At the 2005 AGM, Fusion members decided to proceed with plans for a S207 Preparation Weekend. S207 - The Physical World offers a wide-ranging introduction to physics, covering classical mechanics, thermal physics and fluids, fields, waves and electromagnetism, relativity and quantum physics.

The aim of the preparation weekend is to ease the transition from Level 1 to Level 2 science by consolidating and building on knowledge acquired from courses such as S103 - Discovering Science and S151 - Maths for Science; it is not intended as a substitute for these courses. Proper preparation in both mathematics and physics for S207 will allow students to focus on new material rather than having to play catch-up with ideas that they may have met before but not mastered. Participation in the weekend is anticipated to enhance success in S207.

Fusion plans to present this event on 28-29 January 2006 at Milton Keynes. The weekend will run from Saturday to Sunday, rather than Friday to Sunday, to help keep accommodation costs down and to allow time for travel from outlying regions.

Interested students should register their interest as soon as possible by emailing S207@oufusion.org.uk or by sending a post card to:
Fusion S207, 142 Kingsley Rd, Northampton, NN2 7BY.
Check the Fusion web site for further updates.

Celebrate Einstein Year with a FUSION Einstein T-Shirt

Featuring Einstein's general relativity equation and priced at just £8.50 (including UK post and packing) and available in fashionable black or dark navy, in sizes M, L, XL and XXL. Send your cheque (made out to FUSION), with your delivery address, colour choice(s) and size(s) required to Fusion. Visit our web site for details of all our T-Shirts.

2005 AGM Photo Report

Fusion members pose outside the Royal Pavilion on Sunday.

See more pictures in the 2005 AGM Photo Report by Paul Ruffle.

QUANTA AND CONTINUUM

How I need a drink...

by Frank Buxton

Reading the above in the Winter 2004 Newsletter reminded me of recent researches of my own in the pages of the Encyclopaedia Britannica, (1950 edition). (I acquired the complete set from a friend for £50, during their divorce when they dismantled their home.) Please don't ask what I was looking up, but I came across this little snippet in an article discussing the production of Mathematical Tables: "Prodigies of computation have been achieved by means of some of these modern devices. For example, William Shanks (1812-1882) in 1873 published a value for π to 707 places (of which only 527 are believed to be correct)..." and a little bit further on, "An approximation for e to 707 decimal places was published in 1926 by D H Lehmer..." and then again still further, "Such extreme values have no intrinsic merit in themselves for one may show that if the radius of space is 2.7 × 10¹⁰ parsecs (1 parsec = 3.258 light years) and the diameter of an electron is assumed to be of the order of 2 × 10^-13 cm, then a value of π to 41 decimal places is sufficient to express the circumference of space in electron diameters."

Peter Napier Prizes for 2004

by Stuart Freake

A few years ago, the Physics and Astronomy Department received a legacy from Peter Napier, an OU graduate who had studied many of our physics courses. The Department decided to invest the money and use the income to fund two annual student prizes of £50 book tokens. One prize goes to the student with the best performance in S207 - The Physical World and the other goes to the student with the best performance in one of the Level 3 physics or astronomy courses.

The 2004 winner for S207 is Stephen Portwine from Reading. Stephen wrote about himself as follows: "The Open University has provided me with a fantastic second chance in education. I studied chemistry at Bristol University after leaving school, but rather carelessly left without a degree! I retained an interest in science, although it became clear that it was physics rather than chemistry that really excited me. I took the plunge this year and studied S207 - The Physical World. The course was very intense and I gave up playing cricket for the first time in many years. I did manage to keep playing for my local football team and even managed to attend most home games of my beloved Charlton Athletic (working on the train to and from the games to justify this extravagance). The course was demanding, but hugely rewarding and gave me an insight in matters ranging from star formation to the nature of reality at the quantum level. I will be taking a break from the OU next year as my first child is due to arrive in May, but I hope to return to my studies in 2006. I was very honoured to hear that I had won the Napier Prize. I know my wife too was brimming with pride, as she should be with the help and support she has given throughout the year. I should also thank the students and staff at the SXR207 summer school who were a real inspiration, and my tutor, John Smith."

The Level 3 prize has been awarded to John McKenzie from Stevenage for his superb performance on S357 - Space, Time and Cosmology. In his letter accepting the prize, John wrote about his experience studying with the OU:

"I'm a Cardiffian, now living in Stevenage, married with two sons who have recently gone through university, and am enjoying now being the only student in the family. Since taking early retirement (my last job was in telecoms pricing), I've been slowly working my way through the OU science courses, and hope to eventually get a BSc by around 2010. My original qualifications were in maths, which must have helped with Space, Time and Cosmology."

Both Stephen and John obtained marks in the high 90s for their continuous assessment and for their exam. So congratulations to both of them on their excellent performances! There were quite a few other students who scored in the 90s for both components of the assessment, and they deserve congratulations too.

New OU Initiative

A new Centre for Excellence in Innovative Physics Teaching is to be opened, the HEFCE announced on 27 January. The centre - a collaboration between the Open University and the universities of Leicester and Reading - will offer students "new learning experiences that will make clear the power and fascination of cutting-edge physics and astronomy".

Obituary - Ron Dawson

by Elsie Denham

I am sorry to tell you that Ron Dawson died on Tuesday, at the age of 77. He was past Chair of OUCSTSS and editor of our journal Open File and as many of you know, worked long and tirelessly for the Society. He resigned from office at the end of 2003 because early treatment for his cancer was not successful and he knew he would face a year of difficult treatment. He was in touch, still cheerful, just before Christmas as he prepared to go back into hospital but his condition deteriorated rapidly in the last three weeks. He will be sorely missed by OUCSTSS and I know he was active in other societies.

Ask-a-Boffin

What is Time?

Ron Larter asks: "I often hear or read of scientists saying that a theory of time is not necessary or even useful, yet in some circles I find there are some who persistently search for answers to the age-worn question, 'What is time?' It seems no one to date has been able to offer a satisfactory answer." Ron goes on to ask "Can we assume that there is indeed a direct link between energy and time? Einstein's equation E=mc² tells us that mass and energy are interchangeable. They are two aspects of the same thing. It would appear to me that this interchangeability of mass and energy is the very process that gives rise to the product we call time."

Paul Ruffle comments: "Relativity and quantum physics treat time quite differently. Time is an integral part of relativity, the stretchable 'distance' between two events, where it can be slowed down or speeded up simply by changing the relative velocity of the observer, or by being in the vicinity of a large gravitational field. However, in quantum physics, time is the non-participating fixed background upon which events unfold."

John Small comments: "This is the problem with the nature of time and is the critical issue preventing a union between general relativity and quantum mechanics. Other people, notably Roger Penrose, have suggested that we do need to rethink what time actually means in order to make any real progress in quantum gravity. In my article, An Alternative Point of View, I've taken the view that any serious contribution to an understanding of the nature of time, if it is to be taken seriously, must lead to an understanding of the nature of space too. This issue of time/space energy/momentum has been gone over quite a lot by other people, notably by Julian Barbour in 'The End of Time', plus there are long review papers by Christopher Isham and Carlo Rovelli and others that dwell extensively on the nature of time in different theories. So Ron's not the first to note that energy changes things in time and we can only measure time by the co-ordinated changes of things, and that time is effectively the co-ordinated change of things."

Jim Grozier comments: "Be careful about drawing conclusions from quantities which are 'equivalent' or 'interchangeable'. Physics is full of quantities which are quite distinct but can be related to each other by means of an equation; pressure and temperature, say, to take a random example. An equation such as E=mc² does NOT mean that energy and mass are 'two aspects of the same thing' - as everyday experience tells us (thankfully, the conversion of mass to energy is not an everyday experience, unless you happen to work in a nuclear power station!) Time, on the other hand, IS an everyday experience - it 'flows' whether or not there is an interchange of mass and energy going on. Indeed, time, in the sense of something changing with time, can be experienced even when we simply see two bodies moving at constant speed relative to each other, a situation where the energy is not changing at all; so I don't see that there is any logic in assuming a direct link between energy and time."

What do think?

Do you have a view on the meaning of time? If you do and have the time, write to the editor at Fusion or email editor@oufusion.org.uk.

EVENT REPORT

Daresbury Laboratory

by Fred Muirhead

4 March 2005: After travelling down the motorway for three hours it was nice to get into the lovely countryside of Cheshire and make my way to the laboratories. Not knowing what weather to expect I was surprised to find glorious sunshine, although a little cold, and to be informed that "we haven't had snow in these 'ere parts for some years".

I decided that the most important thing of the day was to go and have lunch, sorry, I mean the second most important thing, and found the restaurant comfortable and reasonably priced. Back to the Laboratory. I hurried to find, er, no one, and, then, like a huge ray of electrons from a cathode-ray tube, (steady Fred) appeared the rest of the party. After having fused together we were welcomed and given introductory information about the laboratory, and in the lecture theatre a jolly good talk on the Synchrotron Radiation Source. This was followed by an excellent guided tour of the machine and experimental area. As we were very ably informed The Synchrotron Radiation Source (SRS) at Daresbury Laboratory was the worlds first dedicated source of synchrotron light. It runs 24 hours a day, providing intense beams of light spanning through infrared to hard X-rays. Over 2000 researchers use the SRS every year, performing experiments that increase our understanding in many areas of material science, biology, chemistry, and physics.

What is Synchrotron Light?

Synchrotron Light is produced at the Synchrotron Radiation Source when an electron beam travelling close to the speed of light is accelerated in a magnetic field. The light covers a broad area of the electro magnetic spectrum, from infra red to hard X-rays. Synchrotron X-rays are much more intense than those from a conventional laboratory source, enabling researchers to carry out experiments in a very short time - vital on samples which are rapidly changing, such as in vigorous chemical reactions. Very dilute samples can also be studied easily. The light from the SRS has other important properties, making it different from ordinary light ; it comes in regular pulses, allowing data to be collected, like a video, on samples which vary with time. The light is also very highly polarised, linearly in the centre of the beam, and circularly above and below centre.

How is Synchrotron Light Produced?

When a charged particle travelling close to the speed of light is accelerated, it produces a broad spectrum of photons known as synchrotron light. At the SRS a beam of electrons is accelerated when it passes through a magnetic field, changing its path. The field is produced by sixteen huge dipole electromagnets which constrain the beam to a roughly circular path 96m around. Synchrotron light is emitted from these magnets and collected from twelve of them to feed experiments and test facilities. The light emerges like a searchlight in front of the emitting particle so it appears at a tangent to the bend. Three special magnets known as insertion devices also produce light at the SRS.

The type of light produced at sources like the SRS depends on both the energy of the electron beam and the magnetic fields used to bend the beam. The higher the beam energy the shorter the wavelength of the light produced. Strong magnetic fields will bend the beam more sharply - a greater acceleration which also gives shorter wavelength light. The electron beam loses a great deal of energy emitting synchrotron light. To replace this energy, the electron beam bunches are pushed along by radio frequency or RF waves, like someone being continually pushed around on a roundabout. The RF is fed into the electron beam in four places as the beam travels around the SRS. This way the electron beam can emit synchrotron light continuously for many hours.

ESA Conference on Mars

by Lorraine Robinson

The European Space Agency conference on Mars (20-25 February 2005, Noorwidjk, The Netherlands) was a very interesting experience. The most important part of it being that as you sat in the conference room listening to the speakers give their graphical descriptions of the Mars data, you saw where your own maths and physics was taking you. Those individual modules, electronics, electromagnetic radiation, data analysis, light, sound and thermal waves, and mathematically; integration, differential equations, Fourier series, vector and scalar fields, suddenly brought together in an array of equipment used to record the data taken from Mars.

The equipment certainly was impressive. Central themes are inbuilt into this equipment; Key words; 'absorption and emission', the signal as a 'line of sight', transmission, parameterization, quantum mechanics, 'virtual lenses', spectrum images, retrieval of 'vertical distributions', 3-D mapping, image correlation, in fact a list of Key Words dealing with interactive telescopes and cameras.

Mars Express in orbit around Mars. Photo: ESA - Illustration by Medialab.

First in line, the MARSIS radar, which 'maps' the subsurface, surface and ionosphere by sending out low frequency radio waves towards the planet. Their 'reflection' on the surface, the 'return signal', is then analysed through an image spectrometer to determine density, thickness and layer structure. Second the HRSC (High Resolution Stereo Camera), a 'scanning instrument' using electromagnetic wave transmission (the 'signal') giving reflectance measurements of selected rocks and soils over a wide range of illumination geometries, towards the construction of' digital elevation models'. Thirdly and fourthly, the OMEGA, (infrared mapping signals) and the SPICAM (ultraviolet and infrared signals), and so the list goes on and the development of this equipment a result of European collaboration, France, Italy, Great Britain, Russia, America, Spain, all coming together to construct the 'payload' on the First Mars Express.

And the result of all these observations? Mars. About half the size of Earth and considered to have had the same environmental conditions at a time when life evolved on Earth. With two ice covered poles and a surface structure of valleys, plains, channels, terraces, slip-offs and undercut slopes. Lava flows, volcanic activities and standing bodies of water. A soil containing clays, sulphates, carbonates, hydrated minerals and a climate spanning ice to dust. And the downside? A planet which lacks a global magnetic field, dust storms and a description of 'a planet which has lost its' atmosphere'. Life on Mars? Well NASA is keeping an open mind about this!

The last point to consider from this conference, the graphical presentations. These come from developed specific software which can translate the 'return signals' into functions of many variables for mapping illumination.

Overall the conference was incredibly 'user friendly' and intellectually stimulating. Each speaker was given fifteen minutes for his/her presentation and on any one day there could be up to 26 presentations. The atmosphere was casual with participants wandering in and out of the conference room carrying cups of coffee and working on their laptops.

Part of Tithonium Chasma, a major trough at the western end of the Valles Marineris canyon on Mars. Photo: ESA/DLR/FU Berlin (G. Neukum).

ESA runs a number of these conferences and for 3rd year Maths and Physics students it is a 'must' that you go to at least one of them before you graduate. They focus the mind towards career options and also, most importantly, give meaning to the maths and physics learnt in the unit modules.

Fusion Weekend and AGM

by Lorraine Robinson
(with contributions from Jim Grozier and Fred Muirhead)

Friday 21st to Sunday 23rd January 2005 at The University of Sussex

Fusion members in the ion beam room at The University of Sussex.

Fusion weekends are a real pleasure to attend and this one was no exception. Jim Grozier organised for us a really interesting agenda of laboratory visits, lectures, presentations and social activities, and the accommodation at the Institute of Development Studies (IDS) on the University's campus was really superb.

Friday evening started with dinner and drinks at the University's atmospheric Union Bar. It was a chance for everyone to meet up and talk 'OU geek speak', a rare language which involves 'long distance communicative learning wavelengths emitted at high frequency-punctuated intervals'; impossible to understand for those sitting at adjacent tables!

Saturday morning at 10.00 a.m. found us all sitting in the conference room at the IDS listening to Rodney Buckland give a presentation on the Huygens Mission. This was about a 'probe', (a transmitter) which was landed on Titan, one of the 18 moons of Saturn. The nature of the probe's transmission allows 'signals' to contour the planet's surface and sub-surface which when received back by the receiver located on the space-craft yields a mass of data about the composition of the surface and the surrounding atmosphere.

Dr. Buckland also gave to the Fusion members advance information on a potential 'space project' course which he is trying to initiate in conjunction with the OU and the Australian Space Research Institute. Essentially the course would involve OU students designing 'payloads' consisting of imaging, sound and data analysis equipment which would then fit onto launched (and subsequently retrieved) rockets. A leaflet will be sent to all Fusion members about this to see how many potential 'rocket scientists' there are doing physics and maths modules. (Watch this space!).

The group then crowded into the Accelerator/Ion Implantation Lab to be told about the 3 MeV Van de Graaff generator which produces Hydrogen and Helium ions with energies between 300 KeV and 3MeV. These ions are subsequently used in Ion Beam Luminescence Analysis, Ion Implantation, Rutherford Backscattering, Nuclear Reaction analysis and particle induced X-Ray analysis. If that was not enough, we then all viewed the 'Micromaser', a device which makes use of quantum behaviour in macroscopic systems. Rubidium atoms are excited by a laser so that the valence electrons go into a very high energy state (n=63). These high 'n' states are known as Rydberg atoms with a size thousands of times more than the original atoms and a single valence electron orbiting an enclosed shell nucleus. These atoms are then velocity selected (by another laser) and then trapped in a microwave cavity unable to change their quantum state. The purpose of this is towards quantum computing; the ability to store, modify, retrieve, transmit and receive vast quantities of data, packaged in this generated 'quantum bit' electromagnetic beam.

After lunch the AGM began. This included detailed analysis and discussions on the performances of the different departments within Fusion, its finance, membership (there are over 500 of us!), newsletter, events, merchandise and the web site. Also discussions took place on the links which Fusion has with the OU Students' Association (OUSA), 'Nexus' - the Student wing of the Institute of Physics and the OU's Department of Physics and Astronomy. New personnel were proposed and seconded for the roles of events, merchandise and the Department of Physics Liaison Officer and delegates to the OUSA Standing Committee and the Nexus Committee were confirmed (see the full 2005 AGM minutes).

After the AGM Dr. Malcolm Cornwall explained the mathematics behind GPS the 'Global Positioning System' (which you will be happy to know does encompass Einstein's Special Theory of Relativity!). See his article The Physics of GPS below. Dinner was in a Greek Restaurant in Brighton itself, which was a chance to view the town since we travelled there by bus from the University campus.

On Sunday, as compensation for having a cloudy night on Friday and therefore not able to use the University's telescopes for some 'observing', Jim Grozier gave us a talk, presentation and tour of the Lab in which he is currently studying for his D.Phil. In this Lab, neutrons are the order of the day and having contained them, positioned them, directed them and counted them, Jim's experiment uses them in order to identify the radiation signature (EDM) of the spatial asymmetry between matter and anti-matter and so explain why there is so little anti-matter compared to matter. This experiment is indeed ingenious since it shows how the scientific community faced with the dilemma of 'no signal' for symmetric matter and anti-matter (a foundation stone of physics) side-stepped this barrier to consider the neutron as 'pear-shaped'. For additional reading on this experiment please refer to Jim's article Pear-shaped neutrons and the meaning of life in the Spring 2004 Newsletter.

To round off the weekend members of the group had a most enjoyable time on a tour of the Royal Pavilion, the Prince Regent's 'onion-domed' seaside palace.

This was indeed a Fusion Weekend and AGM that lived up to all expectations. Many thanks again to Jim for organising this and to all the speakers, presenters and Fusion members who made this visit a real pleasure.

The Physics of GPS

by Malcolm G Cornwall

We've all done it - measure how far away the lightning is by counting the seconds between seeing the flash and hearing the boom. Knowing the speed of sound, a mile in about 5 seconds, it's easy to work out the distance.

The same idea is the basic principle of the Global Positioning System, GPS, now beginning to permeate the every-day world of the general public. For GPS, though, we measure the time a radio signal takes to reach us from several of the 24 GPS satellites (known in the trade as Space Vehicles or SVs) which orbit the earth. Knowing the speed of radio waves, c, the receiver can work out how far away the satellites are. It's then only a matter of geometry - actually a process of trilateration - to work out our exact position on the earth.

In this short article, I can only provide a brief introduction to the myriad aspects of GPS, such as its origins in the '70s as a Pentagon cold-war project, the constellation of satellites needed and their orbits, the structure of the complex signals transmitted by each satellite. It would be interesting, too, to look at some of its numerous and unexpected applications, from precise positioning and speed determination, and monitoring of earthquake and volcano areas, to date/time stamping of financial transactions, and the (somewhat sinister) continual surveillance of children and employees.

You can find out about the technology and applications of GPS from the sources listed at the end. Here, I'll consider some key features of GPS which relate to some basic ideas in physics.

The 24 equally-spaced satellites transmit radio signals at two frequencies in the GHz range, and orbit at precisely known altitudes at about 20,200 km above the earth. This is about half the distance of geostationary communication satellites, like the one which broadcasts 'Sky', so the orbital period, instead of being 24 hours, is about 12 hours. The orbital period of a GPS satellite is actually 11 hours 58 minutes. Combined with the nearly 24 hour (sidereal) period of the earth's rotation, this means that the satellites move over the same track on earth each day.

For the 'distance of a lighting strike' analogy, the flash tells us when the sound waves started. But for GPS, how can we know when the timing signal set off? The solution is to include with the radio signal exact information on the instant that the signal was transmitted. Time of receipt minus time of arrival then enables the distance to be easily calculated, given that we know 'c' extremely accurately. The locations of the satellites are known extremely precisely to centimetre accuracy, and the receivers have a built in 'almanac' that contains the theoretical positions of each satellite. Corrections to these positions are also transmitted by each satellite, so that the absolute receiver positions can be precisely calculated.

It's obvious that time needs to be measured extremely precisely - an error of 0.1μs would mean a location error of ∼30m. To avoid this, each satellite carries four atomic clocks - two caesium and two rubidium, which are accurate to about 7ns. These are continually compared with the average time indicated by an earth-based collection of atomic clocks. Above our heads therefore is an array of easily accessed, always available, precise clocks. This is why many of the users of GPS utilise this precision in time-sensitive applications like financial 'time stamping', astronomy and mobile telephony.

Given the speed of light and the transit time of the signal, it's easy to assume that the calculation of our location is trivial. In fact there are several sources of error related to the assumed constancy of the speed of light, some due to empirical factors, others more fundamental. Among the first kind is the fact that for a small but crucial fraction of its path to earth, the radio signal travels through the atmosphere, which extends to about 250 km above the earth. Extending from about 50-200 km above us is the ionosphere, a layer of ionised particles (mainly electrons), whose density varies from day to day. EM waves are slightly retarded, and are also very slight refracted as they enter this layer. At an altitude of about 50 km the waves enter the troposphere and see a different 'refractive medium', and again they are refracted and retarded. Clearly corrections must be made to the measured time delay. Luckily the effects of the ionosphere can be accurately modelled, and the parameters required by the equations can be measured. This is done by using the fact that the ionosphere is dispersive, with its effective refractive index approximately inversely proportionally to the frequency. Using the two frequencies transmitted by each satellite, the parameters can, therefore, be continually calculated. This information is then transmitted as a correction term to each receiver, which has a copy of the correction algorithm in its memory.

The correction for the troposphere is not so straight forward; it depends in a complex non-dispersive way on the continually changing pressure, temperature and, particularly, humidity, of the troposphere, so only a rough correction can be made.

The SVs are travelling at an orbital speed of about 4km/s, which has two implications.

Firstly, it means that the signal received can have a Doppler shift of up to ∼±2.5kHz around the transmitted frequency. If the receiver is in motion there is an additional Doppler shift, of course. By measuring this shift it's possible to calculate the receiver's velocity, and some receivers use this method (an alternative is to measure the successive positions of the receiver and divide by the interval between measurements).

Secondly, a fundamental correction is required as a result of relativistic effects, both 'special' and 'general'. Although the orbital speed is very small compared with c, it's sufficient to make the time dilation resulting from the relative speed with respect to the observer very significant in timing the signal. (The 'slowing down' of the satellite clocks is 7μs/day). Furthermore, the altitude of the SVs means that the atomic clocks experience a different gravitational field from a clock on the earth's surface. As a result, according to the General Theory of Relativity, the satellite clocks run faster than the earth bound clocks (45μs/day). The net result of the opposing effects of 'special' and 'general' corrections is that the clocks on the satellites need to be offset before launch. Without the relativistic corrections, GPS position measurements would be in error by a massive 38 μs/day, equivalent to a 10km/day position error. The fact that corrections to GPS based on relativity theory result in such a precise system, provides a most convincing proof of Einstein's theories, and a rare example of where relativity impacts directly our every day experience.

Even this brief overview of some of the physics behind the GPS demonstrates that this undoubtedly impressive achievement of engineering and technology, is above all a tribute to the power of physics in understanding and exploiting the laws of our Universe.

Useful sources of further information: www.trimble.com/gps/why.html, www.colorado.edu/geography/gcraft/notes/gps/gps_f.html, N. Ashby, Relativity and the Global Positioning System, Physics Today, May 2002 , p41.

Dr Malcolm Cornwall is a former lecturer at Brighton University and an OU tutor.

An Alternative Point of View

John Small's summary of his lecture given at last year's ICPS

Problems with Quantum Gravity

Nearly 100 years after Einstein laid the foundations for the development of quantum mechanics and general relativity in 1905 all attempts to reconcile the two great developments of the 20th century have met with limited success (see Smolin). String theorists claim that their program holds the best hope for developing a Theory of Everything that will unite these two strands, but even the best string theorists are now questioning whether the theory can ever yield a clear reason as to why the laws of nature have the form that they do (see Susskind).

Even if string theory is successful in unifying all four fundamental forces there would still remain the deep mysteries of quantum mechanics to be explained. Collectively titled the "measurement problem" these strange facets of quantum theory are not even addressed by string theory, the hope is that some kind of solution will pop out of the equations. Hawking has suggested that the problem might be that there is an element of self-referentiality in the Universe, which according to Godel's Theorem means that there can be no mathematically consistent Theory of Everything. Penrose has suggested that any theory that joins quantum mechanics and gravity must include an element of non-computability, which is much the same as saying there can be no computable, and hence mathematically consistent, Theory of Everything, (though I doubt that he would agree!).

The big problem is that the treatment of time in quantum mechanics and general relativity are quite different. Indeed it's so different that Julian Barbour has suggested that time itself may be an illusion. The problem stated in it's simplest form is that quantum field theories require a rigid non-dynamical framework of spacetime which forms the stage on which the actors, in the form of the fields, play. But in general relativity the gravitational field is itself the same thing as spacetime. String Theory may have spin-2 bosons which can be interpreted as gravitons but it keeps spacetime as a rigid non-dynamical background and so goes against the spirit of general relativity.

Is the world self-referential?

But, if it's so hard to bring general relativity within the framework of a standard quantum field theory, then maybe it's easy to show that it can't be done. It would only be necessary to show that there exists some natural phenomenon that embodies self-referentiality. It has been noticed many times that the weirdness of quantum phenomena could be explained if information can go backwards in time (see Aharanov-Vaidman, Cramer, Hadley). Also David Deutsch has pointed out that the formalism of quantum mechanics is ideally suited to representing the logical states that occur if we let information go backwards in time. The answer to that old chestnut "What would happen if someone went back in time and killed one of their ancestors?" which supposedly creates a paradox, is neatly handled in the quantum formalism by saying that they'd end up in a quantum superposition of existing and not existing. The most useful idea in this direction comes from Castagnoli-Finkelstein who suggest that quantum computation is best understood as the result of a quantum computation being part of the initial input to the computation. In other words the answer to a question can be a part of the definition of the question.

By playing around with this idea it's quite easy to generate toy models of quantum mechanics that embody the concept. For example take the statement

5 divided by the number of characters in this sentence plus the answer output as a fraction is 5 / _₉₈ _₉₉ _₁₀₀

I've set this up so that there are two answers consistent with the form of the statement, we can either complete the sentence with 99 or 100. This has useful similarities with a quantum measurement in that before "measurement" the sentence exists in a superposition of the two possible answers and once we've added the information required represented by the answer we reduce these potentialities to one or the other. This is similar to the procedure whereby we add information in the form of energy to a quantum system in order to make a measurement. A quantum system is not completely defined by the information in the initial conditions but also by the information input to the system in the form of the energy required to make the final measurement. Without the additional information input at the point of measurement we can make only a statistical estimate of a particular outcome. This suggests that the operation of quantizing a classical dynamical equation is more than just a technical issue of fiddling with the formula but is in fact a case of finding a way to represent the states of a system that allows the information in an answer to a question become part of the input to a question.

Using this trick we can also create "entangled statements" such as:

X: Calculate a function f(a,y) where a is an input value and y is the result of Y.
Y: Calculate a function f(a,x) where a is an input value and x is the result of X.

Where we can easily find an equivalent quantum mechanical system such as:

X:Set the spin state of particle A be anti-parallel to the result of measurement of particle B in the measurement basis of Y.
Y:Set the spin state of particle B be anti-parallel to the result of measurement of particle A in the measurement basis of X.

Which provides a neat way to understand entanglement as the physical implementation of self-referencing logic. Entanglement is a problem that seems to have no explanation in purely deterministic terms, and it's been suggested that it has to be accepted as axiomatic (see Popescu). But as entanglement looks suspiciously like the physical implementation of a self-referential algorithm that would imply taking self-referentiality as fundamental, which in turn implies there is no Theory of Everything.

The idea that the answer forms part of the question shows up in general relativity but in a totally different form. There's a philosophical argument about the physical meaning of the notion of general covariance in general relativity. One point of view is that it implies the very notion of individual points in spacetime being real "things" is entirely mistaken and that the very notion of spacetime is not something given a priori but is something that is contructed a posteriori as part of the answer to a question (see Christian). If we can find the right concepts, this would make quantum mechanics dual to general relativity under the notion of self-referentiality. In quantum mechanics the background spacetime is strictly non-dynamic and causal, yet the measurements we make on objects or fields within the spacetime framework have the property that the answer is part of the question. In general relativity the very notion of spacetime itself is part of the answer to a question and the physical objects in that spacetime behave in a purely deterministic manner.

Only 4 dimensions! That can't be right!

Casting caution and rigour to the winds for the moment, and adopting the notion that time is the causal ordering of events super-imposed on a reality which is not really causal we find that to model this non-causality we have to make use of the idea that some things behave "as if" information can go backwards in time. If we use directed lines to connect observations that can be causally ordered as in the Causal Set program of Sorkin et al we have to model the logical loops in causal ordering using circles. A simple circle has the property that you can set every point in the circle in motion at the same time. If you do this on the two dimensional surface of a globe there are always two points remaining stationary. This property that you can set every point in motion at the same time is called "parallelisability" and is shared by the 3 and 7 dimensional analogues of the circle. These are labeled in turn as S¹,S³,S⁷. Now each of these is associated with a complex algebra S¹ with the complex numbers, S³ with the quaternions and S⁷ with the octonions (see John Baez for a full discussion). Together with the reals these three complex algebras are called the division algebras. If we model the causal loops using the parallelisable spheres and count causal steps as in the Causal Set program with real numbers then we have to count the non-causal steps using complex numbers. The largest of the parallelisable spheres is S⁷ which has three generators. Which implies that we have to count in three linearly independent bases each of which is complex with respect to the causal steps. This means that space like separation is a notion that arises from placing a causal ordering onto a non-causal reality and we then get a metric s²=t²-(x₁²+x₂²+x₃²). Which is a neat result, and suggests we might even be headed in the right direction. But it also means that all the work on theories which require more than three spatial dimensions is wrong, and we therefore need a proper proof that this is the way to go.

Another curious clue attracts our attention. If quantum measurements are taken to be the result of some self-referential process, then if we put the measurements within a fixed temporal framework we have to model the "causal loop" aspect of quantum information using the parallelisable spheres again. Now the groups that fall out of the division algebras give rise to the symmetry groups U(1) × SU(2) × SU(3), which is the symmetry group of the Standard Model (see Dixon for a fuller explanation).

These clues suggest that the idea is worth investigating more deeply. However it doesn't need an Einstein to see that the assumption that self-referentiality is fundamental lands us straight into very deep philosophical waters. I think it's best to ignore the philosophical problems until the investigation is complete.

References

[Aharanov-Vaidman]

Y. Aharanov and L. Vaidman.

Properties of a quantum system during the time interval between two measurements.

Phys. Rev., A(41):11-20, 1990.

[Baez]

J. Baez.

The octonions.

Bull. Amer. Math. Soc., 39:145-205, 2002.

[Barbour]

Julian Barbour.

The End of Time.

Weidenfield & Nicolson, 1999.

[Christian]

N. Callender, C. Huggett, editors.

In Physics Meets Philosophy at the Planck Scale., chapter Why the quantum must yield to gravity.

Christian, J.

Cambridge University Press, 2001.

[Castagnoli-Finkelstein]

D. R. Castagnoli, G. Finkelstein.

Quantum ground state computation with static gates.

arXiv:quant-ph/0209084, Sep 2003, arXiv:quant-ph/0209084.

[Cramer]

J. G. Cramer.

The transactional interpretation of quantum physics.

Reviews of Modern Physics, 58:647-688, 1986.

[Deutsch]

D. Deutsch.

Quantum mechanics near closed timelike lines.

Physics Review D, 44(10):3197-217, 1991.

[Dixon]

G. Dixon.

Division Algebras: Octonions, quanternions, complex numbers and the algebraic design of physics.

Kluwer, 1994.

[Hadley]

M. Hadley.

The logic of quantum mechanics derived from classical general relativity.

Foundations of Physics Letters, 10(1):43-60, 1997.

[Hawking]

S. Hawking.

Goedel and the end of physics.

http://www.damtp.cam.ac.uk/strtst/dirac/hawking/, 2003.

[Popescu]

S. Rohrlich, D. Popescu.

Nonlocality as an axiom for quantum theory*.

arXiv:quant-ph/9508009, September 1995, arXiv:quant-ph/9508009.

[Smolin]

Lee Smolin.

How far are we from the quantum theory of gravity?

arXiv:hep-th/0303185 v2, April 2003, arXiv:hep-th/0303185 v2.

[Sorkin]

Meyer D., Sorkin R.D., Bombelli L., Lee J.

Space-time as a causal set.

Phys Rev Lett, 5(59):512-24, 1987.

[Susskind]

Leonard Susskind.

A universe like no other.

New Scientist, 180(2419):34, November 2003.

Broken Bones, Treatment Plans & Wheelchairs

Physics In Medicine: An Introduction

by James Cullis and Denise Hoban,
University Hospitals Coventry and Warwickshire

At some point in our lives we have all visited a hospital for one reason or another. If you stopped and thought about any particular visit you would be amazed at the role physicists play in the life of a hospital. Medical Physics is a vast subject area encompassing many different aspects of medicine within the hospital from wheelchair and prosthetic design to lasers and diagnostic radiology.

Career Entry

A career in Medical Physics can follow many different paths but the main path is through a 2-year Postgraduate training course. Entry is usually either through a Physics or Engineering degree. The training is split into two components: a 10-month taught MSc program and a further 14 months hospital-based training. The MSc enables a good grounding in Medical Physics to be obtained and also exposes students to anatomy and physiology of the body. Hospital training is then further split into 3 specialist subject areas chosen from a list of 15. Examples include: Radiotherapy, Radiation Protection, Nuclear Medicine, Ultrasound, MRI and Physiological Measurement and a period of 4 months training in each area is undertaken. Training follows a very different pattern depending upon the subject area, although usually a training plan is formulated and a mentor assigned to help the trainee meet all of the competencies.

Successful completion of the hospital training results in the awarding of a Diploma of the IPEM (Institute in Physics and Engineering In Medicine). Assessment for this diploma is through a local assessor's report, a portfolio of the work undertaken, and a final viva. All aim to meet a number of competencies for the subject area. Completion of the Diploma enables the candidate to apply for higher-grade jobs.

Experiences of Two Trainees

James Cullis

I graduated from Sheffield University with a BSc in Physics with Medical Physics in 1999. Subsequently I obtained a place on the Grade A training scheme in the West Midlands and spent the first year studying for an MSc in Medical and Radiation Physics at Birmingham University. I then trained in the hospitals within the region in MRI, Nuclear Medicine and Radiotherapy. After completion of the training scheme I carried out a PhD in Magnetic Resonance Spectroscopy of Human Cells at the University of Warwick before getting a job in Nuclear Medicine.

Fig 1: 3-Field Radiotherapy Treatment Plan for Prostate Cancer

Radiotherapy training is the most popular area and probably the largest subject area. It involves treatment of cancerous tumours using high energy X-rays. X-ray beams are "fired" at the patient at different angles in order to produce a lethal dose (Dose = energy deposited per unit mass) to the tumour and lower (non-lethal) dose to the surrounding healthy tissues. My training covered all aspects of the physics from computerised planning of the treatment beams tailored specifically for each patient to the calibration of the machines that deliver the X-rays. This was mainly through a series of simple projects to gain understanding. This subsequently led to the undertaking of supervised routine work (patient plans, dose calculations etc). Cross-sectional (CT) imaging of the body allows accurate definition of the tumour and other sensitive organs. Radiation beams can then be superimposed onto the CT images to obtain a dose plan as shown in Figure 1 (a 3-field treatment for prostate cancer). Each plan and treatment is therefore individually tailored to the patient.

Quality Assurance of the machines is also critical in treatment delivery and this formed a regular part of my training. Monitoring of patient doses and calibration of dose monitoring equipment was also routinely undertaken to ensure that the dose prescribed is the dose delivered in the treatment. During the training small research projects were also carried out.

Denise Hoban

I graduated from UMIST in June 2000 with an MPhys in Physics with French. In the final year of my degree I had taken a module in Medical Physics, and had decided that this was the career path for me. I secured a training place in the West Midlands, and began the two-year contract in September 2000. The first year of this was mostly taken up by the MSc in Medical and Radiation Physics at the University of Birmingham. I then chose three areas of specialisation, namely Radiotherapy, Nuclear Medicine and Diagnostic Radiology. Each of these attachments lasted three months, during which time I experienced a wide variety of work undertaken by a physicist working in the healthcare sector. I experienced the everyday duties, and also carried out some projects. One such project was to commission a set of eye shields used to shield the lenses of patients undergoing electron beam therapy to treat skin lesions.

The two years were quite intensive, but very enjoyable. I found the job to be very social, mixing with lots of staff members from different clinical disciplines. The training called on a range of knowledge and skills, from physics to anatomy, and problem solving to report writing.

For my MSc project I investigated the effect of breast position in Nuclear Medicine myocardial perfusion images of female patients. Nuclear Medicine involves the administration of radioactive isotopes (gamma-ray emitters) that are labelled with a pharmaceutical. Each pharmaceutical is taken up in specific organ(s) that then allow images of the organ(s) to be taken and an assessment of the function of the organ made. Myocardial perfusion images are used to diagnose and locate areas of poor or absent perfusion in the myocardium. Patients are injected with Tc^99m (T_1/2 ∼ 6 hrs), which is labelled to a tracer which is preferentially absorbed by the myocardium. After a suitable time delay to allow the radionuclide to distribute through the patient, images are acquired using a dual headed gamma camera. A correction can be made to the acquired images to correct for the attenuating properties of overlying tissue, which is a particular problem in female patients as the breast tissue overlies the myocardium. The accuracy with which this correction works was investigated by building a suitable representation of a female torso. The effect of the breast position was also assessed.

Fig 2: (a) Cross-sectional images through the left ventricle representing a 'normal' well perfused myocardial wall, and (b) showing what appears to be an area of poor perfusion. This is actually due to breast attenuation of the photons.

I am now working as a physicist specialising in diagnostic radiology and radiation protection. I work alongside two other physicists, and between us we cover seven large hospitals, as well as private hospitals, dental surgeries and veterinary surgeries. The work involves all manner of radiographic equipment, from CT scanners, fluoroscopy units and digital radiology to simple mobile X-ray units and dental X-ray equipment. By law all radiological equipment must be checked regularly, and we provide this service, advising on any work necessary on the equipment in order to bring it up to recommended standards.

My work also concerns the legislation surrounding the use of radiation and I provide advice to organisations possessing any such equipment. Along with routine work I also contribute to research teams, both clinical and physics-based. I have designed and built commercially unavailable test objects for use in routine testing. I'm also involved in the teaching and education of staff in relation to radiation safety issues.

Further information on training in Medical Physics is available from the Institute of Physics and Engineering in Medicine www.ipem.ac.uk and the Association of Clinical Scientists www.assclinsci.org.

Nuclear Astrophysics

by Prof Brian Fulton, University of York

Nuclear astrophysics is a branch of nuclear physics which looks at the nuclear reactions which occur in stars and other astrophysical sites. We have known since the 1950's that all the atoms which we see around us were made in the centre of stars, through successions of nuclear reactions. These nuclear reactions occur when the fast moving atoms in the hot interior collide, causing the hydrogen from which the star is made to be built up, first to helium, then to carbon and oxygen, and then to make the heavier elements. If it wasn't for these nuclear reactions there would be no carbon and oxygen in the Universe to enable life to evolve. Indeed, all the atoms of which we ourselves are made were produced in such reactions inside a star - so we are all of us, children of the stars.

Our link with the stars does not just arise from their role in creating the elements of life, for we rely on our own star, the Sun, whose energy output maintains the condition for life here on Earth. This nuclear energy comes from the binding energy released when light nuclei fuse together to form heavier ones. In atoms it is the electric (Coulomb) force which holds the parts of the atom together, and the binding energy reflects the amount of energy it would take to pull all the electrons out of the atom. Typical binding energies for electrons in an atom are of the order of tens to hundreds of eV. When two atoms combine to form a molecule, some of the binding energy can be released and this is the source of the chemical energy which we use when burning coal or petrol. In nuclei, the constituents (positively charged protons and electrically neutral neutrons) are held together by the strong (or nuclear) force, which as its name implies is much stronger than the electric force. Hence the binding energies in nuclei are much larger, typically measured in ten and hundreds of MeV. This means that when two nuclei are fused together, the binding energy released is millions of times greater than in chemical processes.

There is one slight difficulty in fusing together two nuclei. The nuclear force is somewhat strange in having a very short range, unlike the more familiar electric and gravitational forces between two objects which extend to any distance, falling off in strength with an inverse square law. By contrast, the nuclear force only operates over distances out to about 1 femtometre (fm), or 10^-15 m. This causes a problem, because the protons in a nucleus have a positive charge and so there is an electric repulsion between two nuclei. Nuclear physicists get around this by using accelerators to deliver beams of high energy nuclei with enough energy to overcome this repulsion and get within 1 fm of the target nucleus so that the nuclear force can come into play and cause the two nuclei to fuse. Nature is more elegant and achieves the same end simply by using the thermal energy of fast moving nuclei in the hot gas in the interior of a star.

Fig 1: An illustration of the nuclear reactions which occur during the helium burning stage of a star that lead to the creation of carbon and then oxygen.

In the first stage of a star's life, collisions between the hydrogen atoms cause them to be changed into helium, releasing nuclear energy in the process. This energy keeps the star shining, and it is the nuclear energy of our own star, the Sun, which keeps us alive here on Earth. Most of the stars which you can see in the night sky are also in this phase of their life, which is called the "main sequence" because of the striking correlation between the luminosity (energy output) of a star and its colour (temperature). The star can survive in this stage for billions of years, with the energy being produced by the nuclear reactions in the core providing enough heat and pressure in the gas to balance the gravitational attraction which is trying to crush the star. We often refer to the process as "hydrogen burning", by analogy to the release of chemical energy when, for example, coal is burnt. However it is important to remember that the energy release comes from a change in the nuclear binding energy, rather than the Coulomb binding energy of atoms. Eventually the store of hydrogen is exhausted and the core temperature drops, allowing gravity to take over and compress the star. However this compression in turn heats the core to even higher temperatures, with the nuclear collisions becoming more energetic so that helium nuclei, despite the higher repulsion arising from their higher charge, come close enough together to fuse.

It is in this second stage of a star's evolution that the more interesting reactions (in terms of supporting life in the Universe) start to happen. First the helium atoms combine to form carbon atoms and then some of these carbon atoms combine with other helium atoms to form oxygen. Again, nuclear energy is released in the process, which is often called the "helium burning" phase. At this stage in a star's life cycle it swells up to become what is called a Red Giant, like the star Betelgeuse in the constellation of Orion which is visible in the night sky in the winter months. Incidentally, when our Sun does this it will swell up so much that it will swallow up the Earth - but don't worry as that is some billions of years off!

What happens to a star after this stage depends on its mass. The lighter stars don't have enough gravitational attraction for the core temperatures to be raised high enough for the carbon and oxygen nuclei to come close enough together in collisions for nuclear reactions to take place, and so the star can end its life as what is called a White Dwarf. In a larger star a further succession of nuclear reactions with increasingly heavier nuclei may take place, interspersed with periods of gravitational contraction. For the most massive stars, with a mass greater than about ten times our Sun, these reactions produce nuclei up to iron. Here, however, things start to go wrong. Up to this point the star has been able to generate energy because the binding energy of the nuclei being produced in the fusion is greater than that of the two colliding nuclei, and this difference is what is released. However, iron is the most tightly bound nucleus, and for heavier nuclei the binding energy starts to decrease. Hence it is no longer possible to produce energy by fusing the iron nuclei together, indeed, if this does happen it causes a loss of energy. At this stage the star is doomed! With no more possibility of releasing nuclear energy in the core to withstand the force of gravity, gravity finally wins the battle and the star undergoes a catastrophic collapse, producing the stupendous phenomenon of a supernova. In these explosions the heavy elements which have been built up during the lifetime of the star are blown out into the interstellar regions of the galaxy, where they can later become caught up in a new generation of star formation, with their accompanying planetary systems.

Fig 2: The Crab Nebula, the site of a supernova explosion in 1054. The picture illustrates the new elements which were created in the star being blown out into the interstellar medium, where they may later be caught up in the formation of new planetary systems. Picture courtesy of the FORS Team on the 8.2m VLT.

For many years there has been a fruitful collaboration between astronomers, astrophysicists and nuclear physicists, who have worked together to understand these processes. The nuclear physicists carry out experiments to measure the rates of the different nuclear reactions which can occur. The astrophysicists then use these in models of stellar interiors to determine how much energy is produced and how much of each new element is created. Finally the astronomers can carry out observations of the spectra of distant stars to check the accuracy of these predictions. One of the big problems for the nuclear physicists is that, although the temperatures of stellar interiors are high (tens of millions of degrees) the thermal energies of the nuclei are still small (kinetic energies of hundreds of keV). At these collision energies the reaction rates are very small, making them very difficult to measure. Indeed we often have to resort to measuring to as low as we can and then extrapolating to the required energy regime. The main problem is that the experimental rates are so small that the signal in our detectors is swamped by background signals from other sources, such as natural background radioactivity or cosmic rays. One neat solution to this problem is to build your accelerator in one of the deep underground laboratories which have been built for other low background physics experiments, such as solar neutrino detection, dark matter searches, etc. One nice example of this is the LUNA project at the Gran Sasso Laboratory in Italy, where recently they have been able to measure two of the key reactions which occur in the Sun, down to the relevant energies.

Fig 3: LUNA (Laboratory Underground for Nuclear Astrophysics) in the Gran Sasso laboratory deep under the Italian Alps. Courtesy of Gran Sasso Laboratory.

While the above may suggest that we are well on our way to understanding the life cycle of a star, along with the energy generation and element production, this is only a part of the great nuclear astrophysics adventure. Despite their enormous temperatures, stars are relatively gentle environments, in terms of nuclear collisions. There are much more spectacular astrophysical objects, such as novae, X-ray bursters and the previously mentioned supernovae, where much higher temperatures can occur (billions rather than millions of degrees). Developing models of these explosive sites is itself a challenge, but a bigger problem arises when we try and measure the rates of the nuclear reactions which occur. The problem is that many of the reactions occurring in these objects involve collisions between nuclei which are unstable (i.e. one or other is a radioactive nucleus which will undergo beta decay). This presents a major experimental problem, since if the nucleus has a short half life, even if we can produce some in a nuclear reactor or by some other means, it will have decayed before we can make it into a target to bombard with the beams from our accelerator.

This problem doesn't occur in studies of stellar nucleosynthesis. In a star, even though the nuclei in the hot gas are colliding many times a second, it is only the very few nuclei with the very highest energies in the Maxwell Boltzmann velocity distribution that have enough energy to get close enough to fuse. Hence any individual nucleus survives, on average, many years between each nuclear reaction. This is long enough to ensure that if unstable nuclei are produced, they will undergo radioactive decay to become a stable nucleus before they take part in another reaction. This means that the nuclear reactions which are important for understanding what goes on in a star are all between stable nuclei. Hence we have been able to produce targets of these to carry out measurements of the reaction rates.

Fig 4: The ISAC facility at the TRIUMF Laboratory in Vancouver, an example of the new generation of radioactive beam facilities dedicated to nuclear astrophysics research. Courtesy of TRIUMF Laboratory.

Because of this problem, the nuclear astrophysics of explosive astrophysical sites has been poorly understood. Fortunately, in the last few years nuclear physicists have developed the technology to produce and accelerate beams of short-lived, radioactive nuclei. With these facilities we are now able to undertake measurements of the key reactions which govern the energy generation and element production in some of the most spectacular objects in the Universe. It is already apparent from these initial studies that these objects are the origin of many of the elements we see around us, in particular they produce over half of the heavy elements beyond iron. A number of new facilities have recently started operation around the world, with more in construction, to exploit this new opportunity. Within a few years we can hope to have an understanding of what occurs in some of the most spectacular objects which Nature has produced.

For more information visit:
LUNA www.cerncourier.com/main/article/44/%208/15/1;
ISAC www.triumf.info/public/about/isac.php.