# Mach's principle

Mach's principle is a hypothesis first stated by the physicist and philosopher Ernst Mach in 1893, which states that:

"The inertia of any system is the result of the interaction of that system and the rest of the universe. In other words, every particle in the universe ultimately has an effect on every other particle."

According to Mach's principle, which is an example of a relational theory, a single object (for example, the Earth) in an otherwise empty Universe would feel no inertial forces. It would be impossible to determine whether that object is rotating or not. According to Mach, the inertial forces on that object are caused by the sum of the gravitational forces from cosmic bodies such as the distant stars1; the rotation of that object only makes sense relative to these other objects. For an example of the inertial forces on that object, see Coriolis force.

In this sense, Mach's principle can be said to be a form of philosophical holism.

The above version of the principle is largely due to Albert Einstein, who brought the principle into mainstream physics whilst working on general relativity. Indeed it was Einstein who first coined the phrase Mach's principle. There is much debate as to whether Mach really intended to suggest a new physical law since he never states it explicitly. He is more concerned with criticising Newton's mechanics, in particular the idea of absolute space.

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.1 Although Einstein was intrigued by Mach's principle, his general relativity does not fully agree with it. There have been attempts to formulate a theory which is more fully Machian, such as Brans-Dicke theory, but none have been completely successful.

## Note

• Note 1: Max Born, Einstein's Theory of Relativity. Dover 1962, a translation of Born's 1924 book in German, which explained Relativity in non-mathematical terms.

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