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Helgoland and the captivating origins of quantum theory

In June 1925 Werner Heisenberg retreated to Helgoland in the North Sea, a treeless island offering the 23-year-old German physicist a space to think, along with some respite from the extreme hay fever he was suffering. On that remote outpost, Heisenberg had an idea that would revolutionize physics and bring profound implications for philosophy and technology. This was an event that would kickstart quantum mechanics.

Helgoland is the title of the latest book by physicist and science writer Carlo Rovelli. It is essentially a journey through the origins of quantum physics, interwoven with narrative about Heisenberg, Dirac, Einstein and the other luminaries from the first quantum generation. Rovelli also discusses his own interpretations of the quantum world, and connects quantum theory with diverse ideas, from Buddhist thinking to the grand themes of the Russian revolution.

Rovelli speaks about Helgoland in this latest episode of the Physics World Stories podcast. In a wide-ranging conversation with podcast host Andrew Glester, Rovelli discusses quantum concepts, the often overlooked role of philosophy in science, and his minimalist approach to science writing.

If you enjoy this episode, make sure to also join us for the inaugural Physics World Quantum Week. Running on 14–18 June 2021, the event showcases the latest developments in quantum science and technology. It includes a series of free-to-view webinars and a curated selection of quantum articles.

Quantum microscope uses entanglement to reveal biological structures

Quantum entanglement has been used to overcome a key limitation on the speed, sensitivity, and resolution of a bioimaging technique called stimulated Raman scattering (SRS) gain microscopy.

The breakthrough was made by Warwick Bowen and colleagues at the University of Queensland in Australia and Germany’s University of Rostock, who showed how correlations between the detection times of photons from a bright laser could greatly improve the signal-to-noise ratio of SRS — allowing detection of molecular samples with 14% lower concentrations than were previously possible.

SRS is widely used for imaging biological tissues on molecular scales. It works by illuminating samples with two lasers with different frequencies. First light from a “pump” laser undergoes Raman scattering from a molecule of interest, causing the molecule to emit a photon at a different frequency than the pump light. This “Stokes” photon is characteristic of the molecule’s unique vibrational mode and collecting these photons allows the molecule of interest to be imaged in a sample.

Clever trick

However, this Stokes signal is very weak, so a clever trick is used to enhance it. A second laser at the Stokes frequency is used to illuminate the sample, which enhances the emission of Stokes photons and makes the molecular signal easier to measure.

However, for this technique to work, noise in the Stokes laser must be reduced to a minimum. Since photons are discrete energy packets, there is an inherent randomness in the times at which they each arrive at the detector. This creates unavoidable “shot noise” in the detected signal, that can all but drown out the desired signal — putting fundamental limits on the speed, sensitivity, and resolution of the technique. This problem could be overcome by raising the intensities of the pump and Stokes lasers, however this would risk damaging delicate biological samples.

Squeezed states

Now, Bowen’s team have lowered the shot noise of the system by preparing the Stokes laser’s photons in “squeezed-amplitude” quantum states. The photons are entangled quantum mechanically, which means that their quantum states are no longer fully independent of each other. This results in a significant reduction in the randomness of photon detection times.

Biochemical quantitative phase imaging goes photothermal

An artist's impression of the new imaging method

Although the intensity of the molecular signal remained unchanged, this new approach made it far easier for Bowen’s team to distinguish it from noise. Overall, they achieved an improvement in signal-to-noise ratio as high as 35%, allowing them to detect molecular samples with 14% lower concentrations than were previously possible – without increased risk of laser damage.

Although this improvement was relatively modest, it allowed the researchers to observe biological structures that could not otherwise be resolved. The success of their technique also illustrates potential for using quantum-correlated light in other optical imaging applications – which could potentially lead significant improvements in speeds and sensitivities.

The new technique is described in Nature.

Light-squashing ‘spaceplates’ could lead to paper-thin smartphones

The drive to miniaturize optical systems has led to the design of many new devices, from Fresnel lenses to metamaterial wave-plates. However, most optical systems still contain empty space between components – think of the empty barrel between the lenses of a telescope or the camera bump on the back of a smartphone – that could be further reduced. Now, researchers in Canada have tackled this issue and designed three different “spaceplates” that effectively compress space, reducing the size of optical devices and paving the way towards extremely compact optical systems.

Designing materials to squash space

It is relatively simple to stretch space in an optical system by allowing light to travel through a material of higher refractive index. But finding a material that has the opposite effect, compressing space instead of stretching it, is not an easy task. As well as being compressed, the beam of light should not change direction, and the phase and amplitude of the beam should appear exactly as if it had simply travelled a longer distance through empty space. This ideal material should also work over a broad range of frequencies and incident angles. Hence the team at the University of Ottawa, had a tricky problem to solve.

Orad Reshef, lead author of a paper in Nature Communications describing the work, summarized their approach to tackling this issue, “The spaceplate is a fundamentally different imaging element from any type of lens we’ve seen before. Whereas a lens operates on a beam of light as a function of position over the cross section of a beam, a spaceplate operates as a function of the light field’s momentum. It is one of the first optical elements that behaves this way.”

Diagrams showing a spaceplate — How it works: a spaceplate shifts the point at which a beam is focused closer to the lens, reducing the length of the optical path as shown in the upper and middle diagrams. The researchers investigated spaceplates made from a nonlocal metamaterial and a uniaxial medium as shown in the lower diagrams. (Courtesy: Orad Reshef/*Nature Communications*/CC BY 4.0)

With these conditions in mind, the team had a few material options to try. A material with a lower refractive index than its surroundings would work, as would a carefully chosen uniaxial material like calcite – which has an index of refraction along one crystal axis (the extraordinary axis) that is different to the index of refraction along the other two axes. Another possibility is a structured material with optical properties designed to depend on the angle of the incident beam, known as a non-local material. The researchers explored these different approaches and proved that all three could be used to create a spaceplate.

Putting it to the test

Increasing the background refractive index by filling the beam line with oil was the starting point for their first experiment. The team aimed to measure the shift in the focal point of a focused beam after a spaceplate was added and find the compression factor – the factor by which the spaceplate shrinks the local region of space. When a 4.4 mm-long chamber filled with air was inserted into the oil in the path of the light, the focus of the beam was pulled forwards by 2.3 mm, which meant a compression factor of 1.48.

The second experiment involved placing the uniaxial crystal calcite into the oil-filled beam line, to make a 29.84 mm-long spaceplate that advanced the focus of a beam polarized along its extraordinary axis by 3.4 mm – a compression factor of 1.12, which was constant over a large range of incident angles.

However, the largest compression factor measured by the team was achieved using a non-local metamaterial in air. A genetic algorithm selected the ideal thicknesses of 25 alternating layers of silicon and silicon dioxide, and the result was a metamaterial with a refractive index that varies with the incident angle of the beam. This metamaterial was just over 10 μm thick and pulled forward the focus of a beam by 43.2 μm compared to the beam travelling in vacuum, setting the team’s record compression factor of 5.2.

Capturing an image

One thing we may be able to look forward to after this work is more compact lenses for cameras. To demonstrate this, a colour image of a painting (Canadian artist Emily Carr’s, War Canoes, Albert Bay, 1912) was taken inside a vat of glycerol. With the 30 mm long calcite spaceplate in place, the image was formed 3.4 mm closer to the object, with no additional aberrations.

Jeff Lundeen, the team’s principal investigator, shared his vision of the potential impacts of the team’s results: “The spaceplate illustrates a way of manipulating light that when combined with metasurfaces, could allow for completely general image processing, beyond what is possible with conventional computational processing of a recorded image.”

The combination of these very promising experimental results and the design of the super-compact metamaterial spaceplate, mean that surely the future of ultra-thin optical systems is closer than it looks.

Application of electrochemical impedance spectroscopy in lithium-ion batteries

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Be it improving energy density or cycle life or reducing cost, understanding the failure modes of batteries in a non-destructive mode is critical during the design, product development and manufacturing of lithium-ion batteries.

Electrochemical impedance spectroscopy (EIS) provides the ability to access and decouple the failure modes based on the processes’ timescale. Analysis of recorded EIS can be done either through phenomenological modelling or equivalent circuit modelling, with each having its own pros and cons.

This webinar reviews the basics of applying EIS for understanding the phenomena in lithium-ion batteries, the experimental details and protocols, and the types of models with a few case studies.

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Chockkalingam (Chock) Karuppaiah has more than 23 years of experience in electrochemical and energy product development. Products he developed include polymer electrolyte fuel cells, flow batteries and solid oxide fuel cells. He was involved in the design, development and manufacturing scale-up of seven different products. His professional experience includes being vice-president of engineering, Bloom Energy; founder, EC Labs; research professor, Case Western Reserve University, US; manager of the Fundamentals Team, Plug Power; and research staff, Los Alamos National Lab.

Dr Karuppaiah received his BS in chemical and electrochemical engineering from the Central Electrochemical Research Institute, India (1993), and PhD in electrochemistry and fuel cells from Rensselaer Polytechnic Institute, US (1997). He has authored 21 published patents.

Novel stereotactic QA with film-class resolution: First clinical experience with myQA SRS

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This presentation has been submitted for approval by CAMPEP for 1 MPCEC hour and is accredited by EBAMP as a CPD event for Medical Physicists at EQF Level 7 and awarded 9 CPD credit points.

Learn about the physics characteristics and clinical performance of the new, recently released myQA SRS solution. This detector is optimized for your SRS/SBRT Patient QA and features a novel 0.4 mm film-class resolution CMOS technology array with 105,000 measurement points. The solution includes a dedicated phantom to support your efficient QA for different stereotactic delivery methods. First clinical results will be presented.

We are pleased to feature guest speaker Yun Yang, PhD, DABR, Medical Physicist at Rhode Island Hospital, USA. Dr Yang will present his findings from extensive testing of the myQA SRS at Rhode Island Hospital. The presentation will conclude with answers to your live questions.

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Yun Yang, PhD, DABR, is a Medical Physicist at Rhode Island Hospital, USA. He has 10 years’ experience working as a Medical Physicist and has obtained a PhD in medical physics, MSc in radiological sciences and protection and a BE in electronic science and technology. Yun Yang specializes in the area of medical physics, has had numerous research articles published and is a member of AAPM, ASTRO and ACR. In addition to his passion for his field, he also shares his expertise through teaching as an Assistant Professor.

Muons and streetlights: the six-decade quest to pinpoint the value of g–2

I’m sure you know the tale of the police officer who spots a drunk person looking for their wallet beneath a streetlight. The officer asks if the drunkard is sure that’s where it’s lost. “No, I’m not,” the drunkard replies. “It’s just the only place I can see.” Psychologists refer to this observational bias, in which you study something where you can conveniently look, the “streetlight effect”. For experimental high-energy physicists, however, it’s all they can ever do.

Consider the muon – a “fatter” version of an electron – onto which huge resources have been devoted to measuring the way it wobbles. Physicists have been pursuing this quest almost continuously since the 1950s when they began building the theoretical edifice known as quantum electrodynamics (QED). In QED, which describes how light interacts with matter, particles are conceived as spinning magnets, with the ratio of their magnetic moment to spin being a value called g.

The difference between g and 2 is an indication of whether QED is comprehensive enough – or whether there is physics “beyond” it

In QED’s basic versions, g is exactly equal to 2. But when muons whirl around in a magnetic field, they encounter traces of all particles and forces “out there” in nature, and how they wobble depends on the total value of such traces. The experimental value of the difference between g and 2, called the anomalous magnetic moment or g–2, is therefore an indication of whether QED is comprehensive enough – whether there is physics “beyond” it.

To determine a value for g–2, physicists soon realized they’d have to align the spin axes of muons, send them through a magnetic field, and then see how they scatter. Unfortunately, that proved too difficult and it was not until the discovery of “parity violation” in the weak interaction in 1957 that things radically changed. Nature, it turned out, had bestowed a wonderful gift upon particle physicists. Among other things, parity violation meant that muons emit their decay products – electrons – only in certain directions with respect to their spin axis. Complex and difficult polarization and scattering procedures were no longer needed to determine the frequency of muon wobble. Instead, you could just study patterns of electrons.

Changing times

The first “g–2 experiment” began at CERN in 1959. Apart from potentially revealing that QED might be defective, experimentalists hoped that the project might reveal something about the difference between muons and electrons. The experiment also provided an important use for CERN’s first accelerator, the synchrocyclotron, whose value was already in doubt given the new generation of machines called synchrotrons.

Running in spurts for several years, with a final report issued in 1965, that first g–2 experiment was ultimately disappointing. It revealed no breakdown of QED, and heralded nothing new about the muon. As far as one could tell, the QED edifice was solid.

But then CERN’s new accelerator, the Proton Synchrotron, came into operation. Various experimental developments, coupled with a more precise theoretical value, suddenly made another experiment worthwhile. The second CERN g–2 experiment, which began in 1966, arrived at a measurement 25 times more precise than before. This result disagreed with theory by 1.7σ, a sign of a defect in the QED edifice jarring enough to inspire more work from both theorists and experimentalists.

By the time the second CERN g–2 experiment ended, yet more ways to beat back systematic errors had been uncovered, leading to a third version at CERN starting in 1969. One interesting feature was that this experiment was a highly sensitive test of general relativity. Debate was still ongoing about the physical reality of time dilation (i.e. the slowing down of a clock with respect to an observer) and now the measure of time dilation of the muon lifetime in the storage ring ended the debate. The results, which confirmed the QED prediction to a precision of 0.0007%, were published in 1979.

By that year, what was becoming known as the Standard Model of particle physics had come together, linking the known particles and almost all the known forces in a single theoretical package. Predicted particles were discovered, and measurements of various processes turned out to be in accord with theory. The QED edifice looked sounder than ever. Strangely, this attracted renewed attention to g–2, for now physicists sought some way – any way – to look for defects.

Another experiment was duly embarked upon, this time at the Brookhaven National Laboratory in the US. Using a 15 m-diameter storage ring fitted with superconducting magnets providing a vertical 1.45 T magnetic field, it sought to push the measurement down from seven parts per million to just one part per million, testing the limits of the Standard Model. With data collection complete in 2001, the result was published in 2004 and disagreed with theory by around 2.5σ, with an accuracy of 0.5 parts per million in the anomaly (Phys. Rev. Lett. 92 1618102).

Science is not a simple sequence of theoretical test and experimental confirmation or refutation

This was a suggestive, but not definitive, indication of physics beyond the Standard Model. A fifth g–2 experiment duly began at Fermilab in 2013, after Brookhaven bequeathed its magnet to the Illinois lab. Now consisting of about 200 people, the experiment announced its latest findings in April showing a discrepancy of 4.2σ (Phys. Rev. Lett. 126 141801). Despite being a little shy of the 5σ now considered necessary to achieve consensus for a claim, the new result was derived from only the first of several runs.

The critical point

The sequence of five g–2 experiments is an intriguing lesson in the history of physics. Each was undertaken for a different motive, each involved a different set of technologies, and each gave rise to results that had different implications. The story shows that science is not a simple sequence of theoretical test and experimental confirmation or refutation. Rather, many different theoretical and experimental factors come into play in making such a time-consuming and expensive experiment worthwhile.

Ultimately, experimentalists may very well find what they are looking for under the streetlight after all.

Diamond microparticles enable simultaneous MRI and optical imaging

A team of US-based researchers has created an innovative technique that uses diamond microparticles to enable simultaneous optical and MR imaging – a major breakthrough that could pave the way for faster and deeper medical imaging. So, how does the new technique work in practice? What are its advantages over existing imaging approaches? And what are the key research and clinical applications?

Deeper high-resolution images

When researchers or clinicians want to look closely at living tissue, they face a trade-off between the depth and clarity of the images that they can capture. This is because light-based, or optical, microscopes provide detailed, high-resolution images – but only up to depths of around a millimetre. Conversely, MRI uses radio frequencies capable of reaching all parts of the body, but can only capture low-resolution images.

In an effort to overcome these limitations, a research team headed up at the University of California, Berkeley, has demonstrated how microscopic diamond particles can be used to capture information from MRI and optical fluorescence imaging at the same time, potentially enabling observers to obtain high-resolution images up to a centimetre beneath the surface of tissue – 10 times deeper than existing approaches using just light. The researchers describe their new technique in the Proceedings of the National Academy of Sciences.

As author Ashok Ajoy explains, the new method makes use of both optical imaging and hyperpolarized MRI – the first ever implementation of such a combination. The technique uses diamond microparticles with nitrogen vacancy defects that optically fluoresce and allow the nuclei in carbon-13 (¹³C) atoms in the surrounding lattice to be spin hyperpolarized, which allows the diamond particles to light up in MRI.

“In combination, these two imaging modes have a lot of complementary features that make them attractive. Especially powerful is the fact that the imaging in the two modes occurs in Fourier reciprocal spaces,” says Ajoy.

Key applications

The research team envision using the technique primarily for cellular studies and examining tissue samples outside the body. Other likely applications range from helping with the identification of chemical markers of disease in blood to physiological studies in animals.

“While there is wide literature showing that diamond is non-toxic, we don’t envision using these particles inside the body natively,” Ajoy says.

That said, methods by which the diamonds are used to spin hyperpolarize other analytes – for example, water – which can then be injected into the body, might open exciting new background-free avenues of MRI imaging in angiography, he adds.

According to Ajoy, a key advantage of the combined approach is that, by using two modes of observation, it could allow faster imaging. Diamond tracers are also low cost and comparatively simple to work with in research and clinical settings – potentially broadening access to inexpensive nuclear magnetic resonance (NMR) techniques in the future. Other advantages of the new method stem from the fact it provides better imaging in scattering or optically dense media.

“Moreover, these two modes – optics and MRI – sample the image in two Fourier reciprocal spaces, known as x- and k- space. It’s like seeing the same object simultaneously in two conjugate modes; this can yield interesting new ways to significantly speed up image acquisition,” Ajoy says.

Moving forward, Ajoy confirms that the research team has already embarked on the next phase of research, which will focus on enhancing the functionality of the diamond particles. “We are attempting to endow the particles with chemical sensing capabilities so that they can provide information on their local chemical environment via their optical or MRI signatures,” he adds.

Unveiling the minute nanoscale magnetic realm with the Qnami ProteusQ

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In recent years, the need for novel materials to boost storage and computation capabilities to keep up with the ongoing quantum revolution has increased tremendously. Nanoscale magnetism plays a crucial role in the identification of ideal candidate materials for such a challenge. Standard magnetic imaging techniques, however, can not reveal magnetic properties at the nanoscale without invasively perturbing the materials’ magnetic configuration.

Here enters Qnami ProteusQ: the first patented and complete quantum microscope system. It is the first scanning NV (nitrogen-vacancy) magnetometer for the analysis of magnetic materials at the atomic scale. Its proprietary quantum technology provides high-precision images that allow scientists and engineers to see directly the most subtle properties of their samples and the effect of microscopic changes in their design or fabrication processes.

In this talk, we will show how quantum sensing enables us to measure magnetic fields that have never been measurable before. We will provide an overview of the different magnetic imaging modalities of ProteusQ and put this in context of cutting-edge materials science research.

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Alexander Stark is a co-founder and the CIO of Qnami. He received his PhD from the Technical University of Denmark where he developed measurement protocols for quantum sensing applications. Alexander has extensive know-how at the interface between hardware, software and quantum technologies, and is responsible for the development of Qnami’s flagship, the Qnami ProteusQ. He is also co-founder of Qudi, an open-source framework for quantum engineers that now constitutes the backbone of LabQ, the software operating Qnami’s Quantum Microscope.

Peter Rickhaus is the application scientist of Qnami. He has a broad knowledge in nanoscience ranging from biology, chemistry to physics. Within his PhD at Basel University and his Postdoc at the ETH Zurich he acquired a deep understanding of quantum physics and also extended his capabilities towards numerous fabrication and processing techniques. He contributed to more than 30 research publications and hosts a rich hands-on knowledge for investigative and analytical techniques.

Tomography technique could help in the fight against nuclear terrorism

Physicists at the Royal Institute of Technology in Stockholm, Sweden, have developed a new technique to rapidly detect and characterize so-called special nuclear materials like plutonium and enriched uranium. The technique, dubbed neutron-gamma emission tomography, works by measuring the “coincidences” of particles emitted in nuclear fission.

Special nuclear materials are a double-edged sword. As fuel for power stations and reactors, they have enabled great technological advances, but they can damage cities and even threaten human civilization if employed as weapons of mass destruction. They also pose a long-term contamination hazard, from accidents and from potential acts of nuclear terrorism using radiotoxic dispersion devices. Being able to identify, localize and characterize such materials quickly is therefore critical for national security, as well as for detecting radiation leaks and mapping radioactive contamination.

The problem is that the radiation portal monitors commonly used in settings such as airports and seaports are unable to do these things. Instead, they are simply designed to measure the radiation flux as people, vehicles, parcels and other objects pass through them, and set off an alarm if the flux exceeds predefined thresholds. The radiation flux they measure consists primarily of neutrons and gamma photons, both of which are produced during nuclear fission – the decay process by which the nucleus of an atom splits into two or more smaller, lighter “daughter” nuclei.

“Coincidences” of neutron and gamma-ray emissions

In contrast, the new neutron-gamma emission tomography (NGET) technique developed by Bo Cederwall and colleagues can determine the location of special nuclear materials with high precision. It works by measuring the time of arrival of neutrons and gamma photons at specially-designed detector assemblies. The system then looks for “coincidences” – that is, events in which neutrons and gamma rays are detected one after the other – and uses the time-of-arrival information to pinpoint the particles’ source in real time.

“In physics, fast coincidences mean that particles have arrived within a very short time interval, in this case within a couple of 100 nanoseconds or so,” Cederwall explains. “These particles are, in the majority of cases, correlated from the same fission event, or from other types of reactions like alpha-particle induced reactions in the material.”

Test source

The team members demonstrated their new technique using a prototype radiation portal monitor they developed in their laboratory. This system consists of an array of eight 127-mm-diameter by 127-mm-length cylindrical liquid organic scintillator cells arranged in two detector assemblies 1 metre apart. The researchers carried out their tests using a radioactive source of californium-252 (Cf-252) with a mass of 3.2 × 10⁻⁹ g, encapsulated in a 4.6-mm × 6-mm cylindrical ceramic casing.

Cf-252 undergoes spontaneous fission, producing an average of 3.76 neutrons per fission event. The source’s total fission rate of roughly 1900 events per second is thus equivalent to that produced by around 100 g of weapons-grade plutonium (7% plutonium-240 and 93% plutonium-241), which would correspond to an object about 1 cm in size.

Not yet optimized

Although Cederwall and colleagues stress that they have not yet optimized their detector for efficiency, nor designed it for imaging, they were nevertheless able to identify the position of their relatively weak test source within an uncertainty of just 4.2 cm. Using a set of more uniformly distributed detectors or smaller detector cells would, they say, substantially improve the detector’s spatial resolution. What is more, while the current study focused on measuring coincidences from a stationary source, the researchers say the method could readily be adapted to moving objects with the aid of an optical tracking system.

The researchers, who report their work in Science Advances, say they now plan to try out the NGET technique on different configurations and geometries of portal monitors, including some that might be used for vehicles and freight containers rather than pedestrians. They have also begun a project to analyse the contents of radioactive waste containers. “There is a large global stockpile of temporarily stored radioactive waste – for example, from civil and military nuclear research – which is quite often of unknown detailed composition and origin,” Cederwall tells Physics World. “Such materials need careful characterization before they are disposed of to ensure public safety”.

Frequency and distance of human travel follows universal pattern, mobile-phone data reveals

Patterns describing how far and how frequently people travel to different locations within cities are surprisingly universal across the world, according to a new study by an international team of researchers. While it may seem obvious that people will travel to closer locations more often, this aspect of human mobility had not been analysed in detail before and the results could help city planners achieve a wide range of goals from improving public transport to controlling disease.

How people move from one place to another is of fundamental importance. It dictates social, economic and cultural exchanges; how cities develop and grow; traffic congestion and pollution; and the spread of contagious diseases. But despite this, our understanding of human movements is incomplete. Existing models tend to focus on the number of people that travel between different locations, with little consideration of the frequencies of recurring visits by individuals.

Gravity and radiation

The gravity law of human migration says that the movement between two urban areas decrease with distance and increases with population size or importance of the areas. The radiation model adds the component of other places people could stop on their journeys: the less places there are to stop – to go shopping or to work, for example – the further people will travel.

In this latest research, researchers analysed anonymized mobility data from millions of mobile phone users in seven cities around the world: Abidjan, Ivory Coast; Dakar, Senegal; Boston, US; Singapore; and Braga, Lisbon and Porto in Portugal. The data were collected during different periods between 2006 and 2013. Using these data, the researchers were able to estimate were each phone user lived and the places they travelled.

“Analysing not only visitation distance, but also frequency, allows us to gain a deeper understanding of urban mobility patterns, and to develop more accurate models of how people interact with the physical space surrounding them,” team member Paolo Santi of the Senseable City Laboratory at the Massachusetts Institute of Technology says. “These models could be used, for instance, to estimate energy demand in the transition towards more pervasive electric mobility.”

Predictable and universal

Santi and colleagues found that flows to all locations in a city follow a predictable and universal pattern, revealing a simple and robust law that they call the universal visitation law of human mobility. According to this law, the number of visitors to any location decreases as the inverse square of the product of their visiting frequency and travel distance. Or put more simply, people are unlikely to travel far too often.

This scaling law is remarkably consistent across urban areas around the world, according to the researchers, who found that the number of individuals who visited different locations was highly consistent across the different cities. They also found that the number of visitors decreases in a predictable pattern for all locations in a given city, with respect to the frequency of visits and distance travelled. High-density areas were filled with people who had travelled shorter distances.

“We believe that the striking similarity observed across different cities might be caused by some common, fundamental mechanism that drives people’s mobility choices,” Santi told Physics World. He explains that one possibility is that people alternate between returning to already visited locations and exploring new locations. But exploration choices are based on popularity: people are more likely to explore popular locations. “We have shown that this basic mechanism can generate a pattern of visitation distance and frequencies that replicates the visitation law observed in the data,” Santi adds.

Missing component

The research is described in a paper in Nature, and in an accompanying commentary, Laura Alessandretti and Sune Lehmann, at the Technical University of Denmark, write that Santi and colleagues “have identified a key component that was missing from existing theoretical frameworks of human mobility: visitor frequency”. They add that the discovery of the law paves “the way for studies that could deepen our theoretical understanding of how individual and collective mobility patterns are connected”.

Santi says, “We would like to explore more the applications of the visitation law, for example in the field of urban infrastructure design and planning”. “Also, we are applying the visitation law to study epidemics, trying to understand the effect of restrictions on distance and frequency of visitation to the size of the infected population.”

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Helgoland and the captivating origins of quantum theory