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Explaining the second quantum revolution

 

The first quantum revolution was a revolution in atomic and subatomic physics, and it brought us not only the iPad and the Higgs boson but also a range of excellent popular-science books. While the atomic wonderland of the “Mr Tompkins” books now seems dated, George Gamow’s images of gazelles being diffracted by bamboo groves and cars leaking through garage walls still capture vividly the strangeness of the micro world.

The second quantum revolution, in which quantum mechanics was applied first to information theory and then to information technology, is harder to popularize. This is not because quantum information processing is particularly complex but because there are no simple images that will carry you any distance into the field. To understand quantum information is to understand the mathematics describing it; without the mathematics you can have only the haziest picture of what the field is all about.

Fortunately, the crucial mathematics is quite simple and with a few basic results you can make enormous progress. In The Quantum Divide, Christopher Gerry, a theoretical physicist, and Kimberley Bruno, a school teacher and vice principal, have done an impressive job in cutting the necessary mathematics down to the absolute minimum, below what I previously thought was possible. While the proverbial “educated layman” might struggle at times, many readers of Physics World will have little difficulty; anyone who has completed the first year of a physics degree will have more than enough background knowledge to understand the book.

Bell’s theorem is perhaps the founding result of quantum information theory, although the field did not blossom into its current form until many years after John Bell formulated it. In essence, Bell showed that any local realistic theory about how the world works is inconsistent with quantum mechanics. Here “local” means obeying relativity and in particular the requirement that information cannot travel faster than light, while “realistic” means that the results of measurements implicitly exist in the world before the measurements are made, with the measurement acting simply to reveal these pre-existing results. Einstein was unhappy with the ideas that eventually led to this theorem, not just because of the challenge to locality but also because of the apparent implication that observations, in effect, create the world. Unfortunately for Einstein, subsequent experiments have confirmed Bell’s predictions.

In its traditional form, Bell’s theorem is subtle and its derivation quite hard to follow. Gerry and Bruno have sidestepped this by describing a later variant that was invented by Lucien Hardy, developed by Thomas Jordan and subsequently popularized by David Mermin. This version begins with four statements about the outcomes of four possible sets of measurements that could be performed on a pair of particles. These four statements, if taken together, are contradictory: any three of them can be true, but it is easy to show that it is impossible for all four statements to be simultaneously true if measurements are simply revealing a pre-existing reality. It is, however, straightforward to design a quantum mechanical situation in which all four statements are true, thus immediately ruling out any naive description of the quantum world.

Gerry and Bruno carefully describe Hardy’s argument in a particularly simple way, allowing the reader to see how the result can be worked out. Not all of their explanations are equally successful; in particular, I found the discussion of apparent faster-than-light communication in quantum tunnelling unclear. Overall, however, they have done an excellent job.

An unusual feature of The Quantum Divide is that the authors do not content themselves with theory but always describe relatively simple experiments that demonstrate the expected behaviour. These experiments are taken from quantum optics – the study of light and its interactions with matter at the fundamental single-particle level – reflecting Gerry’s research in theoretical quantum optics and his textbook, published jointly with Peter Knight, in the same field. While some of the experiments are subtle and difficult to understand, others are entirely straightforward. Concentrating on this single field allows the reader to gradually build up an understanding of the experimental methods, and therefore to puzzle through the trickier scenarios.

The use of light in these experiments can, at first sight, make the results seem less surprising than they really are. The result of overlapping light waves from two sources – leading to constructive and destructive interference – is studied at school and many quantum information experiments are, in effect, little more than exotic interference effects. This view, however, misses the point: the behaviour of single photons provides a far better conceptual model for the reality underlying the physical world than the behaviour of single billiard balls or other large objects that are commonly used as examples. The debate as to whether objects are really particles or really waves is fundamentally sterile: in fact, they are really just like light.

This leads, of course, to the philosophical problems of quantum mechanics – one of which is apparently answered up front by the book’s subtitle, Why Schrödinger’s Cat is Either Dead or Alive. Gerry and Bruno cheerfully adopt a relatively standard Copenhagen interpretation of quantum mechanics for most of the book. In this approach, sometimes called a “psi-epistemic” view (see “The life of psi”, May pp26–31), quantum mechanics says nothing about how the world really is but only describes what we can know about it. Since I have learnt about quantum information in a many-worlds, “psi-ontic” community, in which the quantum state is considered to be the true reality, this approach seems odd to me and I am not certain whether the authors completely believe their own public view.

However, as they make clear, these philosophical questions determine only how we think about the experiments we perform and in practice all of the different interpretations make the same predictions for any experiment we can imagine performing at the present time. Can we really say whether Schrödinger’s cat is alive and dead at the same time? It is hard to beat Bill Clinton’s reply made in a different context: that depends on what the meaning of the word is is.

Earth’s ‘second moon’ target of proposed mission

 

The Earth’s “second moon” is the target of an innovative concept for a space mission. The proposal – put forward by a researcher in Italy – would see a light and cheap-to-launch satellite travel to the near-Earth asteroid, Cruithne. Among the novel features of the mission is the idea of having two independent “nano platforms” that can be deployed to conduct scientific surveys once the satellite has reached its destination.

Also known as asteroid 3753, Cruithne is a five-kilometre-wide near-Earth object (NEO). While presenting no risk of colliding with us, the asteroid is locked in a 1:1 mean motion resonance with the Earth. This means that the two bodies take approximately the same time to complete an orbit of the Sun, so they appear as if they are chasing each other. Viewed from Earth, Cruithne is seen to weave a bean-shaped path, coming closest at a distance of 12,500,000 kilometres away – a habit that has lent it the nickname of the Earth’s “second moon”.

Relic of the early solar system

Cruithne is of great scientific interest. As with many small asteroids, its composition should still preserve its original chemical make-up – unaltered by high internal pressures and temperatures – which could tell us more about how the solar system formed. For the purposes of a visiting survey satellite, however, Cruithne’s large orbital inclination presents a particular challenge to reaching it, one that certainly tests the mettle of any proposed space mission. “The [new] study proposes a novel mission approach for the survey of near-Earth asteroids based on small and flexible satellites,” says paper author Pierpaolo Pergola, an aerospace engineer from the University of Pisa.

The efficiency of the mission comes primarily from making use of an electric ion-propulsion system. This would use power generated from solar arrays to produce and accelerate high-temperature plasma in two thrusters – which would enable the craft to travel at high speeds while using relatively small amounts of fuel for a space mission of this type. By saving in propellants, launch costs are lowered and mass can instead be allocated to a greater payload. “This is especially convenient for a high-total-impulse mission,” says Pergola, explaining that in a classical chemical-propulsion system – with more conventional trajectories – one would need more fuel.

The proposed payload in this case would be two subsidiary nano-platforms, which could be deployed at the destination to conduct detailed surveys. Pergola explains that the ideal candidate for this would be 2U CubeSats (with dimensions of 20 × 10 × 10 cm), the miniaturized research platforms that have brought affordable research opportunities in recent years. Despite their size, CubeSats can achieve a range of applications – such as employing accelerometers, mass spectrometers or particle probes – while still being lighter together with the mother satellite than one single expansive and less manoeuvrable probe. With the main spacecraft acting as a telecommunications relay to Earth, and as a radiation shield during space travel, the mission design overcomes two of the exiting hazards that are associated with using CubeSats for deep-space applications.

No need to slingshot

Furthermore, as the mission would go straight from Earth to Cruithne without having to slingshot around anything else en route, such a mission would save on transit time and complexity while offering a highly flexible launch window. In total, the spacecraft is expected to weigh around 100 kg and would be expected to reach Cruithne in around 320 days. Such a survey mission could potentially help pave the way to subsequent robotic landing missions, human explorations or even asteroid-mining endeavours, claims Pergola.

While this interesting mission proposal certainly seems to have potential, a trip to Cruithne may not be quite “written in the stars” as yet. “For the time being, [this] is a proof of concept,” explains Pergola, who reports having received positive feedback on the principle from colleagues. He adds: “I’m aware that there is a growing interest worldwide toward applications of the CubeSat standard in more exotic missions, like [this] one.”

As yet, however, Pergola does not have a clear picture of all the expenses involved in such a mission.

The proposed mission is reported in Advances in Space Research.

Tractor beam produced with unstructured light

 

Researchers in Florida and Singapore have produced a method of dragging objects on the surfaces of fluids that they believe could lead to new techniques for micromanipulation. The team has shown that its “tractor beam” can manipulate objects over macroscopic distances along a chosen interface of two materials with different refractive indices.

Push and pull

While science fiction has long relished tales of unfortunate vessels being dragged to their doom by tractor beams, the more benign ambitions of physicists include optical micromanipulation of particles in biomedical experiments and chemical engineering. Any scientist trying to produce an attractive force from radiation has to contend with the fact that photons carry momentum and when a particle absorbs a photon it must absorb that momentum, pushing the particle away from the light source. But what if the object does not absorb the radiation?

Groups such as Pavel Zemánek‘s at the Institute of Scientific Instruments of the Academy of Sciences in the Czech Republic have irradiated objects symmetrically off-axis so that they scatter light forward, giving them recoil momentum directed back toward the light sources. Other researchers such as David Grier’s team at New York University have created “optical conveyor belts” – streams of backward-moving optical traps that reel objects in. These are all approximations, however, to true tractor beams, which would use a single, unstructured beam of light to pull the object.

In the new research, members of Aristide Dogariu‘s group at the University of Central Florida, together with colleagues at the National University of Singapore, show that simple, unstructured light passing from a fluid of low refractive index to one of higher refractive index pulls transparent objects suspended at the interface back towards the light source. In the late 1800s, the mathematician Hermann Minkowski showed that a photon’s momentum increases proportionally as the refractive index of the medium through which it is propagating increases. If a transparent object is suspended at the interface between these two media, photons exit the object with greater momentum than they had on entry. To conserve momentum, therefore, the object at the interface must be pulled in the opposite direction to the photon flow, whatever the refractive index of the object itself. This photonic force will be far too weak to overcome the surface tension and actually free the object from the interface.

Photonic forces

“It’s very hard to take a floating object on the surface of a fluid and either pull it out of the fluid or push it down into the fluid,” Dogariu explains. Practical effects can be produced, however, if the object is illuminated at an oblique angle to the interface, in which case photons still pass through the object from a lower to a higher refractive index medium, but there is a transverse component to the resulting force. This transverse component can be used to pull objects along the interface. The researchers tested this by obliquely illuminating oil droplets on the surface of water. They found that the droplets within the illumination spot of the beam showed an obvious movement towards the light source, whereas droplets not illuminated showed, on average, no such movement.

Despite the fact that it can only pull objects around at the interface between two fluids, Dogariu believes that the research could have important applications. “The properties of many systems are practically determined by their interfaces, from colloidal systems to cell biology,” he says. “What we are after is practically being able to manipulate the properties of these interfaces with optical forces.” He lists optical sorting as one principal application. All particles will absorb some photons passing through them, and when a particle absorbs a photon instead of transmitting it, it will be pushed rather than pulled. “If you have two species that have different levels of absorption, they will have different absolute velocities on the surface,” he explains.

Grier, who was not involved with this work, is more sceptical about the potential for direct application of the work. He points out that a similar technique called photophoresis already exists that sorts particles in suspension according to how much they are pushed by radiation. He is also concerned that, if particles absorb radiation, they will dissipate heat, which could lead to hydrodynamic effects disrupting the movement. Nevertheless, he is intrigued by the fundamental physics of the research and thinks that it could lead to interesting further work. “The medium has largely been ignored in the process of scaling up tractor beams,” he says. “This paper really introduces the idea that you can use the medium as part of the process.”

The research is published in Nature Photonics.

Australian science communicator Peter Pockley dies

Peter Pockley (right) at his his home in Sydney in 2011 with Matin Durrani.

By Matin Durrani

Physics World was saddened to learn today – via a Tweet from the Australian Nobel-prize-winning astronomer Brian Schmidt – of the death of veteran Australian science journalist Peter Pockley.

Peter, who was 78, had contributed numerous articles to Physics World over the years, focusing mainly on the ups and downs of science policy in Australia, of which he had an in-depth knowledge. He died peacefully at his home in Sydney on 11 August 2013.

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Grains colliding in mid-air create stronger sandstorms

 

The colliding of whipped-up grains of sand increases the strength of sandstorms, according to researchers from Brazil, China and Switzerland. Bouncing along above a moving bed of grains, collisions between particles in mid-air can propel them to greater heights – increasing the overall storm flux. These transport processes are vital to sandstorms and similar phenomena, which act to reshape a variety of geological landscapes.

Moving particles in a sandstorm can be grouped into three categories: creepers, leapers and saltons. Creepers are sand grains that remain at ground level, while both leapers and saltons are flung up into the air. The difference in the latter type of grain comes in the height that they can achieve. Saltons gain enough altitude that their impact velocity on landing – the so-called splash – sends other saltons up into the air. Together, these movements form saltation, the main aeolian or wind-based transport process.

Modelling flows

The role of mid-air collisions in such particle transport has long been debated, with the expectation that collisions between grains would cause particle movement to suffer an overall reduction. By creating 3D models of sandstorms, however – both with and without collisions – the researchers discovered that this is not, in fact, the case.

“Surprisingly, we found an enormous enhancement of mass transport by the wind in the presence of mid-air collisions, compared with the case when such collisions are switched off,” explains Nuno Araújo, one of the researchers at the Eidgenössische Technische Hochschule Zürich.

Counterintuitive findings

Unlike previous theories – which argued that saltons could only be formed during a splash – the team’s model revealed that leapers can become saltons through a series of mid-air collisions that gradually increase their altitude. The higher the particles go – as well as the longer they can stay in the air – the greater the acceleration from the wind, which increases the likelihood of saltation formation.

This was not the only counterintuitive finding. The team also observed that the storm flux – a measurement of strength based on the number of particles moving through a given area – actually increased when the sand particles were modelled to lose energy when colliding, compared with correspondingly simulated elastic collisions. This is because inelastic collisions acted to align the exit directions of the interacting grains – thereby increasing the flux in the direction of the wind.

The results of this simulation also help make it clear how sandstorms get going in the first place. As the wind grows stronger, grains are slowly dragged along the surface of the sand bed. “Because of irregularities in the surface profile, some particles will hop, eventually producing small splashes,” Araújo explains. Through this process, and with a high enough wind velocity, such splashes can create sufficient leapers to ultimately begin saltation. In fact, when the team modelled storms without mid-air collisions, all the aerial particles were seen to be leapers.

Whipping up a storm

Previous studies of interactions within sandstorms were hindered by having insufficient computing power to run such detailed collision models. Araújo and his colleagues were able to circumvent this issue by optimizing their simulation and using a logarithmic velocity profile to simplify the calculation of the turbulent air motion.

“[This] study gives us a fresh, physicist’s perspective on the concept of saltation – which is the key mechanism for the movement of sand,” comments Tom Gill, a geologist at the University of Texas-El Paso who was not involved in the study. “Since saltation is also the key to the genesis of dust storms, the new work could also improve the modelling and parameterization of the effect of dust aerosols on the global environment and climate system.”

“An interesting follow up would be to experimentally observe the role of mid-air collisions,” says Araújo. While it would not be possible to “switch off” collisions in real life, it would be possible to experimentally vary the restitution coefficient – the ratio of the relative velocities of the colliding particles – within certain limits. Other possible future work that the team proposes includes studies factoring in the aerodynamic lift of the particles, fluctuations in the turbulent wind speed or electrostatic interaction between the particles, or models that assess the role of saltation in different conditions, such as a terrestrial desert, submarine or Martian environment.

The study is reported in Physical Review Letters.

Fuel cell powers rock guitarist

By Matin Durrani

Running on hydrogen and oxygen and producing just electricity without any nasty emissions, fuel cells have over the years been used to power everything  from bikes and buses to cars and even planes.

But last week saw the debut of a fuel cell at Imperial College London that was used to power a rock band. The fuel cell was unveiled at a summer barbeque organized by the Hydrogen and Fuel Cells (H2FC) Supergen Hub – a scheme funded by the UK’s research councils to boost interest in fuel cells among UK universities and businesses.

(more…)

Skyrmion spin control could help speed up electronics

 

Researchers in Germany have succeeded in controlling tiny magnetic-spin patterns known as “skyrmions” for the first time. The result could be important for future high-density data-storage technologies and nanodigital electronic devices with improved data-transfer speeds and processing power.

Skyrmions are small magnetic vortices that occur in many materials, including manganese–silicide thin films (in which they were first discovered) and cobalt–iron–silicon. In the new work, the researchers studied a palladium–iron bilayer on an irridium-crystal surface. The tiny vortices can be imagined as 2D knots in which the magnetic moments rotate about 360° within a plane (see figure).

Skyrmions could form the basis of future hard-disk technologies. Today’s disks use magnetic domains (in which all of the magnetic spins are aligned in the same direction) to store information, but there are fundamental limits to the size such domains can be made. It might be possible to make skyrmions that are much smaller and that could therefore be used to create storage devices with much higher densities. What is more, flipping all of the spins in conventional domains – to switch a device’s memory state from 1 to 0, for example – requires considerable power and can be slow; skyrmions require fewer spin flips to switch. In addition, the final spin state is not easily disrupted – making these skyrmion structures more stable than conventional magnetic domains.

Creating and annihilating single skyrmions

Before skyrmions can be exploited in hard drives, however, scientists need to figure out a way to control them – something that has proved difficult to date. A team of researchers at the University of Hamburg, led by Kirsten von Bergmann, André Kubetzka and Roland Wiesendanger, has now shown that it is possible to create and annihilate single magnetic skyrmions using a spin-polarized current – one in which spin is mostly aligned in one direction – from a scanning tunnelling microscope (STM) tip, albeit at ultralow temperatures of 4.2 K. According to the researchers, the skyrmions switch from one state to another thanks to spin-transfer torques, and one state (skyrmions present) can be favoured over the other (skyrmions absent).

“To write or delete a skyrmion we position our STM tip at a particular spot on the sample and inject a spin-polarized tunnel-current pulse into it,” explains Von Bergmann. “While at low currents and voltages the sample magnetization is stable, at higher currents and voltages the magnetic state starts to switch between a skyrmion and a simple parallel alignment of magnetic moments,” she told physicsworld.com. “In this situation, the current direction can determine which of the states is favoured over the other – a clear indication that spin-transfer torque is involved in the switching process.”

IT applications

Being able to write and delete skyrmions in this way means that such spin textures can now be exploited in information technology. “In particular, the possibility of using layered thin films in this way, as is the case in conventional IT-device technology, could lead to a big step forward towards applications,” adds Von Bergmann.

The Hamburg team is now busy trying to understand the switching mechanism in more detail and finding out exactly how the spin-polarized current couples to the magnetization. “This will help us to optimize the process of writing and deleting skyrmions,” says Von Bergmann. “We will also be investigating other thin-film materials in an effort to unearth systems that show such skyrmion switching at room temperature.”

Skyrmions are named after the UK particle physicist Tony Skyrme, who in 1962 found that they could explain how subatomic particles such as neutrons and protons exist as discrete entities emerging from a continuous nuclear field.

The results are published in Science.

Emeritus trio scoops the 2013 Dirac Medal

 

The 2013 Dirac Medal has been awarded to three scientists whose wide-ranging work has brought profound advances in cosmology, astrophysics and fundamental physics. Thomas W B Kibble, Philip James E Peebles and Martin Rees all receive the honour, which is bestowed annually by the Abdus Salam International Centre for Theoretical Physics (ICTP) in Trieste, Italy. The three scientists will also each receive a prize of $5000.

Spontaneous symmetries

Thomas Kibble, emeritus professor at Imperial College London, has made major contributions to our understanding of spontaneous symmetry breaking – the process at the heart of the Higgs mechanism. Indeed, in an interview last year with Physics World, Peter Higgs named Kibble as one of at least five other theorists who deserve credit for predicting the existence of the Higgs boson. Kibble also explored the importance of symmetry breaking in a cosmological context – investigating what happens when a symmetry “disappears” as the universe evolves from the Big Bang.

“It is always very gratifying to have one’s work recognized by other physicists,” says Kibble. “This award is particularly special for me because of its association with my former colleague and inspiration, Abdus Salam, who founded the ICTP, and also because the other medallists this year are two astronomers for whose work I have the greatest respect – James Peebles and Martin Rees.”

Across the universe

Philip Peebles, a theoretical cosmologist who holds two emeritus-professor positions at Princeton University in the US, has worked on problems ranging from light-element synthesis to the nature of the dark universe. In the 1960s Peebles predicted some of the most important properties of the cosmic microwave background (CMB). He also quantified how galaxies cluster together to form large-scale structures over time and played a leading role in developing theories of “cold dark matter”.

At the heart of darkness

The third recipient, Martin Rees, is an emeritus professor at the University of Cambridge in the UK, where he has spent most of his research career. Like Peebles, Rees has also done pioneering work of the CMB and in 2005 the pair shared the $500,000 Crafoord Prize with James Gunn for their work on understanding the large-scale structure of the universe. Rees has a string of other achievements in astrophysics, including his work on the origin of quasars and the prediction that supermassive black holes lurk at the heart of galaxies.

In addition to his research achievements, Rees has also been instrumental in science policy and the democratization of scientific ideas, having authored several popular-science books. In 2011 Rees was awarded the £1m Templeton Prize for his “profound insights” into the nature of the cosmos that have “provoked vital questions that address mankind’s deepest hopes and fears”. He was also president of the Royal Society between 2005 and 2010, during which time he spoke to Physics World in this video interview about space, politics and scientific advice.

All three scientists received the prize today. Since 1985, the prize has been awarded annually on 8 August – the day on which the British Nobel-prize-winning theorist Paul Dirac was born in 1902. Dirac was a close friend of the ICTP, which was founded in 1964 by the Nobel laureate Abdus Salam as an international research centre to promote scientific excellence in the developing world.

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Just-in-time physics

 

“Our project concerned optimizing a manual longboard stand-up slide,” said Myles Cooper as he stood on a skateboard at the front of the class, holding an unattached skateboard wheel in his hands. It was the last day of “Advanced Classical Mechanics” (ACM), a course at Olin College in Massachusetts. Myles and two other first-year students, including my son Alex, were presenting their final project.

For non-skateboarders, Myles explained that a “longboard” is an elongated skateboard used for downhill cruising and tricks, “manual” means riding on the two back wheels only and “stand-up slide” means skidding, usually downhill. Longboarders consider slides to be awesome and have “slide jams” (see YouTube) to see who can achieve the longest slide without the wheels spinning. The group’s project was to use the tools of classical mechanics to find a function to optimize the distance that a rider could slide downhill on two wheels.

Was this an awesome diversion or effective pedagogy? I had come to Olin College to find out.

Exciting experiment

The college was conceived of in the 1990s as an ambitious response to repair the dismal state of US undergraduate engineering education. At that time, first-year engineering students came in passionate about their calling but half wound up ultimately changing their degree and a fifth dropped out of college entirely. The problem appeared to be an overemphasis on theory; imagine a music school that forced performance students to take three years of theory and harmony before touching an instrument.

In 1997 the F W Olin Foundation, set up in 1938 by the engineer-turned-businessman Franklin Olin, provided an initial $200m to create a new engineering college to foster students’ passion from day one. Most classes are organized around team projects. Olin’s founders call it “just-in-time” education – giving students the knowledge required to complete a project – versus “just-in-case” education, or loading students with knowledge for its own sake. The college is small, with about 350 students and nearly half of them female. The result is, in my view, the most exciting educational experiment in recent history.

As a parent of one of these students, am I biased? Totally. So don’t trust me, check the statistics. Some 98% of all Olin graduates get jobs or go to graduate school. More than 200 engineering programmes elsewhere have sent representatives to Olin to study the curriculum. Earlier this year three Olin founders, including the current president, Richard Miller, won a National Academy of Engineering prize for their efforts.

Though entranced by the educational concept, I was sceptical that physics could be taught effectively in the same project-based way as engineering. The ACM professor, Yevgeniya Zastavker, who has a PhD from the Massachusetts Institute of Technology, explained that ACM is less project-based than most courses at Olin College. Students do projects only at the end, although this work is integral to their education, providing them with hands-on application of physics to engineering contexts. She invited me to observe.

Complex affair

This is what Alex posted on Facebook the night before the presentation: “After spending 16 hours working in the same room save food breaks, spending two weeks figuring out how to model a two-wheeled longboard stand-up slide, running an extremely ridiculous set of differential equations for five days with no result, and possibly learning more about the physics of longboarding than probably any person ever, I AM FINALLY DONE WITH MY ACM FINAL PROJECT!”

A few hours after this post, the group members presented their work in class. They based their initial model on mass, acceleration caused by gravity, hill slope, angle θ between the slope and direction of wheel roll (θ= 0 follows the slope), and coefficients of static and kinetic friction. They created functions describing the system using these parameters for a given slope and θ, using MATLAB to plot these parameters. They found, for instance, that the longest slide with a slope of 15°, an initial velocity of 8 m/s and a constant θ occurred when θ was roughly 63°.

To maximize the slide path, however, requires constantly changing the value of θ. To analyse this further, the group first studied the energetics of the situation, using the Lagrangian approach to make three second-order differential equations for the relations of the system’s components in the x, y and z axes. They ran this through Maple (more powerful than MATLAB) but the presence of too many recursive functions made it impossible to solve. With their presentation looming they returned to a Newtonian approach in terms of forces, writing a MATLAB program that used equations from their first attempt but for which they had to keep resetting θ by hand. What seemed to be a simple system, in short, required complex analytic methods.

The same was true for the other groups that day. One modelled the forces on the college’s robotic sailboat. Another tried to model Spider-man’s iconic movement down a street by shooting silk strands at building walls – a series of spherical spring-pendulum motions in which he never hits the ground or walls. “It looks like a simple system to describe mathematically,” said Abe, a first-year student, “but it turns out that there’s not really an analytical solution and the system quickly becomes chaotic.”

The critical point

I came away convinced that much of classical mechanics can, indeed, be taught via the rigorous analysis of real-world situations “just in time”.

But not everyone appreciated the students’ work. The following complaint appeared on a Web forum on which Olin students had discussed skateboarding physics: “Why are you all trying to put square science into my fun hippie longboarding?” The students’ sarcastic response: “Don’t worry, we modelled the final trajectory with a quartic function, not a ‘square’ one!”

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