A screenshot from the film 'The Cloverfield Paradox' (2018). Source: Netflix

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 = × 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. 🙂