This rather simple formula has great physical implications. Born hypothesized that the above integral determines that the particle "exists somewhere in space". But how can we find it? We use the integral
formula_22 to formula_23. In other words, all that can be known in advance about a particle in general are probabilities, averages, and other statistical quantities associated with its physical quantities (position, momentum, etc.). Basically, this is the Born interpretation.
An extension of the above ideas can be made. Since the Born interpretation says that the actual position particle cannot be known, we can derive the following. If formula_24 are solutions to the wave equation, then the superposition of those solutions, i.e.
formula_25
is also a solution. This implies, then, that the particle exists in every possible position. When an observer comes and measures the position of the particle, then the superposition is reduced to a single possible wave function. (i.e., formula_26 → formula_27, where formula_27 is any of the possible wave function states.) This idea that a particle's position cannot exactly be known, and that a particle exists in multiple positions simultaneously gives rise to the Uncertainty principle. The mathematical formulation of this principle can be given by
formula_29
Where formula_30 is the uncertainty in position, and formula_31 is the uncertainty in momentum. This principle can be mathematically derived from the Fourier transforms between momentum and position as defined by quantum mechanics, but we will not derive it in this article.
There are various other interpretations, such as the many-worlds interpretation, and quantum determinism.
Nutmeg
Nutmeg ("Myristica fragrans") is a species of evergreen tree in the genus "Myristica". It is found in tropical Southeast Asia and Australia.
Run (island)
Pulau Run is an island in Indonesia. It is one of the smallest Islands of the Banda Islands. It is about 3 km long and less than 1 km wide.
It used to be of great importance, because of the value of the spices nutmeg and "mace". Both spices are from the same tree. The trees were only grown on the Banda Islands. During the history of the spice trade sailors of the British East India Company of the second expedition of James Lancaster, John Davis and John Middleton who stayed in Bantam on Java first reached the Island in 1603. They made good contacts with the people who lived there.
Two wars were fought over the extremely costly spices.
The Treaty of Westminster ended the First Anglo-Dutch War of 1652–1654. According to the treaty, Run should have been returned to England. The first attempt in 1660 failed due to formal constraints by the Dutch; after the second in 1665 the English traders were expelled in the same year and the Dutch destroyed the nutmeg trees.
After the second Anglo-Dutch War of 1665–1667 England and the United Provinces of the Netherlands agreed in the Treaty of Breda to the status quo: The English kept the island of Manhattan which a fleet sent by the Duke of York (the future Charles II), had occupied illegally in 1664 and renamed from New Amsterdam to New York. Run was officially given to the Dutch.
The Dutch monopoly on nutmeg and mace was destroyed by the transfer of nutmeg trees to Ceylon, Singapore and other British colonies in 1817 after the capture of the main Island Bandalontor in 1810 by Captain Cole. This led to the decline of the Dutch supremacy in the spice trade, but there are still nutmeg trees growing on Run today.
Shinty
Shinty a traditional game now mainly played in the Scottish Highlands. It involves 2 teams of twelve players using a stick (known as a "caman" from Scottish Gaelic) to put a ball in the opposing team's net.
It was once played over all Scotland but is now played mostly in the Scottish Highlands and Highland communities in the big Scottish cities. It is also played in universities and in America by enthusiasts.
The sport's rules and regulations are decided by the Camanachd Association.
It has a common ancestor with the Irish game of hurling and hurlers and shinty players sometimes hold internationals.
1229
1626
1399
54
54 is a year in the 1st century.
48
48 is a year in the 1st century. It was a leap year starting on Monday of the Julian calendar. At the time, it was known as the Year of the Consulship of Vitellius and Poplicola.
1244
1253
1627
1645
1072
1263
1264
1641
1680
Year 1680 was a leap year that started on a Monday when using the Gregorian calendar.
814
814 was .
Manx
The word Manx could mean many things related to the Isle of Man:
Hierarchy
A hierarchy (in ; this comes from '-hieros, sacred, and '-arkho, rule) is a way of ranking and organizing things or people. Beneath the top of the hierarchy, each part of it is below some other part. This turns out to be like a pyramid. It is a system to decide who can make decisions, and who is forced to comply with those decisions.
An example with people would be the structure of a company. There is the top manager, and there are a few levels of middle and lower management. At the bottom are the common workers. Another example would be an army that might have a general, followed by colonels, corporals, and sergeants, then privates.
In democracy this is done by educating people in the issues and then voting - in an election to choose leaders, or a referendum to actually choose one option from several. Competing power networks each form a political party and each offers only one leader or one option to the public, to simplify the issues to make decisions possible. After the decision, they typically do not fight it to the point of civil war, but wait for the next election.
In dictatorship this is done by asking one powerful person to make the decision and then agreeing to force everyone to follow it. Any who will not are exiled, imprisoned, or killed, even if the decision is not very important, since the refusal to follow is taken as a challenge to the power structure itself. There is only one power network and all others are forced to become part of it, or fight it. Civil war is much more common in a dictatorship than in a democracy.
In these examples, people who are higher up have more authority and power than people below them.
Sultan
Sultan is a name for Islamic rulers. There is no specific word for a sultan's wife.
The word "sultan" was from Arabic language. It means "strength", "authority", or "rulership". Later, it came to be used as the title of certain Muslim rulers who claimed full sovereignty. They did not have to take orders from any higher monarch, without claiming the overall caliphate.
The dynasty and lands ruled by the Sultan is called a sultanate. During the 20th century several Sultans changed their title to "Malik" which means "king".
States and union territories of India
The Republic of India is divided into twenty-eight States,and eight union territories including the National Capital Territory.
Union territories:
Finnish language
Finnish () is a Uralic language. It is one of the two official languages of Finland. It is also an official minority language in Sweden. Finnish is one of the four national languages of Europe that is not an Indo-European language. The other three are Estonian and Hungarian, which are also Uralic languages, and Basque.