Tuesday, September 25, 2007
From the Ashes of the First Stars
Above, an artist's impression shows a primordial quasar as it might have been, surrounded by sheets of gas, dust, stars and early star clusters. Exacting observations of three distant quasars now indicate emission of very specific colors of the element iron. These Hubble Space Telescope observations, which bolster recent results from the WMAP mission, indicate that a whole complete cycle of stars was born, created this iron, and died within the first few hundred million years of the universe.
Young Stars Hatching in Orion
The latest image released from the Spitzer Space Telescope shows infant stars “hatching” in the head of Orion. Astronomers think that a supernova 3 million years ago sent shockwaves through the region, collapsing clouds of gas and dust, and beginning a new generation of star formation.
The region imaged by Spitzer is called Barnard 30, located about 1,300 light-years from Earth in the constellation of Orion. More specifically, it’s located right beside the star considered to be Orion’s head, Lambda Orionis.
Since the region is shrouded in dark clouds of gas and dust that obscure visible light images, this was an ideal target for Spitzer, which can peer right through them in the infrared spectrum. The tints of orange-red glow are dust particles warmed by the newly forming stars. The reddish-pink dots are the young stars themselves, embedded in the clouds of gas and dust.
The region imaged by Spitzer is called Barnard 30, located about 1,300 light-years from Earth in the constellation of Orion. More specifically, it’s located right beside the star considered to be Orion’s head, Lambda Orionis.
Since the region is shrouded in dark clouds of gas and dust that obscure visible light images, this was an ideal target for Spitzer, which can peer right through them in the infrared spectrum. The tints of orange-red glow are dust particles warmed by the newly forming stars. The reddish-pink dots are the young stars themselves, embedded in the clouds of gas and dust.
Crater for moon settlement
Although ESA’s SMART-1 was smashed into the Moon in 2006, it had the opportunity to gather a tremendous amount of science. Its view of this crater in particular has given ESA scientists the feeling that they might be looking at the perfect spot for a future permanent base on the Moon.
Crater Plaskett sits very close to the Moon’s north pole. This means it’s bathed in eternal sunlight. This would provide plenty of solar energy for future explorers, and creates a predictable temperature - it’s only hot, not hot and cold. Nearby craters bathed in eternal darkness might contain large stores of water ice that could be used for air, fuel and drinking water.
Crater Plaskett might provide a good first step for exploration of the Solar System. It’s close enough that astronauts would still be able to see the Earth. Help could arrive within days, if necessary, and communications would be almost instantaneous. But it’s remote enough to help mission planners understand what would be involved for future, longer duration missions on the Moon, and eventually to Mars.
SMART-1 ended its mission on September 3, 2006, when it ran out of fuel and crashed into the lunar surface. Scientists will be studying its data and images for years.
Crater Plaskett sits very close to the Moon’s north pole. This means it’s bathed in eternal sunlight. This would provide plenty of solar energy for future explorers, and creates a predictable temperature - it’s only hot, not hot and cold. Nearby craters bathed in eternal darkness might contain large stores of water ice that could be used for air, fuel and drinking water.
Crater Plaskett might provide a good first step for exploration of the Solar System. It’s close enough that astronauts would still be able to see the Earth. Help could arrive within days, if necessary, and communications would be almost instantaneous. But it’s remote enough to help mission planners understand what would be involved for future, longer duration missions on the Moon, and eventually to Mars.
SMART-1 ended its mission on September 3, 2006, when it ran out of fuel and crashed into the lunar surface. Scientists will be studying its data and images for years.
The Brightest Supernova Ever
The brightest stellar explosion ever recorded may be a long-sought new type of supernova, according to observations by NASA's Chandra X-ray Observatory and ground-based optical telescopes. This discovery indicates that violent explosions of extremely massive stars were relatively common in the early universe, and that a similar explosion may be ready to go off in our own galaxy.
"This was a truly monstrous explosion, a hundred times more energetic than a typical supernova," said Nathan Smith of the University of California at Berkeley, who led a team of astronomers from California and the University of Texas in Austin. "That means the star that exploded might have been as massive as a star can get, about 150 times that of our sun. We've never seen that before."
Astronomers think many of the first stars in the Universe were this massive, and this new supernova may thus provide a rare glimpse of how those first generation stars died. It is unprecedented, however, to find such a massive star and witness its death. The discovery of the supernova, known as SN 2006gy, provides evidence that the death of such massive stars is fundamentally different from theoretical predictions.
"Of all exploding stars ever observed, this was the king," said Alex Filippenko, leader of the ground-based observations at the Lick Observatory at Mt. Hamilton, Calif., and the Keck Observatory in Mauna Kea, Hawaii. "We were astonished to see how bright it got, and how long it lasted."
The Chandra observation allowed the team to rule out the most likely alternative explanation for the supernova: that a white dwarf star with a mass only slightly higher than the sun exploded into a dense, hydrogen-rich environment. In that event, SN 2006gy should have been 1,000 times brighter in X-rays than what Chandra detected.
"This was a truly monstrous explosion, a hundred times more energetic than a typical supernova," said Nathan Smith of the University of California at Berkeley, who led a team of astronomers from California and the University of Texas in Austin. "That means the star that exploded might have been as massive as a star can get, about 150 times that of our sun. We've never seen that before."
Astronomers think many of the first stars in the Universe were this massive, and this new supernova may thus provide a rare glimpse of how those first generation stars died. It is unprecedented, however, to find such a massive star and witness its death. The discovery of the supernova, known as SN 2006gy, provides evidence that the death of such massive stars is fundamentally different from theoretical predictions.
"Of all exploding stars ever observed, this was the king," said Alex Filippenko, leader of the ground-based observations at the Lick Observatory at Mt. Hamilton, Calif., and the Keck Observatory in Mauna Kea, Hawaii. "We were astonished to see how bright it got, and how long it lasted."
The Chandra observation allowed the team to rule out the most likely alternative explanation for the supernova: that a white dwarf star with a mass only slightly higher than the sun exploded into a dense, hydrogen-rich environment. In that event, SN 2006gy should have been 1,000 times brighter in X-rays than what Chandra detected.
Monday, September 17, 2007
Easy explanation of relativity theory
In the late 19th century scientists attempted to measure the absolute velocity of the earth using the equations of Maxwell and Galileo. Maxwell's equations gave the velocity of the speed of light, and Galileo's gave the way to measure differences between moving and stationery systems. The following is an example of how one would use these to find a velocity:
Imagine a spaceship that could move at a very high speed. Light from behind was shining past this spaceship. If a measurement of the speed of the light gave a result of 2x108m/s, then one can expect the speed of the ship to be 1x108m/s - the difference between the known speed of light (3x108m/s) and the speed measured from the spaceship.
This model could not be used until 1887, because the measuring apparatus was too imprecise. However, when this idea was finally used to try and determine the velocity of the earth, the experiment produced a remarkable result - the earth had zero velocity. Naturally scientists at the time were completely baffled by this and tried to discover where and how the laws of physics had failed.
Several scientists attempted to explain this anomaly before Einstein solved the problem with the Special Theory of Relativity - among them were Henri Poincare who suggested that it was impossible to determine an absolute velocity; H.A. Lorentz who came up with the transformation for motion; Michelson and Morley whose experiment it was that failed and started everyone thinking.
It was left to Einstein to solve the problem with the publication of the Special Theory of Relativity in 1905. He gave up the idea of an absolute velocity, and abolished the idea of the "ether", the mysterious substance through which scientists though light travelled.
Albert Einstein is the most well known physicist of the 20th century. Most famous for his Theory of Relativity, Einstein is also ranked high amongst the scientists responsible for the emergence of quantum mechanics for his proof of light traveling as a particle.
Albert Einstein was born on March 14 1879 to a middle class Jewish family in Ulm, Germany. In 1886 he began his school career in Munich. He disliked school because of the mindless drilling that was involved and he preferred to study at home where he gained an interest in mathematics and science. He began studying Calculus at age twelve at the Luitpold gymnasium. It was at about this time that his studies came into conflict with his deep religious feelings. His realisation that the Bible could not be literally true created his lifelong distrust of authority. He was granted Swiss citizenship a year after graduating from the Polytechnic Institute in Zurich.
He avoided compulsory military service thanks to his flat feet and varicose veins, but he was denied university assistantship. He then began moving around from post to post as a temporary teacher. Through a university contact he eventually gained a permanent job at the Swiss Patent Office as a technical expert, third class. In 1906, four years later, he was promoted to technical expert second class. During this time he wrote a fair amount of theoretical physics literature on a wide range of subjects. Many of these papers, written during his free time, were published and one thesis on a new determination of molecular dimensions earned him a doctorate from the University of Zurich.
During that same year of 1905 Einstein wrote two papers that turned the science world upside down. The first, on the photoelectric effect, contradicted previous perceptions of electromagnetic energy based on Maxwell's equations, and helped establish the nascent science of quantum mechanics. The second linked important parts of mechanics and Maxwell's electrodynamics to form The Special Theory of Relativity. The most important and famous part of this theory was his equation of energy and mass, E=mc2 , which was an undisputed display of pure genius.
He continued to work at the patent office until 1909 in which time he had extended the Special Theory of Relativity to include phenomena involving acceleration. He made significant contributions to the Quantum Theory and in 1908 became a lecturer at the University of Bern after submitting a further thesis for the constitution of radiation. In 1909 he left the patent office and his lectureship at Bern for the University of Zurich, where he was a professor for 2 years before being appointed a full professor at the Karl-Ferdinand University in Prague. By this time Einstein, at age 32, was recognised internationally as a leading scientist and physicist. A year later he began his work on the General Theory of Relativity. He moved to Zurich that same year to take up a chair at the Eidgenssische Technische Hochschule.
Late in 1915 he published the definitive version of the General Theory of Relativity. In 1919 British eclipse expeditions confirmed predictions derived from the General Theory of Relativity and Einstein was idolised by the press the world over.
In 1921 Einstein visited the U.S.A for the first time to raise funds for the planned Hebrew University of Jerusalem. He did lecture a few times on relativity and he received the Barnard Medal. That same year he was awarded the Nobel Prize for his work on the photoelectric effect in 1905, although he was not present for the award.For the next 6 years Einstein travelled around the world, receiving the Copley Medal of the Royal Society in 1925 and the Gold Medal of the Royal Astronomical Society in 1926. His schedule proved too hectic, for in 1928 Einstein experienced a physical collapse due to overwork. Although he did recover, he had to take things easy for the next two years.
He resumed his international visits in 1930 and in December of 1932, while he was in the U.S.A. the Nazis came to power, seizing his property after he had revoked his citizenship. He was granted permanent residence in America in 1935. At Princeton he resumed his quest to unify electromagnetic and gravitational phenomena in a theory he called the Unified Field Theory. He failed despite devoting the last 25 years of his life to this theory. In 1940 he was granted American citizenship and he made many contributions to world peace, he himself being a pacifist. By 1949 he was unwell and he began preparing for death by drawing up a will. He was offered the Presidency of Israel following the death of its first president in 1952 and, although it was difficult for him to do so, he declined the offer.
A week before his death Einstein signed his last letter. It was a letter to Bertrand Russell in which he agreed that his name should be placed on a manifesto urging all nations to give up nuclear weapons. It is fitting that one of his last acts was to argue, as he had done all his life, for world peace. He died peacefully on April 18 1955 at the age of 76.
Albert Einstein is the most well known physicist of the 20th century. Most famous for his Theory of Relativity, Einstein is also ranked high amongst the scientists responsible for the emergence of quantum mechanics for his proof of light traveling as a particle.
Albert Einstein was born on March 14 1879 to a middle class Jewish family in Ulm, Germany. In 1886 he began his school career in Munich. He disliked school because of the mindless drilling that was involved and he preferred to study at home where he gained an interest in mathematics and science. He began studying Calculus at age twelve at the Luitpold gymnasium. It was at about this time that his studies came into conflict with his deep religious feelings. His realisation that the Bible could not be literally true created his lifelong distrust of authority. He was granted Swiss citizenship a year after graduating from the Polytechnic Institute in Zurich.
He avoided compulsory military service thanks to his flat feet and varicose veins, but he was denied university assistantship. He then began moving around from post to post as a temporary teacher. Through a university contact he eventually gained a permanent job at the Swiss Patent Office as a technical expert, third class. In 1906, four years later, he was promoted to technical expert second class. During this time he wrote a fair amount of theoretical physics literature on a wide range of subjects. Many of these papers, written during his free time, were published and one thesis on a new determination of molecular dimensions earned him a doctorate from the University of Zurich.
During that same year of 1905 Einstein wrote two papers that turned the science world upside down. The first, on the photoelectric effect, contradicted previous perceptions of electromagnetic energy based on Maxwell's equations, and helped establish the nascent science of quantum mechanics. The second linked important parts of mechanics and Maxwell's electrodynamics to form The Special Theory of Relativity. The most important and famous part of this theory was his equation of energy and mass, E=mc2 , which was an undisputed display of pure genius.
He continued to work at the patent office until 1909 in which time he had extended the Special Theory of Relativity to include phenomena involving acceleration. He made significant contributions to the Quantum Theory and in 1908 became a lecturer at the University of Bern after submitting a further thesis for the constitution of radiation. In 1909 he left the patent office and his lectureship at Bern for the University of Zurich, where he was a professor for 2 years before being appointed a full professor at the Karl-Ferdinand University in Prague. By this time Einstein, at age 32, was recognised internationally as a leading scientist and physicist. A year later he began his work on the General Theory of Relativity. He moved to Zurich that same year to take up a chair at the Eidgenssische Technische Hochschule.
Late in 1915 he published the definitive version of the General Theory of Relativity. In 1919 British eclipse expeditions confirmed predictions derived from the General Theory of Relativity and Einstein was idolised by the press the world over.
In 1921 Einstein visited the U.S.A for the first time to raise funds for the planned Hebrew University of Jerusalem. He did lecture a few times on relativity and he received the Barnard Medal. That same year he was awarded the Nobel Prize for his work on the photoelectric effect in 1905, although he was not present for the award.For the next 6 years Einstein travelled around the world, receiving the Copley Medal of the Royal Society in 1925 and the Gold Medal of the Royal Astronomical Society in 1926. His schedule proved too hectic, for in 1928 Einstein experienced a physical collapse due to overwork. Although he did recover, he had to take things easy for the next two years.
He resumed his international visits in 1930 and in December of 1932, while he was in the U.S.A. the Nazis came to power, seizing his property after he had revoked his citizenship. He was granted permanent residence in America in 1935. At Princeton he resumed his quest to unify electromagnetic and gravitational phenomena in a theory he called the Unified Field Theory. He failed despite devoting the last 25 years of his life to this theory. In 1940 he was granted American citizenship and he made many contributions to world peace, he himself being a pacifist. By 1949 he was unwell and he began preparing for death by drawing up a will. He was offered the Presidency of Israel following the death of its first president in 1952 and, although it was difficult for him to do so, he declined the offer.
A week before his death Einstein signed his last letter. It was a letter to Bertrand Russell in which he agreed that his name should be placed on a manifesto urging all nations to give up nuclear weapons. It is fitting that one of his last acts was to argue, as he had done all his life, for world peace. He died peacefully on April 18 1955 at the age of 76.Symmetry in physics is generally defined as the ability of something to remain the same after undergoing a certain operation. A sphere for example has total symmetry because it looks exactly the same after being turned in any way. A cylinder on the other hand only has left right symmetry because it only remains the same if the rotation is around the vertical axis.
Not only does the object itself have to be considered, but any outside influences as well. For example if we have a machine that relies on gravity or oxygen then moving it to another place does not necessarily mean that symmetry will hold, so the operation, in this case displacement, would have to be performed on all the components relied upon by that machine to function. Physical phenomena remain unchanged (therefore their laws remain unchanged) after undergoing operations such as:
Displacement in space and time
Rotation around a fixed axis
Constant velocity in a straight line
Reflection in space
Reversal of time
Displacement in space is a seemingly obvious case as is displacement in time. Velocity in a straight line means that if we have an apparatus in a moving vehicle it would work in exactly the same way as it would if it wasn't moving provided the velocity and direction do not change. Reflection in space means that if we had two objects one looking exactly like the others mirror image, they would work exactly the same. It cannot as yet be proven, but it is believed that the physical laws hold true under the reversal of time.
Two operations that seem to conform to symmetry but do not are a change of scale and constant rotation at a fixed angular velocity. Symmetry does not hold under a change of scale because larger things deteriorate faster than smaller things. For example if we had a small bridge over a small space it would last longer than a larger bridge over a larger space and if gravity was increased according to the scale as well then the larger bridge would deteriorate even faster. Therefore increasing something in scale does not mean it will remain the same. An object rotating around a fixed point at a constant angular velocity will experience centrifugal forces. These forces are not around when that object is still, thus the object would have different forces on it and symmetry would not hold.
Constant velocity in a straight line is what Special Relativity is all about. However, the idea that constant velocity in a straight line is symmetrical did not come from Einstein, but was stated by Newton in one of his corollaries to the laws of motion. He stated, "the motions of bodies included in a given space are the same among themselves, whether that space is at rest or moves uniformly forward in a straight line". This means that if a spaceship was moving uniformly forward in a straight line, any experiments performed and any phenomena measured will give the same results as if the spaceship were not moving at all. This is why the experiment to determine the velocity of the earth gave a result of zero - zero is the result it would have given if the earth were not moving at all, so zero is the result it must give when moving uniformly in a straight line. It is when this principle is applied together with the principle that the speed of light also remains the same under all conditions that the strange consequences of relativity become apparent.
The principles of Symmetry are very nice, but we need some way to make them work. We do this by using mathematical devices known as transformations.
What is a transformation? A transformation is a formula which takes co-ordinates in one system, and gives us their corresponding co-ordinates in another. For example, there is a transformation which will give us the co-ordinates of a system in a system whose origin has been rotated relative to ours. Transformations are a vital part of physics, especially as they help us ensure that results are consistent - if we apply the standard transformations, our laws should come out the same before and after.
It was this seemingly simple problem which caused so many headaches at the end of the last century. It appeared as if James Clerk Maxwell's equations governing the speed of light did not obey these transformations - thus violating the principle of relativity. It was Lorentz who first suggested that Maxwell's laws were correct, and Newton's needed changing, and he did so by introducing his Lorentz transformations, which are at the heart of many Relativistic phenomena (these formulas are quite complex, and are given in the Advanced section). Einstein took this idea, and so first derived the Lorentz transformations and introduce the ground shaking ideas of Relativity.
Imagine a spaceship that could move at a very high speed. Light from behind was shining past this spaceship. If a measurement of the speed of the light gave a result of 2x108m/s, then one can expect the speed of the ship to be 1x108m/s - the difference between the known speed of light (3x108m/s) and the speed measured from the spaceship.
This model could not be used until 1887, because the measuring apparatus was too imprecise. However, when this idea was finally used to try and determine the velocity of the earth, the experiment produced a remarkable result - the earth had zero velocity. Naturally scientists at the time were completely baffled by this and tried to discover where and how the laws of physics had failed.
Several scientists attempted to explain this anomaly before Einstein solved the problem with the Special Theory of Relativity - among them were Henri Poincare who suggested that it was impossible to determine an absolute velocity; H.A. Lorentz who came up with the transformation for motion; Michelson and Morley whose experiment it was that failed and started everyone thinking.
It was left to Einstein to solve the problem with the publication of the Special Theory of Relativity in 1905. He gave up the idea of an absolute velocity, and abolished the idea of the "ether", the mysterious substance through which scientists though light travelled.
Albert Einstein is the most well known physicist of the 20th century. Most famous for his Theory of Relativity, Einstein is also ranked high amongst the scientists responsible for the emergence of quantum mechanics for his proof of light traveling as a particle.
Albert Einstein was born on March 14 1879 to a middle class Jewish family in Ulm, Germany. In 1886 he began his school career in Munich. He disliked school because of the mindless drilling that was involved and he preferred to study at home where he gained an interest in mathematics and science. He began studying Calculus at age twelve at the Luitpold gymnasium. It was at about this time that his studies came into conflict with his deep religious feelings. His realisation that the Bible could not be literally true created his lifelong distrust of authority. He was granted Swiss citizenship a year after graduating from the Polytechnic Institute in Zurich.
He avoided compulsory military service thanks to his flat feet and varicose veins, but he was denied university assistantship. He then began moving around from post to post as a temporary teacher. Through a university contact he eventually gained a permanent job at the Swiss Patent Office as a technical expert, third class. In 1906, four years later, he was promoted to technical expert second class. During this time he wrote a fair amount of theoretical physics literature on a wide range of subjects. Many of these papers, written during his free time, were published and one thesis on a new determination of molecular dimensions earned him a doctorate from the University of Zurich.
During that same year of 1905 Einstein wrote two papers that turned the science world upside down. The first, on the photoelectric effect, contradicted previous perceptions of electromagnetic energy based on Maxwell's equations, and helped establish the nascent science of quantum mechanics. The second linked important parts of mechanics and Maxwell's electrodynamics to form The Special Theory of Relativity. The most important and famous part of this theory was his equation of energy and mass, E=mc2 , which was an undisputed display of pure genius.
He continued to work at the patent office until 1909 in which time he had extended the Special Theory of Relativity to include phenomena involving acceleration. He made significant contributions to the Quantum Theory and in 1908 became a lecturer at the University of Bern after submitting a further thesis for the constitution of radiation. In 1909 he left the patent office and his lectureship at Bern for the University of Zurich, where he was a professor for 2 years before being appointed a full professor at the Karl-Ferdinand University in Prague. By this time Einstein, at age 32, was recognised internationally as a leading scientist and physicist. A year later he began his work on the General Theory of Relativity. He moved to Zurich that same year to take up a chair at the Eidgenssische Technische Hochschule.
Late in 1915 he published the definitive version of the General Theory of Relativity. In 1919 British eclipse expeditions confirmed predictions derived from the General Theory of Relativity and Einstein was idolised by the press the world over.
In 1921 Einstein visited the U.S.A for the first time to raise funds for the planned Hebrew University of Jerusalem. He did lecture a few times on relativity and he received the Barnard Medal. That same year he was awarded the Nobel Prize for his work on the photoelectric effect in 1905, although he was not present for the award.For the next 6 years Einstein travelled around the world, receiving the Copley Medal of the Royal Society in 1925 and the Gold Medal of the Royal Astronomical Society in 1926. His schedule proved too hectic, for in 1928 Einstein experienced a physical collapse due to overwork. Although he did recover, he had to take things easy for the next two years.
He resumed his international visits in 1930 and in December of 1932, while he was in the U.S.A. the Nazis came to power, seizing his property after he had revoked his citizenship. He was granted permanent residence in America in 1935. At Princeton he resumed his quest to unify electromagnetic and gravitational phenomena in a theory he called the Unified Field Theory. He failed despite devoting the last 25 years of his life to this theory. In 1940 he was granted American citizenship and he made many contributions to world peace, he himself being a pacifist. By 1949 he was unwell and he began preparing for death by drawing up a will. He was offered the Presidency of Israel following the death of its first president in 1952 and, although it was difficult for him to do so, he declined the offer.
A week before his death Einstein signed his last letter. It was a letter to Bertrand Russell in which he agreed that his name should be placed on a manifesto urging all nations to give up nuclear weapons. It is fitting that one of his last acts was to argue, as he had done all his life, for world peace. He died peacefully on April 18 1955 at the age of 76.
Albert Einstein is the most well known physicist of the 20th century. Most famous for his Theory of Relativity, Einstein is also ranked high amongst the scientists responsible for the emergence of quantum mechanics for his proof of light traveling as a particle.
Albert Einstein was born on March 14 1879 to a middle class Jewish family in Ulm, Germany. In 1886 he began his school career in Munich. He disliked school because of the mindless drilling that was involved and he preferred to study at home where he gained an interest in mathematics and science. He began studying Calculus at age twelve at the Luitpold gymnasium. It was at about this time that his studies came into conflict with his deep religious feelings. His realisation that the Bible could not be literally true created his lifelong distrust of authority. He was granted Swiss citizenship a year after graduating from the Polytechnic Institute in Zurich.
He avoided compulsory military service thanks to his flat feet and varicose veins, but he was denied university assistantship. He then began moving around from post to post as a temporary teacher. Through a university contact he eventually gained a permanent job at the Swiss Patent Office as a technical expert, third class. In 1906, four years later, he was promoted to technical expert second class. During this time he wrote a fair amount of theoretical physics literature on a wide range of subjects. Many of these papers, written during his free time, were published and one thesis on a new determination of molecular dimensions earned him a doctorate from the University of Zurich.
During that same year of 1905 Einstein wrote two papers that turned the science world upside down. The first, on the photoelectric effect, contradicted previous perceptions of electromagnetic energy based on Maxwell's equations, and helped establish the nascent science of quantum mechanics. The second linked important parts of mechanics and Maxwell's electrodynamics to form The Special Theory of Relativity. The most important and famous part of this theory was his equation of energy and mass, E=mc2 , which was an undisputed display of pure genius.
He continued to work at the patent office until 1909 in which time he had extended the Special Theory of Relativity to include phenomena involving acceleration. He made significant contributions to the Quantum Theory and in 1908 became a lecturer at the University of Bern after submitting a further thesis for the constitution of radiation. In 1909 he left the patent office and his lectureship at Bern for the University of Zurich, where he was a professor for 2 years before being appointed a full professor at the Karl-Ferdinand University in Prague. By this time Einstein, at age 32, was recognised internationally as a leading scientist and physicist. A year later he began his work on the General Theory of Relativity. He moved to Zurich that same year to take up a chair at the Eidgenssische Technische Hochschule.
Late in 1915 he published the definitive version of the General Theory of Relativity. In 1919 British eclipse expeditions confirmed predictions derived from the General Theory of Relativity and Einstein was idolised by the press the world over.
In 1921 Einstein visited the U.S.A for the first time to raise funds for the planned Hebrew University of Jerusalem. He did lecture a few times on relativity and he received the Barnard Medal. That same year he was awarded the Nobel Prize for his work on the photoelectric effect in 1905, although he was not present for the award.For the next 6 years Einstein travelled around the world, receiving the Copley Medal of the Royal Society in 1925 and the Gold Medal of the Royal Astronomical Society in 1926. His schedule proved too hectic, for in 1928 Einstein experienced a physical collapse due to overwork. Although he did recover, he had to take things easy for the next two years.
He resumed his international visits in 1930 and in December of 1932, while he was in the U.S.A. the Nazis came to power, seizing his property after he had revoked his citizenship. He was granted permanent residence in America in 1935. At Princeton he resumed his quest to unify electromagnetic and gravitational phenomena in a theory he called the Unified Field Theory. He failed despite devoting the last 25 years of his life to this theory. In 1940 he was granted American citizenship and he made many contributions to world peace, he himself being a pacifist. By 1949 he was unwell and he began preparing for death by drawing up a will. He was offered the Presidency of Israel following the death of its first president in 1952 and, although it was difficult for him to do so, he declined the offer.
A week before his death Einstein signed his last letter. It was a letter to Bertrand Russell in which he agreed that his name should be placed on a manifesto urging all nations to give up nuclear weapons. It is fitting that one of his last acts was to argue, as he had done all his life, for world peace. He died peacefully on April 18 1955 at the age of 76.Symmetry in physics is generally defined as the ability of something to remain the same after undergoing a certain operation. A sphere for example has total symmetry because it looks exactly the same after being turned in any way. A cylinder on the other hand only has left right symmetry because it only remains the same if the rotation is around the vertical axis.
Not only does the object itself have to be considered, but any outside influences as well. For example if we have a machine that relies on gravity or oxygen then moving it to another place does not necessarily mean that symmetry will hold, so the operation, in this case displacement, would have to be performed on all the components relied upon by that machine to function. Physical phenomena remain unchanged (therefore their laws remain unchanged) after undergoing operations such as:
Displacement in space and time
Rotation around a fixed axis
Constant velocity in a straight line
Reflection in space
Reversal of time
Displacement in space is a seemingly obvious case as is displacement in time. Velocity in a straight line means that if we have an apparatus in a moving vehicle it would work in exactly the same way as it would if it wasn't moving provided the velocity and direction do not change. Reflection in space means that if we had two objects one looking exactly like the others mirror image, they would work exactly the same. It cannot as yet be proven, but it is believed that the physical laws hold true under the reversal of time.
Two operations that seem to conform to symmetry but do not are a change of scale and constant rotation at a fixed angular velocity. Symmetry does not hold under a change of scale because larger things deteriorate faster than smaller things. For example if we had a small bridge over a small space it would last longer than a larger bridge over a larger space and if gravity was increased according to the scale as well then the larger bridge would deteriorate even faster. Therefore increasing something in scale does not mean it will remain the same. An object rotating around a fixed point at a constant angular velocity will experience centrifugal forces. These forces are not around when that object is still, thus the object would have different forces on it and symmetry would not hold.
Constant velocity in a straight line is what Special Relativity is all about. However, the idea that constant velocity in a straight line is symmetrical did not come from Einstein, but was stated by Newton in one of his corollaries to the laws of motion. He stated, "the motions of bodies included in a given space are the same among themselves, whether that space is at rest or moves uniformly forward in a straight line". This means that if a spaceship was moving uniformly forward in a straight line, any experiments performed and any phenomena measured will give the same results as if the spaceship were not moving at all. This is why the experiment to determine the velocity of the earth gave a result of zero - zero is the result it would have given if the earth were not moving at all, so zero is the result it must give when moving uniformly in a straight line. It is when this principle is applied together with the principle that the speed of light also remains the same under all conditions that the strange consequences of relativity become apparent.
The principles of Symmetry are very nice, but we need some way to make them work. We do this by using mathematical devices known as transformations.
What is a transformation? A transformation is a formula which takes co-ordinates in one system, and gives us their corresponding co-ordinates in another. For example, there is a transformation which will give us the co-ordinates of a system in a system whose origin has been rotated relative to ours. Transformations are a vital part of physics, especially as they help us ensure that results are consistent - if we apply the standard transformations, our laws should come out the same before and after.
It was this seemingly simple problem which caused so many headaches at the end of the last century. It appeared as if James Clerk Maxwell's equations governing the speed of light did not obey these transformations - thus violating the principle of relativity. It was Lorentz who first suggested that Maxwell's laws were correct, and Newton's needed changing, and he did so by introducing his Lorentz transformations, which are at the heart of many Relativistic phenomena (these formulas are quite complex, and are given in the Advanced section). Einstein took this idea, and so first derived the Lorentz transformations and introduce the ground shaking ideas of Relativity.
Theory of every thing
Flucidity is a new way of thinking. It is what scientists call a "theory of everything" except that unlike any grand theory it can actually be applied to everything, not just physics. It is also easy enough for anyone to understand and can even be used for the very simple as well as the very complex.
Flucidity is a completely ridiculous idea until you actually begin to use it. Its best feature is that it can be used by anyone, in minutes.
You can think of Flucidity as a language. We use language all the time to do everything from solving problems to developing relationships to making our lives better. We also have the language of life, made possible by just four letters of DNA. Flucidity is a language of languages, expressed in four simple "letters" called elements. Knowing how it works will enable you to achieve results limited only by your imagination
Flucidity is a completely ridiculous idea until you actually begin to use it. Its best feature is that it can be used by anyone, in minutes.
You can think of Flucidity as a language. We use language all the time to do everything from solving problems to developing relationships to making our lives better. We also have the language of life, made possible by just four letters of DNA. Flucidity is a language of languages, expressed in four simple "letters" called elements. Knowing how it works will enable you to achieve results limited only by your imagination
History topics
History topic: Special relativity
--------------------------------------------------------------------------------
The classical laws of physics were formulated by Newton in the Principia in 1687. According to this theory the motion of a particle has to be described relative to an inertial frame in which the particle, not subjected to external forces, will move at a constant velocity in a straight line. Two inertial frames are related in that they move in a fixed direction at a constant speed with respect to each other. Time in the frames differs by a constant and all times can be described relative to an absolute time. This 17th Century theory was not challenged until the 19th Century when electric and magnetic phenomena were studied theoretically.
It had long been known that sound required a medium to travel through and it was quite natural to postulate a medium for the transmission of light. Such a medium was called the ether and many 19th Century scientists postulated an ether with various properties. Cauchy, Stokes, Thomson and Planck all postulated ethers with differing properties and by the end of the 19th Century light, heat, electricity and magnetism all had their respective ethers.
A knowledge that the electromagnetic field was spread with a velocity essentially the same as the speed of light caused Maxwell to postulate that light itself was an electromagnetic phenomenon. Maxwell wrote an article on Ether for the 1878 edition of Encyclopaedia Britannica. He proposed the existence of a single ether and the article tells of a failed attempt by Maxwell to measure the effect of the ether drag on the earth's motion. He also proposed an astronomical determination of the ether drag by measuring the velocity of light using Jupiter's moons at different positions relative to the earth.
Prompted by Maxwell's ideas, Michelson began his own terrestrial experiments and in 1881 he reported
The result of the hypothesis of a stationary ether is shown to be incorrect, and the necessary conclusion follows that the hypothesis is erroneous.
Lorentz wrote a paper in 1886 where he criticised Michelson's experiment and really was not worried by the experimental result which he dismissed being doubtful of its accuracy. Michelson was persuaded by Thomson and others to repeat the experiment and he did so with Morley, again reporting that no effect had been found in 1887. It appeared that the velocity of light was independent of the velocity of the observer. [Michelson and Morley were to refine their experiment and repeat it many times up to 1929.]
Also in 1887 Voigt first wrote down the transformations
x' = x - vt, y' = y/g, z' = z/g, t' = t - vx/c2
and showed that certain equations were invariant under these transformations. These transformations, with a different scale factor, are now known as the Lorentz equations and the group of Lorentz transformations gives the geometry of special relativity. All this was unknown to Voigt who was writing on the Doppler shift when he wrote down the transformations.
Voigt corresponded with Lorentz about the Michelson-Morley experiment in 1887 and 1888 but Lorentz does not seem to have learnt of the transformations at that stage. Lorentz however was now greatly worried by the new Michelson-Morley experiment of 1887.
In 1889 a short paper was published by the Irish physicist George FitzGerald in Science. The paper The ether and the earth's atmosphere takes up less than half a page and is non-technical. FitzGerald pointed out that the results of the Michelson-Morley experiment could be explained only if
... the length of material bodies changes, according as they are moving through the ether or across it, by an amount depending on the square of the ratio of their velocities to that of light.
Lorentz was unaware of FitzGerald's paper and in 1892 he proposed an almost identical contraction in a paper which now took the Michelson-Morley experiment very seriously. When it was pointed out to Lorentz in 1894 that FitzGerald had published a similar theory he wrote to FitzGerald who replied that he had sent an article to Science but I do not know if they ever published it . He was glad to know that Lorentz agreed with him for I have been rather laughed at for my view over here . Lorentz took every opportunity after this to acknowledge that FitzGerald had proposed the idea first. Only FitzGerald, who did not know if his paper had been published, believed that Lorentz had published first!
Larmor wrote an article in 1898 Ether and matter in which he wrote down the Lorentz transformations (still not written down by Lorentz) and showed that the FitzGerald-Lorentz contraction was a consequence.
Lorentz wrote down the transformations, now named after him, in a paper of 1899, being the third person to write them down. He, like Larmor, showed that the FitzGerald-Lorentz contraction was a consequence of the Lorentz transformations.
The most amazing article relating to special relativity to be published before 1900 was a paper of Poincaré La mesure du temps which appeared in 1898. In this paper Poincaré says
... we have no direct intuition about the equality of two time intervals.
The simultaneity of two events or the order of their succession, as well as the equality of two time intervals, must be defined in such a way that the statements of the natural laws be as simple as possible.
By 1900 the concept of the ether as a material substance was being questioned. Paul Drude wrote
The conception of an ether absolutely at rest is the most simple and the most natural - at least if the ether is conceived to be not a substance but merely space endowed with certain physical properties.
Poincaré, in his opening address to the Paris Congress in 1900, asked Does the ether really exist? In 1904 Poincaré came very close to the theory of special relativity in an address to the International Congress of Arts and Science in St Louis. He pointed out that observers in different frames will have clocks which will
... mark what on may call the local time. ... as demanded by the relativity principle the observer cannot know whether he is at rest or in absolute motion.
The year that special relativity finally came into existence was 1905. June of 1905 was a good month for papers on relativity, on the 5th June Poincaré communicated an important work Sur la dynamique de l'electron while Einstein's first paper on relativity was received on 30th June. Poincaré stated that It seems that this impossibility of demonstrating absolute motion is a general law of nature. After naming the Lorentz transformations after Lorentz, Poincaré shows that these transformations, together with the rotations, form a group.
Einstein's paper is remarkable for the different approach it takes. It is not presented as an attempt to explain experimental results, it is presented because of its beauty and simplicity. In the introduction Einstein says
... the introduction of a light-ether will prove to be superfluous since, according to the view to be developed here, neither will a space in absolute rest endowed with special properties be introduced nor will a velocity vector be associated with a point of empty space in which electromagnetic processes take place.
Inertial frames are introduced which, by definition, are in uniform motion with respect to each other. The whole theory is based on two postulates:-
1. The laws of physics take the same form in all inertial frames.
2. In any inertial frame, the velocity of light c is the same whether the light is emitted by a body at rest or by a body in uniform motion.
Einstein now deduced the Lorentz transformations from his two postulates and, like Poincaré proves the group property. Then the FitzGerald-Lorentz contraction is deduced. Also in the paper Einstein mentions the clock paradox. Einstein called it a theorem that if two synchronous clocks C1 and C2 start at a point A and C2 leaves A moving along a closed curve to return to A then C2 will run slow compared with C1. He notes that no paradox results since C2 experiences acceleration while C1 does not.
In September 1905 Einstein published a short but important paper in which he proved the famous formula
E = mc2.
The first paper on special relativity, other than by Einstein, was written in 1908 by Planck. It was largely due to the fact that relativity was taken up by someone as important as Planck that it became so rapidly accepted. At the time Einstein wrote the 1905 paper he was still a technical expert third class at the Bern patent office. Also in 1908 Minkowski published an important paper on relativity, presenting the Maxwell-Lorentz equations in tensor form. He also showed that the Newtonian theory of gravitation was not consistent with relativity.
The main contributors to special relativity were undoubtedly Lorentz, Poincaré and, of course, the founder of the theory Einstein. It is therefore interesting to see their respective reactions to the final formulation of the theory. Einstein, although he spent many years thinking about how to formulate the theory, once he had found the two postulates they were immediately natural to him. Einstein was always reluctant to acknowledge that the steps which others were taking due to the Michelson-Morley experiment had any influence on his thinking.
Poincaré's reaction to Einstein's 1905 paper was rather strange. When Poincaré lectured in Göttingen in 1909 on relativity he did not mention Einstein at all. He presented relativity with three postulates, the third being the FitzGerald-Lorentz contraction. It is impossible to believe that someone as brilliant as Poincaré had failed to understand Einstein's paper. In fact Poincaré never wrote a paper on relativity in which he mentioned Einstein. Einstein himself behaved in a similar fashion and Poincaré is only mentioned once in Einstein's papers. Lorentz, however, was praised by both Einstein and Poincaré and often cited in their work.
Lorentz himself poses a puzzle. Although he clearly understood Einstein's papers, he did not ever seem to accept their conclusions. He gave a lecture in 1913 when he remarked how rapidly relativity had been accepted. He for one was less sure.
As far as this lecturer is concerned he finds a certain satisfaction in the older interpretation according to which the ether possesses at least some substantiality, space and time can be sharply separated, and simultaneity without further specification can be spoken of. Finally it should be noted that the daring assertion that one can never observe velocities larger than the velocity of light contains a hypothetical restriction of what is accessible to us, a restriction which cannot be accepted without some reservation.
Despite Lorentz's caution the special theory of relativity was quickly accepted. In 1912 Lorentz and Einstein were jointly proposed for a Nobel prize for their work on special relativity. The recommendation is by Wien, the 1911 winner, and states
... While Lorentz must be considered as the first to have found the mathematical content of the relativity principle, Einstein succeeded in reducing it to a simple principle. One should therefore assess the merits of both investigators as being comparable...
Einstein never received a Nobel prize for relativity. The committee was at first cautious and waited for experimental confirmation. By the time such confirmation was available Einstein had moved on to further momentous work.
Article by: J J O'Connor and E F Robertson
--------------------------------------------------------------------------------
February 1996
MacTutor History of Mathematics
[http://www-history.mcs.st-andrews.ac.uk/HistTopics/Special_relativity.html]
--------------------------------------------------------------------------------
The classical laws of physics were formulated by Newton in the Principia in 1687. According to this theory the motion of a particle has to be described relative to an inertial frame in which the particle, not subjected to external forces, will move at a constant velocity in a straight line. Two inertial frames are related in that they move in a fixed direction at a constant speed with respect to each other. Time in the frames differs by a constant and all times can be described relative to an absolute time. This 17th Century theory was not challenged until the 19th Century when electric and magnetic phenomena were studied theoretically.
It had long been known that sound required a medium to travel through and it was quite natural to postulate a medium for the transmission of light. Such a medium was called the ether and many 19th Century scientists postulated an ether with various properties. Cauchy, Stokes, Thomson and Planck all postulated ethers with differing properties and by the end of the 19th Century light, heat, electricity and magnetism all had their respective ethers.
A knowledge that the electromagnetic field was spread with a velocity essentially the same as the speed of light caused Maxwell to postulate that light itself was an electromagnetic phenomenon. Maxwell wrote an article on Ether for the 1878 edition of Encyclopaedia Britannica. He proposed the existence of a single ether and the article tells of a failed attempt by Maxwell to measure the effect of the ether drag on the earth's motion. He also proposed an astronomical determination of the ether drag by measuring the velocity of light using Jupiter's moons at different positions relative to the earth.
Prompted by Maxwell's ideas, Michelson began his own terrestrial experiments and in 1881 he reported
The result of the hypothesis of a stationary ether is shown to be incorrect, and the necessary conclusion follows that the hypothesis is erroneous.
Lorentz wrote a paper in 1886 where he criticised Michelson's experiment and really was not worried by the experimental result which he dismissed being doubtful of its accuracy. Michelson was persuaded by Thomson and others to repeat the experiment and he did so with Morley, again reporting that no effect had been found in 1887. It appeared that the velocity of light was independent of the velocity of the observer. [Michelson and Morley were to refine their experiment and repeat it many times up to 1929.]
Also in 1887 Voigt first wrote down the transformations
x' = x - vt, y' = y/g, z' = z/g, t' = t - vx/c2
and showed that certain equations were invariant under these transformations. These transformations, with a different scale factor, are now known as the Lorentz equations and the group of Lorentz transformations gives the geometry of special relativity. All this was unknown to Voigt who was writing on the Doppler shift when he wrote down the transformations.
Voigt corresponded with Lorentz about the Michelson-Morley experiment in 1887 and 1888 but Lorentz does not seem to have learnt of the transformations at that stage. Lorentz however was now greatly worried by the new Michelson-Morley experiment of 1887.
In 1889 a short paper was published by the Irish physicist George FitzGerald in Science. The paper The ether and the earth's atmosphere takes up less than half a page and is non-technical. FitzGerald pointed out that the results of the Michelson-Morley experiment could be explained only if
... the length of material bodies changes, according as they are moving through the ether or across it, by an amount depending on the square of the ratio of their velocities to that of light.
Lorentz was unaware of FitzGerald's paper and in 1892 he proposed an almost identical contraction in a paper which now took the Michelson-Morley experiment very seriously. When it was pointed out to Lorentz in 1894 that FitzGerald had published a similar theory he wrote to FitzGerald who replied that he had sent an article to Science but I do not know if they ever published it . He was glad to know that Lorentz agreed with him for I have been rather laughed at for my view over here . Lorentz took every opportunity after this to acknowledge that FitzGerald had proposed the idea first. Only FitzGerald, who did not know if his paper had been published, believed that Lorentz had published first!
Larmor wrote an article in 1898 Ether and matter in which he wrote down the Lorentz transformations (still not written down by Lorentz) and showed that the FitzGerald-Lorentz contraction was a consequence.
Lorentz wrote down the transformations, now named after him, in a paper of 1899, being the third person to write them down. He, like Larmor, showed that the FitzGerald-Lorentz contraction was a consequence of the Lorentz transformations.
The most amazing article relating to special relativity to be published before 1900 was a paper of Poincaré La mesure du temps which appeared in 1898. In this paper Poincaré says
... we have no direct intuition about the equality of two time intervals.
The simultaneity of two events or the order of their succession, as well as the equality of two time intervals, must be defined in such a way that the statements of the natural laws be as simple as possible.
By 1900 the concept of the ether as a material substance was being questioned. Paul Drude wrote
The conception of an ether absolutely at rest is the most simple and the most natural - at least if the ether is conceived to be not a substance but merely space endowed with certain physical properties.
Poincaré, in his opening address to the Paris Congress in 1900, asked Does the ether really exist? In 1904 Poincaré came very close to the theory of special relativity in an address to the International Congress of Arts and Science in St Louis. He pointed out that observers in different frames will have clocks which will
... mark what on may call the local time. ... as demanded by the relativity principle the observer cannot know whether he is at rest or in absolute motion.
The year that special relativity finally came into existence was 1905. June of 1905 was a good month for papers on relativity, on the 5th June Poincaré communicated an important work Sur la dynamique de l'electron while Einstein's first paper on relativity was received on 30th June. Poincaré stated that It seems that this impossibility of demonstrating absolute motion is a general law of nature. After naming the Lorentz transformations after Lorentz, Poincaré shows that these transformations, together with the rotations, form a group.
Einstein's paper is remarkable for the different approach it takes. It is not presented as an attempt to explain experimental results, it is presented because of its beauty and simplicity. In the introduction Einstein says
... the introduction of a light-ether will prove to be superfluous since, according to the view to be developed here, neither will a space in absolute rest endowed with special properties be introduced nor will a velocity vector be associated with a point of empty space in which electromagnetic processes take place.
Inertial frames are introduced which, by definition, are in uniform motion with respect to each other. The whole theory is based on two postulates:-
1. The laws of physics take the same form in all inertial frames.
2. In any inertial frame, the velocity of light c is the same whether the light is emitted by a body at rest or by a body in uniform motion.
Einstein now deduced the Lorentz transformations from his two postulates and, like Poincaré proves the group property. Then the FitzGerald-Lorentz contraction is deduced. Also in the paper Einstein mentions the clock paradox. Einstein called it a theorem that if two synchronous clocks C1 and C2 start at a point A and C2 leaves A moving along a closed curve to return to A then C2 will run slow compared with C1. He notes that no paradox results since C2 experiences acceleration while C1 does not.
In September 1905 Einstein published a short but important paper in which he proved the famous formula
E = mc2.
The first paper on special relativity, other than by Einstein, was written in 1908 by Planck. It was largely due to the fact that relativity was taken up by someone as important as Planck that it became so rapidly accepted. At the time Einstein wrote the 1905 paper he was still a technical expert third class at the Bern patent office. Also in 1908 Minkowski published an important paper on relativity, presenting the Maxwell-Lorentz equations in tensor form. He also showed that the Newtonian theory of gravitation was not consistent with relativity.
The main contributors to special relativity were undoubtedly Lorentz, Poincaré and, of course, the founder of the theory Einstein. It is therefore interesting to see their respective reactions to the final formulation of the theory. Einstein, although he spent many years thinking about how to formulate the theory, once he had found the two postulates they were immediately natural to him. Einstein was always reluctant to acknowledge that the steps which others were taking due to the Michelson-Morley experiment had any influence on his thinking.
Poincaré's reaction to Einstein's 1905 paper was rather strange. When Poincaré lectured in Göttingen in 1909 on relativity he did not mention Einstein at all. He presented relativity with three postulates, the third being the FitzGerald-Lorentz contraction. It is impossible to believe that someone as brilliant as Poincaré had failed to understand Einstein's paper. In fact Poincaré never wrote a paper on relativity in which he mentioned Einstein. Einstein himself behaved in a similar fashion and Poincaré is only mentioned once in Einstein's papers. Lorentz, however, was praised by both Einstein and Poincaré and often cited in their work.
Lorentz himself poses a puzzle. Although he clearly understood Einstein's papers, he did not ever seem to accept their conclusions. He gave a lecture in 1913 when he remarked how rapidly relativity had been accepted. He for one was less sure.
As far as this lecturer is concerned he finds a certain satisfaction in the older interpretation according to which the ether possesses at least some substantiality, space and time can be sharply separated, and simultaneity without further specification can be spoken of. Finally it should be noted that the daring assertion that one can never observe velocities larger than the velocity of light contains a hypothetical restriction of what is accessible to us, a restriction which cannot be accepted without some reservation.
Despite Lorentz's caution the special theory of relativity was quickly accepted. In 1912 Lorentz and Einstein were jointly proposed for a Nobel prize for their work on special relativity. The recommendation is by Wien, the 1911 winner, and states
... While Lorentz must be considered as the first to have found the mathematical content of the relativity principle, Einstein succeeded in reducing it to a simple principle. One should therefore assess the merits of both investigators as being comparable...
Einstein never received a Nobel prize for relativity. The committee was at first cautious and waited for experimental confirmation. By the time such confirmation was available Einstein had moved on to further momentous work.
Article by: J J O'Connor and E F Robertson
--------------------------------------------------------------------------------
February 1996
MacTutor History of Mathematics
[http://www-history.mcs.st-andrews.ac.uk/HistTopics/Special_relativity.html]
Subscribe to:
Posts (Atom)
