Symmetry Redux: Conservation Laws


One of the first topics I ever posted about here on Silhouette of Science is Symmetry. I was fascinated by the manifold ways, both obvious and subtle, that Symmetry pervades our world. In that post I touched upon the presence of Symmetry in processes biological, chemical and physical, and the striking absence of Symmetry in a select few instances. I appealed to cellular automata as an example of simplicity spawning complexity. And lastly I yearned for some deeper symmetry, or a more fundamental rule from which the apparent breaking of symmetries could be explained.

Continue reading “Symmetry Redux: Conservation Laws”

The Question of Science

When I was 12, a friend gave me The Ultimate Hitchhiker’s Guide as a birthday present – 5 books bound together with an ornately engraved gold and black cover. It was a behemoth of a book, chronicling the adventures of Englishman Arthur Dent and his extraterrestrial friend Ford Prefect as they traveled through the galaxy. It seemed like the Bible of Science Fiction, and I absolutely couldn’t put it down. I think I read the entire series over a Spring Break one year, opting out of swimming, instead immersing myself in science fiction lore.

Through Arthur and Ford, I vicariously ventured into all corners of Douglas Adams’ universe. I encountered a cow that wanted to be eaten, a Paranoid Android older than the Universe, and a babel fish, which, when placed in your ear, allows you to understand any language.

In the first installment, The Hitchhiker’s Guide to the Galaxy, a group of hyper-intelligent beings builds a supercomputer called Deep Thought, in order to help them solve the mysteries of the universe. They ask Deep Thought the ‘Answer to the Ultimate Question of Life, the Universe, and Everything’, which turns out to be 42. But, as the computer aptly points out, the Beings know the answer but not the question. In the sequels, armed with an answer, the extraterrestrials backtrack through possible equations and formulas, and build an even more powerful supercomputer to discover the question.

One of the reasons I love the series is that every instance of science or adventure is so incredibly fantastical. But recently I’ve found that some of the ideas in the Hitchhiker’s Guide hit close to home.

When I first thought about writing this blog post, I wanted to write about physical intuition, the ability to qualitatively explain complex processes by thinking about them in terms of everyday experiences. I’ve since come to realize that “everyday experiences” doesn’t quite do justice to the way most people perceive science. Science is about asking questions and, hopefully, getting answers. However, in many ways, we don’t even know which questions we should be asking.

Science asks how, not why. It’s a subtle difference, one that is easy to ignore or overlook. But it lies at the heart of the way we see the world. How looks for an explanation, a sequence of events that brings a system from point A to point B. It is the search for processes that accurately describe the world around us. Even cause and effect lie in the realm of how. Why, on the other hand, begs a purpose, an intention.

These two questions seem so genuinely similar that we group them together, using them interchangeably. The lack of distinction is so ingrained in our society that it has become a part of our language. My roommate here at CERN, Emil Öhman is originally from

Sweden, so English is his second language. Every night over dinner we talk about philosophy and physics, and even though he is fluent in English, he always asks me to clarify what I mean when I use the word reason.

Emil brought to my attention the fact that reason has two completely separate meanings. Sure enough, as attests, we use the word as a synonym for ‘motive’, the why, and ‘cause’, the how. The former connotes purpose, which is inherently human, while the latter seeks to explain natural occurrences. Consciously or not, we often use reason ambiguously, hinting at both meanings simultaneously.

Syntactical quirks aside, this inability to distinguish between how and why is an integral part of the way we interact with science. Through high school and my freshman year of college, I’ve heard the phrase ‘physical intuition’ thrown around in physics and math classes in the likes of “from our physical intuition, we can see that…” and “it’s obvious if you use your physical intuition, that this problem can be distilled down to…”

In many cases it is the most powerful problem solving technique that we have. Sometimes the math required to solve a problem is incredibly involved, and you have to think back on all of the physical processes you’ve observed in your life, pick out a few that share a semblance of similarity, and compare and contrast them in the hopes of developing a hunch. It allows us to run thought experiments in our heads, taking as an axiom that the physical laws that govern all processes are the same.

The classic examples of using physical intuition tend to fit this mold fairly well. Richard Feynman famously asked his students to find the weakest point on an infinitely round table with four evenly spaced legs. In the absence of physical intuition, this problem would require applied physics and intensive mathematical calculation. Using personal experiences, it is easy to guess that the table is weakest between any two of its legs.

Albert Einstein used physical intuition to formulate his theory of relativity. He realized that if he were in a metal box isolated from the outside world, and he felt a downward acceleration, he wouldn’t be able to tell if the box was a rocket accelerating upward, or if a gravitational body was pulling him closer. Einstein didn’t need to run experiments or create a perfectly isolated system out in space in order to come to his conclusion. Instead, the Equivalence Principle, as it became known (for equating inertial and gravitational acceleration) required physical intuition and a bit of creativity.

But it seems like the analogies are now in large part based on social structures. Physical intuition has grown to view particles as people, and subatomic phenomena as social interactions. I remember my Chemistry teacher in high school explaining the force between protons and electrons as “opposites attract”, as if it were an obvious corollary to a similar phenomenon in dating. We colloquially referred to certain elements as “wanting” to have a complete valence shell of electrons, when we really meant that atoms of that element lose or gain electrons because they are unstable.

We even personify Natural Selection, the process by which life evolves to handle environmental and social conditions. I’ve heard over and over again that Evolution “favors” those that are fit. Evolution itself has no wants or desires. It just happens to be true that on average organisms that are more fit to survive, survive.

Whereas physical intuition used to ask how, our personification of science has added an element of why. Instead of asking, “how did such biodiversity come to exist?” we ask, “why were these organisms chosen to survive?” By bringing inanimate objects and abstract processes to life, we give them thoughts, feelings, and even emotions! We impose upon them the human constructs of intent and purpose.

Indeed, it’s such a satisfying way to view the world. Emil thinks of particles as people that push each other away when they get too close and invade personal space, and pull each other closer when they grow too distant.

I only recently realized that my own conception of particles and elements relies heavily on social interaction. On the whole, the more fundamental a particle, the more stable it is, and the larger and more complex it becomes, the more prone it is to decay. Some, like the proton, have lifetimes longer than the existence of the Universe, while others live for fleeting fractions of a second. The same logic applies to elements. Those with more atoms tend to be less stable than elements containing only a few. I think about these particles and elements in terms of social groups; the larger the group, the greater the likelihood that members will disagree, and someone will want to leave. Complexity spurs on collapse.

There’s something poetic in our relationship with Science. We are composed of particles, but we view particles as if they were innately human. We personify elements and assign rationale to mechanisms that have no inherent purpose. Our social, as well as physical experiences, point us to the answer…

Which brings us back to the ‘Answer to the Ultimate Question of Life, the Universe, and Everything’. Is it wrong to incorporate why into our understanding of Science? Does why complement the empiricism of how, or refute it? Clearly viewing particle physics through the lens of social structures has limitations. It could, however, lend new approaches to old problems. After all, why appeals to something deep down, which how alone can never hope to satisfy. Could there be two fundamental questions, two ‘Ultimate Questions of Life, the Universe, and Everything’?

So Much for Symmetry

One of the first ideas that drew me to science was symmetry – the concept that everything has inherent balance, proportionality, and temporal harmony. I know it’s romantic to think that everything, from electrons to elephants, obeys the same universal laws; but for such a simple idea, it holds surprisingly true.

In Biology, plants and animals adhere to many different types of symmetry. Sunflowers and Nautilus shells spiral outward according to the golden ratio; trees and leaves display fractal geometry, in which the same pattern appears on many scales; and animals show bilateral symmetry, where left mirrors right.

Chemical bonding, too, is governed by symmetry – elements that have the same number of electrons in their outer (valence) shell, bond in the same way. The whole periodic table is based on this structure!

Much of Physics revolves around symmetry in the form of invariance, or lack of change based on coordinate system. It only seems right that in space up is no different than down! In fact, when drawing the diagrams that bear his name, Richard Feynman was so taken by symmetry, he concluded that a particle traveling forward in time is the same as its antiparticle traveling backward in time. In 1972, the Nobel Laureate PW Anderson went so far as to declare, “It is only slightly overstating the case to say that physics is the study of symmetry”!

But every once in a while nature throws a curveball our way. The narwal’s tusk is on its left jaw. And the wrybill is the only bird with its beak always bent to the right.

It’s almost frustrating that out of the millions of species on Earth, all but a few fit symmetries so nicely. What makes them different? What allows left-handed fermions to interact with the weak force when right-handed fermions cannot?

Chaos theory (pictured below), is the study of sensitivity to initial conditions. It says that simple systems, like the double rod pendulum, can have extremely complex results. With just two rods connected at a joint and hung as a pendulum, the double rod pendulum is one of the simplest mechanical systems. Yet it exhibits extremely complex behavior. It never retraces its earlier path, and never repeats a pattern. What’s more, changing the initial conditions even slightly leads to entirely unrecognizable results.

Maybe this sensitivity extends to other systems. In his book, A New Kind of Science, Stephen Wolfram studies cellular automata, or small grids of squares colored either black or white. He identifies 256 simple rules for deciding what color each square would be based on the squares around it, and runs each simulation on his computer. While the vast majority of the simulations produce simple, easily identifiable patterns, and fractals, a small fraction of the tests give different results.

Rule 110, although close to many of the other rules, produces results so complicated that it takes thousands of iterations, and millions of cells, for a pattern to emerge. Until then, it is essentially impossible to predict the behavior of a cell from the prior results.

The mathematician Horace Lamb once said of the chaotic nature of turbulence, “When I die and go to Heaven there are two matters on which I hope for enlightenment. One is quantum electrodynamics, and the other is the turbulent motion of fluids. And about the former I am rather optimistic”.

Maybe chaotic systems can’t be predicted. Maybe their rules can’t be solved for with mathematics or computational power. But I’d like to think that our Universe is governed by simple, elementary laws; and that usually these laws produce simple results, but every once in a while produce an unrecognizable pattern which we perceive as disorder. Narwals and wrybirds break bilateral symmetry. But I’d like to believe that there’s some deeper, truer symmetry that we’re missing. As childish an ideal as symmetry is, it’s soothing to think that there is some underlying order.

Maybe nature isn’t throwing us a curveball; we might just be looking at turbulence the wrong way!

Talking with Titans

In just over a week I’ll be packing my things and getting on a plane to Geneva, Switzerland. I’m going to be working at the ATLAS detector at CERN, the

European Organization for Nuclear Research. It is the world’s largest Physics research complex! Every day for two months I’ll collaborate and talk with people who are just as crazy about Physics as I am, and that is saying a lot! It’s a dream come true for me.

Although I’ll see it with my own eyes shortly, for now, my mental image of CERN consists of dream-like silhouettes of science. There are plenty of pictures of the LHC (Large Hadron Collider), and the ATLAS detector online. But it’s hard to grasp their sheer magnitude.

Before teaching the class Big Science at Sprout, I did some research on CERN, and I came upon a few numbers that hint at CERN’s marvel:

  • 99.999997 – percent of speed of light at which particles travel in LHC
  • 1800 – physicists working at ATLAS detector
  • 210,000 – DVDs worth of data per day analyzed by Data Centre
  • 600 million – particle collisions per second in the LHC
  • 13 billion – estimated dollars spent to find Higgs Boson

But these numbers only scratch the surface of CERN’s scientific prowess and its influence on society. CERN scientists discovered the W and Z bosons, which are carrier particles for the Weak Nuclear force, and the Higgs Boson, whose field gives particles mass. Even the internet, which I am using to write this post, was invented at CERN.

The ATLAS experiment, situated in a cavern dug into the Large Hadron Collider, is one of the biggest sites at CERN. Its detector weighs as much as the eiffel tower, and stands five stories tall. Along with its sister experiment, CMS, the ATLAS experiment was instrumental in discovering the Higgs Boson.

While ATLAS is short for A Toroidal LHC Apparatus, it seems to me an apt acronym. In Greek mythology, Atlas was the Titan who held the world in his hands. As the Titan of navigation and astronomy, Atlas also became associatedwith cartography and maps. I think it’s fitting that in a collosal cavern, a titanic detector is piecing together a different type of map – the map to the fundamental particles.

Right now Geneva seems as far away as Mount Olympus; all I see is a silhouette in the distance. But I can’t wait to talk with the titans of physics, and, hopefully, to hold a little bit of the world in my hands.