Originally Posted by mc^2

To be accurate:

Newton - used Galilean spacetime (that is, an absolute space and an absolute time) that followed Euclidian rules of geometry. Newton regarded "Space" as a physical "something" where accelerated motion is not relative.

Leibniz - declared that motion is relative in all respects, and that "space" has no intrinsic physical properties. Space is "nothng" apart from the separation of physical objects as perceived by our senses.

Mach - conjectured that the property of inertia (resistance to acceleration) is due to the average mass distribution of the universe. Mach however, did not supply a mechanism for his conjecture. Like Leibniz, Mach did not regard space as a physical entity.

Einstein SR - space and time are not absolutes. Space and time are each relative. However, now space and time are combined into a single mathematical entity called spacetime. Spacetime is absolute because trajectories within spacetime are used to determine if motion is accelerated or not. SR does away with Galilean spacetime because it allows faster-than-light speeds. Instead, SR uses Minkowski spacetime, which imposes an invariant limit on velocity.

Einstein GR - spacetime is no longer absolute, but changeable. Spacetime is the real and physical manifestation of a gravitational field. All accelerated motion is now relative to the gravitational field. GR reduces to SR when the gravitational field is zero, however a field that measures zero is still a field. Hence, accelerated motion is defined with respect to even a "flat" spacetime (zero gravitational field).

A well-known example of where Mach and GR deviate is where Mach suggested that in an empty universe, accelerated motion could not be detected, as there are no benchmarks against which to measure such motion ("Newton's bucket"). General Relativity does provide a benchmark via the gravitational field, which is real and physical. Thus, GR tells us that accelerated motion is detectable even in an empty universe.

Although Mach did not provide a mechanism to support his conjecture regarding inertia, GR does provide a mechanism via the combined gravitational field, and that's why the conclusions are very different!



Are you referring to Brans-Dicke Theory? Or something else?