Context and question: In a famous paper of 1936 with Garrett Birkhoff, the first work ever to introduce quantum logics, von Neumann and Birkhoff first proved that quantum mechanics requires a propositional calculus substantially different from all classical logics and rigorously isolated a new algebraic structure for quantum logics. The concept of creating a propositional calculus for quantum logic was first outlined in a short section in von Neumann's 1932 work, but in 1936, the need for the new propositional calculus was demonstrated through several proofs. For example, photons cannot pass through two successive filters that are polarized perpendicularly (e.g., one horizontally and the other vertically), and therefore, a fortiori, it cannot pass if a third filter polarized diagonally is added to the other two, either before or after them in the succession, but if the third filter is added in between the other two, the photons will, indeed, pass through. This experimental fact is translatable into logic as the non-commutativity of conjunction . It was also demonstrated that the laws of distribution of classical logic, and , are not valid for quantum theory.
What is the difference of logic in quantum theory?
Answer: laws of distribution of classical logic, and , are not valid for quantum theory
Context and question: Albania has often been called the 51st state for its perceived strongly pro-American positions, mainly because of the United States' policies towards it. In reference to President George W. Bush's 2007 European tour, Edi Rama, Tirana's mayor and leader of the opposition Socialists, said: "Albania is for sure the most pro-American country in Europe, maybe even in the world ... Nowhere else can you find such respect and hospitality for the President of the United States. Even in Michigan, he wouldn't be as welcome." At the time of ex-Secretary of State James Baker's visit in 1992, there was even a move to hold a referendum declaring the country as the 51st American state. In addition to Albania, Kosovo which is predominately Albanian is seen as a 51st state due to the heavily presence and influence of the United States. The US has had troops and the largest base outside US territory, Camp Bondsteel in the territory since 1999.
What is the name of the largest Albanian military base outside of Albanian territory?
Answer: unanswerable
Context and question: At the foundation of the Order, the "Medal of the Order of the British Empire" was instituted, to serve as a lower award granting recipients affiliation but not membership. In 1922, this was renamed the "British Empire Medal". It stopped being awarded by the United Kingdom as part of the 1993 reforms to the honours system, but was again awarded beginning in 2012, starting with 293 BEMs awarded for the Queen's Diamond Jubilee. In addition, the BEM is awarded by the Cook Islands and by some other Commonwealth nations. In 2004, a report entitled "A Matter of Honour: Reforming Our Honours System" by a Commons committee recommended to phase out the Order of the British Empire, as its title was "now considered to be unacceptable, being thought to embody values that are no longer shared by many of the country's population".
How many BEM's were awarded for the Queen's Diamond Jubilee?
Answer:
293