James Clerk Maxwell

Born in 1831 at 14 India Street, Edinburgh, Maxwell was brought up at Glenlair House in Dumfriesshire, and schooled at Edinburgh Academy.

At the age of fourteen, his paper “Oval Curves” was presented on his behalf to the Royal Society of Edinburgh by James Forbes, Professor of Natural Philosophy at the University of Edinburgh, in 1846. This started a friendship with Forbes that would last throughout Maxwell's career; it also helped convince his father that it was mathematics, and not law, that Maxwell should study.

From 1847 to 1850 he attended the University of Edinburgh, and at the age of eighteen had two papers published in the Transactions of the Royal Society of Edinburgh.

Maxwell graduated from the University of Cambridge in 1854, and was made a Fellow of Trinity College in 1855.

Appointed in 1856 to the Chair of Natural Philosophy at the University of Aberdeen, he was made redundant when two colleges merged, and was unsuccessful in applying for the Chair of Natural Philosophy vacated by Forbes in Edinburgh, the post going to another pupil of Edinburgh Academy, Peter Guthrie Tait.

Peter Guthrie Tait, FRSE (b. 1831 d. 1901)RSE General Secretary (1879 –1901)

James David Forbes, FRS FRSE (b. 1809 d. 1868)RSE General Secretary (1840 –1860)

James Clerk Maxwell, FRS FRSE (b. 1831 d. 1879)by Alexander Stoddart FRSE in George Street, Edinburgh

Peter Guthrie Tait, FRSE (b. 1831 d. 1901)

Maxwell was, however, appointed to the corresponding Chair at King’s College, London in the same year. From 1860 to 1865 he made his most significant advances in his understanding of electricity and magnetism.

He resigned from King’s College in 1865 and returned to Glenlair. In 1871 he became the first Cavendish Professor of Physics at Cambridge.

Maxwell died of cancer on 5 November 1879.

During his career Maxwell wrote on electromagnetism, geometry, polarised light, optics, colour theory, Saturn’s rings, viscosity, and the kinetic theory of gases.

James Clerk Maxwell, FRS FRSE (b. 1831 d. 1879)

James David Forbes, FRS FRSE (b. 1809 d. 1868)

Maxwell’s Electromagnetism

Electric charges cause electric fields

Maxwell’s electromagnetic equations

There are no magnetic monopoles: magnets always have North/South pairs

Changing magnetic fields generate electric fields

Electric currents and changing electric fields generate magnetic fields

While at King’s College London, Maxwell was most productive in developing his understanding of the

relation between electricity and magnetism, inspired by the earlier experimental work of Michael Faraday at the Royal Institution.

The concept of an electric or magnetic field pervading the whole of space can be attributed to Faraday. Maxwell extended his work, and predicted the existence of electromagnetic waves (discovered in the form of radio waves by Hertz in 1887) with the same speed as light.

Maxwell concluded that light itself was an electromagnetic wave, along with many other forms of electromagnetic radiation with which we are familiar today, such as radio waves, X-rays and microwaves. All of the modern electrical and optoelectronic devices we use today owe their existence to Maxwell’s work.

Peter Guthrie Tait and Lord Kelvin conjectured that these waves travelled through an imperceptible medium known as the aether: experimental failure to find it would lead to another revolutionary idea.

William Thomson (Lord Kelvin), FRS FRSE (b. 1824 d. 1907)RSE President (1873–78; 1886–90; 1893–1907)

Michael Faraday, FRS Hon FRSE (b. 1791 d. 1867)

William Thomson (Lord Kelvin), FRS FRSE (b. 1824 d. 1907)

Einstein and Special Relativity

When Maxwell discovered that light was a form of electromagnetic radiation, it was assumed that it would

propagate through a supporting medium, just as sound travels through air but not a vacuum.

Lord Kelvin and others conjectured that there existed an invisible aether pervading space, through which light travelled. As the Earth orbited the Sun at 66,000 miles per hour, waves in the aether would travel at different speeds relative to the Earth depending on whether they were travelling with the Earth’s motion through the aether, against it, or at right-angles to it.

In 1887, Albert Michelson and Edward Morley devised an experiment to test this idea and found that there was no effect: the aether did not exist, and the speed of light is the same in all reference frames.

Inspired by this result, Albert Einstein used the invariance of the speed of light to build his Special Theory of Relativity in 1905. This had profound consequences, and theories involving fast moving elementary particles had to be written to be consistent with relativity. One unexpected consequence is that relativity permits the creation of new matter out of energy, according to the famous equation E = mc2. 

The Michelson-Morley experiment, shown mounted on a stone slab, floating on a pool of mercury to isolate the experiment from vibrations: an attempt to detect the Earth’s passage through the aether. Beams of light were shone at right-angles, reflected, and then sensitive measurements made to determine if the speed of the light waves had been altered according to their initial direction, but no variations were detected.

Michelson and Morley’s work has been called the most famous failed experiment in history: its negative conclusions had far-ranging consequences.

Albert Einstein, Hon FRSE (b. 1879 d. 1955)

Albert Michelson, Hon FRSE (b. 1852 d. 1931) Edward Morley (b. 1838 d. 1923)

To give precise position data, navigation satellites use highly accurate atomic clocks, which nevertheless have to be corrected by taking into account Einstein's Special and General theories of Relativity.

The mass-energy equivalence embodied in the equation E = mc2 allows for both the generation of nuclear power and the production of new matter in elementary particle collisions.

Albert Michelson, Hon FRSE (b. 1852 d. 1931) Edward Morley (b. 1838 d. 1923)

The Tait Institute ofMathematical Physicsand Peter Higgs

The development of quantum theory took place over the three decades following the early work of Max Planck and Einstein.

In 1909, Ernest Rutherford discovered that the atom consisted of electrons orbiting a tiny, dense, nucleus. Using such a model, the pioneers of quantum mechanics – Niels Bohr, Max Born, Paul Dirac, Erwin Schrödinger and Werner Heisenberg – were able to explain the atomic elements that made up the Periodic Table. Dirac combined special relativity and quantum mechanics to describe the electron, and predicted its antimatter partner, the positron.

In the following two decades the quantum theory of fields was developed, combining electromagnetism, relativity and quantum mechanics, culminating in quantum electrodynamics (QED).

Max Born was appointed in 1936 to the University of Edinburgh Tait Chair of Natural Philosophy. On his retirement in 1952 the Tait Chair passed to Nicholas Kemmer FRS FRSE, who in 1938 had predicted the p0 particle. In 1954 Kemmer established the Tait Institute of Mathematical Physics at 1 Roxburgh Street in Edinburgh.

Max Born, FRS FRSE (b. 1882 d. 1970) The Royal Medal, awarded toPeter Higgs by the RSE in 2000.

Peter Higgs, FRS FRSE (b. 1929)Peter Higgs, FRS FRSE (b. 1929)

Peter Higgs was born in Newcastle, on 29 May 1929. He spent a great part of his early life in Bristol, and attended Cotham School, where Dirac had also been a pupil.

Higgs was an undergraduate, postgraduate and post-doctoral researcher at King’s College London. He spent a short period in Edinburgh as a postdoctoral fellow in 1954, and in 1960 was appointed to a lectureship at the Tait Institute.

He was awarded a Personal Chair in Theoretical Physics in 1980, and became Professor Emeritus on his retirement in 1996. The Queen presented him with the RSE Royal Medal in its inaugural year (2000).

The 1964 papers (The boson is born)

Experiments in nuclear and particle physics have shown, surprisingly, that symmetries may be exact or they may be

broken in certain circumstances. For example, most forces respect a left-right symmetry, whilst the force that drives radioactive beta-decay breaks this symmetry. Symmetries may either be explicitly broken in the nature of the force, or the breaking may arise ‘spontaneously’ from the vacuum.

The ‘Goldstone theorem’ showed that this spontaneous symmetry-breaking always gives rise to a massless scalar boson, but no such particle has ever been found.

What is a boson?Particles of matter (such as electrons) – collectively known as fermions – can only be created and destroyed as matter-antimatter pairs. By contrast, the quanta of radiation (photons) can be created individually, and are called bosons. Bosons with the symmetry of a sphere (looking the same in all directions) are called scalar bosons. Amongst more complex particles are vector bosons, such as the photon.

The Higgs ‘wine-bottle’ potential and equations: blackboard courtesy of the University of Edinburgh and Peter Higgs.

The Higgs boson is born: the revised paper by Peter Higgs that first introduces the massive scalar boson.

The Higgs boson: a publication historyA number of people worked on incorporating Maxwell’s electromagnetic field in theories of spontaneous symmetry-breaking, sometimes referred to as the Higgs mechanism. Peter Higgs alone stated explicitly that the theory implies that a massive scalar boson must exist.

August 1964: Robert Brout and Francois Englert publish a paper on the evasion of the Goldstone theorem.

September 1964: Higgs independently publishes a paper showing that the Goldstone theorem is not necessarily true.

October 1964: A second Higgs paper describes a simple model of spontaneous symmetry-breaking combining two scalar fields with the field for a massless vector boson, resulting in a massive vector boson and a single massive scalar boson. This paper is surprisingly rejected.

Higgs adds a note about the necessary existence of massive scalar particles as a consequence of such models; this revised paper is accepted by another journal, and the Higgs boson is born.

November 1964: Similar work is carried out independently by Gerry Guralnik, Carl Hagen and Tom Kibble.

May 1966: Higgs third paper is published, outlining the properties of the massive scalar boson.

March 1967: A paper by Kibble shows how to make some vector bosons massive while leaving others (such as the photon) massless.

Before agreeing to fund the Large Hadron Collider (LHC), governments in over a dozen CERN member states needed

to be satisfied of the project’s scientific scope and importance, the technological stimulus and benefits it would provide, and its impact on public attitudes to fundamental science.

In 1993 William Waldegrave as Minister for Science held a competition to explain the Higgs boson; the prize-winning allegory by David Miller is adapted in the cartoon below.

The vacuum is not truly empty: it is like a cocktail party full of CERN scientists chatting to their nearest neighbours.

Suppose breaking news now arrives at the party, about the discovery of a new particle. The scientists are keen to hear it, and crowd around the door.

Eager to be first to bring the news, a knot of scientists struggles through the crowded room. The throng causes the news to cross the room slowly: because of its slowness it has acquired mass. That is the Higgs boson, a massive object built solely out of vacuum.

A famous scientist enters, and an eager crowd forms round him. They impede his motion as he struggles to get through, and so increase his mass. That is the Higgs mechanism, which makes material objects massive.

The Higgs mechanismillustrated

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The Holy Grail for the theory of fundamental particles becomes the search for the Higgs boson: the LHC is the machine to power this search.

Electroweak interactionand the Standard Model

Combining relativity and quantum theory led to ‘Quantum Electrodynamics’, in which the force between electrically-

charged particles is carried by the exchange of photons (γ), the massless quanta of light. Extraordinary precision was achieved, agreeing with experiment to within 1 part in a trillion; this theory is one of the most precisely tested in the history of science.

A similar theory, ‘Quantum Chromodynamics’, successfully describes the reactions of particles like protons and neutrons. The carrier of the force between them is the massless gluon (g).

The weak particle interactions, however, that describe both nuclear decay and fusion processes in the Sun, are mediated by massive particles known as weak bosons: W+, W– and Z0.

A theory with massive W+/W–/Z0 bosons, however, gave contradictory answers at very high energies.

Weinberg and Salam solved this problem by starting with massless weak bosons and four Higgs fields. Three of these Higgs fields were absorbed to make the W and Z bosons massive, whilst leaving the photon massless. The remaining Higgs field – the –became massive, but the theory did not fix a value for its mass.

Parallel work revealed three families of matter particles (quarks and leptons) all acquiring their mass via the Higgs mechanism.

Neutrinos were found to change from one type to another through ‘neutrino oscillations’ or ‘mixing’: this means that each type has a different, but very small, mass.

The Standard ModelThe Standard Model of particle physics is a theory concerning the electromagnetic, weak, and strong nuclear interactions, which mediate the dynamics of the known subatomic particles.

Developed throughout the mid to late 20th century, The Standard Model is truly “a tapestry woven by many hands” (Glashow), sometimes driven forward by new experimental discoveries, sometimes by theoretical advances. It was a collaborative effort in the largest sense, spanning continents and decades.

The current formulation was finalised following experimental confirmation of the existence of quarks. Discoveries of the bottom and top quarks and the tau neutrino gave further credence to the model. More recently, the apparent detection of the Higgs boson completes the set of predicted particles.

Because of its success in explaining a wide variety of experimental results, the Standard Model is sometimes regarded as a “theory of almost everything” (Oerter).

Acceleratorsand detectors: CERN

Peter Higgs FRS FRSE, standing in the 27 km LHC collider ring at CERN.

Location of the LHC tunnel, over 100 m underground. The 27 km circumference accelerator straddles the Franco-Swiss border, shown in blue. Geneva airport is at the bottom of the image, for scale.

Right: a side- and end-view of a typical Z-boson event produced in the ALEPH detector at LEP, in 1992.

Colliding beams enter from both sides, and annihilate in the centre of the detector.

The tracks of the two jets of created particles are curved by a magnetic field: higher energy particles have straighter tracks. 

To make massive new particles like W, Z and the Higgs, particle accelerators of increasing energy were constructed

at CERN over a period of years using a circular tunnel (27 km around) with a ring of magnets to contain and store ‘beams’ of particles moving in both directions. These collide head-on at four points around the ring, where large detector systems observe the collision products.

Proton-antiproton collisions were studied from 1983. The Large Electron Positron collider (LEP) investigated electron-positron annihilation from 1989, and the Large Hadron Collider made its first very high energy proton-proton collisions in 2008.

CERNSince 1954 the European Organisation for Nuclear Research (CERN in Geneva) has provided the facilities needed to produce and study new particles. The UK is one of twenty Member States. It costs everyone in Europe the same as one cup of coffee per year.

Four vital technologies have Scottish origins1894 C T R Wilson FRS FRSE invents the cloud chamber. Cosmic

rays and elementary particles leave tracks, rather like a plane flying through a clear blue sky. (Nobel Prize 1927)

1944 Sir Samuel Curran FRS FRSE invents the scintillation counter, used to detect and time the passage of subatomic particles.

1948 Sir Samuel Curran FRS FRSE invents the proportional counter, used in complex detector systems and energy measurements.

1960 Bruno Touschek (PhD, Glasgow) invents the colliding-beam storage ring.

Peter Higgs FRS FRSE, standing in the 27km LHC collider ring at CERN.

CERN, 1983 – In a bold project the CERN SPS accelerator ring was turned into a proton-antiproton collider. Antiprotons

were created, stored, raised in energy, and then collided head-on with protons. W± bosons can be produced in such a matter-antimatter annihilation, and the figure below shows such an event.

The isolated straight track, identified as a high-energy electron, is balanced by an unseen particle, as predicted by theory. A collection of such events points to a common cause in the production of a W± boson decaying to high-energy electrons or muons.

The Z0 boson is produced more rarely, but those decays in which all the resultant particles can be measured permit the identification and measurement of the Z0.

This work won the 1984 Nobel Prize for Carlo Rubbia and Simon van der Meer.

Detecting the decay of a W– boson, the result of the collision between a proton and anti-proton. (From Carlo Rubbia’s 1984 Nobel Lecture.)

Precision at LEPEarlier data supported the Standard Model, describing three ‘generations’ of quarks and leptons, with none missing and no extra particles.

1989: The LEP collider at CERN made Z0 particles in profusion, and allowed many precision tests to be made. The combined LEP measurement of the number of generations is 2.9840 ± 0.0082, a number so close to 3 that it severely limits the possibilities of additional unknown particles and interactions.

A wide range of precisely measured properties of the W and Z provides detailed support for the standard model, of electroweak interactions leaving one unanswered question...

… where is the Higgs?

A graph showing the rate of Z0 production as a function of energy. The curves show the theoretical predictions if there were 2, 3 or 4 generations of quarks and leptons. The black dots are the results from the ALEPH experiment at LEP, confirming that there are only three generations.

Discovery and precisionestablish the Standard Model

Discovery at theLarge Hadron Collider

An ATLAS computer display showing a candidate Higgs production event. The particle tracks emerging from the collision are a signature of the decay of the Higgs boson.

A 27 km superconducting magnet ring stores beams of protons, accelerating the beams until

each particle has an energy thousands of times that of normal atoms. At four points around the ring the clockwise and anticlockwise beams collide head on. Reactions producing a wide range of particles occur billions of times each second.

To ensure that the scientific investigations are independently tested, two rival collaborations have built and now operate giant detector systems to catch the elusive Higgs-production events. ATLAS and CMS each have over 100 institutes from over 30 countries.

Scientists from the Universities of Edinburgh and Glasgow are members of the ATLAS collaboration, and have developed technologies for precision particle-tracking, and for organising the world-wide computer power needed to store and analyse the data (the ‘Grid’).

Detecting the Higgs boson• OnebillioneventspersecondcanbecapturedandanalysedforHiggsproduction.

• OneeventinmanybillionsmaycontainarecognisableHiggsboson.

• DifferentHiggsdecaymodesarepossible,suchastwophotons,ortwoelectronsplus two muons (see figure opposite).

• EventsfromseparatedecaymodescanbeusedtodeterminetheHiggsbosonmass.

• Combiningresultsfordifferentdecaymodescanprovideevidencefortheproduction of a new boson.

• July4,2012:bothATLASandCMSreportdiscoveryofanewbosonwithHiggs-like properties, and a mass about 135 times that of the proton.

The ATLAS detector during construction. The eight toroidal magnets bend the tracks of the particles formed from the energy of the colliding proton beams. A typical collision snapshot can be seen in the figure on the left.

The discovery of the scalar boson announced on 4 July 2012 was published separately by the ATLAS and CMS experiments at

the end of August using improved analysis. The Large Hadron Collider continued running until the end of 2012, collecting more data. The updated results give the strongest evidence that the scalar particle discovered is indeed the Standard Model Higgs boson. Measurements of the properties of this particle known as spin and parity are also consistent with that of the Higgs boson.

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The Large Hadron Collider shut down at the beginning of 2013 for upgrades to both the accelerators and the experimental detectors. It will restart in 2015-16 and will run at a higher energy of 13-14TeV allowing improved determination of the properties of the boson and for searches for new physics that lie beyond the present Standard Model. It may shed light on some of the big outstanding questions about how our Universe works.

In June 2013, the Royal Society of Edinburgh unveiled a newly commissioned portrait by the leading Scottish artist Victoria Crowe OBE, FRSE.

The left hand figure plots the probability p0 that the observed signal is due to a background fluctuation rather than a true Higgs signal. Since December 2011, this has decreased from one part in a thousand to one part in a thousand million! The right hand figure shows that measurements of the spin J and parity P of the observed particle agree well with the expected value of J P = O+.

In the painting there are elements personal to Peter Higgs that include a glass bowl in the shape of the Higgs potential, engraved with a simulated decay of the Higgs boson to four muons. © Victoria Crowe 2013. Photographs by Antonia Reeve.

Peter Higgs has been widely acclaimed and has received many prestigious awards, including Honorary Degrees from several world-leading universities; other major awards are also listed below. In October 2013 Peter Higgs achieved the ultimate recognition when he was awarded the Nobel Prize in Physics, jointly with Francois Englert, for their work on the theory of how particles acquire mass.

January 2012 City of Edinburgh 2011 Edinburgh Award

October 2012 Royal Society of Edinburgh ‘Higgs Medal’

December 2012 Companion of Honour

January 2013 Premio Nonino 2013 Award ‘Man of Our Time’

January 2013 Honorary Fellow Royal Scottish Society for the Arts

March 2013 Edinburgh International Science Festival Edinburgh Medal*

April 2013 Honorary Member Saltire Society Scotland

May 2013 Prince of Asturias Science and Technology Prize 2013*

July 2013 Freedom of the City of Bristol

* Shared with CERN.

The Nobel Prize in Physics, awarded to Peter Higgs

on 8 October 2013. ® The Nobel Foundation. Photo: Lovisa Engblom.

Higgs boson discovery confirmed

“This is for everyone”

A range of technological advances and innovations were devised to create and exploit both the LHC and its detectors, and to

enable over 2000 scientists to work together on a common project.

Technologies stimulated by accelerator and detector advances include the following:

•TheWorld-WideWeb:inventedin1990atCERNbySirTimBerners-Lee, and made available to everyone. Berners-Lee won the IEEE/RSE/Wolfson James Clerk Maxwell Award in 2008.

•PracticalsuperconductingmagnetsforMRImedicalimaging.

•PETandSPECTmedicalimagingscanners.

•Thecomputergridtobringworld-wideresourcestothelargestdata-handling problems.

•Imagingtechnologyforsecuritypurposes.

•Semiconductordevicedesign.

•High-vacuumtechnology.

•Superfluidrefrigerators:colderthanouterspace.

•Makingenemiesintofriends:evenatthe heightoftheColdWar,European-USSR collaboration thrived.

•World-widecollaborativeprojectstoutilisetheskillsofmanycountries. (ATLAS has over 3000 members at 174 institutes in 38 countries, for example.)

Theory triumphantly predicts what occurs• Energy≡ matter. (E =mc2, Einstein 1905)• Generalrelativitymakesspace-timecurved.(Einsten1915,1917)• Wave-particleduality.(deBroglie1924)• Existenceofanti-matter.(Dirac1928)• Predictionofthep0 meson. (Kemmer 1938)• W and Z bosons. (1983)• Threegenerationsofquarksandneutrinos.(1989)• Higgsboson.(2012)

Theory challenged and new ideas needed• Arethereadditionalparticlesmirroringthoseweknow

(‘supersymmetry’ and ‘naturalness’)?• Cangravitybeunifiedwiththeotherforces(‘superstrings’and

‘supergravity’)?• Whydoneutrinosmix?• Wherehastheanti-matterfromtheBigBanggone?• Whatisthedarkmatter(22%)thatseemstodominateordinary

matter(only4%)intheUniverse?• Whatisthedarkenergy(74%)thatcausestheUniverse’s

expansion to accelerate?

MRI scans of a human head – an example of one of the technological benefits arising from the development of superconducting magnets.

The theory and techniques for the discovery of the Higgs boson have their genesis in the work of James Clerk Maxwell.

To quote the man who discovered electromagnetic waves:

“Radio waves are of no use whatsoever” — Heinrich Hertz (1887)

As Peter Higgs said: we have no idea if the Higgs boson will be of any practical use.