by neufer » Thu Oct 24, 2013 1:39 am
http://en.wikipedia.org/wiki/Mach%27s_principle wrote:
<<Mach's principle (or Mach's conjecture) is the name given by Einstein to an imprecise hypothesis often credited to the physicist and philosopher Ernst Mach. The idea is that the local motion of a rotating reference frame is determined by the large scale distribution of matter, as exemplified by this anecdote:
"You are standing in a field looking at the stars. Your arms are resting freely at your side, and you see that the distant stars are not moving. Now start spinning. The stars are whirling around you and your arms are pulled away from your body. Why should your arms be pulled away when the stars are whirling? Why should they be dangling freely when the stars don't move?"
Mach's principle says that this is not a coincidence—that there is a physical law that relates the motion of the distant stars to the local inertial frame. If you see all the stars whirling around you, Mach suggests that there is some physical law which would make it so you would feel a centrifugal force. There are a number of rival formulations of the principle. It is often stated in vague ways, like "mass out there influences inertia here". A very general statement of Mach's principle is "Local physical laws are determined by the large-scale structure of the universe." The basic idea also appears before Mach's time, in the writings of George Berkeley.
Newton tried to demonstrate that one can always decide if one is rotating with respect to the absolute space, measuring the apparent forces that arise only when an absolute rotation is performed. If a bucket is filled with water, and made to rotate, initially the water remains still, but then, gradually, the walls of the vessel communicate their motion to the water, making it curve and climb up the borders of the bucket, because of the centrifugal forces produced by the rotation. Newton says that this thought experiment demonstrates that the centrifugal forces arise only when the water is in rotation with respect to the absolute space (represented here by the earth's reference frame, or better, the distant stars); instead, when the bucket was rotating with respect to the water no centrifugal forces were produced, this indicating that the latter was still with respect to the absolute space. “
Ernst Mach debunked this notion of absolute space and argued that the inertia existed because the water was spinning relative to the rest of the matter in the universe. Indeed, the same effects would be observed if the bucket was still and the rest of the universe was rotating around it, he said.”
This concept was a guiding factor in Einstein's development of the general theory of relativity. Einstein realized that the overall distribution of matter would determine the metric tensor, which tells you which frame is rotationally stationary. Frame dragging and conservation of gravitational angular momentum makes this into a true statement in the general theory in certain solutions. But because the principle is so vague, many distinct statements can be (and have been) made which would qualify as a Mach principle, and some of these are false.
The Gödel rotating universe is a solution of the field equations which is designed to disobey Mach's principle in the worst possible way. In this example, the distant stars seem to be revolving faster and faster as one moves further away. This example doesn't completely settle the question, because it has closed timelike curves.
Most physicists believe Mach's principle was never developed into a quantitative physical theory that would explain a mechanism by which the stars can have such an effect. Although Einstein was intrigued and inspired by Mach's principle, Einstein's formulation of the principle is not a fundamental assumption of general relativity. There have been attempts to formulate a theory which is more fully Machian, such as Brans–Dicke theory, but most physicists argue that none have been fully successful.>>
Walter Isaacson, Einstein wrote:
<<
“The Olympia Academy’s reading list included some classics with themes that Einstein could appreciate, such as Sophocles’ searing play about the defiance of authority, Antigone, and Cervantes’ epic about stubbornly tilting at windmills, Don Quixote. But mostly the three academicians read books that explored the intersection of science and philosophy: David Hume’s A Treatise of Human Nature, Ernst Mach’s Analysis of the Sensations and Mechanics and Its Development, Baruch Spinoza’s Ethics, and Henri Poincaré’s Science and Hypothesis. It was from reading these authors that the young patent examiner began to develop his own philosophy of science.”
“Einstein had two scientific heroes he had never met—Ernst Mach (February 18, 1838 – February 19, 1916) and Hendrik Lorentz—and he was able to visit them both before his move to Prague. When he went to Vienna for his formal presentation to the ministers there, he called on Mach, who lived in a suburb of that city. The aging physicist and preacher of empiricism, who so deeply influenced the Olympia Academy and instilled in Einstein a skepticism about unobservable concepts such as absolute time, had a gnarly beard and gnarlier personality. “Please speak loudly to me,” he barked when Einstein entered his room. “In addition to my other unpleasant characteristics I am also almost stone deaf.””
“As a young empiricist, excited by his readings of Ernst Mach, Einstein had been willing to reject any concepts that could not be observed, such as the ether and absolute time and space and simultaneity. But the success of his general theory convinced him that Mach’s skepticism, even though it might be useful for weeding out superfluous concepts, did not provide much help in constructing new theories.”
“Meanwhile, another approach to quantum mechanics had been developed in the summer of 1925 by a bright-faced 23-year-old hiking enthusiast, Werner Heisenberg, who was a student of Niels Bohr in Copenhagen and then of Max Born in Göttingen. As Einstein had done in his more radical youth, Heisenberg started by embracing Ernst Mach’s dictum that theories should avoid any concepts that cannot be observed, measured, or verified. For Heisenberg this meant avoiding the concept of electron orbits, which could not be observed.”>>
[quote=" http://en.wikipedia.org/wiki/Mach%27s_principle"]
<<Mach's principle (or Mach's conjecture) is the name given by Einstein to an imprecise hypothesis often credited to the physicist and philosopher Ernst Mach. The idea is that the local motion of a rotating reference frame is determined by the large scale distribution of matter, as exemplified by this anecdote: [b][i][color=#0000FF]"You are standing in a field looking at the stars. Your arms are resting freely at your side, and you see that the distant stars are not moving. Now start spinning. The stars are whirling around you and your arms are pulled away from your body. Why should your arms be pulled away when the stars are whirling? Why should they be dangling freely when the stars don't move?"[/color][/i][/b]
Mach's principle says that this is not a coincidence—that there is a physical law that relates the motion of the distant stars to the local inertial frame. If you see all the stars whirling around you, Mach suggests that there is some physical law which would make it so you would feel a centrifugal force. There are a number of rival formulations of the principle. It is often stated in vague ways, like "mass out there influences inertia here". A very general statement of Mach's principle is "Local physical laws are determined by the large-scale structure of the universe." The basic idea also appears before Mach's time, in the writings of George Berkeley.
Newton tried to demonstrate that one can always decide if one is rotating with respect to the absolute space, measuring the apparent forces that arise only when an absolute rotation is performed. If a bucket is filled with water, and made to rotate, initially the water remains still, but then, gradually, the walls of the vessel communicate their motion to the water, making it curve and climb up the borders of the bucket, because of the centrifugal forces produced by the rotation. Newton says that this thought experiment demonstrates that the centrifugal forces arise only when the water is in rotation with respect to the absolute space (represented here by the earth's reference frame, or better, the distant stars); instead, when the bucket was rotating with respect to the water no centrifugal forces were produced, this indicating that the latter was still with respect to the absolute space. “[b][i][color=#0000FF]Ernst Mach debunked this notion of absolute space and argued that the inertia existed because the water was spinning relative to the rest of the matter in the universe. Indeed, the same effects would be observed if the bucket was still and the rest of the universe was rotating around it, he said.[/color][/i][/b]”
This concept was a guiding factor in Einstein's development of the general theory of relativity. Einstein realized that the overall distribution of matter would determine the metric tensor, which tells you which frame is rotationally stationary. Frame dragging and conservation of gravitational angular momentum makes this into a true statement in the general theory in certain solutions. But because the principle is so vague, many distinct statements can be (and have been) made which would qualify as a Mach principle, and some of these are false. [b][color=#FF0000]The Gödel rotating universe is a solution of the field equations which is designed to disobey Mach's principle in the worst possible way. In this example, the distant stars seem to be revolving faster and faster as one moves further away. This example doesn't completely settle the question, because it has closed timelike curves.[/color][/b]
Most physicists believe Mach's principle was never developed into a quantitative physical theory that would explain a mechanism by which the stars can have such an effect. Although Einstein was intrigued and inspired by Mach's principle, Einstein's formulation of the principle is not a fundamental assumption of general relativity. There have been attempts to formulate a theory which is more fully Machian, such as Brans–Dicke theory, but most physicists argue that none have been fully successful.>>[/quote][quote="Walter Isaacson, Einstein"]
[float=right][img3="[b]'[i]Please speak loudly to me[/i],' Mach
barked when Einstein entered his room.
'[i]In addition to my other unpleasant
characteristics I am also almost stone deaf.[/i]'[/b]"]http://www.zyx2.org/PEOPLE/Fig861.jpg[/img3][/float]
<<[b][i][color=#0000FF]“The [url=http://en.wikipedia.org/wiki/Olympia_Academy]Olympia Academy[/url]’s reading list included some classics with themes that Einstein could appreciate, such as Sophocles’ searing play about the defiance of authority, Antigone, and Cervantes’ epic about stubbornly tilting at windmills, Don Quixote. But mostly the three academicians read books that explored the intersection of science and philosophy: David Hume’s A Treatise of Human Nature, Ernst Mach’s Analysis of the Sensations and Mechanics and Its Development, Baruch Spinoza’s Ethics, and Henri Poincaré’s Science and Hypothesis. It was from reading these authors that the young patent examiner began to develop his own philosophy of science.”
“Einstein had two scientific heroes he had never met—Ernst Mach (February 18, 1838 – February 19, 1916) and Hendrik Lorentz—and he was able to visit them both before his move to Prague. When he went to Vienna for his formal presentation to the ministers there, he called on Mach, who lived in a suburb of that city. The aging physicist and preacher of empiricism, who so deeply influenced the Olympia Academy and instilled in Einstein a skepticism about unobservable concepts such as absolute time, had a gnarly beard and gnarlier personality. “Please speak loudly to me,” he barked when Einstein entered his room. “In addition to my other unpleasant characteristics I am also almost stone deaf.””
“As a young empiricist, excited by his readings of Ernst Mach, Einstein had been willing to reject any concepts that could not be observed, such as the ether and absolute time and space and simultaneity. But the success of his general theory convinced him that Mach’s skepticism, even though it might be useful for weeding out superfluous concepts, did not provide much help in constructing new theories.”
“Meanwhile, another approach to quantum mechanics had been developed in the summer of 1925 by a bright-faced 23-year-old hiking enthusiast, Werner Heisenberg, who was a student of Niels Bohr in Copenhagen and then of Max Born in Göttingen. As Einstein had done in his more radical youth, Heisenberg started by embracing Ernst Mach’s dictum that [u]theories should avoid any concepts that cannot be observed, measured, or verified[/u]. For Heisenberg this meant avoiding the concept of electron orbits, which could not be observed.”[/color][/i][/b]>>[/quote]