Categories

## Time and the pandemic

There is this idea in physics that the fundamental laws of nature apply the same way for processes moving both forwards and backwards in time. So you can’t actually measure the passage of time by studying these processes. Where does our sense of time, rather the passage of time, come from then? How do we get to tell that the past and future are two different things, and that time flows from the former to the latter?

We sense time because things change. Clock time is commonly understood to be a way to keep track of when and how often things change but in physics, time is not the master: change doesn’t arise because of time but time arises because of change. So time manifests in the laws of nature through things that change in time. One of the simplest such things is entropy. Specifically, the second law of thermodynamics states that as time moves forward, the entropy of an isolated system cannot decrease. Entropy thus describes an arrow of time.

This is precisely what the pandemic is refusing to do, at least as seen through windows set at the very back of a newsroom. Many reporters writing about the coronavirus may have the luxury of discovering change, and therefore the forward march of time itself, but for someone who is somewhat zoomed out – watching the proceedings from a distance, as it were – the pandemic has only suffused the news cycle with more and more copies of itself, like the causative virus itself.

It seems to me as if time has stilled. I have become numb to news about the virus, which I suspect is a coping mechanism, like a layer of armour inserted between a world relentlessly pelting me with bad news and my psyche itself. But the flip side of this protection is an inability to sense the passage of time as well as I was able before.

My senses are alert to mistakes of fact, as well as mostly of argument, that reporters make when reporting on the coronavirus, and of course to opportunities to improve sentence construction, structure, flow, etc. But otherwise, and thanks in fact to my limited engagement with this topic, it feels as if I wake up every morning, my fingers groaning at the prospect of typing the words “lockdown”, “coronavirus”, “COVID-19”, “herd immunity” and whatever else1. And since this is what I feel every morning, there is no sense of change. And without change, there is no time.

1. I mean no offence to those suffering the pandemic’s, and the lockdown’s, brutal health, economic, social, cultural and political consequences.

I would desperately like to lose my armour. The bad news will never stop coming but I would still like to get back to bad news that I got into journalism to cover, the bad news that I know what to do about… to how things were before, I suppose.

Oh, I’m aware of how illogical this line of introspection is, yet it persists! I believe one reason is that the pandemic is a passing cloud. It leapt out of the horizon and loomed suddenly over all of us, over the whole world; its pall is bleak but none of us doubts that it will also pass. The pandemic will end – everybody knows this, and this is perhaps also why the growing desperation for it to dissipate doesn’t feel misplaced, or unjustified. It is a cloud, and like all clouds, it must go away, and therefrom arises the frustration as well: if it can go away, why won’t it?

Is it true that everything that will last for a long time also build up over a long time? Climate change, for example, doesn’t – almost can’t – have a single onset event. It builds and builds all around us, its effects creeping up on us. With each passing day of inaction, there is even less that we can do than before to stop it; in fact, so many opportunities have been squandered or stolen by bad actors that all we have left to do is reduce consumption and lower carbon emissions. So with each passing day, the planet visits us with more reminders of how we have changed it, and in fact may never have it back to the way it once was.

Almost as if climate change happened so slowly, on the human scale at least, that it managed to weave itself into our sense of time, not casting a shadow on the clock as much as becoming a part of the clock itself. As humankind’s grandest challenge as yet, one that we may never fully surmount, climate change doesn’t arise because of time but time arises because of climate change. Perhaps speed and surprise is the sacrifice that time demands of that which aspires to longevity.

The pandemic, on the other hand, likely had a single onset… right? At least it seems so until you realise the pandemic is in fact the tip of the proverbial iceberg – the thing jutting above the waterline, better yet the tip of the volcano. There is a complicated mess brewing underground, and out of sight, to which we have all contributed. One day the volcano shoots up, plastering its surroundings with lava and shooting smoke and soot kilometres into the air. For a time, the skies are a nuclear-winter grey and the Sun is blotted out. To consider at this time that we could stave off all future eruptions by pouring tonnes of concrete into the smouldering caldera would be folly. The pandemic, like magma, like the truth itself, will out. So while the nimbuses of each pandemic may pass, all the storm’s ingredients will persist.

I really hope the world, and I do mean the world, will heed this lesson as the novel coronavirus’s most important, if only because our sense of time and our expectations of what the passage of time could bring need to encompass the things that cause pandemics as much as they have come to encompass the things that cause Earth’s climate to change. We’ve become used to thinking about this outbreak, and likely the ones before it, as transitory events that begin and end – but really, wrapped up in our unrelenting yearning for the pandemic to pass is a conviction that the virus is a short-lived, sublunary creature. But the virus is eternal, and so our response to it must also transform from the mortal to the immortal.

Then again, how I wish my mind submitted, that too just this once, to logic’s will sans resistance. No; it yearns still for the pandemic to end and for ‘normal’ to recommence, for time to flow as it once did, with the promise of bringing something new to the threshold of my consciousness every morning. I sense there is a line here between the long- and the short-term, between the individual and the collective, and ultimately between the decision to change myself and the decision to wait for others before I do.

I think, as usual, time will tell. Heh.

Categories

## Amorphous topological insulators

A topological insulator is a material that conducts electricity only on its surface. Everything below, through the bulk of the material, is an insulator. An overly simplified way to understand this is in terms of the energies and momenta of the electrons in the material.

The electrons that an atom can spare to share with other atoms – and so form chemical bonds – are called valence electrons. In a metal, these electrons can have various momenta, but unless they have a sufficient amount of energy, they’re going to stay near their host atoms – i.e. within the valence band. If they do have energies over a certain threshold, then they can graduate from the valence band to the conduction band, flowing throw the metal and conducting electricity.

In a topological insulator, the energy gap between the valence band and the conduction band is occupied by certain ‘states’ that represent the material’s surface. The electrons in these states aren’t part of the valence band but they’re not part of the conduction band either, and can’t flow throw the entire bulk.

The electrons within these states, i.e. on the surface, display a unique property. Their spins (on their own axis) are coupled strongly with their motion around their host atoms. As a result, theirs spins become aligned perpendicularly to their momentum, the direction in which they can carry electric charge. Such coupling staves off an energy-dissipation process called Umklapp scattering, allowing them to conduct electricity. Detailed observations have shown that the spin-momentum coupling necessary to achieve this is present only in a few-nanometre-thick layer on the surface.

If you’re talking about this with a physicist, she will likely tell you at this point about time-reversal symmetry. It is a symmetry of nature that is said to (usually) ‘protect’ a topological insulator’s unique surface states.

There are many fundamental symmetries in nature. In particle physics, if a force acts similarly on left- and right-handed particles, it is said to preserve parity (P) symmetry. If the dynamics of the force are similar when it is acting against positively and negatively charged particles, then charge conjugation (C) symmetry is said to be preserved. Now, if you videotaped the force acting on a particle and then played the recording backwards, the force must be seen to be acting the way it would if the video was played the other way. At least if it did it would be preserving time-reversal (T) symmetry.

Physicists have known some phenomena that break C and P symmetry simultaneously. T symmetry is broken continuously by the second law of thermodynamics: if you videographed the entropy of a universe and then played it backwards, entropy will be seen to be reducing. However, CPT symmetries – all together – cannot be broken (we think).

Anyway, the surface states of a topological insulator are protected by T symmetry. This is because the electrons’ wave-functions, the mathematical equations that describe some of the particles’ properties, do not ‘flip’ going backwards in time. As a result, a topological insulator cannot lose its surface states unless it undergoes some sort of transformation that breaks time-reversal symmetry. (One example of such a transformation is a phase transition.)

This laboured foreword is necessary – at least IMO – to understand what it is that scientists look for when they’re looking for topological insulators among all the materials that we have been, and will be able, to synthesise. It seems they’re looking for materials that have surface states, with spin-momentum coupling, that are protected by T symmetry.

Physicists from the Indian Institute of Science, Bengaluru, have found that topological insulators needn’t always be crystals – as has been thought. Instead, using a computer simulation, Adhip Agarwala and Vijay Shenoy, of the institute’s physics department, have shown that a kind of glass also behaves as a topological insulator.

The band theory described earlier is usually described with crystals in mind, wherein the material’s atoms are arranged in a well-defined pattern. This allows physicists to determine, with some amount of certainty, as to how the atoms’ electrons interact and give rise to the material’s topological states. In an amorphous material like glass, on the other hand, the constituent atoms are arranged randomly. How then can something as well-organised as a surface with spin-momentum coupling be possible on it?

As Michael Schirber wrote in Physics magazine,

In their study, [Agarwala and Shenoy] assume a box with a large number of lattice sites arranged randomly. Each site can host electrons in one of several energy levels, and electrons can hop between neighboring sites. The authors tuned parameters, such as the lattice density and the spacing of energy levels, and found that the modeled materials could exhibit symmetry-protected surface currents in certain cases. The results suggest that topological insulators could be made by creating glasses with strong spin-orbit coupling or by randomly placing atoms of other elements inside a normal insulator.

The duo’s paper was published in the journal Physical Review Letters on June 8. The arXiv preprint is available to read here. The latter concludes,

The possibility of topological phases in a completely random system opens up several avenues both from experimental and theoretical perspectives. Our results suggest some new routes to the laboratory realization of topological phases. First, two dimensional systems can be made by choosing an insulating surface on which suitable [atoms or molecules] with appropriate orbitals are deposited at random (note that this process will require far less control than conventional layered materials). The electronic states of these motifs will then [interact in a certain way] to produce the required topological phase. Second is the possibility of creating three dimensional systems starting from a suitable large band gap trivial insulator. The idea then is to place “impurity atoms”, again with suitable orbitals and “friendly” chemistry with the host… The [interaction] of the impurity orbitals would again produce a topological insulating state in the impurity bands under favourable conditions.

Agarwala/Shenoy also suggest that “In realistic systems the temperature scales over which one will see the topological physics … may be low”, although this is not unusual. However, they don’t suggest which amorphous materials could be suitable topological insulators.

Thanks to penflip.com and its nonexistent autosave function, I had to write the first half of this article twice. Not the sort of thing I can forgive easily, less so since I’m loving everything else about it.