Mach's principle

• 1. Origins And Philosophical Roots

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  Ernst Mach published The Science of Mechanics in 1883, introducing a radical idea about motion. Before this book appeared, George Berkeley had written similar thoughts in his work De Motu decades earlier. Mach argued that we cannot define rotation without referencing other bodies in the universe. He questioned why water climbs up the sides of a spinning bucket if there is no absolute space to measure against. This philosophical stance challenged the prevailing Newtonian view that space exists independently of matter. Mach suggested that all motion must be understood as relative to other objects. His writing did not explicitly state a new physical law but rather offered a redescription of how we experience movement. Albert Einstein later read these pages and found them deeply inspiring for his own theories.

• 2. Einstein And General Relativity

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  Albert Einstein coined the phrase Mach's principle in a letter dated the 25th of June 1913 sent to Ernst Mach himself. He believed that the distribution of matter in the universe determined which frames were stationary with respect to rotation. Einstein hoped that general relativity would prove that inertia arises from interactions between distant stars. He wrote to Mach expressing satisfaction when he discovered an effect where a spinning shell of mass caused internal reference frames to precess. This discovery seemed to confirm that matter influences inertia here. However, Einstein never made Mach's principle a fundamental assumption of his final theory. The principle remained vague while the mathematics of general relativity became precise. Many physicists now argue that general relativity does not fully satisfy Mach's original vision. An expert poll held in Tübingen in 1993 showed most respondents believed general relativity was not perfectly Machian.

• 3. The Newton Bucket Argument

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  Isaac Newton described a thought experiment involving a bucket filled with water in his book Philosophiae Naturalis Principia Mathematica. When the bucket rotates, the water eventually climbs up the sides due to centrifugal forces. Newton claimed this proved the existence of absolute space because the water rotated relative to something invisible yet real. Mach countered that we cannot know how the water behaves if the bucket walls become leagues wide. He argued that the apparent forces arise only because our reference system treats small bodies as moving and large bodies like the earth as still. Mach suggested that every motion has sense only in reference to other bodies. If the bucket were replaced by the entire universe, the result might differ entirely from what Newton predicted. This critique formed the core of Mach's challenge to classical mechanics.

• 4. Lense-Thirring Frame Dragging

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  A spinning spherical shell of mass causes the reference frame inside it to precess with respect to a fixed background. This phenomenon is known as the Lense, Thirring effect. Einstein viewed this manifestation as evidence supporting Mach's principle. The plane of a pendulum would not be dragged around if the shell of matter were absent or stationary. Modern relativists see imprints of Machian ideas in the initial-value problem of spacetime geometry. In an asymptotically flat universe, boundary conditions at infinity define a frame where inertia has meaning. A Lorentz transformation on the distant universe can transform this inertia into another state. Some theories require spacetime to be spatially compact and globally hyperbolic for stronger forms of the principle to apply. These models suggest that the distribution of matter determines the inertial frame at each point in the universe.

• 5. Quantitative Formulations And Sciama

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  Dennis W. Sciama proposed adding an acceleration-dependent term to the Newtonian gravitation equation in 1953. He worked at Cambridge University when developing this quantitative expression of Mach's Principle. His formula included variables such as distance r, gravitational constant G, relative acceleration a, and speed of light c. Sciama called the resulting effect inertial induction. This attempt sought to explain how distant stars could influence local inertia through a measurable mechanism. Most physicists believe no fully successful quantitative theory exists yet. Hermann Bondi and Joseph Samuel later listed eleven distinct statements labeled Mach0 through Mach10. Their list highlighted the variety possible within the broad notion that mass there influences inertia here. Despite these efforts, the principle remains imprecise compared to other physical laws.

• 6. Competing Gravity Theories

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  The Brans, Dicke theory represents one attempt to incorporate Mach's principle more fully into gravitational physics. Another approach is the Hoyle, Narlikar theory of gravity developed by Fred Hoyle and Jayant Narlikar. Most physicists argue that none of these alternatives have been entirely successful so far. An exit poll of experts held in Tübingen in 1993 asked whether general relativity was perfectly Machian. Only three respondents answered yes while twenty-two replied no. When asked if general relativity with appropriate boundary conditions was very Machian, fourteen said yes and seven said no. These results reflect ongoing debate about the validity and scope of Mach's original hypothesis. Some formulations require the universe to be spatially closed or assert that total energy equals zero. Others claim that if all matter were removed, space itself would cease to exist.