I always figured this was because of acceleration. If an object is rotating it will experience a constant acceleration because it's path through spacetime is curved (equivalence principle).

So being at rest you experience no forces in your local reference frame, rotating = acceleration in your local reference frame.

I'm not sure why the rest of the universe rotating around the bucket would impart acceleration upon it because the rest of the universe is outside the buckets local reference frame. What sort of mechanism can transfer acceleration through rotation from one reference frame to another? (genuine question)

After all, it's acceleration within the local reference frame that lets the object 'feel' the acceleration rotation - it lets the object 'feel' it's curved path through spacetime, so it knows it is rotating and not the universe around it.

This is begging the question though -- relativity presupposes the existence of a 4D spacetime upon which you can do your calculations, so at that moment when you state that the local reference frame is not accelerating, is the moment that you declared that the object is not rotating but the universe is.

However relativity also admits the description of spacetime where the entire universe rotates and the object's edges are experiencing constant acceleration.

One way to look at relativity is note that local observers can disagree about apparent distances, times, velocities, and accelerations, they are all able to use Lorentz transforms to answer the question of 'what would another observer see'. So in any relativistic description of this universe, all observers need to agree on whether the object in the middle is rotating or not -- but this appears to be a free parameter.

In other words, General Relativity fails to fully follow Mach's principle on a global scale.

>Tie two rocks together with a rope, he suggested, and go into deep space far from the gravitation of the Earth or the sun...Rotate the rope about its centre and it will become taut as the rocks pull outwards. The rocks will create an outward force pulling the rope tight. If one does this in an empty universe then what can it mean for the system to be rotating. There is nothing to measure rotation with respect to. Newton deduced from this thought experiment that there had to be something to measure rotation with respect to, and that something had to be space itself.

Eh? You measure the rotation against the thing that performed the “rotate the rope” step in the experiment.

Thought experiments that contain the step “now magically remove X from the observable universe” should be treated with caution! :-)

If you change it to just “There exists a universe empty except for a rotating set of rocks connected by a rope”, rotation needs no meaning as it’s one of the axioms. Also, there is no observer in that universe, so you’re making a pretty dangerous assumption about the ability to observe a universe without being a part of it.

If the rotation needs no meaning, what stretches the rope then?

Well, it's a thought experiment. You can think of the same with two rocket powered capsules, tied with a rope, so that nothing has to disappear. If they are rotating, they are rotating against something (space itself), if they are not rotating, rocket power is strangely not having any effect, which violates Newton's Third Law.

That’s easy then; they’re rotating relative to the exhaust stream that they’re creating.

Now if you’re talking quantum vacuum thrusters, exploring exactly how that works should also give you a good idea of what space is! ;-)

But, how could you measure or perceive that rotation, relative only to the exhaust stream created by each rocket? If you are picturing the rockets doing any more than pulling the rope taut with the force of their motion, ie the rockets are turning around like a wheel in your mental image, you are actually picturing them rotating relative to you, the stationary observer.

The conundrum is: what is the rotation without the relative perspective of the stationary observer? What pulls the rope taut?

>What pulls the rope taut?

Ok, this seems to be a clash of intuitions explained by reference frames —

When you imagine an object in deep space or its own empty universe, you intuitively use an “inertial reference frame”, where “the physics of a system in an inertial frame have no causes external to the system”. I.e. you do not see any “fictitious” forces like the centrifugal force, so the rope would not be taut.

https://en.m.wikipedia.org/wiki/Inertial_frame_of_reference

If you are imagining the rope to be taut, you are imagining a force pulling it taut, but this force that you’re imagining is only explained by physics if you’re using a rotational (non-inertial) reference frame.

So if your system has unexplained “centrifugal” forces, those forces can be modelled as the system rotating within an inertial reference frame, without having any evidence of any “non-rotating” matter.

It just so happens that deep space is pretty close to an inertial reference frame, so your mind sort of makes that assumption.

Or, in other words, you could measure and perceive the rate of the rope’s rotation by analyzing the forces in system, without having any physical external point of reference.

I posted an explanation on the top level that some may find useful.