mathematical physics

You’re allowed to be interested in particle physics

This page appeared in The Hindu’s e-paper today.

I wrote the lead article, about why scientists are so interested in an elementary particle called the top quark. Long story short: the top quark is the heaviest elementary particle, and because all elementary particles get their masses by interacting with Higgs bosons, the top quark’s interaction is the strongest. This has piqued physicists’ interest because the Higgs boson’s own mass is peculiar: it’s more than expected and at the same time poised on the brink of a threshold beyond which our universe as we know it wouldn’t exist. To explain this brinkmanship, physicists are intently studying the top quark, including measuring its mass with more and more precision.

It’s all so fascinating. But I’m well aware that not many people are interested in this stuff. I wish they were and my reasons follow.

There exists a sufficiently healthy journalism of particle physics today. Most of it happens in Europe and the US, (i) where famous particle physics experiments are located, (ii) where there already exists an industry of good-quality science journalism, and (iii) where there are countries and/or governments that actually have the human resources, funds, and political will to fund the experiments (in many other places, including India, these resources don’t exist, rendering the matter of people contending with these experiments moot).

In this post, I’m using particle physics as itself as well as as a surrogate for other reputedly esoteric fields of study.

This journalism can be divided into three broad types: those with people, those concerned with spin-offs, and those without people. ‘Those with people’ refers to narratives about the theoretical and experimental physicists, engineers, allied staff, and administrators who support work on particle physics, their needs, challenges, and aspirations.

The meaning of ‘those concerned with spin-offs’ is obvious: these articles attempt to justify the money governments spend on particle physics projects by appealing to the technologies scientists develop in the course of particle-physics work. I’ve always found these to be apologist narratives erecting a bad expectation: that we shouldn’t undertake these projects if they don’t also produce valuable spin-off technologies. I suspect most particle physics experiments don’t because they are much smaller than the behemoth Large Hadron Collider and its ilk, which require more innovation across diverse fields.

‘Those without people’ are the rarest of the lot — narratives that focus on some finding or discussion in the particle physics community that is relatively unconcerned with the human experience of the natural universe (setting aside the philosophical point that the non-human details are being recounted by human narrators). These stories are about the material constituents of reality as we know it.

When I say I wish more people were interested in particle physics today, I wish they were interested in all these narratives, yet more so in narratives that aren’t centred on people.

Now, why should they be concerned? This is a difficult question to answer.

I’m concerned because I’m fascinated with the things around us we don’t fully understand but are trying to. It’s a way of exploring the unknown, of going on an adventure. There are many, many things in this world that people can be curious about. It’s possible there are more such things than there are people (again, setting aside the philosophical bases of these claims). But particle physics and some other areas — united by the extent to which they are written off as being esoteric — suffer from more than not having their fair share of patrons in the general (non-academic) population. Many people actively shun them, lose focus when reading about them, and at the same time do little to muster focus back. It has even become okay for them to say they understood nothing of some (well-articulated) article and not expect to have their statement judged adversely.

I understand why narratives with people in them are easier to understand, to connect with, but none of the implicated psychological, biological, and anthropological mechanisms also encourage us to reject narratives and experiences without people. In other words, there may have been evolutionary advantages to finding out about other people but there have been no disadvantages attached to engaging with stories that aren’t about other people.

Next, I have met more than my fair share of people that flinched away from the suggestion of mathematics or physics, even when someone offered to guide them through understanding these topics. I’m also aware researchers have documented this tendency and are attempting to distil insights that could help improve the teaching and the communication of these subjects. Personally I don’t know how to deal with these people because I don’t know the shape of the barrier in their minds I need to surmount. I may be trying to vault over a high wall by simplifying a concept to its barest features when in fact the barrier is a low-walled labyrinth.

Third and last, let me do unto this post what I’m asking of people everywhere, and look past the people: why should we be interested in particle physics? It has nothing to offer for our day-to-day experiences. Its findings can seem totally self-absorbed, supporting researchers and their careers, helping them win famous but otherwise generally unattainable awards, and sustaining discoveries into which political leaders and government officials occasionally dip their beaks to claim labels like “scientific superpower”. But the mistake here is not the existence of particle physics itself so much as the people-centric lens through which we insist it must be seen. It’s not that we should be interested in particle physics; it’s that we can.

Particle physics exists because some people are interested in it. If you are unhappy that our government spends too much on it, let’s talk about our national R&D expenditure priorities and what the practice, and practitioners, of particle physics can do to support other research pursuits and give back to various constituencies. The pursuit of one’s interests can’t be the problem (within reasonable limits, of course).

More importantly, being interested in particle physics and in fact many other branches of science shouldn’t have to be justified at every turn for three reasons: reality isn’t restricted to people, people are shaped by their realities, and our destiny as humans. On the first two counts: when we choose to restrict ourselves to our lives and our welfare, we also choose to never learn about what, say, gravitational waves, dark matter, and nucleosynthesis are (unless these terms turn up in an exam we need to pass). Yet all these things played a part in bringing about the existence of Earth and its suitability for particular forms of life, and among people particular ways of life.

The rocks and metals that gave rise to waves of human civilisation were created in the bellies of stars. We needed to know our own star as well as we do — which still isn’t much — to help build machines that can use its energy to supply electric power. Countries and cultures that support the education and employment of people who made it a point to learn the underlying science thus come out on top. Knowing different things is a way to future-proof ourselves.

Further, climate change is evidence humans are a planetary species, and soon it will be interplanetary. Our own migrations will force us to understand, eventually intuitively, the peculiarities of gravity, the vagaries of space, and (what is today called) mathematical physics. But even before such compulsions arise, it remains what we know is what we needn’t be afraid of, or at least know how to be afraid of. 😀

Just as well, learning, knowing, and understanding the physical universe is the foundation we need to imagine (or reimagine) futures better than the ones ordained for us by our myopic leaders. In this context, I recommend Shreya Dasgupta’s ‘Imagined Tomorrow’ podcast series, where she considers hypothetical future Indias in which medicines are tailor-made for individuals, where antibiotics don’t exist because they’re not required, where clean air is only available to breathe inside city-sized domes, and where courtrooms use AI — and the paths we can take to get there.

Similarly, with particle physics in mind, we could also consider cheap access to quantum computers, lasers that remove infections from flesh and tumours from tissue in a jiffy, and communications satellites that reduce bandwidth costs so much that we can take virtual education, telemedicine, and remote surgeries for granted. I’m not talking about these technologies as spin-offs, to be clear; I mean technologies born of our knowledge of particle (and other) physics.

At the biggest scale, of course, understanding the way nature works is how we can understand the ways in which the universe’s physical reality can or can’t affect us, in turn leading the way to understanding ourselves better and helping us shape more meaningful aspirations for our species. The more well-informed any decision is, the more rational it will be. Granted, the rationality of most of our decisions is currently only tenuously informed by particle physics, but consider if the inverse could be true: what decisions are we not making as well as we could if we cast our epistemic nets wider, including physics, biology, mathematics, etc.?

Consider, even beyond all this, the awe astronauts who have gone to Earth orbit and beyond have reported experiencing when they first saw our planet from space, and the immeasurable loneliness surrounding it. There are problems with pronouncements that we should be united in all our efforts on Earth because, from space, we are all we have (especially when the country to which most of these astronauts belong condones a genocide). Fortunately, that awe is not the preserve of spacefaring astronauts. The moment we understood the laws of physics and the elementary constituents of our universe, we (at least the atheists among us) may have realised there is no centre of the universe. In fact, there is everything except a centre. How grateful I am for that. For added measure, awe is also good for the mind.

It might seem like a terrible cliché to quote Oscar Wilde here — “We are all in the gutter, but some of us are looking at the stars” — but it’s a cliché precisely because we have often wanted to be able to dream, to have the simple act of such dreaming contain all the profundity we know we squander when we live petty, uncurious lives. Then again, space is not simply an escape from the traps of human foibles. Explorations of the great unknown that includes the cosmos, the subatomic realm, quantum phenomena, dark energy, and so on are part of our destiny because they are the least like us. They show us what else is out there, and thus what else is possible.

If you’re not interested in particle physics, that’s fine. But remember that you can be.

Featured image: An example of simulated data as might be observed at a particle detector on the Large Hadron Collider. Here, following a collision of two protons, a Higgs boson is produced that decays into two jets of hadrons and two electrons. The lines represent the possible paths of particles produced by the proton-proton collision in the detector while the energy these particles deposit is shown in blue. Caption and credit: Lucas Taylor/CERN, CC BY-SA 3.0.

The Kapitza pendulum

Rarely does a ‘problem’ come along that makes you think more than casually about the question of mathematics’s reality, and problems in mathematical physics are full of them. I came across one such problem for the first time yesterday, and given its simplicity, thought I should make note of it.

I spotted a paper yesterday with the title ‘The Inverted Pendulum as a Classical Analog of the EFT Paradigm’. I’ve never understood the contents of such papers without assistance from a physicist, but I like to go through them in case a familiar idea or name jumps up that warrants a more thorough follow-up or I do understand something and that helps me understand something else even better.

In this instance, the latter happened, and I discovered the Kapitza pendulum. In 1908, a British mathematician named Andrew Stephenson described the problem but wasn’t able to explain it. That happened at the hands of the Russian scientist Pyotr Kapitsa, for whom the pendulum is named, who worked it out in the 1950s.

You are familiar with the conventional pendulum:

Here, the swinging bob is completely stable when it is suspended directly below the pivot, and is unmoving. The Kapitza pendulum is a conventional pendulum whose pivot is rapidly moved up and down. This gives rise to an unusual stable state: when the bob is directly above the pivot! Here’s a demonstration:

As you can see, the stable state isn’t a perfect one: the bob still vibrates on either side of a point above the pivot, yet it doesn’t move beyond a particular distance, much less drop downward under the force of gravity. If you push the bob just a little, it swings across a greater distance for some time before returning to the narrow range. How does this behaviour arise?

I’m fascinated by the question of the character of mathematics because of its ability to make predictions about reality – to build a bridge between something that we know to be physically true (like how a conventional pendulum would swing when dropped from a certain height, etc.) and something that we don’t, at least not yet.

If this sounds wrong, please make sure you’re thinking of the very first instantiation of some system whose behaviour is defying your expectations, like the very first Kapitza pendulum. How do you know what you’re looking at isn’t due to a flaw in the system or some other confounding factor? A Kapitza pendulum is relatively simple to build, so one way out of this question is to build multiple units and check if the same behaviour exists in all of them. If you can be reasonably certain that the same flaw is unlikely to manifest in all of them, you’ll know that you’re observing an implicit, but non-intuitive, property of the system.

But in some cases, building multiple units isn’t an option – such as a particle-smasher like the Large Hadron Collider or the observation of a gravitational wave from outer space. Instead, researchers use mathematics to check the likelihood of alternate possibilities and to explain something new in terms of something we already know.

Many theoretical physicists have even articulated that while string theory lacks experimental proof, it has as many exponents as it does because of its mathematical robustness and the deep connections they have found between its precepts and other, distant branches of physics.

In the case of the Kapitza pendulum, based on Newton’s laws and the principles of simple harmonic motion, it is possible to elucidate the rules, or equations, that govern the motion of the bob under the influence of its mass, the length of the rod connecting the bob to the pivot, the angle between the line straight up from the pivot and the rod (θ), acceleration due to gravity, the length of the pivot’s up-down motion, and how fast this motion happens (i.e. its frequency).

From this, we can derive an equation that relates θ to the distance of the up-down motion, the frequency, and the length of the rod. Finally, plotting this equation on a graph, with θ on one axis and time on the other, and keeping the values of the other variables fixed, we have our answer:

When the value of θ is 0º, the bob is pointing straight up. When θ = 90º, the bob is pointing sideways and continues to fall down, to become a conventional pendulum, under the influence of gravity. But when the frequency is increased from 10 arbitrary units in this case to 200 units, the setup becomes a Kapitza pendulum as the value of θ keeps shifting but only between 6º on one side and some 3º on the other.

The thing I’m curious about here is whether mathematics is purely descriptive or if it’s real in the way a book, a chair or a planet is real. Either way, this ‘problem’ should remind us of the place and importance of mathematics in modern life – by virtue of the fact that it opens paths to understanding, and then building on, parts of reality that experiences based on our senses alone can’t access.

Featured image: A portrait of Pyotr Kapitsa (left) in conversation with the chemist Nikolai Semyonov, by Boris Kustodiev, 1921. Credit: Kapitsa Collection, public domain.

The problem with rooting for science

The idea that trusting in science involves a lot of faith, instead of reason, is lost on most people. More often than not, as a science journalist, I encounter faith through extreme examples – such as the Bloch sphere (used to represent the state of a qubit) or wave functions (‘mathematical objects’ used to understand the evolution of certain simple quantum systems). These and other similar concepts require years of training in physics and mathematics to understand. At the same time, science writers are often confronted with the challenge of making these concepts sensible to an audience that seldom has this training.

More importantly, how are science writers to understand them? They don’t. Instead, they implicitly trust scientists they’re talking to to make sense. If I know that a black hole curves spacetime to such an extent that pairs of virtual particles created near its surface are torn apart – one particle entering the black hole never to exit and the other sent off into space – it’s not because I’m familiar with the work of Stephen Hawking. It’s because I read his books, read some blogs and scientific papers, spoke to physicists, and decided to trust them all. Every science journalist, in fact, has a set of sources they’re likely to trust over others. I even place my faith in some people over others, based on factors like personal character, past record, transparency, reflexivity, etc., so that what they produce I take only with the smallest pinch of salt, and build on their findings to develop my own. And this way, I’m already creating an interface between science and society – by matching scientific knowledge with the socially developed markers of reliability.

I choose to trust those people, processes and institutions that display these markers. I call this an act of faith for two reasons: 1) it’s an empirical method, so to speak; there is no proof in theory that such ‘matching’ will always work; and 2) I believe it’s instructive to think of this relationship as being mediated by faith if only to amplify its anti-polarity with reason. Most of us understand science through faith, not reason. Even scientists who are experts on one thing take the word of scientists on completely different things, instead of trying to study those things themselves (see ad verecundiam fallacy).

Sometimes, such faith is (mostly) harmless, such as in the ‘extreme’ cases of the Bloch sphere and the wave function. It is both inexact and incomplete to think that quantum superposition means an object is in two states at once. The human brain hasn’t evolved to cognate superposition exactly; this is why physicists use the language of mathematics to make sense of this strange existential phenomenon. The problem – i.e. the inexactitude and the incompleteness – arises when a communicator translates the mathematics to a metaphor. Equally importantly, physicists are describing whereas the rest of us are thinking. There is a crucial difference between these activities that illustrates, among other things, the fundamental incompatibility between scientific research and science communication that communicators must first surmount.

As physicists over the past three or four centuries have relied increasingly on mathematics rather than the word to describe the world, physics, like mathematics itself, has made a “retreat from the word,” as literary scholar George Steiner put it. In a 1961 Kenyon Review article, Steiner wrote, “It is, on the whole, true to say that until the seventeenth century the predominant bias and content of the natural sciences were descriptive.” Mathematics used to be “anchored to the material conditions of experience,” and so was largely susceptible to being expressed in ordinary language. But this changed with the advances of modern mathematicians such as Descartes, Newton, and Leibniz, whose work in geometry, algebra, and calculus helped to distance mathematical notation from ordinary language, such that the history of how mathematics is expressed has become “one of progressive untranslatability.” It is easier to translate between Chinese and English — both express human experience, the vast majority of which is shared — than it is to translate advanced mathematics into a spoken language, because the world that mathematics expresses is theoretical and for the most part not available to our lived experience.
Samuel Matlack, ‘Quantum Poetics’, The New Atlantic, 2017

However, the faith becomes more harmful the further we move away from the ‘extreme’ examples – of things we’re unlikely to stumble on in our daily lives – and towards more commonplace ideas, such as ‘how vaccines work’ or ‘why GM foods are not inherently bad’. The harm emerges from the assumption that we think we know something when in fact we’re in denial about how it is that we know that thing. Many of us think it’s reason; most of the time it’s faith. Remember when, in Friends, Monica Geller and Chandler Bing ask David the Scientist Guy how airplanes fly, and David says it has to do with Bernoulli’s principle and Newton’s third law? Monica then turns to Chandler with a knowing look and says, “See?!” To which Chandler says, “Yeah, that’s the same as ‘it has something to do with wind’!”

The harm is to root for science, to endorse the scientific enterprise and vest our faith in its fruits, without really understanding how these fruits are produced. Such understanding is important for two reasons.

First, if we trust scientists, instead of presuming to know or actually knowing that we can vouch for their work. It would be vacuous to claim science is superior in any way to another enterprise that demands our faith when science itself also receives our faith. Perhaps more fundamentally, we like to believe that science is trustworthy because it is evidence-based and it is tested – but the COVID-19 pandemic should have clarified, if it hasn’t already, the continuous (as opposed to discrete) nature of scientific evidence, especially if we also acknowledge that scientific progress is almost always incremental. Evidence can be singular and thus clear – like a new avian species, graphene layers superconducting electrons or tuned lasers cooling down atoms – or it can be necessary but insufficient, and therefore on a slippery slope – such as repeated genetic components in viral RNA, a cigar-shaped asteroid or water shortage in the time of climate change.

Physicists working with giant machines to spot new particles and reactions – all of which are detected indirectly, through their imprints on other well-understood phenomena – have two important thresholds for the reliability of their findings: if the chance of X (say, “spotting a particle of energy 100 GeV”) being false is 0.27%, it’s good enough to be evidence; if the chance of X being false is 0.00006%, then it’s a discovery (i.e., “we have found the particle”). But at what point can we be sure that we’ve indeed found the particle we were looking for if the chance of being false will never reach 0%? One way, for physicists specifically, is to combine the experiment’s results with what they expect to happen according to theory; if the two match, it’s okay to think that even a less reliable result will likely be borne out. Another possibility (in the line of Karl Popper’s philosophy) is that a result expected to be true, and is subsequently found to be true, is true until we have evidence to the contrary. But as suitable as this answer may be, it still doesn’t neatly fit the binary ‘yes’/’no’ we’re used to, and which we often expect from scientific endeavours as well (see experience v. reality).

(Minor detour: While rational solutions are ideally refutable, faith-based solutions are not. Instead, the simplest way to reject their validity is to use extra-scientific methods, and more broadly deny them power. For example, if two people were offering me drugs to suppress the pain of a headache, I would trust the one who has a state-sanctioned license to practice medicine and is likely to lose that license, even temporarily, if his prescription is found to have been mistaken – that is, by asserting the doctor as the subject of democratic power. Axiomatically, if I know that Crocin helps manage headaches, it’s because, first, I trusted the doctor who prescribed it and, second, Crocin has helped me multiple times before, so empirical experience is on my side.)

Second, if we don’t know how science works, we become vulnerable to believing pseudoscience to be science as long as the two share some superficial characteristics, like, say, the presence and frequency of jargon or a claim’s originator being affiliated with a ‘top’ institute. The authors of a scientific paper to be published in a forthcoming edition of the Journal of Experimental Social Psychology write:

We identify two critical determinants of vulnerability to pseudoscience. First, participants who trust science are more likely to believe and disseminate false claims that contain scientific references than false claims that do not. Second, reminding participants of the value of critical evaluation reduces belief in false claims, whereas reminders of the value of trusting science do not.

(Caveats: 1. We could apply the point of this post to this study itself; 2. I haven’t checked the study’s methods and results with an independent expert, and I’m also mindful that this is psychology research and that its conclusions should be taken with salt until independent scientists have successfully replicated them.)

Later from the same paper:

Our four experiments and meta-analysis demonstrated that people, and in particular people with higher trust in science (Experiments 1-3), are vulnerable to misinformation that contains pseudoscientific content. Among participants who reported high trust in science, the mere presence of scientific labels in the article facilitated belief in the misinformation and increased the probability of dissemination. Thus, this research highlights that trust in science ironically increases vulnerability to pseudoscience, a finding that conflicts with campaigns that promote broad trust in science as an antidote to misinformation but does not conflict with efforts to install trust in conclusions about the specific science about COVID-19 or climate change.
In terms of the process, the findings of Experiments 1-3 may reflect a form of heuristic processing. Complex topics such as the origins of a virus or potential harms of GMOs to human health include information that is difficult for a lay audience to comprehend, and requires acquiring background knowledge when reading news. For most participants, seeing scientists as the source of the information may act as an expertise cue in some conditions, although source cues are well known to also be processed systematically. However, when participants have higher levels of methodological literacy, they may be more able to bring relevant knowledge to bear and scrutinise the misinformation. The consistent negative association between methodological literacy and both belief and dissemination across Experiments 1-3 suggests that one antidote to the influence of pseudoscience is methodological literacy. The meta-analysis supports this.

So rooting for science per se is not just not enough, it could be harmful vis-à-vis the public support for science itself. For example (and without taking names), in response to right-wing propaganda related to India’s COVID-19 epidemic, quite a few videos produced by YouTube ‘stars’ have advanced dubious claims. They’re not dubious at first glance, if also because they purport to counter pseudoscientific claims with scientific knowledge, but they are – either for insisting a measure of certainty in the results that neither exist nor are achievable, or for making pseudoscientific claims of their own, just wrapped up in technical lingo so they’re more palatable to those supporting science over critical thinking. Some of these YouTubers, and in fact writers, podcasters, etc., are even blissfully unaware of how wrong they often are. (At least one of them was also reluctant to edit a ‘finished’ video to make it less sensational despite repeated requests.)

Now, where do these ideas leave (other) science communicators? In attempting to bridge a nearly unbridgeable gap, are we doomed to swing only between most and least unsuccessful? I personally think that this problem, such as it is, is comparable to Zeno’s arrow paradox. To use Wikipedia’s words:

He states that in any one (duration-less) instant of time, the arrow is neither moving to where it is, nor to where it is not. It cannot move to where it is not, because no time elapses for it to move there; it cannot move to where it is, because it is already there. In other words, at every instant of time there is no motion occurring. If everything is motionless at every instant, and time is entirely composed of instants, then motion is impossible.

To ‘break’ the paradox, we need to identify and discard one or more primitive assumptions. In the arrow paradox, for example, one could argue that time is not composed of a stream of “duration-less” instants, that each instant – no matter how small – encompasses a vanishingly short but not nonexistent passage of time. With popular science communication (in the limited context of translating something that is untranslatable sans inexactitude and/or incompleteness), I’d contend the following:

Awareness: ‘Knowing’ and ‘knowing of’ are significantly different and, I hope, self-explanatory also. Example: I’m not fluent with the physics of cryogenic engines but I’m aware that they’re desirable because liquefied hydrogen has the highest specific impulse of all rocket fuels.
Context: As I’ve written before, a unit of scientific knowledge that exists in relation to other units of scientific knowledge is a different object from the same unit of scientific knowledge existing in relation to society.
Abstraction: 1. perfect can be the enemy of the good, and imperfect knowledge of an object – especially a complicated compound one – can still be useful; 2. when multiple components come together to form a larger entity, the entity can exhibit some emergent properties that one can’t derive entirely from the properties of the individual components. Example: one doesn’t have to understand semiconductor physics to understand what a computer does.

An introduction to physics that contains no equations is like an introduction to French that contains no French words, but tries instead to capture the essence of the language by discussing it in English. Of course, popular writers on physics must abide by that constraint because they are writing for mathematical illiterates, like me, who wouldn’t be able to understand the equations. (Sometimes I browse math articles in Wikipedia simply to immerse myself in their majestic incomprehensibility, like visiting a foreign planet.)
Such books don’t teach physical truths; what they teach is that physical truth is knowable in principle, because physicists know it. Ironically, this means that a layperson in science is in basically the same position as a layperson in religion.
Adam Kirsch, ‘The Ontology of Pop Physics’, Tablet Magazine, 2020

But by offering these reasons, I don’t intend to over-qualify science communication – i.e. claim that, given enough time and/or other resources, a suitably skilled science communicator will be able to produce a non-mathematical description of, say, quantum superposition that is comprehensible, exact and complete. Instead, it may be useful for communicators to acknowledge that there is an immutable gap between common English (the language of modern science) and mathematics, beyond which scientific expertise is unavoidable – in much the same way communicators must insist that the farther the expert strays into the realm of communication, the closer they’re bound to get to a boundary beyond which they must defer to the communicator.