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austrian physicist
(1838 – 1916)
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[in ‘theoretical physics’, particularly in discussions of ‘gravitation theories’, mach’s principle (or Mach’s conjecture) is the name given by ‘einstein to an imprecise hypothesis often credited to the physicist/philosopher ‘ernst mach’]
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(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?
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(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 were whirling around you, ‘Mach’ suggests that there is some physical law which would make it so you would feel a ‘centrifugal force’)
(the principle is often stated in vague ways, like mass out there influences ‘inertia’ here”)
(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 rotating faster and faster as one moves further away)
(this example doesn’t completely settle the question, because it has ‘closed timelike curves’)
(the basic idea also appears before mach’s time, in the writings of ‘george berkeley’)
(the book Absolute or Relative Motion? (1896) by Benedict Friedländer and his brother Immanuel contained ideas similar to Mach’s principle)
(a very general statement of Mach’s principle is “local physical laws are determined by the large-scale structure of the universe”)
(in plain words, the question, raised by Ernst Mach, was: “how do rotating bodies know their rate of rotation?”)
(‘mach’ surmised that it requires an action-at-a-distance from distant matter, informing the rotating object about its angular velocity)
(however, mach’s question contains its own answer. “the totality of the universe’s particles can be regarded as a single multiparticle celestial body, without any external celestial bodies it could interact with”)
(thus, following mach’s logic, neither an individual ‘proton’ (sufficiently remote from other ‘protons’) nor the ‘totality of protons’ (the ‘universe’) have any ‘inertia’)
(this implies that the ‘mutual gravitation’ of ‘inertialess individual protons’ would result in an ‘instantaneous gravitational collapse’ of their ‘inertialess totality’—’the universe’)
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(which means ‘mach’s principle’ is WRONG!)
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*🌈✨ *TABLE OF CONTENTS* ✨🌷*
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🔥🔥🔥🔥🔥🔥*we won the war* 🔥🔥🔥🔥🔥🔥