First a warm welcome to all you new FUSION members who have joined in the last few months. We hope to see you at one of our forthcoming events. In the meantime, don't forget to visit our Web site at www.oufusion.org.uk. We also welcome all physics Associate Lecturers (aka course tutors) as readers, courtesy of the Physics and Astronomy Department.

Secondly an apology for the late appearance of this issue; yours truly managed to break his leg while strolling in the countryside. Not the most dangerous of sports you might think, but what with upping sticks for postgrad studies in Manchester, getting the Newsletter out has been a bit of a struggle. Still it does mean we have reports on our recent trips to CERN and Jodrell Bank (see the Photo Reports links above for pictures from these visits). Rumour has it that NEXUS will be organising a visit to DESY in Germany next year!

As well as the special report opposite, we have a staff profile on Bob Lambourne, arguably the best dressed man at Walton Hall - how else did he get on all those committees? Plus more on quantum computers and an interesting profile on Stephen Wolfran. Enjoy!

Paul Ruffle - Newsletter Editor

QUANTA AND CONTINUUM

NEXUS 10th Anniversary

The Fusion Newsletter is published with support from NEXUS, the student section of the Institute of Physics. To find out more about NEXUS (which is ten years old this year) contact Sam Rae the Student Officer at the IoP or visit their Web site at www.nexus.iop.org.

News of New Courses

There are plans for several new science and mathematics courses that may be of interest to students following a physics profile. The information given here, particularly presentation dates, is subject to confirmation and you should check with your regional centre before including these courses in your degree profile. The courses are S390 Science Project, MS324 Waves, Diffusion and Variational Principles and MS325 Computer Algebra and Modern Dynamics.

S390 is a project course based in physics or astronomy that is currently being developed for first presentation in 2004. It is likely to be a requirement for the a new named degree BSc in Physical Science that is currently under consideration and may also be first awarded in 2004.

MS324 covers several topics in mathematical physics that also have applications in other areas of mathematical modelling. Wave Motion starts with a derivation of and methods for solving the wave equation and then proceeds to discuss the d'Alembert solution and some characteristic properties of wave motion. Random Walks and Diffusion introduces the diffusion equation which describes the flow of heat and the mixing of substances due to the random microscopic motion of their atoms. Its solutions are discussed and the Laplace and Poisson equations, describing the special case of steady state flow, are introduced. Random walks and stationary random functions are also introduced and the macroscopic diffusion equation is derived from the fact that the microscopic motion of each atom is a random walk. Variational Principles covers the Euler-Lagrange equations for simple systems and goes on to consider symmetries and constrained systems. Variational principles are then applied to the dynamics of a system of particles and Hamilton's variational principle and the Lagrangian equations of motion are introduced. These equations are then extended to systems described by classical fields and an alternative derivation of the wave equation is given. The first presentation of MS324 is expected in 2004.

No details are available at present for MS325 which is scheduled for presentation in 2005.

From John Pollard

New Element Discovered...

Important scientific breakthrough in bureaucratic physics.

A major research institution has recently announced the discovery of the heaviest element yet known to science. This new element has been tentatively named "administratium." Administratium has one neutron, 12 assistant neutrons, 75 deputy neutrons, and 112 assistant deputy neutrons, giving it an atomic mass of 313.

These 313 particles are held together by force-like particles called morons, which are surrounded by vast quantities of lepton-like particles called peons. Since administratium has no electrons, it is inert. However, it can be detected as it impedes every reaction with which it comes into contact. A minute amount of administratium causes one reaction to take over four days to complete when it would normally take less than a second.

Administratium has a normal half-life of three years; it does not decay but instead undergoes a reorganization in which a portion of the assistant neutrons and deputy neutrons exchange places. In fact, administratium's mass will actually increase over time, since each reorganization causes some morons to become neutrons, forming isodopes. This characteristic of moron-promotion leads some scientists to speculate that administratium is formed whenever morons reach a certain quantity in concentration. This hypothetical quantity is referred to as "critical morass". You will know it when you see it.

From Mike Nugent.

Boring, Boring!

"...small changes in seemingly boring excited states of nuclei could easily have led to a solar system in which boredom would not be a problem, because nobody could be around to be bored."

Author A.C. Phillips commenting on the proportions of carbon and oxygen produced during stellar helium burning, and the anthropic principle, in his book The Physics of Stars (S381 course book).

Renewal Reminder

We recently started sending out membership renewal invitations to those of you who joined FUSION in the first part of last year. We are pleased to report a renewal rate of around 60% with nearly everyone opting for the three year deal for £10. So if you have not yet renewed your membership, please do so as we would hate to lose you! Look out for Jim Grozier's renewal invitation letter arriving around one year from the date you originally joined.

Summer School Reps Required!

We are looking for FUSION members who would like to promote the Society and sign up new members during this year's Summer Schools. All you have to do is print off 20-30 FUSION Membership Forms (from the Web site), take them with you and use your charm and persuasion to get fellow students to part with £5 (or £12 if they want to join the IoP as well). Last year we gained a lot of new members this way. For more info call Jim on 01273 505550.

TRIP REPORTS

Open Day

FUSION was well represented at the OU's Open Day in June, with five people volunteering to staff the Society's stall - in fact that was more than we needed, even allowing for a shift system, so we were able to help out the Physics and Astronomy Department who had rather more stalls than helpers.

Beagle II was on show, and FUSION managed to interrupt Professor Colin Pillinger's lunch to ask about the availability of a webcam on Mars. "We expect much more than the shots you saw of the Pathfinder mission" he said "there'll be daily updates on TV when it starts into operation".

Lee McDonald won a FUSION T-shirt for getting the most right answers in our light hearted quiz.

Open Day 2002 Photo Report

Jodrell Bank

by Jacqui Dodds

On 6th July sixteen of us gathered in the heart of the Cheshire countryside (some dedicated members travelling from as far as Brighton and Cornwall) at Jodrell Bank Observatory (JBO). Our guide for the day was Ian Morison co-ordinator of the SETI programme at JBO and former Operations Engineer there. Ian is also an OU tutor in the North West region for S281 Astronomy and Planetary Science.

This was no ordinary tour of the Jodrell Bank Visitor Centre; we were to go behind the scenes and see where the cutting edge research is taking place.

MERLIN (Multi Element Radio Linked Interferometer Network) operated by JBO is an array of radio telescopes distributed around Great Britain with separations up to 217km, operating at frequencies from 151MHz to 24 GHz. The control room where the synchronizing of MERLIN takes place offers an impressive view of the Lovell Telescope.

The giant 76m Lovell Telescope has been a feature of the Cheshire landscape since 1957. At the moment it is going through a £2 million upgrade to improve the sensitivity and frequency range. The old surface panels have been replaced by galvanized steel plate which has been mounted without welding to make a smoother parabolic shape. The drive and control system are also being replaced by new technology to give independent control of the individual drive motors and the track and foundations have also been refurbished.

Our first port of call was in the Technical Development Labs. One of the major projects undertaken by the Receiver Group at JBO has been to design and build the 30GHz receivers required for the Very Small Array (VSA) installed at the observatory on Mount Teide, Tenerife. The VSA is being used to make exceedingly sensitive measurements of the Cosmic Microwave Background radiation to learn about the early Universe. Observations at such high frequencies are not practical in the UK due to the amount of water vapour in the atmosphere. The receivers with their horn antennas will form an aperture synthesis array to give the resolution of a much larger system - defined by the size of the array - but capable of simultaneously observing a much larger area of the sky than a single large antenna.

The broad band 30GHz low noise amplifiers have a noise temperature around 15K. The receiver and part of the feed horn is mounted within a cryostat cooled to approximately 15K by the use of a compressed helium refrigeration system. The system noise temperature of the VSA receivers is of order 30K, which is a factor of two better than the earlier generation receivers currently in use on Mount Teide.

In another part of the building fibre optic engineering is providing the astronomers with efficient data transfer technology, which has the advantage of high speed, high reliability and low interference. Data used to be transferred across continents by tapes, whereas fibre optics offers alternative data transfer of signals in highly sensitive antenna arrays.

We took a look at COBRA (Coherent On-Line Baseband Receiver for Astronomy) which is a high performance supercluster that can be programmed to perform any function of existing radio receiver instruments simply by modest changes in the software coding. The primary use of the system is in the observation (using the 76m Lovell Telescope) of pulsars, the search for new pulsars and as a high performance computer facility for running simulations of astrophysical phenomena.

Ian Morison gave two talks: 'The Story of Jodrell Bank' and 'Merlin - how and why'. Ian also told us that VSA results in the last few weeks had been cited in about 20 papers about exciting new things that were happening in cosmology. The visit was one of the best I have been on.

Jodrell Bank Photo Report

CERN

by Jim Grozier

In June, nine FUSION members took part in the annual visit to CERN, the world's largest particle physics research centre, organised by NEXUS, the student wing of the Institute of Physics.

CERN occupies a site on the outskirts of Geneva; its most well-known feature is a circular tunnel 27km in circumference in which the particle beams are accelerated prior to collision. You could actually fit quite a large town - Milton Keynes, maybe even Coventry - into a 27km ring; but the tunnel is about 100 metres under the ground, so that all you see from the surface are fields, cows, sheep and the odd building or two; CERN itself takes up about a tenth the area of the ring.

As the equipment is currently being upgraded - from the LEP (Large Electron-Positron) collider to the LHC (Large Hadron Collider), we were not able to go down into the tunnel itself. But we did see one of the huge new detectors being constructed on the surface prior to being lowered down into its place in the ring. The Compact Muon Solenoid (CMS) will be 20 metres long by 14 metres wide, and weigh 12,000 tonnes, when finished; another new detector, ATLAS, will be even bigger. Our guide gave us all the relevant facts and figures, and the tour was prefaced by a general talk about what goes on at CERN and details of the upgrade.

When we had had our fill of CMS we were allowed to wander around the exhibition area, which includes some impressive educational exhibits reminiscent of the Science Museum, and, in the garden, some lovingly restored relics of a previous era - such as bubble chambers and resonant RF cavities - which appear to have crossed the boundary between science and art.

We also had a 'free day' to explore Geneva, and several opportunities to sample the local ale, including one evening with FUSION member Jorge Sanchez (who works at CERN).

CERN Photo Report

The Future for OU Physics

A special report from Nigel Mason the OU's new Professor of Physics

Recently the Institute of Physics (IoP) sent out an appeal asking members to define 'What is physics' in two sentences. It was a rewarding exercise making many of us think about how to describe physics in the 21st century and how to explain it to the public, the media and potential students. For many of us the words of President Clinton that 'the 20th century was the century of Physics, the 21st will be that of biology' echoed. Falling numbers of physics students, departmental closures, decreasing research funding, difficulties in attracting postgraduate and postdoctoral researchers all seem to confirm the demise of physics as we enter the 21st century! Thus in assuming the post of Professor of Physics it would seem that I should be depressed facing a quarter of century of fruitless toil - like Sisyphus pushing his boulder eternally up hill. In fact I am delighted to join the OU Department of Physics and Astronomy at this time since I believe that there is a unique opportunity for the OU to place itself in the vanguard of a new era of physics research, education and exploitation.

Physics is the science that underpins many or all of the other sciences. In the last decade the life sciences have recognised that their 'nanoworld' - governed by quantum phenomena - makes physics as relevant to them as it is astronomy and technology. Physics and physicists are therefore in great demand. As Departmental Careers Officer at UCL it was my job to determine the destinations of our graduates and learn how much they were paid. A sobering experience when you found that students having graduated 18 months before were earning more than yourself but it also had its perks when city companies eager to attract your students invited you to lunch at the Savoy! Nonetheless in every developed country there are fewer physics graduates. Why?

I believe that, in part, physicists are themselves to blame - quite simply we have not answered the IoP's question - What do physicists do? If we can not answer that how can we convince others to 'do physics'? Have we been slowly bludgeoned by the 'Clintonesque propaganda', leaving us defensive and unsure as to our role?

So to the OU and you!! You are direct evidence that there remains a keen interest in physics and a desire to learn more about it. That is of course the role of the OU, to provide the opportunity for anyone to study physics with all its complexity of quantum mechanics, electromagnetism and relativity such that they may gain an understanding and appreciation of the world about them. However physics must also be put into context and here again the OU is perhaps unique. As an OU student you can take a range of science of courses and thus appreciate for yourselves how and where physics is applied and relevant.

This is also the ethos of my own research and will be that of the new Centre of Molecular and Optical Sciences (CeMOS) - which will act as an 'umbrella' for the physics department's research at the OU. However such research must embrace other disciplines developing joint research with colleagues at the OU, other UK Universities and abroad. Already areas for collaboration have emerged. My own laboratory studies of astrophysics together with the observational and modelling studies of the astronomers and the varied studies of PSSRI being recognised as worthy of co-ordination in a new 'Centre of Astrobiology' which, if not the first in the UK, has the potential to be the most wide ranging and largest. There are also common interests with researchers in chemistry on the study of radiation interactions with DNA and with the Oxford Research Unit in technological plasmas. Thus I believe that we may look forward to a renaissance in (physics) research at the OU as staff from several departments are drawn together to work on the themes that will dominate 21st century science:

• The Environment and climate change.
• Technological advances in plasmas and development of quantum devices.
• Astrobiology and the search for origins of life.
• The life sciences.

Of course even with the appointment of further new staff in physics the OU can not expect to cover all areas of modern physics, thus it must build strong partnerships with other UK universities to share resources and personnel to form research teams with 'critical mass'. The OU with its regional networks and emphasis on collaboration can play a unique role in acting both as a forum and example for such collaborative partnerships in which the future for UK academic research and technology surely lies. Indeed the Faculty has already been able to attract several internationally renowned researchers as 'affiliated Professors' to work on joint projects within the CeMOS remit. I am likewise a great supporter of international research collaboration and presently co-ordinate several European research projects. Once again this is in accord with OU tradition, the OU having successfully exported its teaching across Europe and the world - the appointment of the new VC from South Africa being testimony to the OU's global reach and appeal. The future requires that we seek to further such international links attracting international students, researchers and funds to the new research centres at the OU. How better than by offering an environment that is 'open for ideas, open for research and open learning for all? As our students I hope you may spread the word that at the Open University we are indeed open to all and to use a popular advert 'The Future is Bright, The Future is Physics'.

Why don't you attempt to define physics in two sentences? Send your suggestions to n.j.mason@open.ac.uk.

STAFF PROFILE - Dr Robert Lambourne

I first became interested in science as a result of reading 'space' comics when I was about 5. I left primary school at the age of 11 with the school science prize and a determination to study science. I went to a small secondary school in Reading, where I was lucky enough to be inspired by a wonderful physics teacher called Charles Pearce. Mr Pearce knew relatively little physics. He had been trained as an English teacher, but following World War II there was a shortage of physics teachers and he chose to become one. Whatever he lacked in subject knowledge he certainly made up for in enthusiasm and wisdom. He took an enormous delight in the intricate wonder of the physical world and in the creative role of humanity.

At the age of 16 I transferred to a larger school to take my A-levels (Physics, Maths and Further Maths) and from there went to Queen Mary College, University of London to read Physics where I obtained a 1st. I then spent three more years earning a PhD in theoretical particle physics (my thesis concerned the distribution of quarks and antiquarks inside strongly interacting particles such as the proton and the neutron).

Following my PhD I moved to the University of Durham as a Temporary Lecturer in Mathematics and while there taught, amongst other things, relativity, cosmology and part of a Pure Maths MSc course in differential geometry (the mathematics that underpins general relativity), as well as continuing my research work in particle physics.

From Durham I moved to the OU, initially as a Temporary Lecturer, subsequently becoming a permanent member of staff. Since arriving at the OU I have worked on a variety of courses and my interests have broadened to accommodate many areas of mathematics and physics, particularly astrophysics. I no longer regard myself as an active particle physicist, having taken the decision some years ago to abandon work in that field in favour of a full-time commitment to all aspects of physics education. Since then the main projects I have been involved in have been:

S281 Astronomy and Planetary Science, where amongst various contributions on the Sun, the Milky Way and other galaxies, I also helped to edit the book Images of the Cosmos, co-published by the OU and Hodder.

FLAP - The Flexible Learning Approach to Physics - this was a large project funded by the Higher Education Funding Council that aimed to provide conventional universities (i.e. not the OU) with an extensive package of maths and physics teaching resources so that tutors in those universities could easily put together high quality courses that would help their students negotiate the difficult transition from school to university.

The production of these teaching resources drew heavily on the teaching experience, team management skills and resource production experience I had gained through working at the OU. The FLAP project was a great success and the enormous amount of material it produced is still in use at many universities in the UK and abroad. The project lives on with another five FLAP modules being edited and two CD-ROMs being developed, one in association with the University of British Columbia.

S207 The Physical World, where, apart from chairing the course, helping to write The Restless Universe and editing or co-editing Describing Motion and Predicting Motion, I contributed to the materials on mechanics, thermodynamics and quantum physics. I am particularly pleased that, through a co-publishing deal with Institute of Physics Publishing, money from the sales of these books outside the OU is being used to enable the OU's astronomy research group to participate in SALT - the South African Large Telescope that is currently being built.

My present teaching project is S282 Astronomy, where I shall be helping to produce a book on galaxies and cosmology. Since becoming the Head of the Physics and Astronomy Department last January, it has been hard to find the time for my OU writing, but it is a very rewarding activity and one that I greatly enjoy.

Along with other members of the OU Physics and Astronomy Department, I am currently involved in efforts to establish an OU Physics Education Research Group.

Outside the OU, I am very active in the Institute of Physics. I am currently on an IoP working party looking at the possibility of introducing a new style of physics degree. I represent the IoP on the University section of the Physics Education Division of the European Physical Society, and I am a member of the Divisional Committee. I am also involved in an Advisory Group on an 11-14 physics initiative that the IoP is running. I have a strong interest in the Public Understanding of Science, and a long standing involvement with the Oxford University Department of Continuing Education, where I help to organise a range of public outreach activities. Last year this included two day schools on cosmology, one on quantum physics, one on volcanoes and an Astronomy Weekend. The audiences often include past, present and future OU students.

My main relaxation is reading science fiction. In 1990 I co-authored a book on the role and image of science in science fiction called Close Encounters? Science and Science Fiction.

Leading Lights of Contemporary Science

Stephen Wolfram

Born in London in 1959, Stephen Wolfram is a gifted scientist. His family background was intellectual, his mother being an analytic philosopher at Oxford University, and his father a novelist. In his teens he had written a scientific paper for a physics journal and an unpublished book about particle physics. His 1976 paper for the journal Nuclear Physics, "Neutral Weak Interactions and Particle Decays", sets out the possibility of deducing the form of such interactions from measurements of particle decays.

This was only the beginning of his achievements in fundamental physics. He obtained an early PhD in theoretical physics from CalTech in 1979, awarded in part for the ten scientific papers he had by then published. These included the invention of the Fox-Wolfram variables for the analysis of event shapes in particle physics, and for the discovery of the Politzer-Wolfram upper bound on masses of quarks in the Standard Model.

At CalTech he made important connections with the physicist Murray Gell-Mann, who will be discussed in a later article. Wolfram then started writing a computer algebra package called SMP which he released in 1981. About that time he also made friends with Gregory Chaitin (another important mathematician, more later).

Described as brash and demanding, Wolfram naturally ruffled some feathers in American academic scientific circles. He left CalTech for the Institute for Advanced Study at Princeton in 1983, because he could not come to an agreement with CalTech about how to commercialise his work. In 1986, disappointed by the general scientific reception of his latest work, he founded the Centre for Complex Systems Research at the University of Illinois.

At the same time, Wolfram began writing a new package in order to assist him in his own research, that was later to become Mathematica, one of the earliest and most successful computer mathematics packages. This has made him very wealthy.

Over the last ten years, Wolfram worked on his magnum opus, "A New Kind of Science" - promising to publish it on a regular basis. However, he kept extending the deadline for publication. Becoming a virtual recluse, he worked almost exclusively on material for this book, having pretty much given up on academic recognition. Thus he has published the work himself, using his own personal finances.

The book itself contains a fundamental reworking of mathematics in general - an ambitious pursuit as you can well imagine - replacing mathematics with computer programs written in a simple pictorial binary language. In many ways, this approach is that of the structuralist program in the foundations of mathematics, a kind of generalization of category theory.

In foundational issues in mathematics there are several conflicting formalisms. One cluster of formal logic holds that mathematics is based upon sets as fundamental atomic primitives. Thus all maths can be described in terms of logical set manipulations. However, this runs into problems, the most famous of which is named after the philosopher Bertrand Russell who discovered it, and is a deceptively simple but knotty paradox of set self-membership.

Another approach, mathematical category theory, sidesteps these paradoxes by taking a structuralist approach. Thus it does not demand any fundamental primitives at all, but instead shows how mathematical structures in one area are related to structures in another.

Wolfram's approach is to take Turing machines as the foundations of mathematics. Wolfram argues that programming a Turing machine is really describing how data can be converted from one form to another using simple transformation rules, not unlike those in category theory.

These transformation rules can then describe the behaviour, development, dynamics and existence of a vast array of naturally observed phenomena, from explanations of fracture and regular lattice formation in crystals undergoing annealing through motorway traffic jams, from oscillating spiral chemical reactions to patterns in coral skeletons! Along the way, Wolfram promises to place fundamental physics on the same footing, with potentially a fundamental theory of everything to boot!

To be fair, Sejnowski, an important neuroscientist says that "Steve Wolfram is the smartest scientist on the planet, and if anyone is capable of creating a new science, he is the one." If you wish to find out more information about Stephen Wolfram, his homepage www.stephenwolfram.com is stuffed full of interesting articles.

Max Little - a nocturnal OU Mathematical Sciences creature who, when the sun rises, emerges, into the real world as an audio programmer for video games consoles.

The 76m Lovell Telescope at Jodrell Bank.

QUANTUM COMPUTERS - Part 2

In the second of a series of articles Andy Greentree explains how Quantum Physics comes into play in modern computing. > Part 1 > Part 3

The physics of the very small is quantum physics and this point represents a barrier beyond which no classical computer can go. So is that really it? In 2030 do we have to stop building new computers? In order to progress further we need to understand the 'quantum barrier' and learn how this problem can be turned into an opportunity to build the most powerful devices yet.

Quantum Physics

Clearly this can be no more than a brief, idiosyncratic summary of quantum physics. In broad terms I will introduce two of the most important concepts of quantum mechanics which serve to illustrate the differences between the quantum and the classical worlds. These concepts are Heisenberg's Uncertainty Principle and wave-particle duality. Along the way we will encounter the concept of measurements and superposition states, and we will show how the Uncertainty Principle will stop classical computers in their tracks.

Heisenberg's Uncertainty Principle

"What we observe is not nature itself, but nature exposed to our method of questioning." This quotation is from Heisenberg and encapsulates something profound of the workings of the universe itself. Before quantum mechanics, we could think of the universe as a machine, ticking away. Indeed some thinkers even believed that it would be possible to exactly determine any future state of the universe (and past state too, no doubt) by understanding some set of conditions to arbitrary accuracy (Newton? Fourier?). Of course it is obvious that scientists could affect the systems they were observing (for example by a bad choice of experiment, or dropping a spanner on it)3, but it was always possible to consider an ideal observer. One who could know the internal state of whatever was under discussion. Quantum physics forces us to reconsider this assumption and indeed shows it to be false.4

So let's ask ourselves a fundamental question - "How do we measure something?" Let's suppose I have a particle, say an atom, and I want to know where it is. One way to do it is just to look at it. Well, in order to do this I need a light source, say a laser, but in theory even just a light bulb, and I need a stream of photons (particles of light) fired in the direction of the atom. Some of the light will miss the atom all together, we ignore these, and some will hit the atom, and bounce off in some random direction. To detect these I'm going to have a lens focussing the scattered light onto a detector, for example a CCD camera.

Now the resolution of my detection is governed by several things, the pixels on the camera, well we'll ignore these, and the wavelength of the light we use. The wavelength of the light varies with the colour of the light. The redder the light is, the longer the wavelength, the bluer the shorter. It affects our measurement in two important ways. Firstly it alters the probability of the photon interacting with the atom⁵ (is it easier to hit a cricket stump with a ping-pong ball, a cricket ball or a football?). Secondly the shorter the wavelength of light used, the more tightly it can be focussed. This is the so-called diffraction limited spot size, and the smallest spot that can be focussed is of order the wavelength of the light. Combined, these two factors gives a minimum resolution to how well we can detect where an atom is. The better we want to locate the atom, the smaller the wavelength (the bluer in colour) of light we must use.

All well and good, but there is a problem here, and that is that photons carry momentum. Not much momentum, so little that we can't feel it, but an atom, being extremely light, feels a kick every time it is hit by a photon. So every time a photon hits an atom and bounces off in a random direction, the atom recoils in the opposite direction. Now the shorter the wavelength of light used (for the greater resolving power), the larger the momentum kick imparted to the atom. So the better we know where an atom is, the less well we can predict where it is going.

Mathematically we can write this as ΔxΔp >= h/2 where Δx is the uncertainty in the position, Δp is the uncertainty in the momentum and h is Planck's constant (divided by 2π). It's important to realise that Planck's constant is independent of how we actually perform our measurement. This is a fundamental law of nature.

Planck's constant is a very small number, and understanding it is vitally important to understanding the difference between the quantum and classical worlds and why the quantum world is so elusive. Just as the speed of light sets the scale for which we need to worry about relativity, Planck's constant sets the scale for which we need to worry about quantum mechanics. You can also see that this uncertainty relationship tells us why quantum mechanics will foil Moore's Law. Quite literally, Heisenberg's Uncertainty relationship sets a scale beyond which it is impossible to define positions, so it will be impossible to put transistors closer than (of order) this minimum scale.⁶

Waves or Particles

Our description of the Uncertainty Principle was a very particle-like description, but to delve further into the nature of quantum mechanics, we need to really address what we mean by 'particles' and 'waves'. A long-standing observation has been that we can classify 'things' as being either particles or waves. What are some of the properties that we associate with either?

We naturally think of particles as structures that are localised. So by that we mean that they are only in one place (or finite region) at any one time. Also, on some scale they usually indivisible, so you can't really have half a particle, and if you can split it up, it's usually to make something new. Examples of particles from the classical world might be grains of sand, or billiard balls.

Waves, on the other hand, are entities which tend to spread out. They're not localised and can shrink and grow freely. We never really associate classical waves with a number of particles, its more sensible to think of an intensity, and we can always reduce this freely if we want. An example of a classical wave would be a wave at a beach, or a loud shout. An important property of waves is interference. When two waves meet, depending on their phase they will either add up constructively, or could cancel out. After this interaction, the waves travel through each other unchanged.⁷

Now, let's consider an experiment to try and determine whether electrons are particles or waves. To do this we take a source of electrons, an electron gun, and fire it at a pair of slits. The purpose of this is to take our single source and turn it into two sources. The electrons will then travel through a region of space before being detected on a screen.

Before doing an experiment it is often a good idea to try and work out what will happen, that helps in interpreting the results. In this case, if the electrons are particles, we expect to build up a pattern that is reminiscent of a sand pile, with most of the electrons in the centre and fewer near the wings. If the electrons are waves, then we expect to see a pattern similar to interference in a ripple tank, and so on the screen we will see alternating regions of bright and dark, the characteristic signature of waves.

This experiment can be done and the results are instructive. When the apparatus is first turned on, individual bright spots of light are noticed on the screen. The spots of light are due to interactions between electrons and the phosphorescent screen. Appearing randomly, it seems to offer good evidence for a particle-like explanation. But as the experiment continues, we start to notice something strange. The arrival of the electrons is not truly random, there are definitely places where no electrons are being detected. As the experiment continues, the fringe pattern, which is indicative of wave behaviour, is now quite obvious. Somehow the electrons have managed to travel like waves, but be detected like particles.⁸

The modern description of this is that the electron starts out as a particle like structure, goes through both slits simultaneously, and interferes with itself to form a fringe pattern just before detection, when it localises into a particle. The process by which the electron goes from being a wave to a particle is called the collapse of the wave function. Just before the collapse, we say that the electron is in a superposition of all the different places where it can be found.

In order to try and learn more about this particle-wave duality, we perform another experiment. This time, in addition to the electron gun, the slits and the screen, we add an X-ray source which shines on one of the slits. To make things concrete, we'll assume that the slits are 1nm (10^-9 metres) wide and 10nm apart. We start off by shining x-ray photons of wavelength 3nm, so that we can completely resolve which slit the electrons have gone through.

This is possible, but when we view the screen we notice something mysterious. The fringe pattern we had seen earlier has disappeared. Why? Perhaps we hit the electrons too hard. Let's turn down the energy of each photon, which increases the wavelength. Now we choose a wavelength of 5nm. Not short enough to completely resolve which slit the electron went through, but we still get some information. Performing such a measurement gives a pattern which has a faint ghost of interference superimposed on a constant background. It's as if we're halfway between particle-like and wave-like behaviour. If we turn down the energy of the photons until their wavelength is 10nm, the same as the spacing between the slits, we can no longer discern which path was taken by the electrons and the fringe pattern reappears.

The only consistent way to explain these results is to say that if we don't measure the electrons, they follow both paths, which gives rise to wavelike properties. If we spot an electron going one way or the other, it is localised and behaves like a particle (superposition is destroyed). Partial measurement destroys some of the properties.

It is actually important to realise that although we might like to think of an electron splitting in two and following two paths simultaneously, no such thing occurs! Quantum mechanics forces us to rethink the world and one thing it forces us to reconsider is the existence of particles and waves. The model used by physicists today is that the electron is neither a particle nor a wave. It is described by a probability wavefunction and it is this wavefunction which splits up. If the wavefunction is localised, then it is natural to think of the entity as being particle like, if it is diffuse or following many paths, then it is natural to consider our entity as being a wave.

In theory everything can be considered as having both wave and particle like properties. Light was first interpreted as a wave, but later shown to have particle-like properties. The particle of light is called the photon. Sound is thought of as a wave, but in special circumstances can be thought of as a particle, the phonon.

In properly designed experiments almost all of the elementary particles have been shown to have wavelike properties. The most massive particles shown to have wave-like properties are Carbon 70 Bucky Balls. The molecules have 70 carbon atoms and on the quantum scale they are truly enormous. The experiment showing their wavelike nature was performed in Anton Zeilinger's group in Austria and stands as a truly titanic feat of experimental physics. > Part 3

³Actually the original argument included the state of mind of all people, and so was fully deterministic. It is important to realise that quantum mechanics does not necessarily give us back free will. ⁴Actually it just shows us that we can't conceive any methods for an ideal observer, and barring magic or an omnipotent being is a complete description of the universe. ⁵We are ignoring any resonances in the atom. ⁶Actually there are far more ways for quantum mechanics to ruin future computers and it can be fun to think up your own. ⁷Formally, for the waves to be unaltered after interaction the interaction must be linear. The opposite of such interactions are non-linear and understanding them is very important in the field of photonics. ⁸It is interesting to note that J.J. Thomson won the Nobel Prize in 1906 for showing that electrons were particles, and in 1937 his son, G.P. Thompson was a co-recipient of the 1937 prize for showing electrons were waves. As you can see, they were both right!

Fusion members needing a yard (metre?) of ale after their visit to CERN.