Define an event to have spacetime coordinates in system "S" and in a reference frame moving at a velocity v with respect to that frame, "S"′. Then the Lorentz transformation specifies that these coordinates are related in the following way:
is the Lorentz factor and "c" is the speed of light in vacuum, and the velocity "v" of "S"′ is parallel to the "x"-axis. For simplicity, the "y" and "z" coordinates are unaffected; only the "x" and "t" coordinates are transformed. These Lorentz transformations form a one-parameter group of linear mappings, that parameter being called rapidity.
Solving the above four transformation equations for the unprimed coordinates yields the inverse Lorentz transformation:
Enforcing this "inverse" Lorentz transformation to coincide with the Lorentz transformation from the primed to the unprimed system, shows the unprimed frame as moving with the velocity "v′" = −"v", as measured in the primed frame.
There is nothing special about the "x"-axis. The transformation can apply to the "y"- or "z"-axis, or indeed in any direction, which can be done by directions parallel to the motion (which are warped by the "γ" factor) and perpendicular; see the article Lorentz transformation for details.
A quantity invariant under Lorentz transformations is known as a Lorentz scalar.
Writing the Lorentz transformation and its inverse in terms of coordinate differences, where one event has coordinates and , another event has coordinates and , and the differences are defined as
we get
If we take differentials instead of taking differences, we get
In special relativity, the momentum formula_17 and the total energy formula_18 of an object as a function of its mass formula_19 are
and
A frequently made error (also in some books) is to rewrite this equation using a "relativistic mass" (in the direction of motion) of formula_22.
The reason why this is incorrect is that light, for example, has no mass, but has energy. If we use this formula, the photon (particle of light) has a mass, which is according to experiments incorrect.
In special relativity, an object's mass, total energy and momentum are related by the equation
For an object at rest, formula_24 so the above equation simplifies to formula_25. Hence, a massive object at rest still has energy. We call this rest energy and denote it by formula_26:
The need for special relativity arose from Maxwell's equations of electromagnetism, which were published in 1865. It was later found that they call for electromagnetic waves (such as light) to move at a constant speed (i.e., the speed of light).
To have James Clerk Maxwell's equations be consistent with both astronomical observations and Newtonian physics, Maxwell proposed in 1877 that light travels through an ether which is everywhere in the universe.
In 1887, the famous Michelson-Morley experiment tried to detect the "ether wind" generated by the movement of the Earth. The persistent null results of this experiment puzzled physicists, and called the ether theory into question.
In 1895, Lorentz and Fitzgerald noted that the null result of the Michelson-Morley experiment could be explained by the ether wind contracting the experiment in the direction of motion of the ether. This effect is called the Lorentz contraction, and (without ether) is a consequence of special relativity.
In 1899, Lorentz first published the Lorentz equations. Although this was not the first time they had been published, this was the first time that they were used as an explanation of the Michelson-Morley's null result, since the Lorentz contraction is a result of them.
In 1900, Poincaré gave a famous speech in which he considered the possibility that some "new physics" was needed to explain the Michelson-Morley experiment.
In 1904, Lorentz showed that electrical and magnetic fields can be modified into each other through the Lorentz transformations.
In 1905, Einstein published his article introducing special relativity, ""On the Electrodynamics of Moving Bodies"", in "Annalen der Physik". In this article, he presented the postulates of relativity, derived the Lorentz transformations from them, and (unaware of Lorentz's 1904 article) also showed how the Lorentz Transformations affect electric and magnetic fields.
Later in 1905, Einstein published another article presenting "E" = "mc".
In 1908, Max Planck endorsed Einstein's theory and named it "relativity". In that same year, Hermann Minkowski gave a famous speech on "Space and Time" in which he showed that relativity is self-consistent and further developed the theory. These events forced the physics community to take relativity seriously. Relativity came to be more and more accepted after that.
In 1912, Einstein and Lorentz were nominated for the Nobel prize in physics due to their pioneering work on relativity. Unfortunately, relativity was so controversial then, and remained controversial for such a long time that a Nobel prize was never awarded for it.
1964
1964 (MCMLXIV) was .
1894
587
Year 587 (DLXXXVII) was a common year starting on Wednesday (link will display the full calendar) of the Julian calendar. The denomination 587 for this year has been used since the early medieval period, when the Anno Domini calendar era became the prevalent method in Europe for naming years.
September 7
1191
1191 (MCXCI) was .
This is the year the popular game for Xbox 360, Assassin's Creed, is set.
1539
May 30
1431
1574
1984
1984 (MCMLXXXIV) was .
1985
1985 (MCMLXXXV) was .
1986
1986 (MCMLXXXVI) was .
August 12
1918
1918 was a common year starting on Tuesday in the Gregorian calendar, and a common year starting on Monday in the Julian calendar.
Wombat
A wombat is a marsupial in the family Vombatidae. It lives in the Australian eucalyptus forests. There are two genera with three living wombat species; the Common Wombat and the Hairy-nosed Wombats.
It is a medium-sized animal that makes a burrow by digging holes in the ground. Wombats are usually around a metre (40 in) long when they are fully grown. It is a kind of animal known as a marsupial because it has a pouch on its belly that holds its young, although it faces back instead of forward like most marsupials. Having the pouch face backwards prevents dirt from building up in the pouch and hitting the offspring in the face when digging. When its young are born they spend some time growing in their mother's pouch before going into the world. Wombats are herbivores. They eat plants, roots, and grasses. They are nocturnal which means they sleep in the day and come out at night. Some wombats have thick brown fur and very small ears. They can weigh from 20 to 35 kilograms (45 to 80 lb). They can live up to 7 years.
Wombats are commonly known and recognised by their waste products. They are the only known mammals that excrete feces in cubic shape. This lets people easily know when wombat habitats are nearby. It also tells simply what the wombat may have eaten by examining the feces thoroughly.
January 10
N.C. Wyeth
Newell Convers Wyeth (October 22, 1882 – October 19, 1945) was an American painter and book illustrator. He was born in Needham, Massachusetts. He was known for his illustrations for such books as "Robin Hood", "Robinson Crusoe", "The Yearling", "The Last of the Mohicans", and King Arthur. His daughters Henriette and Carolyn, his son, Andrew and grandson Jamie Wyeth were also painters. Wyeth's son Nathaniel was an inventor.
Wyeth was born in Needham, Massachusetts. He died in an accident at a railway crossing in Chadds Ford, Pennsylvania.
Turkey (bird)
Turkeys are a family of bird in the genus "Meleagrididae". They are like a chicken but much bigger. Wild turkeys live in forests in North America and Central America. In the United States, people traditionally eat turkey on the holiday of Thanksgiving.
The family "Meleagrididae" has one genus in it, "Meleagris". This genus has two species: