Monthly Archives: November 2016

Consistency in the Hierarchy

When writing on this blog, I try to share nuggets here and there of phenomena, experiments, sociological observations and other peoples’ opinions I find illuminating. Unfortunately, this format can leave readers wanting when it comes to some sort of coherent message. Precisely because of this, I would like to revisit a few blog posts I’ve written in the past and highlight the common vein running through them.

Condensed matter physicists of the last couple generations have grown up ingrained with the idea that “More is Different”, a concept first coherently put forth by P. W. Anderson and carried further by others. Most discussions of these ideas tend to concentrate on the notion that there is a hierarchy of disciplines where each discipline is not logically dependent on the one beneath it. For instance, in solid state physics, we do not need to start out at the level of quarks and build up from there to obtain many properties of matter. More profoundly, one can observe phenomena which distinctly arise in the context of condensed matter physics, such as superconductivity, the quantum Hall effect and ferromagnetism that one wouldn’t necessarily predict by just studying particle physics.

While I have no objection to these claims (and actually agree with them quite strongly), it seems to me that one rather (almost trivial) fact is infrequently mentioned when these concepts are discussed. That is the role of consistency.

While it is true that one does not necessarily require the lower level theory to describe the theories at the higher level, these theories do need to be consistent with each other. This is why, after the publication of BCS theory, there were a slew of theoretical papers that tried to come to terms with various aspects of the theory (such as the approximation of particle number non-conservation and features associated with gauge invariance (pdf!)).

This requirement of consistency is what makes concepts like the Bohr-van Leeuwen theorem and Gibbs paradox so important. They bridge two levels of the “More is Different” hierarchy, exposing inconsistencies between the higher level theory (classical mechanics) and the lower level (the micro realm).

In the case of the Bohr-van Leeuwen theorem, it shows that classical mechanics, when applied to the microscopic scale, is not consistent with the observation of ferromagnetism. In the Gibbs paradox case, classical mechanics, when not taking into consideration particle indistinguishability (a quantum mechanical concept), is inconsistent with the idea the entropy must remain the same when dividing a gas tank into two equal partitions.

Today, we have the issue that ideas from the micro realm (quantum mechanics) appear to be inconsistent with our ideas on the macroscopic scale. This is why matter interference experiments are still carried out in the present time. It is imperative to know why it is possible for a C60 molecule (or a 10,000 amu molecule) to be described with a single wavefunction in a Schrodinger-like scheme, whereas this seems implausible for, say, a cat. There does again appear to be some inconsistency here, though there are some (but no consensus) frameworks, like decoherence, to get around this. I also can’t help but mention that non-locality, à la Bell, also seems totally at odds with one’s intuition on the macro-scale.

What I want to stress is that the inconsistency theorems (or paradoxes) contained seeds of some of the most important theoretical advances in physics. This is itself not a radical concept, but it often gets neglected when a generation grows up with a deep-rooted “More is Different” scientific outlook. We sometimes forget to look for concepts that bridge disparate levels of the hierarchy and subsequently look for inconsistencies between them.

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The Struggle

Haruki Murakami, the world-renowned Japanese novelist, has garnered a large following because one can easily relate to his protagonists. I have been reading his novels for around ten years now, and recently picked up his unique memoir What I Talk About When I Talk About Running. It is a quirky book, at once about his marathon and ultra-marathon running endeavors, his writing struggles, and how the two are interwoven.

To me, the most inspirational part of this book lies in how through mundaneness and mediocrity springs a rather unique exceptionalism. Murakami is an outstanding writer, but his talents have a limit, and he is honest about this. Most of the book is about struggling, with running and with writing. When I reflect on the book, the image I have in my mind is of a  truck wheel, bearing huge weight, going around and around, yet somehow trudging forward.

Here is a passage from the book I particularly enjoyed, which is applicable in many contexts:

…writers who aren’t blessed with much talent — those who barely make the grade — need to build up their strength at their own expense. They have to train themselves to improve their focus, to increase their endurance. To a certain extent, they’re forced to make these qualities stand in for talent. And while they’re getting by on these, they may actually discover real, hidden talent within them. They’re sweating, digging out a hole at their feet with a shovel, when they run across a deep, secret water vein. It’s a lucky thing, but what made this good fortune possible was all the training they did that gave them the strength to keep on digging. I imagine that late-blooming writers have all gone through a similar process.

Naturally, there are people in the world (only a handful, for sure) blessed with enormous talent that, from beginning to end, doesn’t fade, and whose works are always of the highest quality. These fortunate few have a water vein that never dries up, no matter how much they tap into it. For literature, this is something to be thankful for. It’s hard to imagine the history of literature without such figures as Shakespeare, Balzac and Dickens. But the giants are, in the end, giants — exceptional, legendary figures. The remaining majority of writers who can’t reach such heights (including me, of course) have to supplement what’s missing from their store of talent through whatever means they can. Otherwise it’s impossible for them to keep on writing novels of any value. The methods and directions a writer takes in order to supplement himself becomes part of that writer’s individuality, what makes him special.

Most of what I know about writing I’ve learned through running everyday. These are practical, physical lessons. How much can I push myself? How much rest is appropriate — and how much is too much? How far can I take something and still keep it decent and consistent? When does it become narrow-minded and inflexible? How much should I be aware of the world outside, and how much should I  focus on my inner world? To what extent should I be confident in my abilities, and when should I start doubting myself? I know that if I hadn’t become a long-distance runner when I became a novelist, my work would have been vastly different. How different? Hard to say, but something would have definitely been different.

The book ends with what Murakami hopes his tombstone will read:

Haruki Murakami

1949-20**

Writer (and Runner)

At Least He Never Walked

Kapitza-Dirac Effect

We are all familiar with the fact that light can diffract from two (or multiple) slits in a Young-type experiment. After the advent of quantum mechanics and de Broglie’s wave description of matter, it was shown by Davisson and Germer that electrons could be diffracted by a crystal. In 1927, P. Kapitza and P. Dirac proposed that it should in principle be possible for electrons to be diffracted by standing waves of light, in effect using light as a diffraction grating.

In this scheme, the electrons would interact with light through the ponderomotive potential. If you’re not familiar with the ponderomotive potential, you wouldn’t be the only one — this is something I was totally ignorant of until reading about the Kapitza-Dirac effect. In 1995, Anton Zeilinger and co-workers were able to demonstrate the Kapitza-Dirac effect with atoms, obtaining a beautiful diffraction pattern in the process which you can take a look at in this paper. It probably took so long for this effect to be observed because it required the use of high-powered lasers.

Later, in 2001, this experiment was pushed a little further and an electron-beam was used to demonstrate the effect (as opposed to atoms), as Dirac and Kapitza originally proposed. Indeed, again a diffraction pattern was observed. The article is linked here and I reproduce the main result below:

dirac-kaptiza

(Top) The interference pattern observed in the presence of a standing light wave. (Bottom) The profile of the electron beam in the absence of the light wave.

Even though this experiment is conceptually quite simple, these basic quantum phenomena still manage to elicit awe (at least from me!).

Diversity in and of Physics

When someone refers to a physicist from the early twentieth century, what kind of person do you imagine? Most people will think of an Einstein-like figure, but most likely, one will think of a white male from western Europe or the US.

Today, however, things have changed considerably; physics, both as a discipline and in the people that represent it, has become more diverse. This correlation is probably not an accident. In my mind, the increased diversity is an excellent development, but as with everything, it can be further improved. There are a couple excellent podcasts I listened to recently that have championed diversity in different contexts.

The first podcast was an episode of Reply All entitled Raising the Bar (which you should really start listening to at 11:52 after the rather cringe-worthy Yes-Yes-No segment!). The episode focuses on the lack of diversity in many companies in Silicon Valley. In doing so, they interview an African-American man named Leslie Miley who was a security guard at Apple and went on to work as a software developer and manager at Twitter, Apple, and Google among other companies (i.e. he possessed a completely unorthodox background by Silicon Valley standards). He makes an interesting statement about companies in general (while referring specifically to Twitter) saying:

If you don’t have people of diverse backgrounds building your product, you’re going to get a very narrowly focused product.

He also goes onto say that including people from different backgrounds is not just appropriate from a moral standpoint, but also that:

Diverse teams have better outcomes.

There is plenty of research to support this viewpoint. In particular, Scott Page from the Santa Fe institute and University of Michigan – Ann Arbor is interviewed in the episode and suggests that when teams of people are selected and asked to perform a task, teams of “good people” from diverse backgrounds generally outperform many “excellent people”/experts from similar backgrounds (i.e. the same Ivy League schools, socio-economic status, age etc.).

There is a caveat that is presented in this episode, however. They suggest that it may take longer for a diverse team to gel and to communicate and understand each other. But again, the outcomes in the long-term are generally better.

There is an excellent episode of Hidden Brain that also covers similar topics, but focuses on building a better workplace. The host of the podcast, Shankar Vendantam, interviews the (then) head of human resources at Google, Laszlo Bock, to gain some insight into how Google has been able to build their talent pool. Of specific interest to physicists was how much Google borrows from places like Bell Labs to build a creative workplace environment. Again, Bock stresses the importance of diversity among the employees at Google in order for the company to be successful.

In physics departments across the country, I think it is necessary to take a similar approach. Departments should strive to be diverse and hire people from different backgrounds, schools, genders, and countries. Not only that, graduate students with unorthodox backgrounds should also be welcomed. This again, is not just important for the health of the department, but for the health of the discipline in general.

I strongly suspect that Michael Faraday was one of the greatest experimental physicists in the past few hundred years not in spite of his lack of mathematical acuity, but probably because of it. His mathematical ability famously did not extend much beyond basic algebra and not even as far as trigonometry.