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George Butterworth

George Sainton Kaye Butterworth, MC (12 July 1885 – 5 August 1916) was an English composer who was best known for the orchestral idyll The Banks of Green Willow and his song settings of A. E. Housman's poems from A Shropshire Lad. He was awarded the Military Cross for his gallantry during the fighting at Pozières in the First World War, and died in the Battle of the Somme.

Early years
Butterworth was born in Paddington, London. Soon after his birth, his family moved to York so that his father Sir Alexander Kaye Butterworth could take up an appointment as general manager of the North Eastern Railway, which was based there. Their home was at Riseholme, a house on Driffield Terrace, which later became part of the Mount School. In 2016, the centenary year of his death on the Somme, biographer Anthony Murphy unveiled on behalf of the York Civic Trust a blue plaque to his memory at College House, Driffield Terrace, part of the Mount School.

George received his first music lessons from his mother, who was a singer, and he began composing at an early age. As a young boy, he played the organ for services in the chapel of his preparatory school, Aysgarth School, before gaining a scholarship to Eton College. He showed early musical promise at Eton, a "Barcarolle" for orchestra being played during his time there (it is long since lost).

Butterworth then went up to Trinity College, Oxford, where he became more focused on music, becoming President of the University Music Club. He also made friends with the folk song collector Cecil Sharp; the composer and folk song enthusiast Ralph Vaughan Williams; the future Director of the Royal College of Music, Hugh Allen; and a baritone and future conductor, Adrian Boult. Butterworth and Vaughan Williams made several trips into the English countryside to collect folk songs (Butterworth collected over 450 himself, many in Sussex in 1907, and sometimes using a phonograph) and the compositions of both were strongly influenced by what they collected. Butterworth was also an expert folk dancer, being particularly keen in the art of morris dancing. He was employed for a while by the English Folk Dance and Song Society (of which he was a founder member in 1906) as a professional morris dancer, and was a member of the Demonstration Team.

Upon leaving Oxford, Butterworth began a career in music, writing criticism for The Times, composing, and teaching at Radley College, Oxfordshire. He also briefly studied piano and organ at the Royal College of Music, where he worked with Hubert Parry among others, though he stayed less than a year as the academic life was not for him.

Vaughan Williams and Butterworth became close friends. It was Butterworth who suggested to Vaughan Williams that he turn a symphonic poem he was working on into his London Symphony. Vaughan Williams recalled:

"We were talking together one day when he said in his gruff, abrupt manner: ‘You know, you ought to write a symphony’. I answered...that I’d never written a symphony and never intended to...I suppose Butterworth’s words stung me and, anyhow, I looked out some sketches I had made for...a symphonic poem about London and decided to throw it into symphonic form...From that moment, the idea of a symphony dominated my mind. I showed the sketches to George bit by bit as they were finished, and it was then that I realised that he possessed in common with very few composers a wonderful power of criticism of other men’s work and insight into their ideas and motives. I can never feel too grateful to him for all he did for me over this work and his help did not stop short at criticism."

When the manuscript for that piece was lost (having been sent to Germany, either to the conductor Fritz Busch or for engraving, just before the outbreak of war), Butterworth, together with Geoffrey Toye and the critic Edward J. Dent, helped Vaughan Williams reconstruct the work. Vaughan Williams dedicated the piece to Butterworth's memory after his death.

First World War
At the outbreak of the First World War, Butterworth, together with several of his friends, including Geoffrey Toye and R. O. Morris, joined the British Army as a private in the Duke of Cornwall's Light Infantry, but he soon accepted a commission as a subaltern (2nd Lieutenant) in the 13th Battalion Durham Light Infantry, and he was later temporarily promoted to lieutenant. He was known as G. S. Kaye-Butterworth in the Army. Butterworth's letters are full of admiration for the ordinary miners of County Durham who served in his platoon. As part of 23rd Division, the 13th DLI was sent into action to capture the western approaches of the village of Contalmaison on The Somme. Butterworth and his men succeeded in capturing a series of trenches near Pozières on 16–17 July 1916, the traces of which can still be found within a small wood. Butterworth was slightly wounded in the action. For his action Temporary Lt. George Butterworth, aged 31, was awarded the Military Cross, gazetted 25 August 1916, though he did not live to receive it. The citation for the medal reads as follows:

"For conspicuous gallantry in action. After his captain had been wounded, Butterworth commanded his company with great ability and coolness, and with his energy and utter disregard of danger he set a fine example on the front line. His name had previously been brought to notice for good and gallant work."

The Battle of the Somme was now entering its most intense phase. On 4 August, 23rd Division was ordered to attack a communications trench known as Munster Alley that was in German hands. The soldiers dug an assault trench and named it 'Butterworth Trench' in their officer's honour. In desperate fighting during the night of 4–5 August, and despite friendly fire from Australian artillery, Butterworth and his miners captured and held on to Munster Alley, albeit with heavy losses. At 04:45 on 5 August, amid frantic German attempts to recapture the position, Butterworth was shot through the head by a sniper. His body was hastily buried by his men in the side of the trench, but was never recovered for formal reburial following the fierce bombardments of the final two years of conflict.

When his brigade commander, Brigadier General Page Croft, wrote to Butterworth's father to inform him of his death, it transpired that he had not known that his son had been awarded the Military Cross. Similarly, the brigadier was astonished to learn that Butterworth had been one of the most promising English composers of his generation. Brigadier Croft wrote that Butterworth was "A brilliant musician in times of peace, and an equally brilliant soldier in times of stress."

There is confusion about exactly what award(s) Butterworth received. It is said that he won the MC twice, but this is incorrect. This misunderstanding may have arisen because Butterworth's bravery was regularly in evidence during the Somme campaign. Firstly, he was mentioned in despatches early in July, and was then recommended for the MC "for conspicuous gallantry in action" on 9 July at Bailiff Wood, then again – successfully – "for commanding his company with great ability and coolness" when wounded on 16–17 July. Brigadier Page-Croft also mentioned to Butterworth's father that he had 'won' the medal again on the night he died. However, the Military Cross was not awarded posthumously at the time, and so he could never have been awarded it twice.

Butterworth's body was never recovered (although his unidentified remains may well lie at nearby Pozières Memorial, a Commonwealth War Graves Commission cemetery), and his name appears on the Thiepval Memorial. George Butterworth's The Banks of Green Willow has become synonymous for some with the sacrifice of his generation and has been seen by some as an anthem for all 'Unknown Soldiers'. Sir Alexander Butterworth erected a plaque at St Mary's Priory Church, Deerhurst, Gloucestershire in memory of his son and of his nephew, Hugh, who died at Loos in 1915. (The Rev. George Butterworth, the composer's grandfather, had been vicar of St Mary's in the previous century.) Sir Alexander also arranged the printing in 1918 of a memorial volume in his son's memory. His name is one of the 38 on the War Memorial at the Royal College of Music.

Almost all Butterworth's manuscripts were left to Vaughan Williams, after whose death Ursula Vaughan Williams lodged the original works in the Bodleian, Oxford, and the folk song collection with the EFDSS.

A Shropshire Lad, and other compositions
Butterworth did not write a great deal of music, and before and during the war he destroyed many works he did not care for, lest he should not return and have the chance to revise them. Of those that survive, his works based on A. E. Housman's collection of poems A Shropshire Lad are among the best known. Many English composers of Butterworth's time set Housman's poetry, including Ralph Vaughan Williams.

In 1911 and 1912, Butterworth wrote eleven settings of Housman's poems from A Shropshire Lad. The poems are

 * 1) "Loveliest of Trees"
 * 2) "When I Was One and Twenty"
 * 3) "Look Not in My Eyes"
 * 4) "Think No More, Lad"
 * 5) "The Lads in Their Hundreds"
 * 6) "Is My Team Ploughing?"
 * 7) "Bredon Hill"
 * 8) "Oh Fair Enough Are Sky and Plain"
 * 9) "When the Lad for Longing Sighs"
 * 10) "On the Idle Hill of Summer"
 * 11) "With Rue My Heart Is Laden"

He used no known folk tunes in the songs, although one ("When I Was One and Twenty") was said to be based on a folk tune that has defied identification. The songs were dedicated to Victor Annesley Barrington-Kennett, a friend from Eton and Oxford, who was also to die in France in 1916. They were eventually published in two sets, Six Songs from A Shropshire Lad (1–6 above) and Bredon Hill and Other Songs (7–11), although the composer never settled on a preferred order. Nine of the songs were first performed by James Campbell McInnes (baritone) and Butterworth (piano) on 16 May 1911 at a meeting of the Oxford University Musical Club, organized by Boult. Shortly thereafter Boult sang several of the songs at a private function. At this stage, Butterworth still had not completed "On the idle hill of summer" and did not do so until he was living at Cheyne Gardens in London. It is unusual for the songs to be given publicly in full, although each of the published sets is often performed separately and recorded regularly – in fact, they can be said to be among the most frequently performed English art songs. Six Songs from A Shropshire Lad is the more popular set, with "Is My Team Ploughing?" being the most famous song. Another, "Loveliest of Trees", is the basis for his 1912 orchestral rhapsody, also called A Shropshire Lad, which quotes two songs from the whole – "Loveliest of Trees" and "With Rue My Heart Is Laden".

The parallel is regularly made between the often gloomy and death-obsessed subject matter of A Shropshire Lad, written in the shadow of the Second Boer War, and Butterworth's subsequent death during the Great War. In particular, the song "The lads in their hundreds" tells of young men who leave their homeland to 'die in their glory and never be old'.

The Rhapsody, A Shropshire Lad – a sort of postlude to the songs – employs a normal sized symphony orchestra, and was first performed on 2 October 1913 at the Leeds Festival, conducted by Arthur Nikisch. It was influential upon Vaughan Williams (A Pastoral Symphony), Gerald Finzi (A Severn Rhapsody) and Ernest Moeran (First Rhapsody). Butterworth's other orchestral works are short and based on folksongs he had collected in Sussex in 1907: Two English Idylls (1911) and The Banks of Green Willow (1913). They are often performed and recorded, Banks particularly so. The latter work was premiered by the 24-year-old Adrian Boult on 27 February 1914, at West Kirby, Wirral, (this was in fact Boult's very first professional concert).

Love Blows As the Wind Blows is a setting of poems by W. E. Henley. It exists in three forms: for voice and string quartet, voice and piano and voice and small orchestra. The orchestral version differs from the others quite markedly, not least in having only three songs: "In the Year That's Come and Gone", "Life in Her Creaking Shoes", and "On the Way to Kew" (the other versions include "Fill a Glass with Golden Wine"). The orchestral version was in fact the last music Butterworth worked on before leaving for France, and shows the composer's familiarity with Vaughan Williams' style, as well as with the music of Wagner, Elgar and Debussy.

Butterworth showed real talent that might have flourished but for his early death. The Two English Idylls and The Banks of Green Willow show an ability to handle folk song in a way that eluded many other composers – as the true building blocks of larger forms. His original music (especially the Rhapsody: A Shropshire Lad and the orchestral song cycle Love Blows As The Wind Blows) have a delicacy that brings to mind Debussy or Ibert. However, there is reasonable evidence that he had put composition behind him by the time he went to France, and it is by no means certain that he would have resumed it had he returned. It is certainly likely that he would have faced considerable pressure from friends to compose again, since his orchestral works (particularly the Rhapsody: A Shropshire Lad) had made a great impression, but he was a single-minded man who was unlikely to bow easily to such pressure. He remains perhaps the most obvious case of "what if...?" that is left to us from the battlefields of northern France, and he joins the Frenchman Albéric Magnard, the Spaniard Enrique Granados, and the German Rudi Stephan as possibly the greatest losses to music from the First World War. The great conductor Carlos Kleiber saw in Butterworth a special gift. In his 1978 appearance with the Chicago Symphony Orchestra he programmed, to the surprise of many, Butterworth's English Idyll No. 1.

List of compositions
Butterworth's complete extant works are:

 * Two English Idylls for orchestra (1910–1911)
 * A Shropshire Lad, Rhapsody for orchestra (1911)
 * The Banks of Green Willow for orchestra (1913)
 * Love Blows As the Wind Blows, a song cycle for voice and piano (or string quartet) (both 1911–12) or small orchestra (1914) [words William Ernest Henley]
 * Suite for String Quartet (1910)
 * Eleven Songs from A Shropshire Lad (i.e., Six Songs from A Shropshire Lad, and Bredon Hill and Other Songs) (1910–1911) [words A. E. Housman]
 * Folk Songs From Sussex (1912)
 * Haste On, My Joys!, song (date unknown, probably pre-1906) [words Robert Bridges]
 * I Will Make You Brooches (date unknown) [words Robert Louis Stevenson]
 * I Fear Thy Kisses (1909) [words Percy Bysshe Shelley]
 * Requiescat, song (1911) [words Oscar Wilde]
 * In The Highlands, for female voices and piano (poss. 1912) [words R. L. Stevenson]
 * On Christmas Night, for male chorus (poss. 1912) [folksong]
 * We Get Up In The Morn, for male chorus (poss. 1912) [folksong]
 * Morris Dance Tunes Books 8 & 9 (1914)

Arrangements of Butterworth's compositions

 * Fantasia for Orchestra (1914), edited and completed by Martin Yates
 * Fantasia for Orchestra (1914), edited and completed by Kriss Russman
 * Two English Idylls (arranged for piano duet by John Mitchell) (1999)
 * A Shropshire Lad: Rhapsody (arranged for piano by John Mitchell) (2011)
 * Suite for Small Orchestra (arrangement of the Suite for String Quartet by Phillip Brookes) (2012)
 *  Suite for String Quartette  (arranged for String Orchestra by Kriss Russman) (2015)
 * Eleven Songs from A Shropshire Lad (with accompaniment for small orchestra, arranged by Phillip Brookes) (2006)
 * Six Songs from  A Shropshire Lad  (with accompaniment for orchestra by Kriss Russman) (2015)

Other writings
The Country Dance Book, parts 3 (1912) and 4 (1916) with Cecil Sharp

Recordings

 * All three orchestral works (Two English Idylls, A Shropshire Lad: Rhapsody. and The Banks of Green Willow)
 * Boult/LPO (rec. 1973); Lyrita SRCD 245
 * Marriner/ASMF (rec. 1976); Decca 468 802-2
 * Boughton/English String Orchestra (rec. 1986); Nimbus NI 5068
 * Llewellyn/RLPO (rec. 1991); Decca 436 401-2
 * Elder/Hallé Orchestra (rec. 2002); Hallé CD HLL 7503
 * Russman/BBC National Orchestra of Wales (rec. 2015); BIS Records BIS-2195

 * Two English Idylls only
 * Boult/British Symphony Orch. (No. 1 only, rec. 1922); HMV Cc1129
 * Dilkes/English Sinfonia (rec. 1971); HMV ESD 7101
 * Carlos Kleiber/Chicago SO (No. 1 only, rec. 2 June 1983); Memories CD
 * Tate/English Chamber Orchestra (rec. 1987); EMI CDC7 47945-2
 * Horvay/Prague Radio SO (No. 2 only, date unknown); Artist’s Rifles CD41
 * Wilson/Royal Liverpool PO (rec. 2011) Avie

 * A Shropshire Lad: Rhapsody only
 * Boult/British Symphony Orch. (rec. 1920); HMV 4618AF
 * Boult/Hallé Orchestra (rec. 1942); VAI Audio VAIA 1067-2
 * Stokowski/NBC SO (rec. 1944); Cala CACD 0528
 * Goossens/Sydney SO (rec 1952); HMV DB 9792-3
 * Boult/LPO (rec. 1954); Belart CD 461354-2
 * Barbirolli/ Hallé Orchestra (rec. 1956); Barbirolli Society SJB 1022
 * Barbirolli/ Hallé Orchestra; EMI 4577672
 * Dilkes/English Sinfonia (rec. 1971); HMV CSD 3696
 * Elder/Halle Orchestra (rec. 2002); BBC MM 289

 * The Banks of Green Willow
 * See the separate page

Fantasia for Orchestra (completed by Kriss Russman)
 * Russman/BBC National Orchestra of Wales (rec.2015) BIS Records BIS 2195

 * Songs (complete):
 * The Complete Butterworth Songbook: Stone/Barlow; Stone Records 5060192780024 (All Butterworth’s songs, including the voice/piano version of Love Blows. It also includes a short silent film of Butterworth morris dancing. The tracks from this disc are included among the details below.)

 * All eleven Shropshire Lad songs ('Six Songs' and 'Bredon Hill and Other Songs')
 * Cameron/Moore; Dutton
 * Luxon/Willison (rec. 1976); Decca 468 802-2
 * Luxon/Willison (rec. 1990); Chandos CHAN 8831
 * Williams/Burnside; Naxos 8.572426
 * Rolfe-Johnson/Johnson; Hyperion CDD22044
 * Terfel/Martineau(rec. 1995); DG 445946
 * Allen/Parsons (rec. 2001) EMI 67428
 * Maltman/Vignoles; Hyperion CDA 67378
 * Stone/Barlow; Stone Records 5060192780024
 * Keenlyside/Martineau; Sony Classical 88697 94424-2
 * Rutherford/Asti (rec. 2012); BIS SACD 1610

 * Six Songs from A Shropshire Lad only
 * Henderson/Moore (rec. 1941); Dutton CDLX 7038
 * Shirley-Quirk/Isepp (rec. 1966); Saga STXID5260
 * Rayner Cook/Benson; Unicorn
 * Gehrman/Farmer; Nimbus NI 5033
 * Rolfe-Johnson/Willinson; EMI
 * Lemalu/Burnside (rec. 2003); BBC MM298
 * Allen/Martineau; Wigmore Hall Live WHLIVE0002
 * Polegato/Burnside CBC Records
 * Trew/Vignoles; Meridian CDE84185
 * Varcoe/Hickox/City of London Sinfonia (orch. Lance Baker) (rec. 1989); Chandos CHAN 8743

 * I will Make You Brooches
 * Williams/Burnside; Naxos 8.572426
 * Stone/Barlow; Stone Records 5060192780024

 * I Fear Thy Kisses
 * Williams/Burnside; Naxos 8.572426
 * Stone/Barlow; Stone Records 5060192780024

 * Requiescat
 * Varcoe/Benson; Hyperion CDA 6621/2
 * Williams/Burnside; Naxos 8.572426
 * Stone/Barlow; Stone Records 5060192780024

 * Love Blows as the Wind Blows

 * (Voice and piano)
 * Stone/Barlow; Stone Records 5060192780024

 * (Voice and string quartet)
 * Oxenham/Bingham String Quartet; Meridian DUOCD 89026
 * Lemalu/Belcea Quartet (rec. 2005); EMI 5 58050

 * (Voice and orchestra)
 * Rutherford/Russman/BBC NOW (rec.2015) BIS Records BIS 2195
 * Tear/Handley/CBSO; EMI CDM7 64731-2
 * Varcoe/Hickox/City of London Sinfonia (rec. 1989); Chandos CHAN 8743

 * Folk Songs from Sussex
 * Williams/Burnside; Naxos 8.572426
 * Stone/Barlow; Stone Records 5060192780024

 * Folk songs collected by Butterworth
 * Triple Echo by Coope, Boyes and Simpson contains songs from the Butterworth collection. The Banks of Green Willow, The Cuckoo and The Turtle Dove are given with all verses. There are also songs collected by Vaughan Williams and Grainger. (Rec 2005); No Masters NMCD22

Roads
Three roads are named after Butterworth:
 * Butterworth Road, Trichirappali, Tamil Nadu, India (10.83047°N, 78.69789°W).
 * Butterworth Close in Newport, south Wales (51.59082°N, -2.93484°W), one of several named after composers.
 * Chemin George Butterworth (George Butterworth Lane; 50.04117°N, 2.73311°W), at Pozières on the Somme battlefield.

title: George Butterworth


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Magnetic monopole

In particle physics, a magnetic monopole is a hypothetical elementary particle that is an isolated magnet with only one magnetic pole (a north pole without a south pole or vice versa). A magnetic monopole would have a net north or south "magnetic charge". Modern interest in the concept stems from particle theories, notably the grand unified and superstring theories, which predict their existence. The known elementary particles that have electric charge are electric monopoles.

Magnetism in bar magnets and electromagnets is not caused by magnetic monopoles, and indeed, there is no known experimental or observational evidence that magnetic monopoles exist.

Some condensed matter systems contain effective (non-isolated) magnetic monopole quasi-particles, or contain phenomena that are mathematically analogous to magnetic monopoles.

Early science and classical physics
Many early scientists attributed the magnetism of lodestones to two different "magnetic fluids" ("effluvia"), a north-pole fluid at one end and a south-pole fluid at the other, which attracted and repelled each other in analogy to positive and negative electric charge. However, an improved understanding of electromagnetism in the nineteenth century showed that the magnetism of lodestones was properly explained not by magnetic monopole fluids, but rather by a combination of electric currents, the electron magnetic moment, and the magnetic moments of other particles. Gauss's law for magnetism, one of Maxwell's equations, is the mathematical statement that magnetic monopoles do not exist. Nevertheless, Pierre Curie pointed out in 1894 that magnetic monopoles could conceivably exist, despite not having been seen so far.

Quantum mechanics
The quantum theory of magnetic charge started with a paper by the physicist Paul Dirac in 1931. In this paper, Dirac showed that if any magnetic monopoles exist in the universe, then all electric charge in the universe must be quantized (Dirac quantization condition). The electric charge is, in fact, quantized, which is consistent with (but does not prove) the existence of monopoles.

Since Dirac's paper, several systematic monopole searches have been performed. Experiments in 1975 and 1982 produced candidate events that were initially interpreted as monopoles, but are now regarded as inconclusive. Therefore, whether monopoles exist remains an open question. Further advances in theoretical particle physics, particularly developments in grand unified theories and quantum gravity, have led to more compelling arguments (detailed below) that monopoles do exist. Joseph Polchinski, a string theorist, described the existence of monopoles as "one of the safest bets that one can make about physics not yet seen". These theories are not necessarily inconsistent with the experimental evidence. In some theoretical models, magnetic monopoles are unlikely to be observed, because they are too massive to create in particle accelerators (see below), and also too rare in the Universe to enter a particle detector with much probability.

Some condensed matter systems propose a structure superficially similar to a magnetic monopole, known as a flux tube. The ends of a flux tube form a magnetic dipole, but since they move independently, they can be treated for many purposes as independent magnetic monopole quasiparticles. Since 2009, numerous news reports from the popular media have incorrectly described these systems as the long-awaited discovery of the magnetic monopoles, but the two phenomena are only superficially related to one another. These condensed-matter systems remain an area of active research. (See  below.)

Poles and magnetism in ordinary matter
All matter isolated to date, including every atom on the periodic table and every particle in the Standard Model, has zero magnetic monopole charge. Therefore, the ordinary phenomena of magnetism and magnets do not derive from magnetic monopoles.

Instead, magnetism in ordinary matter is due to two sources. First, electric currents create magnetic fields according to Ampère's law. Second, many elementary particles have an intrinsic magnetic moment, the most important of which is the electron magnetic dipole moment, which is related to its quantum-mechanical spin.

Mathematically, the magnetic field of an object is often described in terms of a multipole expansion. This is an expression of the field as the sum of component fields with specific mathematical forms. The first term in the expansion is called the monopole term, the second is called dipole, then quadrupole, then octupole, and so on. Any of these terms can be present in the multipole expansion of an electric field, for example. However, in the multipole expansion of a magnetic field, the "monopole" term is always exactly zero (for ordinary matter). A magnetic monopole, if it exists, would have the defining property of producing a magnetic field whose monopole term is non-zero.

A magnetic dipole is something whose magnetic field is predominantly or exactly described by the magnetic dipole term of the multipole expansion. The term dipole means two poles, corresponding to the fact that a dipole magnet typically contains a north pole on one side and a south pole on the other side. This is analogous to an electric dipole, which has positive charge on one side and negative charge on the other. However, an electric dipole and magnetic dipole are fundamentally quite different. In an electric dipole made of ordinary matter, the positive charge is made of protons and the negative charge is made of electrons, but a magnetic dipole does not have different types of matter creating the north pole and south pole. Instead, the two magnetic poles arise simultaneously from the aggregate effect of all the currents and intrinsic moments throughout the magnet. Because of this, the two poles of a magnetic dipole must always have equal and opposite strength, and the two poles cannot be separated from each other.

Maxwell's equations
Maxwell's equations of electromagnetism relate the electric and magnetic fields to each other and to the distribution of electric charge and current. The standard equations provide for electric charge, but they posit zero magnetic charge and current. Except for this constraint, the equations are symmetric under the interchange of the electric and magnetic fields. Maxwell's equations are symmetric when the charge and electric current density are zero everywhere, as in vacuum.

Maxwell's equations can also be written in a fully symmetric form if one allows for "magnetic charge" analogous to electric charge. With the inclusion of a variable for the density of magnetic charge, say $ρ_{m}$, there is also a "magnetic current density" variable in the equations, $j_{m}$.

If magnetic charge does not exist – or if it exists but is absent in a region of space – then the new terms in Maxwell's equations are all zero, and the extended equations reduce to the conventional equations of electromagnetism such as $∇ ⋅ B = 0$ (where $∇⋅$ is the divergence operator and $B$ is the magnetic flux density).

In Gaussian cgs units
The extended Maxwell's equations are as follows, in CGS-Gaussian units:

In these equations $ρ_{m}$ is the magnetic charge density, $j_{m}$ is the magnetic current density, and $q_{m}$ is the magnetic charge of a test particle, all defined analogously to the related quantities of electric charge and current; $v$ is the particle's velocity and $c$ is the speed of light. For all other definitions and details, see Maxwell's equations. For the equations in nondimensionalized form, remove the factors of $c$.

In SI units
In the International System of Quantities used with the SI, there are two conventions for defining magnetic charge $q_{m}$, each with different units: weber (Wb) and ampere-meter (A⋅m). The conversion between them is $q_{m}^{[Wb]}$ = $μ_{0}q_{m}^{[A⋅m]}$, since the units are, where H is the henry – the SI unit of inductance.

Maxwell's equations then take the following forms (using the same notation above):

Potential formulation
Maxwell's equations can also be expressed in terms of potentials as follows: where
 * $$\Box = \nabla^2 - \frac{1}{c^2}\frac{\partial^2}{{\partial t}^2}$$

Tensor formulation
Maxwell's equations in the language of tensors makes Lorentz covariance clear. We introduce electromagnetic tensors and preliminary four-vectors in this article as follows:

where:
 * The signature of the Minkowski metric is (+ − − −).
 * The electromagnetic tensor and its Hodge dual are antisymmetric tensors:
 * $$F^{\alpha\beta} = -F^{\beta\alpha},\quad {\tilde F}^{\alpha\beta} = -{\tilde F}^{\beta\alpha}$$

The generalized equations are:

Alternatively, where the $ε^{αβμν}$ is the Levi-Civita symbol.

Duality transformation
The generalized Maxwell's equations possess a certain symmetry, called a duality transformation. One can choose any real angle $ξ$, and simultaneously change the fields and charges everywhere in the universe as follows (in Gaussian units): where the primed quantities are the charges and fields before the transformation, and the unprimed quantities are after the transformation. The fields and charges after this transformation still obey the same Maxwell's equations.

Because of the duality transformation, one cannot uniquely decide whether a particle has an electric charge, a magnetic charge, or both, just by observing its behavior and comparing that to Maxwell's equations. For example, it is merely a convention, not a requirement of Maxwell's equations, that electrons have electric charge but not magnetic charge; after a $ξ = \pi/2$ transformation, it would be the other way around. The key empirical fact is that all particles ever observed have the same ratio of magnetic charge to electric charge. Duality transformations can change the ratio to any arbitrary numerical value, but cannot change that all particles have the same ratio. Since this is the case, a duality transformation can be made that sets this ratio at zero, so that all particles have no magnetic charge. This choice underlies the "conventional" definitions of electricity and magnetism.

Dirac's quantization
One of the defining advances in quantum theory was Paul Dirac's work on developing a relativistic quantum electromagnetism. Before his formulation, the presence of electric charge was simply "inserted" into the equations of quantum mechanics (QM), but in 1931 Dirac showed that a discrete charge naturally "falls out" of QM. That is to say, we can maintain the form of Maxwell's equations and still have magnetic charges.

Consider a system consisting of a single stationary electric monopole (an electron, say) and a single stationary magnetic monopole, which would not exert any forces on each other. Classically, the electromagnetic field surrounding them has a momentum density given by the Poynting vector, and it also has a total angular momentum, which is proportional to the product $q_{e}q_{m}$, and is independent of the distance between them.

Quantum mechanics dictates, however, that angular momentum is quantized as a multiple of $ħ$, so therefore the product $q_{e}q_{m}$ must also be quantized. This means that if even a single magnetic monopole existed in the universe, and the form of Maxwell's equations is valid, all electric charges would then be quantized.

Although it would be possible simply to integrate over all space to find the total angular momentum in the above example, Dirac took a different approach. This led him to new ideas. He considered a point-like magnetic charge whose magnetic field behaves as $q_{m}⁄r^{ 2}$ and is directed in the radial direction, located at the origin. Because the divergence of $B$ is equal to zero everywhere except for the locus of the magnetic monopole at $r = 0$, one can locally define the vector potential such that the curl of the vector potential $A$ equals the magnetic field $B$.

However, the vector potential cannot be defined globally precisely because the divergence of the magnetic field is proportional to the Dirac delta function at the origin. We must define one set of functions for the vector potential on the "northern hemisphere" (the half-space $z > 0$ above the particle), and another set of functions for the "southern hemisphere". These two vector potentials are matched at the "equator" (the plane $z = 0$ through the particle), and they differ by a gauge transformation. The wave function of an electrically charged particle (a "probe charge") that orbits the "equator" generally changes by a phase, much like in the Aharonov–Bohm effect. This phase is proportional to the electric charge $q_{e}$ of the probe, as well as to the magnetic charge $q_{m}$ of the source. Dirac was originally considering an electron whose wave function is described by the Dirac equation.

Because the electron returns to the same point after the full trip around the equator, the phase $φ$ of its wave function $e^{iφ}$ must be unchanged, which implies that the phase $φ$ added to the wave function must be a multiple of $2\pi$. This is known as the Dirac quantization condition. In various units, this condition can be expressed as:

 * {| class="wikitable"

! Units ! Condition where $ε_{0}$ is the vacuum permittivity, $ħ = h/2\pi$ is the reduced Planck constant, $c$ is the speed of light, and $$\mathbb{Z}$$ is the set of integers.
 * SI units (weber convention)
 * $$\frac{q_{\mathrm e} q_{\mathrm m}}{2 \pi \hbar} \in \mathbb{Z}$$
 * SI units (ampere-meter convention)
 * $$\frac{q_{\mathrm e} q_{\mathrm m}}{2 \pi \varepsilon_0 \hbar c^2} \in \mathbb{Z}$$
 * Gaussian-cgs units
 * $$2 \frac{q_{\mathrm e} q_{\mathrm m}}{\hbar c} \in \mathbb{Z}$$
 * }
 * Gaussian-cgs units
 * $$2 \frac{q_{\mathrm e} q_{\mathrm m}}{\hbar c} \in \mathbb{Z}$$
 * }
 * }

The hypothetical existence of a magnetic monopole would imply that the electric charge must be quantized in certain units; also, the existence of the electric charges implies that the magnetic charges of the hypothetical magnetic monopoles, if they exist, must be quantized in units inversely proportional to the elementary electric charge.

At the time it was not clear if such a thing existed, or even had to. After all, another theory could come along that would explain charge quantization without need for the monopole. The concept remained something of a curiosity. However, in the time since the publication of this seminal work, no other widely accepted explanation of charge quantization has appeared. (The concept of local gauge invariance—see Gauge theory—provides a natural explanation of charge quantization, without invoking the need for magnetic monopoles; but only if the U(1) gauge group is compact, in which case we have magnetic monopoles anyway.)

If we maximally extend the definition of the vector potential for the southern hemisphere, it is defined everywhere except for a semi-infinite line stretched from the origin in the direction towards the northern pole. This semi-infinite line is called the Dirac string and its effect on the wave function is analogous to the effect of the solenoid in the Aharonov–Bohm effect. The quantization condition comes from the requirement that the phases around the Dirac string are trivial, which means that the Dirac string must be unphysical. The Dirac string is merely an artifact of the coordinate chart used and should not be taken seriously.

The Dirac monopole is a singular solution of Maxwell's equation (because it requires removing the worldline from spacetime); in more sophisticated theories, it is superseded by a smooth solution such as the 't Hooft–Polyakov monopole.

Dirac string
A gauge theory like electromagnetism is defined by a gauge field, which associates a group element to each path in space time. For infinitesimal paths, the group element is close to the identity, while for longer paths the group element is the successive product of the infinitesimal group elements along the way.

In electrodynamics, the group is U(1), unit complex numbers under multiplication. For infinitesimal paths, the group element is $1 + iA_{μ}dx^{μ}$ which implies that for finite paths parametrized by $s$, the group element is:

$\prod_s \left( 1+ieA_\mu {dx^\mu \over ds} \, ds \right) = \exp \left( ie\int A\cdot dx \right). $

The map from paths to group elements is called the Wilson loop or the holonomy, and for a U(1) gauge group it is the phase factor which the wavefunction of a charged particle acquires as it traverses the path. For a loop:

$e \oint_{\partial D} A\cdot dx = e \int_D (\nabla \times A) \, dS = e \int_D B \, dS.$

So that the phase a charged particle gets when going in a loop is the magnetic flux through the loop. When a small solenoid has a magnetic flux, there are interference fringes for charged particles which go around the solenoid, or around different sides of the solenoid, which reveal its presence.

But if all particle charges are integer multiples of $e$, solenoids with a flux of $2\pi/e$ have no interference fringes, because the phase factor for any charged particle is $exp(2\pii) = 1$. Such a solenoid, if thin enough, is quantum-mechanically invisible. If such a solenoid were to carry a flux of $2\pi/e$, when the flux leaked out from one of its ends it would be indistinguishable from a monopole.

Dirac's monopole solution in fact describes an infinitesimal line solenoid ending at a point, and the location of the solenoid is the singular part of the solution, the Dirac string. Dirac strings link monopoles and antimonopoles of opposite magnetic charge, although in Dirac's version, the string just goes off to infinity. The string is unobservable, so you can put it anywhere, and by using two coordinate patches, the field in each patch can be made nonsingular by sliding the string to where it cannot be seen.

Grand unified theories
In a U(1) gauge group with quantized charge, the group is a circle of radius $2\pi/e$. Such a U(1) gauge group is called compact. Any U(1) that comes from a grand unified theory (GUT) is compact – because only compact higher gauge groups make sense. The size of the gauge group is a measure of the inverse coupling constant, so that in the limit of a large-volume gauge group, the interaction of any fixed representation goes to zero.

The case of the U(1) gauge group is a special case because all its irreducible representations are of the same size – the charge is bigger by an integer amount, but the field is still just a complex number – so that in U(1) gauge field theory it is possible to take the decompactified limit with no contradiction. The quantum of charge becomes small, but each charged particle has a huge number of charge quanta so its charge stays finite. In a non-compact U(1) gauge group theory, the charges of particles are generically not integer multiples of a single unit. Since charge quantization is an experimental certainty, it is clear that the U(1) gauge group of electromagnetism is compact.

GUTs lead to compact U(1) gauge groups, so they explain charge quantization in a way that seems logically independent from magnetic monopoles. However, the explanation is essentially the same, because in any GUT that breaks down into a U(1) gauge group at long distances, there are magnetic monopoles.

The argument is topological:
 * 1) The holonomy of a gauge field maps loops to elements of the gauge group. Infinitesimal loops are mapped to group elements infinitesimally close to the identity.
 * 2) If you imagine a big sphere in space, you can deform an infinitesimal loop that starts and ends at the north pole as follows: stretch out the loop over the western hemisphere until it becomes a great circle (which still starts and ends at the north pole) then let it shrink back to a little loop while going over the eastern hemisphere. This is called lassoing the sphere.
 * 3) Lassoing is a sequence of loops, so the holonomy maps it to a sequence of group elements, a continuous path in the gauge group. Since the loop at the beginning of the lassoing is the same as the loop at the end, the path in the group is closed.
 * 4) If the group path associated to the lassoing procedure winds around the U(1), the sphere contains magnetic charge. During the lassoing, the holonomy changes by the amount of magnetic flux through the sphere.
 * 5) Since the holonomy at the beginning and at the end is the identity, the total magnetic flux is quantized. The magnetic charge is proportional to the number of windings $N$, the magnetic flux through the sphere is equal to $2\piN/e$. This is the Dirac quantization condition, and it is a topological condition that demands that the long distance U(1) gauge field configurations be consistent.
 * 6) When the U(1) gauge group comes from breaking a compact Lie group, the path that winds around the U(1) group enough times is topologically trivial in the big group. In a non-U(1) compact Lie group, the covering space is a Lie group with the same Lie algebra, but where all closed loops are contractible. Lie groups are homogeneous, so that any cycle in the group can be moved around so that it starts at the identity, then its lift to the covering group ends at $P$, which is a lift of the identity. Going around the loop twice gets you to $P^{2}$, three times to $P^{3}$, all lifts of the identity. But there are only finitely many lifts of the identity, because the lifts can't accumulate. This number of times one has to traverse the loop to make it contractible is small, for example if the GUT group is SO(3), the covering group is SU(2), and going around any loop twice is enough.
 * 7) This means that there is a continuous gauge-field configuration in the GUT group allows the U(1) monopole configuration to unwind itself at short distances, at the cost of not staying in the U(1). To do this with as little energy as possible, you should leave only the U(1) gauge group in the neighborhood of one point, which is called the core of the monopole. Outside the core, the monopole has only magnetic field energy.

Hence, the Dirac monopole is a topological defect in a compact U(1) gauge theory. When there is no GUT, the defect is a singularity – the core shrinks to a point. But when there is some sort of short-distance regulator on spacetime, the monopoles have a finite mass. Monopoles occur in lattice U(1), and there the core size is the lattice size. In general, they are expected to occur whenever there is a short-distance regulator.

String theory
In the universe, quantum gravity provides the regulator. When gravity is included, the monopole singularity can be a black hole, and for large magnetic charge and mass, the black hole mass is equal to the black hole charge, so that the mass of the magnetic black hole is not infinite. If the black hole can decay completely by Hawking radiation, the lightest charged particles cannot be too heavy. The lightest monopole should have a mass less than or comparable to its charge in natural units.

So in a consistent holographic theory, of which string theory is the only known example, there are always finite-mass monopoles. For ordinary electromagnetism, the upper mass bound is not very useful because it is about same size as the Planck mass.

Mathematical formulation
In mathematics, a (classical) gauge field is defined as a connection over a principal G-bundle over spacetime. $G$ is the gauge group, and it acts on each fiber of the bundle separately.

A connection on a $G$-bundle tells you how to glue fibers together at nearby points of $M$. It starts with a continuous symmetry group $G$ that acts on the fiber $F$, and then it associates a group element with each infinitesimal path. Group multiplication along any path tells you how to move from one point on the bundle to another, by having the $G$ element associated to a path act on the fiber $F$.

In mathematics, the definition of bundle is designed to emphasize topology, so the notion of connection is added on as an afterthought. In physics, the connection is the fundamental physical object. One of the fundamental observations in the theory of characteristic classes in algebraic topology is that many homotopical structures of nontrivial principal bundles may be expressed as an integral of some polynomial over any connection over it. Note that a connection over a trivial bundle can never give us a nontrivial principal bundle.

If spacetime is $$\mathbb{R}^4$$ the space of all possible connections of the $G$-bundle is connected. But consider what happens when we remove a timelike worldline from spacetime. The resulting spacetime is homotopically equivalent to the topological sphere $S^{2}$.

A principal $G$-bundle over $S^{2}$ is defined by covering $S^{2}$ by two charts, each homeomorphic to the open 2-ball such that their intersection is homeomorphic to the strip $S^{1}×I$. 2-balls are homotopically trivial and the strip is homotopically equivalent to the circle $S^{1}$. So a topological classification of the possible connections is reduced to classifying the transition functions. The transition function maps the strip to $G$, and the different ways of mapping a strip into $G$ are given by the first homotopy group of $G$.

So in the $G$-bundle formulation, a gauge theory admits Dirac monopoles provided $G$ is not simply connected, whenever there are paths that go around the group that cannot be deformed to a constant path (a path whose image consists of a single point). U(1), which has quantized charges, is not simply connected and can have Dirac monopoles while $$\mathbb{R}$$, its universal covering group, is simply connected, doesn't have quantized charges and does not admit Dirac monopoles. The mathematical definition is equivalent to the physics definition provided that—following Dirac—gauge fields are allowed that are defined only patch-wise, and the gauge field on different patches are glued after a gauge transformation.

The total magnetic flux is none other than the first Chern number of the principal bundle, and depends only upon the choice of the principal bundle, and not the specific connection over it. In other words, it is a topological invariant.

This argument for monopoles is a restatement of the lasso argument for a pure U(1) theory. It generalizes to $d + 1$ dimensions with $d ≥ 2$ in several ways. One way is to extend everything into the extra dimensions, so that U(1) monopoles become sheets of dimension $d − 3$. Another way is to examine the type of topological singularity at a point with the homotopy group $\pi_{d−2}(G)$.

Grand unified theories
In more recent years, a new class of theories has also suggested the existence of magnetic monopoles.

During the early 1970s, the successes of quantum field theory and gauge theory in the development of electroweak theory and the mathematics of the strong nuclear force led many theorists to move on to attempt to combine them in a single theory known as a Grand Unified Theory (GUT). Several GUTs were proposed, most of which implied the presence of a real magnetic monopole particle. More accurately, GUTs predicted a range of particles known as dyons, of which the most basic state was a monopole. The charge on magnetic monopoles predicted by GUTs is either 1 or 2 gD, depending on the theory.

The majority of particles appearing in any quantum field theory are unstable, and they decay into other particles in a variety of reactions that must satisfy various conservation laws. Stable particles are stable because there are no lighter particles into which they can decay and still satisfy the conservation laws. For instance, the electron has a lepton number of one and an electric charge of one, and there are no lighter particles that conserve these values. On the other hand, the muon, essentially a heavy electron, can decay into the electron plus two quanta of energy, and hence it is not stable.

The dyons in these GUTs are also stable, but for an entirely different reason. The dyons are expected to exist as a side effect of the "freezing out" of the conditions of the early universe, or a symmetry breaking. In this scenario, the dyons arise due to the configuration of the vacuum in a particular area of the universe, according to the original Dirac theory. They remain stable not because of a conservation condition, but because there is no simpler topological state into which they can decay.

The length scale over which this special vacuum configuration exists is called the correlation length of the system. A correlation length cannot be larger than causality would allow, therefore the correlation length for making magnetic monopoles must be at least as big as the horizon size determined by the metric of the expanding universe. According to that logic, there should be at least one magnetic monopole per horizon volume as it was when the symmetry breaking took place.

Cosmological models of the events following the Big Bang make predictions about what the horizon volume was, which lead to predictions about present-day monopole density. Early models predicted an enormous density of monopoles, in clear contradiction to the experimental evidence. This was called the "monopole problem". Its widely accepted resolution was not a change in the particle-physics prediction of monopoles, but rather in the cosmological models used to infer their present-day density. Specifically, more recent theories of cosmic inflation drastically reduce the predicted number of magnetic monopoles, to a density small enough to make it unsurprising that humans have never seen one. This resolution of the "monopole problem" was regarded as a success of cosmic inflation theory. (However, of course, it is only a noteworthy success if the particle-physics monopole prediction is correct. ) For these reasons, monopoles became a major interest in the 1970s and 80s, along with the other "approachable" predictions of GUTs such as proton decay.

Many of the other particles predicted by these GUTs were beyond the abilities of current experiments to detect. For instance, a wide class of particles known as the X and Y bosons are predicted to mediate the coupling of the electroweak and strong forces, but these particles are extremely heavy and well beyond the capabilities of any reasonable particle accelerator to create.

Searches for magnetic monopoles
Experimental searches for magnetic monopoles can be placed in one of two categories: those that try to detect preexisting magnetic monopoles and those that try to create and detect new magnetic monopoles.

Passing a magnetic monopole through a coil of wire induces a net current in the coil. This is not the case for a magnetic dipole or higher order magnetic pole, for which the net induced current is zero, and hence the effect can be used as an unambiguous test for the presence of magnetic monopoles. In a wire with finite resistance, the induced current quickly dissipates its energy as heat, but in a superconducting loop the induced current is long-lived. By using a highly sensitive "superconducting quantum interference device" (SQUID) one can, in principle, detect even a single magnetic monopole.

According to standard inflationary cosmology, magnetic monopoles produced before inflation would have been diluted to an extremely low density today. Magnetic monopoles may also have been produced thermally after inflation, during the period of reheating. However, the current bounds on the reheating temperature span 18 orders of magnitude and as a consequence the density of magnetic monopoles today is not well constrained by theory.

There have been many searches for preexisting magnetic monopoles. Although there has been one tantalizing event recorded, by Blas Cabrera Navarro on the night of February 14, 1982 (thus, sometimes referred to as the "Valentine's Day Monopole" ), there has never been reproducible evidence for the existence of magnetic monopoles. The lack of such events places an upper limit on the number of monopoles of about one monopole per 1029 nucleons.

Another experiment in 1975 resulted in the announcement of the detection of a moving magnetic monopole in cosmic rays by the team led by P. Buford Price. Price later retracted his claim, and a possible alternative explanation was offered by Luis Walter Alvarez. In his paper it was demonstrated that the path of the cosmic ray event that was claimed due to a magnetic monopole could be reproduced by the path followed by a platinum nucleus decaying first to osmium, and then to tantalum.

High-energy particle colliders have been used to try to create magnetic monopoles. Due to the conservation of magnetic charge, magnetic monopoles must be created in pairs, one north and one south. Due to conservation of energy, only magnetic monopoles with masses less than half of the center of mass energy of the colliding particles can be produced. Beyond this, very little is known theoretically about the creation of magnetic monopoles in high-energy particle collisions. This is due to their large magnetic charge, which invalidates all the usual calculational techniques. As a consequence, collider-based searches for magnetic monopoles cannot, as yet, provide lower bounds on the mass of magnetic monopoles. They can however provide upper bounds on the probability (or cross section) of pair production, as a function of energy.

The ATLAS experiment at the Large Hadron Collider currently has the most stringent cross section limits for magnetic monopoles of 1 and 2 Dirac charges, produced through Drell–Yan pair production. A team led by Wendy Taylor searches for these particles based on theories that define them as long lived (they do not quickly decay), as well as being highly ionizing (their interaction with matter is predominantly ionizing). In 2019 the search for magnetic monopoles in the ATLAS detector reported its first results from data collected from the LHC Run 2 collisions at center of mass energy of 13 TeV, which at 34.4 fb−1 is the largest dataset analyzed to date.

The MoEDAL experiment, installed at the Large Hadron Collider, is currently searching for magnetic monopoles and large supersymmetric particles using nuclear track detectors and aluminum bars around LHCb's VELO detector. The particles it is looking for damage the plastic sheets that comprise the nuclear track detectors along their path, with various identifying features. Further, the aluminum bars can trap sufficiently slowly moving magnetic monopoles. The bars can then be analyzed by passing them through a SQUID.

The astrophysicist Igor Novikov argues that the fields of macroscopic black holes are potential magnetic monopoles, representing the entrance to an Einstein–Rosen bridge.

"Monopoles" in condensed-matter systems
Since around 2003, various condensed-matter physics groups have used the term "magnetic monopole" to describe a different and largely unrelated phenomenon.

A true magnetic monopole would be a new elementary particle, and would violate Gauss's law for magnetism $∇⋅B = 0$. A monopole of this kind, which would help to explain the law of charge quantization as formulated by Paul Dirac in 1931, has never been observed in experiments.

The monopoles studied by condensed-matter groups have none of these properties. They are not a new elementary particle, but rather are an emergent phenomenon in systems of everyday particles (protons, neutrons, electrons, photons); in other words, they are quasi-particles. They are not sources for the $B$-field (i.e., they do not violate $∇⋅B = 0$); instead, they are sources for other fields, for example the $H$-field, the "$B*$-field" (related to superfluid vorticity), or various other quantum fields. They are not directly relevant to grand unified theories or other aspects of particle physics, and do not help explain charge quantization—except insofar as studies of analogous situations can help confirm that the mathematical analyses involved are sound.

There are a number of examples in condensed-matter physics where collective behavior leads to emergent phenomena that resemble magnetic monopoles in certain respects,  including most prominently the spin ice materials. While these should not be confused with hypothetical elementary monopoles existing in the vacuum, they nonetheless have similar properties and can be probed using similar techniques.

Some researchers use the term magnetricity to describe the manipulation of magnetic monopole quasiparticles in spin ice,  in analogy to the word "electricity".

One example of the work on magnetic monopole quasiparticles is a paper published in the journal Science in September 2009, in which researchers described the observation of quasiparticles resembling magnetic monopoles. A single crystal of the spin ice material dysprosium titanate was cooled to a temperature between 0.6 kelvin and 2.0 kelvin. Using observations of neutron scattering, the magnetic moments were shown to align into interwoven tubelike bundles resembling Dirac strings. At the defect formed by the end of each tube, the magnetic field looks like that of a monopole. Using an applied magnetic field to break the symmetry of the system, the researchers were able to control the density and orientation of these strings. A contribution to the heat capacity of the system from an effective gas of these quasiparticles was also described. This research went on to win the 2012 Europhysics Prize for condensed matter physics.

In another example, a paper in the February 11, 2011 issue of Nature Physics describes creation and measurement of long-lived magnetic monopole quasiparticle currents in spin ice. By applying a magnetic-field pulse to crystal of dysprosium titanate at 0.36 K, the authors created a relaxing magnetic current that lasted for several minutes. They measured the current by means of the electromotive force it induced in a solenoid coupled to a sensitive amplifier, and quantitatively described it using a chemical kinetic model of point-like charges obeying the Onsager–Wien mechanism of carrier dissociation and recombination. They thus derived the microscopic parameters of monopole motion in spin ice and identified the distinct roles of free and bound magnetic charges.

In superfluids, there is a field $B*$, related to superfluid vorticity, which is mathematically analogous to the magnetic $B$-field. Because of the similarity, the field $B*$ is called a "synthetic magnetic field". In January 2014, it was reported that monopole quasiparticles for the $B*$ field were created and studied in a spinor Bose–Einstein condensate. This constitutes the first example of a quasi-magnetic monopole observed within a system governed by quantum field theory.

Updates to the theoretical and experimental searches in matter can be found in the reports by G. Giacomelli (2000) and by S. Balestra (2011) in the Bibliography section.

license: Creative Commons - Attribution Share-Alike - https://creativecommons.org/licenses/by-sa/4.0/

title: Magnetic monopole


text:
Tokyo Rose

Tokyo Rose (alternative spelling Tokio Rose) was a name given by Allied troops in the South Pacific during World War II to all female English-speaking radio broadcasters of Japanese propaganda. The programs were broadcast in the South Pacific and North America to demoralize Allied forces abroad and their families at home by emphasizing troops' wartime difficulties and military losses. Several female broadcasters operated using different aliases and in different cities throughout the territories occupied by the Japanese Empire, including Tokyo, Manila, and Shanghai. The name "Tokyo Rose" was never actually used by any Japanese broadcaster, but it first appeared in U.S. newspapers in the context of these radio programs during 1943.

During the war, Tokyo Rose was not any one individual, but rather a group of largely unassociated women working for the same propagandist effort throughout the Japanese Empire. In the years soon after the war, the character "Tokyo Rose" – whom the Federal Bureau of Investigation (FBI) now avers to be "mythical" – became an important symbol of Japanese villainy for the United States. American cartoons, movies, and propaganda videos between 1945 and 1960 tend to portray her as sexualized, manipulative, and deadly to American interests in the South Pacific, particularly by revealing intelligence of American losses in radio broadcasts. Similar accusations concern the propaganda broadcasts of Lord Haw-Haw and Axis Sally, and in 1949 the San Francisco Chronicle described Tokyo Rose as the "Mata Hari of radio".

Tokyo Rose ceased to be merely a symbol during September 1945 when Iva Toguri D'Aquino, a Japanese-American disc jockey for a propagandist radio program, attempted to return to the United States. Toguri was accused of being the "real" Tokyo Rose, arrested, tried, and became the seventh person in U.S. history to be convicted of treason. Toguri was eventually paroled from prison in 1956, but it was more than twenty years later that she received an official presidential pardon for her role in the war.

Iva Toguri and The Zero Hour
Although she broadcast using the name "Orphan Ann", Iva Toguri has been known as "Tokyo Rose" since her return to the United States in 1945. An American citizen and the daughter of Japanese immigrants, Toguri traveled to Japan to tend to a sick aunt just prior to the attack on Pearl Harbor. Unable to leave the country when war began with the United States, unable to stay with her aunt's family as an American citizen, and unable to receive any aid from her parents who were placed in internment camps in Arizona, Toguri eventually accepted a job as a part-time typist at Radio Tokyo (NHK). She was quickly recruited as a broadcaster for the 75-minute propagandist program The Zero Hour, which consisted of skits, news reports, and popular American music.

According to studies conducted during 1968, of the 94 men who were interviewed and who recalled listening to The Zero Hour while serving in the Pacific, 89% recognized it as "propaganda", and less than 10% felt "demoralized" by it. 84% of the men listened because the program had "good entertainment," and one G.I. remarked, "[l]ots of us thought she was on our side all along."

After World War II ended in 1945, the U.S. military detained Toguri for a year before releasing her due to lack of evidence. Department of Justice officials agreed that her broadcasts were "innocuous". But when Toguri tried to return to the United States, an uproar ensued because Walter Winchell (a powerful broadcasting personality) and the American Legion lobbied relentlessly for a trial, prompting the Federal Bureau of Investigation (FBI) to renew its investigation of Toguri's wartime activities. Her 1949 trial resulted in a conviction on one of eight counts of treason.

In 1974, investigative journalists found that important witnesses had asserted that they were forced to lie during testimony. They stated that FBI and US occupation police had coached them for more than two months about what they should say on the stand, and that they had been threatened with treason trials themselves if they did not cooperate. U.S. President Gerald Ford pardoned Toguri in 1977 based on these revelations and earlier issues with the indictment.

Tokyo Mose
Walter Kaner (May 5, 1920 – June 26, 2005) was a journalist and radio personality who broadcast using the name Tokyo Mose during and after World War II. Kaner broadcast on U.S. Army Radio, at first to offer comic rejoinders to the propaganda broadcasts of Tokyo Rose and then as a parody to entertain U.S. troops abroad. In U.S.-occupied Japan, his "Moshi, Moshi Ano-ne" jingle was sung to the tune of "London Bridge is Falling Down" and became so popular with Japanese children and G.I.s that the U.S. military's Stars and Stripes newspaper called it "the Japanese occupation theme song." In 1946, Elsa Maxwell referred to Kaner as "the breath of home to unknown thousands of our young men when they were lonely."

Popular culture
Tokyo Rose has been the subject of songs, movies, and documentaries:
 * 1945: The Mr. Hook propaganda cartoon Tokyo Woes, directed by Bob Clampett and featuring Seaman Hook. The cartoon's titular character (voiced by an uncredited Sara Berner) is a parody of Tokyo Rose broadcasts. Tokyo Rose is portrayed as an overly enthusiastic, crooked-toothed Japanese woman speaking on a propaganda broadcast with a loud voice and an American accent. When she criticizes war bonds, Seaman Hook fires a projectile from a naval gun to blow up Japan.
 * 1945: Tokyo Rose "Voice of Truth", five-minute film short produced by the U.S. Treasury Department to promote public support of the 7th war loan.
 * 1946: Tokyo Rose, movie drama directed by Lew Landers. Lotus Long played "Tokyo Rose", a "seductive jap traitress"; Byron Barr played the G.I. protagonist sent to kidnap her.
 * 1949: In the musical South Pacific, sailors mention getting "advice from Tokyo Rose" in the song "There Is Nothing Like a Dame".
 * 1957: The Hollywood service comedy Joe Butterfly, about U.S. military journalists in Japan just after World War II, includes a fictionalized subplot about the search for the "real" Tokyo Rose.
 * 1957: In the movie The Bridge on the River Kwai, a Tokyo Rose broadcast is briefly heard on the demolition team's portable radio.
 * 1958: In the movie , a Tokyo Rose broadcast details ships and sailors lost at sea based on information gained from trash jettisoned by U.S. submarines.
 * 1959: In the movie Operation Petticoat, a Tokyo Rose broadcast warns the crew of a U.S. submarine to surrender.
 * 1960: The Andy Griffith Show makes a brief reference to Tokyo Rose in the episode titled "Stranger in Town". Andy is trying to persuade his deputy, Barney Fife, that he's being unreasonably suspicious of the stranger in town. "Say, do you reckon he could be a foreign spy?" Barney asks. Andy replies, "He don't sound foreign to me." Barney says, "They learn to talk better than any of us! Remember Tokyo Rose?"
 * 1969: The Story of "Tokyo Rose", a CBS-TV and WGN radio documentary written and produced by Bill Kurtis.
 * 1974: UK rock band Chapman Whitney Streetwalkers recorded a song titled "Tokyo Rose" for their album Chapman Whitney Streetwalkers.
 * 1976: Tokyo Rose, CBS-TV documentary segment on 60 Minutes.
 * 1976: "Harbor Lights", a successful song by Boz Scaggs on his album Silk Degrees, begins with the line "Son of a Tokyo Rose, I was bound to wander from home".
 * 1977: "Tokyo Rose," title of a song by American metal band Riot (now known as Riot V) as part of their first album, Rock City. The band would also go on to reference Tokyo Rose in several other songs, such as "Feel the Same," and "The Land of the Rising Sun."
 * 1978: Dutch rock band Focus released a song entitled "Tokyo Rose" on their album Focus con Proby.
 * 1978: Tokyo Rose made a brief appearance in Tsubame Kamogawa's manga Macaroni Hôrensô in an episode originally published in Weekly Shonen Champion on August 14, 1978.
 * 1984: Italo-disco group City-O' released a song entitled "Rose of Tokyo".
 * 1985: Canadian rock band Idle Eyes had a Top 20 success in their homeland with the song "Tokyo Rose" from their self-titled debut album. The song's narrator addresses his lover, saying she "tells a story like Tokyo Rose".
 * 1987: American heavy metal band Shok Paris released the song "Tokyo Rose" on their 1987 album Steel and Starlight. It's about a lonely G.I. who fell in love with the propaganda broadcaster during the war, and remembers her voice many years later.
 * 1988: Canadian singer-songwriter Joni Mitchell mentions "Tokyo Rose on the radio" in her song "The Tea Leaf Prophecy (Lay Down Your Arms)" on the album Chalk Mark in a Rainstorm.
 * 1989: American composer and musician Van Dyke Parks released a concept album titled Tokyo Rose, on the subject of American and Japanese relations.
 * 1992: In season 7 episode 5 ("Where's Charlie?") of the American television situation comedy The Golden Girls, terminally naive Rose Nylund mistakenly believes her roommate Blanche Devereaux's beau has left Blanche for Tokyo Rose.
 * 1993: Filmmaker Rika Ohara’s performance piece Tokyo Rose premiered at Los Angeles Contemporary Exhibitions in 1993.
 * 1995: Tokyo Rose: Victim of Propaganda, A&E Biography documentary, hosted by Peter Graves, available on VHS (AAE-14023).
 * 1997: The Vigilantes of Love released the song "Tokyo Rose" on their album Slow Dark Train.
 * 2002: Japanese band Cali Gari released the song "Tokyo Rose au Monde Club" on their album Dai 7 Jikkenshitsu.
 * 2006: In Flags of Our Fathers, an American war drama film directed, co-produced, and scored by Clint Eastwood and written by William Broyles Jr. and Paul Haggis about the five Marines and one Navy corpsman who were involved in raising the flag on Iwo Jima, the night before the battle's start those responsible for the radio on one of the ships connect the Tokyo Rose program to the public address system.
 * 2010: In his dissent from Justice Stevens remarked: "If taken seriously, our colleagues' assumption that the identity of a speaker has no relevance to the Government's ability to regulate political speech would lead to some remarkable conclusions. Such an assumption would have accorded the propaganda broadcasts to our troops by 'Tokyo Rose' during World War II the same protection as speech by Allied commanders".
 * 2011: American country-rockabilly band Whiskey Kill released the song "Tokyo Rose", the initial track for their debut album Pissed Off Betty.
 * 2015: Japanese artist Miwa Yanagi's theater piece Zero Hour: Tokyo Rose’s Last Tape was staged at REDCAT Theater, Los Angeles, on February 26-28. The work was presented by Japan Society New York as part of series Stories from the War.
 * 2024: New York Times columnist calls Tucker Carlson the 'Tokyo Rose of our day',

Other uses
The first registered rock group using the name Tokyo Rose was formed in the summer of 1980. They are most known for their video which tells the story of the war time Tokyo Rose. Tokyo Rose is also the name of an emo/pop band hailing from New Jersey.

In 2019, Burnt Lemon Theatre brought the musical theatre production Tokyo Rose to the Edinburgh Fringe Festival, and New Diorama Theatre. An extended version toured in 2021 in several UK cities, accompanied by the release of a cast album.

In 2022, Tokyo Rose – Zero Hour (A Graphic Novel): A Japanese American Woman's Persecution and Ultimate Redemption After World War II was published by Tuttle. It was authored by Andre R. Frattino and illustrated by Kate Kasenow (Illustrator). The Foreword was written by Janice Chiang.

title: Tokyo Rose


text:
Pedestrian

A pedestrian is a person traveling on foot, whether walking or running. In modern times, the term usually refers to someone walking on a road or pavement (US: sidewalk), but this was not the case historically. Pedestrians may also be wheelchair users or other disabled people who use mobility aids.

Etymology
The meaning of pedestrian is displayed with the morphemes ped- ('foot') and -ian ('characteristic of'). This word is derived from the Latin term pedester ('going on foot') and was first used (in the English language) during the 18th century. It was originally used, and can still be used today, as an adjective meaning plain or dull. However, in this article it takes on its noun form and refers to someone who walks.

The word pedestrian may have been used in middle French in the Recueil des Croniques et Anchiennes Istories de la Grant Bretaigne.

History
Walking has always been the primary means of human locomotion. The first humans to migrate from Africa, about 60,000 years ago, walked. They walked along the coast of India to reach Australia. They walked across Asia to reach the Americas, and from Central Asia into Europe.

With the advent of the cars at the beginning of the 20th century, the main story is that the cars took over, and "people chose the car", but there were many groups and movements that held on to walking as their preferred means of daily transport and some who organised to promote walking, and to counterbalance the widely-held view that often favoured cars, e.g. as related by Peter Norton.

During the 18th and 19th centuries, pedestrianism (walking) was a popular spectator sport, just as equestrianism (riding) still is in places. One of the most famous pedestrians of that period was Captain Robert Barclay Allardice, known as "The Celebrated Pedestrian", of Stonehaven in Scotland. His most impressive feat was to walk 1 mi every hour for 1000 hours, which he achieved between 1 June and 12 July 1809. This feat captured many people's imagination, and around 10,000 people came to watch over the course of the event. During the rest of the 19th century, many people tried to repeat this feat, including Ada Anderson who developed it further and walked a half-mile (800 m) each quarter-hour over the 1000 hours.

Since the 20th century, interest in walking as a sport has dropped. Racewalking is still an Olympic sport, but fails to catch public attention as it did. However major walking feats are still performed, such as the Land's End to John o' Groats walk in the United Kingdom, and the traversal of North America from coast to coast. The first person to walk around the world was Dave Kunst who started his walk traveling east from Waseca, Minnesota on 20 June 1970 and completed his journey on 5 October 1974, when he re-entered the town from the west. These feats are often tied to charitable fundraising and are undertaken, among others, by celebrities such as Sir Jimmy Savile and Ian Botham.

Outdoor pedestrian networks

Roads often have a designated footpath for pedestrian traffic, called the sidewalk in North American English, the pavement in British English, and the footpath in Australian and New Zealand English. There are also footpaths not associated with a road; these include urban short cuts and also rural paths used mainly by ramblers, hikers, or hill-walkers. Footpaths in mountainous or forested areas may also be called trails. Pedestrians share some footpaths with horses and bicycles: these paths may be known as bridleways. Other byways used by walkers are also accessible to vehicles. There are also many roads with no footpath. Some modern towns (such as the new suburbs of Peterborough in England) are designed with the network of footpaths and cycle paths almost entirely separate from the road network.

The term trail is also used by the authorities in some countries to mean any footpath that is not attached to a road or street. If such footpaths are in urban environments and are meant for both pedestrians and pedal cyclists, they can be called shared use paths or multi-use paths in general and official usage.

Some shopping streets are for pedestrians only. Some roads have special pedestrian crossings. A bridge solely for pedestrians is a footbridge.

In Britain, regardless of whether there is a footpath, pedestrians have the legal right to use most public roads, excluding motorways and some toll tunnels and bridges such as the Blackwall Tunnel and the Dartford Crossing — although sometimes it may endanger the pedestrian and other road users. The UK Highway Code advises that pedestrians should walk in the opposite direction to oncoming traffic on a road with no footpath.

Indoor pedestrian networks
Indoor pedestrian networks connect the different rooms or spaces of a building. Airports, museums, campuses, hospitals and shopping centres might have tools allowing for the computation of the shortest paths between two destinations. Their increasing availability is due to the complexity of path finding in these facilities. Different mapping tools, such as OpenStreetMap, are extending to indoor spaces.

Pedestrianisation
Pedestrianisation might be considered as a process of removing vehicular traffic from city streets or restricting vehicular access to streets for use by pedestrians, to improve the environment and safety.

Efforts are under way by pedestrian advocacy groups to restore pedestrian access to new developments, especially to counteract newer developments, 20% to 30% of which in the United States do not include footpaths. Some activists advocate large pedestrian zones where only pedestrians, or pedestrians and some non-motorised vehicles, are allowed. Many urbanists have extolled the virtues of pedestrian streets in urban areas. In the US the proportion of households without a car is 8%, but a notable exception is New York City, the only locality in the United States where more than half of all households do not own a car (the figure is even higher in Manhattan, over 75%).

The use of cars for short journeys is officially discouraged in many parts of the world, and construction or separation of dedicated walking routes in city centres receives a high priority in many large cities in Western Europe, often in conjunction with public transport enhancements. In Copenhagen, the world's longest pedestrian shopping area, Strøget, has been developed over the last 40 years, principally due to the work of Danish architect Jan Gehl, a principle of urban design known as copenhagenisation.

Safety issues
Safety is an important issue where cars can cross the pedestrian way. Drivers and pedestrians share some responsibility for improving safety of road users. Road traffic crashes are not inevitable; they are both predictable and preventable.

Key risks for pedestrians are well known. Among the well-documented factors are driver behaviour (including speeding and drunk driving); infrastructure missing facilities (including pavements, crossings and islands); and vehicle designs which are not forgiving to pedestrians struck by a vehicle. The Traffic Injury Research Foundation describes pedestrians as vulnerable road users because they are not protected in the same way as occupants of motor vehicles. There is an increasing focus on pedestrians versus motor vehicles in many countries.

Most pedestrian injuries occur while they are crossing a street. Most crashes involving a pedestrian occur at night. Most pedestrian fatalities are killed by a frontal impact. In such a situation, an adult pedestrian is struck by a car front (for instance, the bumper touches either the leg or knee-joint area), accelerating the lower part of the body forward while "the upper body is rotated and accelerated relative to the car," at which point the pelvis and thorax are hit. Then the head hits the windscreen at the velocity of the striking car. Finally, the victim falls to the ground.

Research has shown that urban crimes, or the mere perception of crimes, severely affect the mental and physical health of pedestrians. Inter-pedestrian behaviour, without the involvement of vehicles, is also a key factor to pedestrian safety.

Some special interest groups consider pedestrian fatalities on American roads a carnage. Five states – Arizona, California, Florida, Georgia and Texas – are the site of 46% of all pedestrian deaths in the country. The advent of SUVs is considered a leading cause; speculation of other factors includes population growth, driver distraction with mobile phones, poor street lighting, alcohol and drugs and speeding.

Cities have had mixed results in addressing pedestrian safety with Vision zero plan: Los Angeles fails while NYC has had success. Nonetheless, in the US, some pedestrians have just 40 seconds to cross a street 10 lanes wide.

Pedestrian fatalities are much more common in accident situations in the European Union than in the United States. In the European Union countries, more than 200,000 pedestrians and cyclists are injured annually. Also, each year, more than 270 000 pedestrians lose their lives on the world's roads. At a global level pedestrians constitute 22% of all road deaths, but might be two-thirds in some countries. Pedestrian fatalities, in 2016, were 2.6 per million population in the Netherlands, 4.3 in Sweden, 4.5 in Wales, 5.3 in New Zealand, 6.0 in Germany; 7.1 in the whole United Kingdom, 7.5 in Australia, 8.4 in France, 8.4 in Spain, 9.4 in Italy, 11.1 in Israel, 13 in Japan, 13.8 in Greece, 18.5 in the United States, 22.9 in Poland, and 36.3 in Romania.

Road design impact on safety
It is well documented that a minor increase in speed might greatly increase the likelihood of a crash, and exacerbate resulting casualties. For this reason, the recommended maximum speed is 30 km/h or 40 km/h in residential and high pedestrian traffic areas, with enforced traffic rules on speed limits and traffic-calming measures.

The design of road and streets plays a key role in pedestrian safety. Roads are too often designed for motorized vehicles, without taking into account pedestrian and bicycle needs. The non-existence of sidewalk and signals increases risk for pedestrians. This defect might more easily be observed on arterial roadways, intersections and fast-speed lanes without adequate attention to pedestrian facilities. For instance, an assessment of roads in countries from many continents shows that 84% of roads are without pedestrian footpaths, while maximum limited speed is greater than 40 km/h.

Among the factors which reduce road safety for pedestrians are wider lanes, roadway widening, and roadways designed for higher speeds and with increased numbers of traffic lanes.

For this reason, some European cities such as Freiburg (Germany) have lowered the speed limit to 30 km/h on 90% of its streets, to reduce risk for its 15 000 people. With such policy, 24% of daily trips are performed by foot, against 28% by bicycles, 20% by public transport and 28% by car. (See Zone 30.)

A similar set of policies to discourage the use of cars and increase safety for pedestrians has been implemented by the Northern European capitals of Oslo and Helsinki. In 2019, this resulted in both cities counting zero pedestrian deaths for the first time.

Seasonality
In Europe, pedestrian fatalities have a seasonal factor, with 6% of annual fatalities occurring in April but 13% (twice more) in December. The rationale for such a change might be complex.

Health benefits and environment
Regular walking is important both for human health and for the natural environment. Frequent exercise such as walking tends to reduce the chance of obesity and related medical problems. In contrast, using a car for short trips tends to contribute both to obesity and via vehicle emissions to climate change: internal combustion engines are more inefficient and highly polluting during their first minutes of operation (engine cold start). General availability of public transportation encourages walking, as it will not, in most cases, take one directly to one's destination.

Unicode
In Unicode, the hexadecimal code for "pedestrian" is 1F6B6. In XML and HTML, the string  produces 🚶.

title: Pedestrian


text:
Spectra (poetry collection)

Spectra: A Book of Poetic Experiments was a small volume of poetry published in 1916 by American writers Witter Bynner, who wrote under the pseudonym "Emanuel Morgan", and Arthur Davison Ficke, who wrote as "Anne Knish." The book was intended as satire directed at the Imagism poetry movement.

Spectra was preceded by a brief manifesto outlining the Spectric method as a school:

 * "In the first place, it speaks, to the mind of that process of diffraction by which are disarticulated the several colored and other rays of which light is composed. . . ."
 * "In its second sense, the term Spectric relates to the reflex vibrations of physical sight, and suggests the luminous appearance which is seen after the exposure of the eye to intense light, and, by analogy, the after-colors of the poets initial vision."
 * "In its third sense, Spectric connotes the overtones, adumbrations, or spectres which for the poet haunt all objects of both the seen and unseen world. . . ."

The poems in the collection were identified by opus numbers rather than titles, and mostly take on a silly tone.

From "Opus 6" by Emanuel Morgan:

 * If I were only dafter
 * I might be making hymns
 * To the liquor of your laughter
 * And the lacquer of your limbs.

Anne Knish's Opus 118:

 * If bathing were a virtue, not a lust
 * I would be dirtiest.

 * To some, housecleaning is a holy rite.
 * For myself, houses would be empty
 * But for the golden motes dancing in sunbeams.

 * Tax-assessors frequently overlook valuables.
 * Today they noted my jade.
 * But my memory of you escaped them.

Spectra was intended solely as a joke. Initially, even the publisher was fooled by the book, but he was let in on the joke before going to press. The authors assumed the ridiculousness of the work would shine through, but it was actually accepted as a legitimate poetic movement for two years. In 1918, Bynner admitted in a public speech that he had co-authored the book and explained the hoax.

Both Bynner and Ficke were accomplished poets of their time, but the Spectra poems are probably the most widely remembered of their work. Both authors admitted to the hoax having backfired to a certain extent, as it overshadowed their more serious work. Nonetheless, Ficke stated that he learned a good deal about composition while writing as Knish, adding that it actually influenced his later work.

title: Spectra (poetry collection)