thinking something about their way of reasoning is broken. And so they’re sitting at an impasse, as if at the threshold of a higher-dimensional universe they may never be allowed to enter.

I think this is important in the study of the philosophy of science because if we’re able to keep in mind that humans are emotional and that our emotions have significant real-world consequences, we’d not only be better at understanding where knowledge comes from. We’d also become more sensitive to the various sources of knowledge (whether scientific, social, cultural or religious) and their unique domains of applicability, even if we’re pretty picky, and often silly, at the moment about how each of them ought to be treated (Related/recommended: Hilary Putnam’s way of thinking).

*I don’t like dichotomies. They’re too cut-and-dried a conceptualisation.

The intricacies of being sold on string theory

If you are seeking an appreciation for the techniques of string theory, then Brian Greene’s The Elegant Universe could be an optional supplement. If, on the other hand, you want to explore the epistemological backdrop against which string theory proclaimed its aesthetic vigor, then the book is a must-read. As the title implies, it discusses the elegance of string theory in great and pleasurable detail, beginning from a harmonious resolution of the conflicts between quantum mechanics and general relativity being its raison d’être to why it commands the attention of some of the greatest living scientists.

A bigger victory it secures, however, is not in simply laying out string theory but getting you interested in it – and this has become a particularly important feature of science in the 21st century.

The counter-intuitive depiction of nature by the principles of modern physics have, since the mid-20th century, foretold that reality can be best understood in terms of mathematical expressions. This contrasted the simplicity of its preceding paradigm: Newtonian physics, which was less about the mathematics and more about observations, and therefore required fewer interventions to bridge reality as it seemed and reality as it said it was.

Modern physics – encompassing quantum mechanics and Albert Einstein’s theories of relativity – overhauled this simplicity. While reality as it seemed hadn’t changed, reality as they said it was bore no semblence to any of Newton’s work. The process of understanding reality became much more sophisticated, requiring years of training just to prepare oneself to be able to understand it, while probing it required the grandest associations of intellect and hardware.

The trouble getting it across

An overlooked side to this fallout concerned the instruction of these subjects to non-technical audiences, to people who liked to know what was going on but didn’t want to dedicate their lives to it1. Both quantum mechanics and general relativity are dominated by advanced mathematics, yet spelling out such abstractions is neither convenient nor effective for non-technical communication. As a result, science communicators have increasingly resorted to metaphors, using them to negotiate with the knowledge their readers already possessed.

This is where The Elegant Universe is most effective, especially since string theory is admittedly more difficult to understand than quantum mechanics or general relativity ever was. In fact, the book’s first few chapters – before Greene delves into string theory – are seasoned with statements of how intricate string theory is, while he does a tremendous job of laying the foundations of modern physics.

Especially admirable is his seamless guidance of the reader from time dilation and Lorentzian contraction to quantum superposition to the essentials of superstring theory to the unification of all forces under M-theory, with nary a twitch in between. The examples with which he illustrates important concepts are never mundane, too. His flamboyant writing makes for the proverbial engaging read. You will often find words you wouldn’t quickly use to describe the world around you, endorsing a supreme confidence in the subject being discussed.

Consider: “… the gently curving geometrical form of space emerging from general relativity is at loggerheads with the frantic, roiling, microscopic behavior of the universe implied by quantum mechanics”. Or, “With the discovery of superstring theory, musical metaphors take on a startling reality, for the theory suggests that the microscopic landscape is suffused with tiny strings whose vibrational patterns orchestrate the evolution of the cosmos. The winds of charge, according to superstring theory, gust through an aeolian universe.”

More importantly, Greene’s points of view in the book betray a confidence in string theory itself – as if he thinks that it is the only way to unify quantum mechanics and general relativity under an umbrella pithily called the ‘theory of everything’. What it means for you, the reader, is that you can expect The Elegant Universe not to be an exploratory stroll through a garden but more of a negotiation of the high seas.

Taking recourse in emotions

Does this subtract from the objectivity an enthused reader might appreciate as it would have prepared her to tackle the unification problem by herself? Somewhat. It is a subtle flaw in Greene’s reasoning throughout the book: while he devotes many pages to discussing solutions, he spends little time annotating the flaws of string theory itself. Even if no other theory has charted the sea of unification so well, Greene could have maintained some objectivity about it.

At the same time, by the end of the book, you start to think there is no other way to expound on string theory than by constantly retreating into the intensity of emotions and the honest sensationalism they are capable of yielding. For instance, when describing his own work alongside Paul Aspinwall and David Morrison in determining if space can tear in string theory, Greene introduces the theory’s greatest exponent, Edward Witten. As he writes,

“Edward Witten’s razor-sharp intellect is clothed in a soft-spoken demeanor that often has a wry, almost ironic, edge. He is widely regarded as Einstein’s successor in the role of the world’s greatest living physicist. Some would go even further and describe him as the greatest physicist of all time. He has an insatiable appetite for cutting-edge physics problems and he wields tremendous influence in setting the direction of research in string theory.”

Then, in order to convey the difficulty of a problem that the trio was facing, Greene simply states: Witten “lit up upon hearing the ideas, but cautioned that he thought the calculations would be horrendously difficult”. If Witten expects them to be horrendously difficult, then they must indeed be as horrendous as they get.

Such descriptions of magnitude are peppered throughout The Elegant Universe, often clothed in evocative language, and constitute a significant portion of its appeal to a general audience. They rob string theory of its esoteric stature, making the study of its study memorable. Greene has done well to not dwell on the technical intricacies of his subject while still retaining both the wonderment and the frustration of dealing with something as intractable. This, in fact, is his prime achievement through writing the book.

String theory is not about technique

It was published in 1999. In the years since, many believe that string theory has become dormant. However, that is also where the book scores: not by depicting the theory as being unfalsifiable but as being resilient, as being incomplete enough to dare physicists to follow their own lead in developing it, as being less of a feat in breathtaking mathematics and more of constantly putting one’s beliefs to the test.

Simultaneously, it is unlike the theories of inflationary cosmology that are so flexible that disproving them is like fencing with air. String theory has a sound historical basis in the work of Leonhard Euler, and its careful derivation from those founding principles to augur the intertwined destinies of space and time have concerned the efforts of simply the world’s best mathematicians.

Since the late 1960s, when string theory was first introduced, it has gone through alternating periods of reaffirmation and discreditation. Each crest in this journey has been introduced by a ‘superstring revolution’, a landmark hypothesis or discovery that has restored its place in the scientific canon. Each trough, on the other hand, has represented a difficult struggle to attempt to cohere the implications of string theory into a convincing picture of reality.

These struggles are paralleled by Greene’s efforts in composing The Elegant Universe, managing to accomplish what is often lost in the translation of human endeavors: the implications for the common person. This could be in the form of beauty, or a better life, or some form of intellectual satisfaction; in the end, the book succeeds by drawing these possibilities to the fore, for once overshadowing the enormity of the undertaking that string theory will always be.

Buy the book on Amazon.

1Although it can also be argued that science communication as a special skill was necessitated by science becoming so complex.

‘No string theorists in non-elite institutions’

Shiraz Naval Minwalla, a professor of theoretical physics at the Tata Institute of Fundamental Research (TIFR), Mumbai, won the New Horizons in Physics Prize for 2013 on November 5. The prize – which recognizes ‘promising researchers’ and comes with a cash prize of $100,000 – is awarded by the Fundamental Physics Prize Foundation, set up by Russian billionaire Yuri Milner in 2012.

Shiraz has been cited for his contributions to the study of string theory and quantum field theory, particularly for improving our understanding of the equations governing fluid dynamics, and using them to verify the predictions of all quantum field theories as opposed to a limited class of theories before.

On November 12, Shiraz was also awarded the Infosys Foundation Prize in the physical sciences category. He was the youngest among this year’s winners.

I interviewed him over Skype for The Hindu (major hat-tip to Akshat Rathi), which is where this interview first appeared (on November 13, 2013). Shiraz had some important things to say, including the now-proverbial ‘the Indian elementary school system sucks’, and that India is anomalously strong in the arena of string theory research, although it doesn’t yet match up to the US’s output qualitatively, but that almost none of it happens in non-elite institutions.

Here we go.

Why do you work with string theory and quantum field theory? Why are you interested in these subjects?

Because it seems like one of the roads to completing one element of the unfinished task of physics. In the last century, there have been two big developments in physic. The quantum revolution, which established the language of quantum mechanics for dealing with physical systems, and the general theory of relativity, which established the dynamic nature of spacetime as reality in the world and realized it was responsible for gravity. These two paradigms have been incredibly successful in their domains of applicability. Quantum theory is ubiquitous in physics, and is also the basis for theories of elementary particle physics. The general relativity way of thinking has been successful with astrophysics and cosmology, i.e. successful at larger scales.

These paradigms have been individually confirmed and individually very successful, yet we have no way of putting them together, no single mathematically consistent framework. This is why I work with string theory and quantum field theory because I think it is the correct path to realize a unified quantum theory of gravity.

What’s the nature of your work that has snagged the New Horizons Prize? Could you describe it in simpler terms?

The context for this discussion is the AdS/CFT correspondence of string theory. AdS/CFT asserts that certain conformal quantum field theories admit a reformulation as higher dimensional theories of gravity under appropriate circumstances. Now it has long been expected that the dynamics of any quantum field theory reduces, under appropriate circumstances, to the equations of hydrodynamics. If you put these two statements together it should follow that Einstein’s equations of gravity reduce, under appropriate circumstances, to the equations of hydrodynamics.

My collaborators and I were able to directly verify this expectation. The equations of hydrodynamics that Einstein’s equations reduce have particular values of transport coefficients. And there was a surprise here. It turns out that the equations charged relativistic hydrodynamics that came out of this procedure were slightly different in form from those listed in textbooks on the subject, like the text of [Lev] Landau and [Evgeny] Lifshitz. The resolution of this apparent paradox was obtained by [Dam] Son and [Piotr] Surowka and in subsequent work, where it was demonstrated that the textbook expectations for the equations of hydrodynamics are incomplete. The correct equations sometimes have more terms, in agreement with our constructions.

The improved understanding of the equations of hydrodynamics is general in nature; it applies to all quantum field theories, including those like quantum chromodynamics that are of interest to real world experiments. I think this is a good (though minor) example of the impact of string theory on experiments. At our current stage of understanding of string theory, we can effectively do calculations only in particularly simple – particularly symmetric – theories. But we are able to analyse these theories very completely; do the calculations completely correctly. We can then use these calculations to test various general predictions about the behaviour of all quantum field theories. These expectations sometimes turn out to be incorrect. With the string calculations to guide you can then correct these predictions. The corrected general expectations then apply to all quantum field theories, not just those very symmetric ones that string theory is able to analyse in detail.

How do you see the Prize helping your research work? Does this make it easier for you to secure grants, etc.?

It pads my CV. [Laughs] So… anything I apply for henceforth becomes a little more likely to work out, but it won’t have a transformative impact on my career nor influence it in any way, frankly. It’s a great honour, of course. It makes me happy, it’s an encouragement. But I’m quite motivated without that. [After being asked about winning the Infosys Foundation Prize] I’m thrilled, but I’m also a little overwhelmed. I hope I live up to all the expectations. About being young – I hope this means that my best work is ahead of me.

What do you think about the Fundamental Physics Prize in general? About what Yuri Milner has done for the world of physics research?

Until last week, I hadn’t thought about it very much at all. The first thing to say is when Milner explained to me his motivations in constituting this prize, I understood it. Let me explain. As you know, Milner was a PhD student in physics before he left the field to invest in the Internet, etc. He said he left because he felt he wasn’t good enough to do important work.

He said one motivation was that people who are doing well needn’t found Internet companies. This is his personal opinion, one should respect that. Second: He felt that 70 or 80 years ago, physicists were celebrities who played a large role in motivating some young people to do science. Nowadays, there are no such people. I think I agree. Milner wants to do what he can to push the clock back on that. Third: Milner is uniquely well-positioned because he understands physics research because of his own background and he understands the world of business. So, he wanted to bridge these worlds. All these are reasonable ways of looking at the world.

If I had a lot of money, this isn’t the way I would have gone about it. There are many more efficient ways. For instance, more smaller prizes for younger people makes more sense than few big prizes for well established people. Some of the money could have gone as grants. I haven’t seriously thought about this, though. The fact is Milner didn’t have to do this but he did. It’s a good thing. This is his gesture, and I’m glad.

Are the Fundamental Physics Prizes in any way bringing “validity” to your areas of research? Are they bringing more favourable attention you wouldn’t have been able to get otherwise?

Well, of late, it has become fashionable sometimes to attack string theory in certain parts of the world of physics. In such an environment, it is nice to see there are other people who think differently.

What are your thoughts on the quality of physics research stemming from India? Are there enough opportunities for researchers at all levels of their careers?

Let me start with string theoretic work, which I’m aware of, and then extrapolate. String theory work done in India is pretty good. If you compared the output from India to the US, the work emerging from the US is way ahead qualitatively. But if you compared it to Japan’s output, I would say it’s clear that India does better. Japan has a large string theory community supported by American-style salaries whereas India runs on a shoestring. Given that and the fact that India is a very poor country, that’s quite remarkable. There’s no other country with a GDP per capita comparable to India’s whose string theoretic output is anywhere as good. In fact, the output is better than any country in the European Union, but at the same time not comparable to the EU’s as a whole. So you get an idea of the scale: reasonably good, not fantastic.

The striking weakness of research in India is that research happens by and large only in a few elite institutions. But in the last five years, it has been broadening out a bit. TIFR and the Harish-Chandra Research Institute [HRI] have good research groups; there are some reasonably good young groups in Indian Institute of Science [IIS], Bengaluru; Institute of Mathematical Sciences, Chennai; some small groups in the Chennai Mathematical Institute, IIT-Madras, IIT-Bombay, IIT-Kanpur, all growing in strength, The Indian Institute of Science Education and Research (IISER), Pune, has also made good hires in string theory.

So, it’s spreading out. The good thing is young people are being hired in many good places. What is striking is we don’t yet have participation from universities; there are no string theorists in non-elite institutions. Delhi University has a few, very few. This is in striking contrast with the US, where there are many groups in many universities, which gives the community great depth of research.

If I were to give Indian research a grade sheet, I’d say not bad but could do much better. There are 1.2 billion people in the country, so we should be producing commensurate output in research. We shouldn’t content ourselves by thinking we’re doing better than [South] Korea. Of course it is an unfair thing to ask for, but that should be the aim. For example, at TIFR, when we interview students for admission, we find that we usually have very few really good candidates. It’s not that they aren’t smart; people are smart everywhere. It’s just one reason: that the elementary school system in the country is abysmal. Most Indians come out of school unable to contribute meaningfully to any intellectual activity. Even Indian colleges have the same quality of output. The obvious thing is to make every school in India a reasonable school [laughs]. Such an obvious thing but we don’t do it.

Is there sufficient institutional and governmental support for researchers?

At the top levels, yes. I feel that places with the kind of rock-solid support that TIFR gives its faculty are few and far between. In the US many such places exist. But if you went to the UK, the only comparable places are perhaps Cambridge and Oxford. Whereas if you went to the second tier Durham University, you’ll see it’s not as good a place to be as TIFR. In fact, this is true for most universities around the world.

Institutions like TIFR, IIS, HRI and the National Centre for the Biological Sciences give good support and scientists should recognize this. There are few comparable places in the Third World. What we’re missing however is the depth. The US research community has got so good because of its depth. Genuine, exciting research is not done just in the Ivy League institutions. Even small places have a Nobel Laureate teaching there. So, India may have lots of universities but they are somehow not able to produce good work.

We’ve had a couple Indians already in what’s going to be three years of the Fundamental Physics Prizes – before you, there was Ashoke Sen. But in the Nobel Prizes in physics, we’ve had a stubborn no-show since Subramanyan Chandrasekhar won it in 1983. Why do you think that is?

There are two immediate responses. First is that, as I mentioned, India has an anomalously strong string theory presence. Why? I don’t know. India is especially strong with string theory. And the Fundamental Physics Prize Foundation has so far had some focus on this. The Nobel Prizes on the other hand require experimental verification of hypotheses. So, for as long as the Foundation has focused on the mathematics in physics, India has done well.

What are you going to do with your $100,000?

I haven’t seriously thought about it.

At the time of my interview, I had no idea he was about to win the Infosys Foundation Prize as well. It seems he’s in great demand! Good luck, Shiraz. 🙂