There is nothing outside the universe. - Lee Smolin

So, there can't be any absolute frame. Everything must be measured relative to an entity that exists in the universe. Thus, space is relative. But, what about the Bucket argument that Newton proposed in favour of his absolute rotation theory? Can a relationist explain the Bucket Argument? If reality is relative how to disprove Newton's Bucket Argument that establish Absolute rotation?

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    $\begingroup$ The bucket argument merely shows that a rotating frame of reference is non-inertial. Nothing to see here. Move on. $\endgroup$ – John Dvorak Dec 27 '14 at 8:37
  • $\begingroup$ The Wikipedia article you (attepmt to) link explains things pretty well, actually. $\endgroup$ – John Dvorak Dec 27 '14 at 8:42
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    $\begingroup$ Moreover, if you're worried about relativities of rotating frames, then General Relativity actually tells the difference between the frame where the bucket is rotating and a relatively rotating frame wherein the bucket is still. At most one of these frames is inertial, and it is the frame wherein a fixed bucket has a flat surface. Acceleration, in the sense of what an accelerometer measures, is absolute in General Relativity: it is a fallacy that "relativity teaches us that everything is relative". $\endgroup$ – WetSavannaAnimal Dec 27 '14 at 8:50
  • $\begingroup$ @user36790 Wow! In the times of Newton the Wikipedia already existed? I pressed on your words "Bucket argument", and what I found was "Donate to Wikipedia !" $\endgroup$ – Sofia Dec 27 '14 at 9:30
  • $\begingroup$ Newton could have done his experiment with the bucket and water, while walking toward the College. Both for him and for a person at rest, the water would appear as rising toward the sides of the pail. $\endgroup$ – Sofia Dec 27 '14 at 10:04

From the context of non-relativistic classical mechanics, Newton's bucket argument says that angular velocity is absolute, just as Newton's first law says that translational acceleration is absolute.

The modern view of Newton's first law is that it says there exists a set of preferred frames of reference (frames in which the laws of physics take on their simplest form) called inertial frames. In classical mechanics, all inertial frames have two things in common: That the origin of one inertial frame as viewed from the perspective of some other inertial frame is moving at a constant velocity, and that the axes of any two inertial frames are not rotating with respect to one another.

What this means is that any two inertial observers will agree on the translational acceleration and angular velocity of any object. Another way to say this is that translational acceleration and angular velocity are absolute in non-relativistic classical mechanics.

Things get a bit trickier from the perspective of general relativity. General relativity preserves the basic concept of an inertial frame, but inertial frames in general relativity are not the same as those in non-relativistic classical mechanics. Inertial frames in general relativity are local rather than universal, and a non-rotating frame centered on a free-falling object is inertial in general relativity (but not in Newtonian mechanics).

Nonetheless, angular velocity and acceleration still have a bit of absoluteness to them in general relativity. One can construct local experiments that measure proper angular velocity and proper translational acceleration. A modern smartphone contains (low quality) versions of such devices, a MEMS gyro and a MEMS accelerometer.


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