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Mach's principle
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{{short description|Concept of absolute rotation}} In [[theoretical physics]], particularly in [[discussions]] of [[:Category:Theories of gravity|gravitation theories]], '''Mach's principle''' (or '''Mach's conjecture'''<ref>Hans Christian Von Bayer, ''The Fermi Solution: Essays on Science'', Courier Dover Publications (2001), {{ISBN|0-486-41707-7}}, [https://books.google.com/books?id=VhJr9Qx8ohsC&dq=mach's+conjecture&pg=PA79 page 79].</ref>) is the name given by [[Albert Einstein]] to an imprecise hypothesis often credited to the [[physicist]] and [[philosopher]] [[Ernst Mach#Philosophy of science|Ernst Mach]]. The hypothesis attempted to explain how rotating objects, such as [[gyroscope]]s and spinning celestial bodies, maintain a [[frame of reference]]. The proposition is that the existence of [[absolute rotation]] (the distinction of local [[inertial frame]]s vs. [[rotating reference frame]]s) is determined by the large-scale distribution of matter, as exemplified by this anecdote:<ref name=":1">{{Cite book |title=Gravitation and Cosmology |last=Weinberg |first=Steven |publisher=Wiley |year=1972 |isbn=978-0-471-92567-5 |location=USA |pages=[https://archive.org/details/gravitationcosmo00stev_0/page/17 17] |url-access=registration |url=https://archive.org/details/gravitationcosmo00stev_0/page/17 }}</ref> <blockquote> 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? {{efn|name=fn1}}<ref name=":1" /> </blockquote> 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, 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".<ref name=Hawking>{{cite book |title=The Large Scale Structure of Space–Time |author1=Stephen W. Hawking |author2=George Francis Rayner Ellis |name-list-style=amp |isbn=978-0-521-09906-6 |date=1973 |publisher=[[Cambridge University Press]] |page=1 |url=https://books.google.com/books?id=QagG_KI7Ll8C&q=Ellis+inauthor:Hawking}}</ref> Mach's 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 (general relativity)|metric tensor]] which indicates which frame is stationary with respect to rotation. [[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 have been made which would qualify as a '''Mach principle''', some of which are false. The [[Gödel metric|Gödel rotating universe]] is a solution of the field equations that 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 does not completely settle the question of the physical relevance of the principle because it has [[closed timelike curve]]s.
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