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Novikov self-consistency principle

The Novikov self-consistency principle known as the Novikov self-consistency conjecture and Larry Niven's law of conservation of history, is a principle developed by Russian physicist Igor Dmitriyevich Novikov in the mid-1980s. Novikov intended it to solve the problem of paradoxes in time travel, theoretically permitted in certain solutions of general relativity that contain what are known as closed timelike curves; the principle asserts that if an event exists that would cause a paradox or any "change" to the past whatsoever the probability of that event is zero. It would thus be impossible to create time paradoxes. Physicists have long known that some solutions to the theory of general relativity contain closed timelike curves—for example the Gödel metric. Novikov discussed the possibility of closed timelike curves in books he wrote in 1975 and 1983, offering the opinion that only self-consistent trips back in time would be permitted. In a 1990 paper by Novikov and several others, "Cauchy problem in spacetimes with closed timelike curves", the authors state: The only type of causality violation that the authors would find unacceptable is that embodied in the science-fiction concept of going backward in time and killing one's younger self.

Some years ago one of us considered the possibility that CTCs might exist and argued that they cannot entail this type of causality violation: events on a CTC are guaranteed to be self-consistent, Novikov argued. The other authors have arrived at the same viewpoint. We shall embody this viewpoint in a principle of self-consistency, which states that the only solutions to the laws of physics that can occur locally in the real Universe are those which are globally self-consistent; this principle allows one to build a local solution to the equations of physics only if that local solution can be extended to a part of a global solution, well defined throughout the nonsingular regions of the space-time. Among the co-authors of this 1990 paper were Kip Thorne, Mike Morris, Ulvi Yurtsever, who in 1988 had stirred up renewed interest in the subject of time travel in general relativity with their paper "Wormholes, Time Machines, the Weak Energy Condition", which showed that a new general relativity solution known as a traversable wormhole could lead to closed timelike curves, unlike previous CTC-containing solutions, it did not require unrealistic conditions for the universe as a whole.

After discussions with another co-author of the 1990 paper, John Friedman, they convinced themselves that time travel needn't lead to unresolvable paradoxes, regardless of the object sent through the wormhole. By way of response, physicist Joseph Polchinski wrote them a letter arguing that one could avoid the issue of free will by employing a paradoxical thought experiment involving a billiard ball sent back in time through a wormhole. In Polchinski's scenario, the billiard ball is fired into the wormhole at an angle such that, if it continues along its path, it will exit in the past at just the right angle to collide with its earlier self, knocking it off track and preventing it from entering the wormhole in the first place. Thorne would refer to this scenario as "Polchinski's paradox" in 1994. Upon considering the scenario, Fernando Echeverria and Gunnar Klinkhammer, two students at Caltech, arrived at a solution to the problem that managed to avoid any inconsistencies. In the revised scenario, the ball emerges from the future at a different angle than the one that generates the paradox, delivers its younger self a glancing blow instead of knocking it away from the wormhole.

This blow alters its trajectory by just the right degree, meaning it will travel back in time with the angle required to deliver its younger self the necessary glancing blow. Echeverria and Klinkhammer found that there was more than one self-consistent solution, with different angles for the glancing blow in each situation. Analysis by Thorne and Robert Forward illustrated that for certain initial trajectories of the billiard ball, there could be an infinite number of self-consistent solutions. Echeverria and Thorne published a paper discussing these results in 1991. Thus, it is plausible that there exist self-consistent extensions for every possible initial trajectory, although this has not been proven; this only applies to initial conditions outside of the chronology-violating region of spacetime, bounded by a Cauchy horizon. This could mean that the Novikov self-consistency principle does not place any constraints on systems outside of the region of space-time where time travel is possible, only inside it.

If self-consistent extensions can be found for arbitrary initial conditions outside the Cauchy Horizon, the finding that there can be multiple distinct self-consistent extensions for the same initial condition—indeed, Echeverria et al. found an infinite number of consistent extensions for every initial trajectory they analyzed—can be seen as problematic, since classically there seems to be no way to decide which extension the laws of physics will choose. To get around this difficulty and Klinkhammer analyzed the billiard ball scenario using quantum mechanics, performing a quantum-mechanical sum over histories using only the consistent extensions, found that this resulted in a well-defined probability for each consistent extension; the au

Green measure

In mathematics — in stochastic analysis — the Green measure is a measure associated to an Itō diffusion. There is an associated Green formula representing suitably smooth functions in terms of the Green measure and first exit times of the diffusion; the concepts are named after the British mathematician George Green and are generalizations of the classical Green's function and Green formula to the stochastic case using Dynkin's formula. Let X be an Rn-valued Itō diffusion satisfying an Itō stochastic differential equation of the form d X t = b d t + σ d B t. Let Px denote the law of X given the initial condition X0 = x, let Ex denote expectation with respect to Px. Let LX be the infinitesimal generator of X, i.e. L X = ∑ i b i ∂ ∂ x i + 1 2 ∑ i, j i, j ∂ 2 ∂ x i ∂ x j. Let D ⊆ Rn be an open, bounded domain. Intuitively, the Green measure of a Borel set H is the expected length of time that X, having started at x, stays in H before it leaves the domain D; that is, the Green measure of X with respect to D at x, denoted G, is defined for Borel sets H ⊆ Rn by G = E x, or for bounded, continuous functions f: D → R by ∫ D f G = E x The name "Green measure" comes from the fact that if X is Brownian motion G = ∫ H G d y, where G is Green's function for the operator LX on the domain D.

Suppose that Ex < +∞ for all x ∈ D, let f: Rn → R be of smoothness class C2 with compact support. F = E x − ∫ D L X f G. In particular, for C2 functions f with support compactly embedded in D, f = − ∫ D L X f G; the proof of Green's formula is an easy application of Dynkin's formula and the definition of the Green measure: E x = f + E x = f + ∫ D L X f G. Øksendal, Bernt K.. Stochastic Differential Equations: An Intro

Tolleshunt Major

Tolleshunt Major is a small village five miles north east of Maldon, in the Maldon District of Essex, England. It forms part of the electoral ward of Tolleshunt D'Arcy and is situated on the northern bank of the River Blackwater; the Tolleshunt group of villages grew up in the area settled by the Saxon chief Toll who cleared areas of forest round local water sources. Tolleshunta was the Anglo Saxon name for Toll's spring; the name Tolleshunt Major, was granted by King Henry VIII to Stephen Beckenham, in 1544. Beckenham bought various landscapes in and around the village and built a semi-fortified manor house with a turreted gatehouse within a red-brick boundary wall; this became known as "Beckingham House". The house was replaced by a farmhouse; the former gatehouse which formed part of Beckingham Manor, complete with turrets and boundary wall still remain. In 1609, Beckingham completed the design and construction of a heraldic shield which featured statuettes of himself and his wife Alvis Beckingham.

The monument was displayed at the parish church of St. Nicholas; this scrapped. The Beckingham family came from Wiltshire. Stephen’s son Thomas Beckingham received a knighthood and died in 1633, his son, became heir to the estate aged 12. The estate was sold to Sir Thomas Adams, an alderman from London; the manor house changed hands several times before becoming the property of the current owners. Tolleshunt Major's only streets are Beckingham Street, Bakers Lane, Mill Lane, Witham Road, Tudwick Road and Tolleshunt D'Arcy Road, all situated within the built up part of the village, which consists of just over one hundred dwellings; the village's parish boundaries stretch as far as Little Totham, taking in parts of Sawyers Lane and Plains Road. Other rural parts of the village include Church Road to the east, Tudwick Road to the north, Sawyers Lane and Plains Road to the west, parts of Scraley Road, Wash Lane and Bakers Green to the south; the village, not on any main road, is bordered by the villages of Little Totham, Tolleshunt D'Arcy, Tolleshunt Knights and Great Totham North and South.

Nearby towns include Maldon District, Colchester and Tiptree. Tolleshunt Major is host to The Beckingham Business park which has a small number of businesses, ranging from a transport company to a sports equipment manufacturing company. There are no street lights, mains gas supply or bus service apart from a schools service in the village; the village has one public house called the Beckingham Bell, situated in Beckingham Street. The village does have one small shop on Wicks Manor Farm situated in Tolleshunt Major, owned by Howies & Sons. Wicks Manor Farm is a Local Essex farm which produces dry cured bacon, ham and pork. Other shops can be found in Tiptree, about a ten-minute drive where large supermarkets can be found as well as fast food restaurants, newsagents, a post office, hair salons and pharmacists. In Tiptree is the jam factory owned by Wilkin & Sons Limited. Bigger shopping centres are at Chelmsford City about 30 minutes drive away and Colchester Town about 30 minutes away. There are several elected representatives at different levels of government which act for Tolleshunt Major and the surrounding villages.

There are two Tolleshunt D'arcy district councillors which represent the area at Maldon District Council. The current district councillors are Maddie Thompson; the current MEPs are Vicky Ford, Andrew Duff, Stuart Agnew, Robert Sturdy, Geoffrey Van Orden, Richard Howitt and David Campbell Bannerman. There is no bus service that runs through Tolleshunt Major apart from the school bus, operated by Stephensons of Essex. Buses can be boarded from the nearby village of Tolleshunt D’arcy which commutes through Colchester or Great Totham. Other villages served are Maldon and Witham; the closest National Rail service is located in Witham or Hatfield Peveral, is operated by Abellio Greater Anglia. Destinations served from these stations include London Liverpool Street and Ipswich, Harwich and Norwich via the Great Eastern Main Line; the nearest London Underground line is the central line at Stratford International. There are no schools in the village of Tolleshunt Major, there nearest primary school is in Tolleshunt D'arcy.

Tolleshunt D'arcy has one primary school in the village on Tollesbury Road called St. Nicholas School C of E; this school serves the villages of Tolleshunt D’Arcy, Tolleshunt Major, Tolleshunt Knights and Little Totham. The school is situated in the centre of Tolleshunt D'Arcy village and has acres of open grassland and wild-life area, it has views over the Blackwater Estuary. St. Nicholas primary school provides a broad and balanced education for pupils between the ages of 4 and 11 years, it was founded according to the practices of the Church of England. The school is a single story building built in 1983 which has 7 classrooms which includes a large reception class room with its own playground. There has been a school in Tolleshunt D’Arcy since before 1900; the school has a large hall used for assemblies, Physical education, teaching and plays. It has a library, ICT suite and wildlife quad with a pond; the schools latest Ofsted inspection dated November 2011 achieved an overall grade of 3, satisfactory.

There is no pre school either is Tolleshunt Major, the nearest again being in the neig

Leverton, Lincolnshire

Leverton is a village and civil parish in the Boston district of Lincolnshire, about 6 mi east-north-east from Boston, on the A52 road. The population of the civil parish at the 2011 census was 689, it is one of eighteen parishes which, together with Boston, form the Borough of Boston in the county of Lincolnshire, England. The local government has been arranged in this way since the reorganisation of 1 April 1974, which resulted from the Local Government Act 1972; this parish forms part of the Coastal electoral ward. Hitherto, the parish had formed part of Boston Rural District, in the Parts of Holland. Holland was one of the three divisions of the traditional county of Lincolnshire. Since the Local Government Act of 1888, Holland had been in a county in itself. Before this, Leverton had been in Parts of Holland. Leverton Grade I listed Anglican church is dedicated to St Helen. Media related to Leverton at Wikimedia Commons "Leverton" See details of the parish Council See map

Charles Fairfax (soldier)

Sir Charles Fairfax was an English soldier. Fairfax was the fourth son of Sir Thomas Fairfax of Denton and Nun Appleton in Yorkshire, brother of Thomas Fairfax, 1st Lord Fairfax of Cameron, he was born in or about 1567, when young he went with his brother to serve under Sir Francis Vere in the Low Countries. Fairfax became a distinguished commander. At the battle of Nieuwport he rallied the English companies at a critical moment, he was one of the defenders during the siege of Ostend. By desire of Francis Vere he went to the camp of the Archduke Albert as a hostage, he fought in the breach when the Spanish forces assaulted the works in December 1601. In May 1604 he was at the siege of Sluis, commanding troops which routed the Spanish general Luis de Velasco in the battle of Oostberg line. According to Dutch military historians François de Bas and F. J. G. Ten Raa, Fairfax became commander of the English companies still fighting at Ostend, he landed there on 7 June with five companies of reinforcements, but was killed in the last stages of fighting on 17 September, only three days before the general surrender of the stronghold.

This article incorporates text from a publication now in the public domain: "Fairfax, Charles". Dictionary of National Biography. London: Smith, Elder & Co. 1885–1900

List of African musicians

This is a list of African musicians and musical groups. See: List of Algerian musicians See: List of Angolan musicians Angélique Kidjo Wally Badarou Banjo Mosele Franco and Afro Musica Matsieng Zeus Balaké Cheikh Lô Dramane Kone Farafina Best Life Music Khadja Nin Kebby Boy Sat-B See: List of Cameroonian musicians Cesaria Evora Gil Semedo Alpha Blondy Magic System Ernesto Djédjé Tiken Jah Fakoly DJ Arafat Serge Beynaud Youlou Mabiala Pierre Moutouari Werrason Papa Wemba Ferre Gola Fally Ipupa Mbilia Bel Abeti Masikini Madilu System Youlou Mabiala Franco Luambo Makiadi See: List of Democratic Republic of the Congo musicians See: List of Egyptian musicians Abraham Afewerki Oliver N'Goma Patience Dabany Annie-Flore Batchiellilys Sona Maya Jobarteh Foday Musa Suso See: List of Ghanaian musicians Sona Tata Condé Sekouba Bambino Daddi Cool Les Ballets Africains Balla et ses Balladins Bembeya Jazz Djeli Moussa Diawara Famoudou Konaté Mory Kanté Mamady Keita Ballet Nimba José Carlos Schwarz Eneida Marta See: List of Kenyan musicians Sundaygar Dearboy Knero Takun-J See: List of Malagasy musicians Boubacar Traoré Mory Kanté Salif Keita Toumani Diabaté Kandia Kouyaté Habib Koité Issa Bagayogo Rokia Traoré Tinariwen Ali Farka Touré Amadou et Mariam Oumou Sangaré Afel Bocoum Lobi Traoré Fatoumata Diawara Djelimady Tounkara Rail Band Dimi Mint Abba Malouma Noura Mint Seymali Wazimbo Ghorwane Fany Pfumo Stewart Sukuma Moreira Chonguica Lizha James Neyma Mingas Al Bowlly Wazimbo 340ml Afric Simone Mamar Kassey Mdou Moctar See: List of Nigerian musicians Alpha Rwirangira Tom Close Riderman King James Knolwess Butera Benjami Mugisha Urban Boyz Kate Bashabe Simon Bikindi Corneille Miss Jojo Akon Baaba Maal Ismaël Lô Orchestra Baobab Positive Black Soul Thione Seck and Raam Daan Star Band Touré Kunda Youssou N'Dour and Étoile de Dakar Xalam Bai Kamara S. E. Rogie Steady Bongo K-Man Emmerson Anis Halloway Supa Laj Xiddigaha Geeska Mohamed Mooge Liibaan Waayaha Cusub Hasan Adan Samatar Aar Maanta Maryam Mursal K'naan Guduuda'Arwo Magool See: List of South African musicians Yaba Angelosi Mary Boyoi Emmanuel Jal Silver X Abdel Aziz El Mubarak AlKabli Mohammed Wardi Dusty & Stones Kambi Tendaness Joseph Lusungu Mnenge Ramadhani Muhiddin Maalim Hassani Bitchuka Saidi Mabera Wilson Kinyonga Remmy Ongala Kasaloo Kyanga Mr. Nice Saida Karoli Diamond Platnumz Lady Jaydee Professor Jay TID Rose Mhando Vanessa Mdee A.

Y. Ruby Ali Kiba Rayvanny Bi Kidude Carola Kinasha Imani Sanga Tudd Thomas Bella Bellow King Mensah See: List of Ugandan musicians See: List of Zambian musicians See: List of Zimbabwean musicians List of Soukous musicians List of African guitarists