Universality

(Published on iopblog )

What qualifies as “fundamental” physics? The answer might seem straightforward. It is science that investigates the universal properties of nature, like the interactions between quantum fields studied at CERN or the shape of the cosmos observed by astronomers. In the other camp, science that is not fundamental includes things like strength testing of new materials, or sports science to optimize the trajectory of a javelin. Both types of research use scientific methods to design good experiments that remove any potential observer-bias.

Straightforward as it seems, I posed the question because I want to tell you about research on Non-equilibrium Statistical Physics. Because it contains the word “Statistical”, you might put this subject into the non-fundamental category. To see why that would be wrong, you need to know some little-understood facts about how nature works – about which aspects of nature are in fact universal.

Some of the fundamental properties of nature can be found by studying matter in ever finer detail. By doing so, our predecessors have discovered that matter is made of atoms that are made of electrons and nuclei that are made of quantum fields constituting quarks, gluons, leptons etc. These are clearly fundamental properties of nature. The universe has, for some as-yet unknown reason, decided to allow these particular fields to exist, so we must study them to find out, fundamentally, how the universe works.

But nature has other fundamental properties that evade detection by this microscopic exploration. They are properties that emerge only when a large number of particles interact. Of course, once you know the behaviours of elementary particles, you can use a computer to simulate a large number of them and predict what they will do en masse. The particles’ motions become more complicated the more of them you have. For instance, here (right) is a picture of the paths of two classical particles attracted by gravity, or they could be charged particles interacting via electrostatic attraction. They follow simple elliptical paths. Introduce a third particle (below right) and their paths become chaotic.

Say you wanted to know how much force will be applied to the piston of an engine by a large collection of particles that constitute some gas. The pressure felt by the piston fluctuates wildly in the presence of three or more molecules that sporadically collide with it. But it turns out that, for a large enough collection of particles, although their individual trajectories become effectively random, their collective motion becomes completely predictable. Here’s the crucial point. The pressure averages out as the number of molecules approaches infinity and, amazingly, the pressure ceases to depend on what the molecules are made of or how they interact. Its value is given by the ideal gas law that you probably learned at school. It only depends on how densely the molecules are packed into the container and on the temperature.

As Ludwig Boltzmann, the founding father of statistical physics discovered, even the temperature doesn’t depend on any detailed features of the gas molecules, only on the amount of energy that they have been given and on their symmetries – the number of ways you can rotate one of the molecules without changing its appearance.

This is a very important fact. It means that the detailed features of elementary particles do not determine how the universe works. Large-scale physics is not controlled by those details, but only by a few of their symmetries and by the statistical properties of large numbers.

Specifically, most of the macroscopic properties of matter depend only on how many different ways there are to rearrange its particles and energy. The preceding sentence sounds too bizarre to be true, and needs to be read several times. All that we experience around us; the wetness of water, the clarity of glass, the viscosity of treacle and the conductivity of silicon, are manifestations of combinatorics. They result from the mathematics of large numbers of interactions, not from the microscopic properties of those interactions.

If you still doubt that a theory based on statistics (on counting arrangements of particles) can constitute fundamental physics, you need look no further than the second law of thermodynamics, that most intriguing of laws, which states that the amount of entropy (disorder) in the universe can only increase with time. It is a consequence of statistical physics. Boltzmann realised that entropy is simply a way of counting large numbers of configurations, and yet it is responsible for our sense of the direction of time, a fundamental concept.

As a crude example of the unifying effect of large numbers, look at the flowing fluids depicted below. Their macroscopic properties, such as flow rate, diffusivity, compressibility, viscosity... are affected by a few basic features like the hardness of their particles, the packing density of those particles and the presence of gravity. At this scale, we don't notice what the constituent particles are made of, or their detailed features like the fact that the fluid on the right is made of red blood cells in a capillary, whereas that on the left is composed of athletes in the Engadin Ski Marathon.

A more precise (but rather complicated) correspondence exists between the behaviour of a fluid, such as water, at its critical point (where the pressure is just high enough to make the gas identical to the liquid, thus removing the boiling transition) and certain types of magnet, known as Ising magnets, at their Curie point (the temperature where they lose their permanent magnetism). These very different systems behave in identical ways as they approach the critical/Curie temperature. Fundamentally, the reason for this is that they both comprise large numbers of interacting particles that can each be found in one of two states: for Ising magnets, each atom's magnetic north pole can point either up or down while, within a sample of water, at any given location, a molecule can be either present or absent. No other microscopic features of these radically disparate sets of particles govern their collective behaviour. As a result, water and Ising magnets share identical large-scale physics and are said to belong to the same universality class.

Another material sharing the same universal features as these two is the "surfactant sponge phase". It is an arrangement of molecules that often forms spontaneously when you mix washing-up liquid with water. The detergent molecules group together, forming thin membranes that curve and connect into a sponge-like arrangement of pipes, depicted here.

This elaborate surface divides the water into two interpenetrating labyrinths. So, once again, within the sponge phase, each point in space can be characterised by a single binary digit, specifying which of the two labyrinths it belongs to. It also undergoes a transition at a critical temperature - not from gas to liquid, or from non-magnetic to magnetic, but from a "symmetric" state in which the labyrinths have equal volumes, to a state in which their symmetry is broken, with one region bigger than the other. [Roux D, Coulon C and Cates ME, "Sponge phases in surfactant solutions", J. Phys. Chem 96, 4174-4187 (1992)].

Since Kenneth Wilson's Nobel-prize-winning development of "Renormalization Group" theory in the 1970s - the mathematical tool for dealing with universality - many different “universality classes” have been discovered amongst a mid-boggling variety of interacting systems. Wilson and Boltzmann's theories apply to systems of particles at thermodynamic equilibrium, meaning that they are not flowing. More recently, there have been hints that the behaviour of flowing systems may be governed by a unifying statistical theory of “Large Deviations”, giving them universal features that are not obvious in the microscopic laws of nature. I honestly cannot image a more captivating subject to research.

Images:

1. Two particles attracted to each other following simple ellipitcal paths.
2. Three mutually attracting particles create more complicated, chaotic paths. Credit: Daniel Piker
3. Athletes in the Engadin ski marathon behaving like particles of a fluid
4. Red blood cells flowing through a capillary.
5. A sponge-like arrangement of molecules, such as that which forms when mixing detergent and water. Source: Physical Review Focus
   
   

Soldiers in Schools

(Published on iopblog as "Why Michael Gove's plan to fast-track soldiers into schools is worrying")

Could anything be more important to the future of our society than education? I truly believe not. That’s partly why I chose a career in lecturing, believing it a worthwhile use of my skills as a physicist. There are plenty of other topics causing concern at the moment, such as unemployment, crime and international tensions. We, as a society, need to tackle those issues but, in doing so, we are treating symptoms, not solving the problems. The root causes all involve shortcomings in people’s attitudes and in the quality of their decisions. Education is the means to improve things in the long term.

Tomorrow’s society is shaped by today’s parents and teachers. Bad education and upbringing is where our future problems begin. Good quality education creates the best chance of a socially and economically healthy world. I don’t imagine many people would disagree with those self-evident assertions.

Obviously then, being intelligent folk not intent on self-destruction, we only entrust this most crucial and difficult task — of educating and shaping the next generation — to the brightest and best. Surely, as a nation of sane people wanting a harmonious future, education is our top priority, into which we channel the majority of our resources, right? We don’t? Then I hope the government is going to put that right and turn teaching into the most prestigious and highly-trained of all professions.

What’s that you say about out-of-work soldiers? I thought we were discussing the future of education. Please tell me that the Secretary of State for Education, Michael Gove, is joking about the new ‘Troops to Teachers’ scheme, introduced this month, for fast-tracking ex-military personnel into the classroom! Under the scheme, those leaving the armed forces will be the only people able to start training as a teacher without a degree and be qualified within two years.

I don’t intend to make a party-political point, since I have not seen any recent government give education the priority that it’s due. ‘Troops to Teachers’ is just the latest down-grading of the kudos afforded to academic excellence. According to this policy, being successful in a particular academic subject at school apparently makes you less suitable to teach it than someone who trained for a career in the army.

According to BBC News:

A DfE spokesman stressed that top military specialists often have relevant experience, particularly in science and technology which could help redress the shortage of teachers in some subjects.

Well that’s a relief then. The DfE spokesman says science doesn’t need all the years of methodical rigour that university degrees squander on it. It can be picked up on the job by non-graduates trained to operate some electronic equipment. Now I feel foolish for wasting my time on all that pointless study.

I fear for our children’s prospects in the mathematical sciences if they are taught by people who share the spokesman’s confusion between technological proficiency and scientific education. And, while some schoolchildren would benefit from bootcamp drill, the DfE’s implicit endorsement of military discipline, as an adequate substitute for nurturing critical thinking, is a worrying message.

Don’t get me wrong, I don’t mean to disparage military personnel. In fact, I admire them for their extraordinary bravery and unquestioning loyalty. I don’t primarily admire them for their scholarship and child-rearing skills. Undoubtedly, some ex-forces people have those skills and could become excellent teachers. Rightly, they have always had the same opportunities as anyone else to embark on teacher training. But the idea that everyone else is less suitable, requiring more training than an ex-soldier before educating our children, is ridiculous.

This strikes me as a transparent ruse to use our education system to absorb the impact of the recent downsizing of the armed forces. What next? I hear there’s a mounting crisis in hospital overcrowding. Why not fast-track patients into the classroom. I’m sure that, like soldiers, many of them have a rich life-experience to draw upon, so there’s no need to consider their academic achievements.

Perhaps I shouldn’t be facetious about this most crucial and disappointing turn of events. But I begin to wonder whether the government is being facetious when it so often proclaims its commitment to promoting STEM subjects (Science, Technology, Engineering and Mathematics), and claims to appreciate their importance to our society and economy. STEM subjects require a great deal of dedication, inspirational teaching and uninterrupted hard study by academically gifted people. I would like to see more young people arriving at university well prepared for higher education in the STEM subjects. That would require a real commitment to academic excellence in schools. I can hardly believe I need to say this, Mr Gove: academic excellence is not the same as military training.

The English Patient

(As published on iopblog)

I’m writing this post from Room 7 of the paediatric emergency ward of l’Hopitale Sud in Rennes, France. It’s my fifth day spent in the room, distantly separated from my holiday luggage. It might seem like a strange priority, writing a piece for physicsfocus at this juncture, but there’s not a lot to do in the evenings, other than watch a cathode ray tube plotting graphs of the electrical signals emanating from my four year old son in the bed next to mine. I’m fine. He will be too, thanks to several dozen outstanding French doctors and the miracles of medical physics.

It has been a week that we’ll never forget; a week that has tested our emotional stamina and my O-level French to the limit. I could write about the turmoil caused by the cruel and dangerous condition that suddenly afflicted my son, or about the sheer brilliance of the French doctors who managed to diagnose an illness that only affects one person in a hundred thousand, with unique symptoms each time. But in view of this blog’s remit, I’ll tell you about a physical phenomenon that helped to preserve my sanity by providing a distraction from an otherwise bleak day.

Some of the vital diagnostic clues were provided by an MRI machine. You might know that MRI (Magnetic Resonance Imaging) uses an incredibly strong magnetic field, only realisable by modern superconducting electromagnets that can carry high electric currents without the resistance that would make ordinary metal wires heat up to melting point. Consequently, I was told, before approaching the machine, to remove any metal objects including my belt, phone, etc, that might fly towards the magnet, causing injury. Surprisingly, I was allowed to keep my gold wedding ring.

Entering the MRI room, I noticed the heavy door was edged with copper contacts that meshed with similar contacts in the door frame, to complete a Faraday cage: a metal enclosure completely surrounding the machine, screening its sensitive magnetic probes from stray radio noise in the outside world, and also preventing its own radio signals spilling out into the hospital.

My little one lay in the machine’s central tunnel, and the compassionate technician in charge let me lean in to hold his hand. The technician was ad-libbing, since this was an adult hospital, to which we had been diverted due to a broken MRI in the local children’s hospital. So perhaps she had overlooked the fact that my left hand – complete with wedding ring – would be inside the high-field region. In the event, the ring remained obediently on my finger and caused no problems, but I was treated to the distracting sensation of the gold band dancing and vibrating on my ring finger as the magnetic field was switched back and forth to elicit informative radio broadcasts from all the atomic nuclei in my son’s brain.

By tugging magnetically on the tiny bar magnet that is an atomic nucleus, then nudging it with a radio wave, the machine makes it precess exactly like a wobbling spinning top. That wobbling nucleus makes its own magnetic field wobble, generating radio waves that are picked up by the machine. As a side effect, the switching magnetic field made electric currents flow around my gold ring, turning it into an electromagnet that pushed and pulled against the field. Understanding the process made it seem no less magical when an invisible force shook my hand.

I’m very glad to be living in an age when this incredible technology, which would have been science fiction only a few years ago, has developed out of the curiosity-driven research of academic physicists. The non-invasive MRI scan was able to rule out all the common ailments, leading to a swift diagnosis and treatment.

They tell me he’s going to be OK; we just have to wait. The French medical staff have been excellent and the medical physics has been state-of-the-art. Call me a harsh critic, but I’m afraid, all in all, the holiday still gets a thumbs down.

Image: Kondor83/Shutterstock.com

"What do you do?"

(As published on iopblog)

Physics has always been my vocation. Perhaps it’s because my dad is an engineer, so my earliest memories are of soldering irons, microscopes and torque gauges. For whatever reason, I have always cared very deeply about trying to understand how the world works, and have never lost the childish impulse to ask “why” on every possible occasion. I pursued physics, and am now lucky enough to do it for a living. So when someone asks me “What do you do?” you might expect me to have a good answer at the ready.

It’s a question we all get asked whenever we meet someone, whether at a party, a bus-stop or (so we are led to believe) an audience with the Queen. Unless your life conforms to some standard set of labels, you probably find the question as tricky to answer as I do. You could just give your job title, but that doesn’t really summarise you, does it?

“I’m a university lecturer,” I’ll say.

I could have told them I’m a physicist, teaching and researching at Leeds University Department of Applied Maths, or that I’m a proud father – the activities that occupy most of my time. But I usually go with the job title. This prompts the response,

“What’s your subject?”

As any physicists out there will know, the traditional course of this conversation goes as follows:

“Physics.”

“Oh, I wasn’t any good at physics at school,” …followed by an uncomfortable silence.

I never know how to respond to that. “Oh dear” just sounds patronising, and “I was” would be worse. I would be grateful to hear your suggestions for diverting this social train-crash.

But ever since physics celebs Brian Cox and (fellow physicsfocus blogger) Jim Al-Khalili have captured the public imagination, I am pleased to report that the conversation these days tends to run more like this:

“Physics”

“Oh, that’s really interesting. What do you work on? Is it astronomy or subatomic particles?”

Of course, like anyone with properly functioning goose-pimples, I am filled with fascinated awe by both the vast and tiny extremes of our universe. But my own research is in a less well-publicised area of fundamental physics: statistical mechanics.

Statistical mechanics is the third pillar which, together with General Relativity and Quantum Mechanics, underpins our understanding of the physical world. Stat mech, as it’s known to its friends, lies between the realms of the very large and the very small, linking the two. It is the theory that explains why ice is hard and water is runny and liquid-crystals are weird.

Often the next question I am asked is:

“So, what substance are you working on at the moment?”

This is the point at which my interlocutor might reasonably begin to lose patience. I would love to be able to give a straight answer to that question, as a chemist or an engineer or even many physicists could.

“It’s not like that,” I have to say.

You see, some types of research apply to specific substances or specific gadgets. Some scientists study graphene, for instance, and some technologists design solar cells. But often, it’s more useful to classify research by the ideas that it addresses, rather than its applications.

Stat mech describes what happens when vast numbers of tiny particles interact with each other to form large-scale materials. Its principles can be applied equally well to water molecules, electrons in a metal, or the neutrons in a pulsar, to predict their behaviour en masse. The only proviso is that the collection of particles must be at equilibrium, meaning that they are not flowing.

Image: This artist’s concept shows young, blue stars encircling a supermassive black hole at the core of a spiral galaxy like the Milky Way. Credit: NASA, ESA, and A. Schaller (for STScI)

In my research, I am working to extend the well-established theory, to find the principles governing non-equilibrium systems, ie collections of objects that are in a state of flux, whether they are molecules of molten plastic flowing into a mould, or stars swirling round a black hole. I study the universal principles behind these types of collective motion, rather than focussing on a particular case. Any progress that can be made in this area will have countless applications that haven’t been imagined yet, so it’s a worthwhile thing to do, as well as being fascinating.

I believe that we need both types of research – ideas-based and applications-based – in order to achieve a really broad, deep and productive understanding of the physical world. I know which type I personally find more interesting. Unfortunately, it’s the one that’s hardest to explain at parties. It’s probably a blessing that I’ve never met the queen – I’m not sure she’s got the stamina for it.

In Focus

This week, the Institute of Physics launched physicsfocus, a new forum for discussion on all aspects of physics, from education to research to whimsy. The nine regular bloggers contributing to physicsfocus include a bloke with whom you may be familiar. It's a pleasure to rub shoulders (electronically) with such informed, provocative and erudite writers. I recommend you have a look at physicsfocus, and join the discussions. Meanwhile, just for completeness, I'll be reproducing my own physicsfocus posts here at PhysicsBloke.com, as well as posting other articles that don't appear on the IoP's site.

Gravitons

Since beginning my occasional series “The Big Questions” in Sky At Night Magazine, I have been contacted by people asking me to explain other enigmas of physics. Many of them are already extremely well informed, so it’s a real challenge to give an accurate and satisfying answer – a challenge that I find myself enjoying. Writing for the magazine has been an elevating and refreshing experience in many ways.

It would be wrong to mention Sky at Night this week without paying tribute to Sir Patrick Moore, whose inspirational life came to an end on Sunday. I won't attempt an obituary, as many have been published this week, far better than I could manage. Brian May, writing in The Guardian, put it particularly well: "the world has lost a priceless treasure that can never be replaced". But I will just add my ha'peth, as one of the legion of scientists who owe their earliest interest in astronomy to Sir P. I would like to express my gratitude for his enormous enthusiasm and thought-provoking presentation. Unfortunately, unlike the presenters of the TV programme, contributors to the magazine do not tend to meet, working instead by email and telephone. Nevertheless I feel fortunate to have my name appearing in a few of the same issues as his.

Returning to the point, one of the readers recently e-mailed me with a really deep question. It's a bit more technical than my usual blog entries, but I know it's something that a lot of physicists wonder about. So, with my correspondent's permission, I’ll reproduce his question and my answer here in full.

Subject: Gravitons

Dear Dr Evans

As a Sky at Night reader I have seen and enjoyed your first two articles, so look forward to the others.

Separately, in the last year or so, I have make making an effort to understand, or at least, get a better feel for Einstein’s relativity.

I have been able to (sort of) follow the steps that lead to Special Relativity and the how the problem of gravity (instantaneous action at a distance and so on) was resolved by the development of General Relativity simplistically as a geometric description – curved space-time.

What still does confuse me however is that elsewhere gravity continues to be described as a force with attempts being made to combine it with the electromagnetic, strong and weak forces into a theory of everything. In this context  the graviton is described as the force carrier for gravity (analogous to the photon, W & Z bosons, and the gluons for the other forces) on the way to the development of a quantum theory of gravity.

I suppose the question is whether gravitons are reconcilable with general relativity, or whether this means that the latter in itself is still not a complete description. I have looked at various websites to try and get some light thrown on this but without much success – references to stress energy tensors, and so on don’t mean anything to me, and I doubt are ever likely to!

It would be useful to know from someone working is this field what the current thinking is – definitely not in terms of any technical description, but just a summary that could be understood by the interested non specialist as to the status of the various theories.

If you are able to find time to respond, that would be useful, but quite understand if not.

Regards

Brian Radesk             

---

Dear Brian,

Thanks for your message. I'm glad you've been enjoying my articles.

It's a very interesting question that you ask. The short answer is that General Relativity hasn't been overturned. It has been built upon. Or, more accurately, it is being built upon, since there isn't yet a complete quantum version of it.

First, I should say, gravity is a force. I mentioned in my last article that "in a sense" there is no force, only geometry, but that's really just a way of understanding the nature of this particular force. Look in detail at any type of force, and you'll find an alternative way of describing it. So there is no contradiction between General Relativity and descriptions of the "force" of gravity.

Gravitons, like photons and the other "gauge bosons" (force carriers) are very confusing, and almost universally misunderstood. They are called "particles", but things that are called "particles" in quantum field theory (the "standard model") are not really particles at all in any sense that we would normally use the word. You might have heard of the idea of wave-particle duality in quantum mechanics, where an object like an electron sometimes seems to behave like a particle, and sometimes like a wave. In fact, all quantum mechanical "particles" behave almost entirely like waves. The only thing that they have in common with classical particles is that, under certain very specific conditions, they can be countable.

Take the theory of electromagnetism, for instance. This was all worked out by the Victorians, culminating in James Clerk Maxwell's theory that unified electricity and magnetism by describing them both with four elegant equations. That theory predicted the existence of electromagnetic waves, including light. 

Subsequently, those waves were found to exist with only a discrete set of possible amplitudes (or energies). So you can count the amount of energy possessed by those waves in discrete steps. One of these countable increments in the energy of an electromagnetic wave is called a photon. You see, it's not really much like a particle. And the existence of photons doesn't over-throw Maxwell's theory of electromagnetism.

Similarly, Einstein's field equations of General Relativity have solutions describing gravitational waves. Applying the principles of quantum mechanics, people expect those waves only to be allowed to exist with a discrete set of possible energies. These countable excitations of gravitational waves are called gravitons, but we don't yet have a full self-consistent mathematical description of them. Whatever the correct theory of quantum gravity turns out to be, you can bet it will incorporate the field equations of General Relativity.

I hope this helps.

Best wishes.

Mike Evans.

_______________

Dr R Mike L Evans

Lecturer

Department of Applied Mathematics

University of Leeds, LS2 9JT, UK

@PhysicsBloke

The Sky's the limit

Breaking News: The biggest name in popular astronomy publishing, Sky At Night Magazine, has a new writer. It's me! 

Over the next three issues (November 2012 – January 2013), I'll have a series of four-page feature articles about the physics of space – what it is, how it works and where it comes from. The series is called “The Big Questions” and, in each article, I’ll tackle one of the enduring questions about the Universe, and try to convince the readers that they don’t need to be Albert Einstein to understand the answers. 

The first article will be called “What is spacetime?”. I guess everyone has heard of “spacetime” and felt curious about what it really means, but most people assume that you need to be good at maths or have a degree in physics to have any chance of really knowing about it. I believe that no topic is too advanced to be explained in an entertaining way. 

So my articles are aimed at everyone. Curiosity is the only qualification that my readers need. The style is going to be irreverent, but never at the expense of accuracy. I expect to answer more "Big Questions" later in the year, as well as more news-based features on areas of applied maths and theoretical physics.

I enjoy writing, and I think that helping to make science more accessible is one of the most worthwhile things I can do. So I'm very excited to be embarking on this new project. Sky At Night Magazine has a great reputation, and it turns out that the editorial staff are really friendly and easy to work with. It's been great to see my scribblings being turned into polished and visually stunning articles.

As a theoretical physicist, I regularly talk about my research in academic circles - in seminars and at conferences. So I often rub shoulders with the great and the good - I've met a few Nobel laureates, and am no longer easily star-struck. But I have to admit that writing for the partner publication to the world-renowned television programme, founded and presented by Patrick Moore, does give me a frisson of pride and excitement. Or, to put it another way, Woohoo!

The November issue will be in the shops from 16th October.