The problem is: how does the bucket know that it's rotating, and not the rest of the universe that's rotating around it?

Maybe this will help: http://www-groups.dcs.st-and.ac.uk/history/HistTopics/Newton...

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.

The difficulty comes when you ask the next question: What causes inertia? Why do particles “want” to move in a straight line?

As the article points out, the highest rise happens when the water is in sync with the bucket, so you can’t attribute the phenomenon to friction.

What causes magnetism?

These questions won’t really stress me until we run out of ideas for physics experiments. :-)

Drop the bucket and look at the equatorial bulge problem of a planet stated in the article. The planet is effectively spinning in a vacuum so there is no "outer friction."

You aren't the only one. I thought the same thing while reading this and felt the mechanics behind the atoms' movement was easy to understand and explain in what the article seems to suggest is difficult to explain. Perhaps either the bucket example was a bad one, not explained correctly as to what was difficult to understand, or Newton didn't understand certain aspects of the physics of atoms at the time. I'm not a physics or history expert, but it seems like a failure of the article to make the problem clear, not you.

It's possible that the confusion comes from the weirdness of non-inertial reference frames. Switching from [rotating bucket] to [universe rotating around the bucket] is not an intuitive operation.

To build on the atom-level view, imagine you take a snapshot in time of a cross-section of the bucket and the universe. Then you put debuggers on four particles. These debuggers tell us the linear velocities of each particle. Two of the particles, A and B, are part of the water in the bucket. The other two particles are somewhere out in the universe, but aligned in a line with C and D.

Here's the picture so far, with the size of the arrow indicating the linear velocity of each particle. The bucket+water has been rotating for a long time, so all the water is rotating normally.

  [center of bucket]
  A -->
  B ---->
  [edge of bucket]
  .
  .
  C
  D

Now let's switch reference frames so the the universe (containing particles C and D) is rotating around the bucket. C an D are going faster since they are further from the center of rotation.

  [center of bucket]
                A
                B
  [edge of bucket]
                .
                .
        <------ C
  <------------ D

In this new reference frame, A and B have no difference in velocity. This is very worrisome! The information containing the relative velocities of A and B (and, therefore, the forces on them) has essentially been destroyed. We might need to add new forces to get the information back - information which is crucial to explaining the water getting pushed outwards.

This is a sketch, definitely not rigorous. But my main point is that you can't say "imagine the universe is rotating around the bucket" without introducing a lot of messiness. That's what it means to have a non-inertial/accelerating reference frame.

On another note, I do think the Nautilus article is conflating two different points of confusion. First, as I described above, rotating reference frames are weird. But despite that weirdness, we can fully explain it in terms of the underlying physical concepts (acceleration, inertia, space, etc). Second, we haven't fully explained the origin of those concepts yet. But that's a very different matter. It seems like a stretch to say that we can't explain the water vortex, or that we can't explain the bulging planet.

based on the article, i think the problem of momentum (which you invoke) is the crux of the question.

You gotta prove it mathematicly which is the hardest part

>What is it?

Hubris. Programmers believe they can solve anything. The belief is so strong that they can look at a centuries old problem, which has puzzled the greatest minds in science, and think they have the simple answer in minutes.

Programmers are engineers in a complex domain with many opportunities for establishing new best practices. A big part of their job is to analyze how complex systems function, and design changes to those systems that achieve a desired result.

The belief that they have a simple answer is a result of applying their engineering skills to a domain that they understand poorly but think they know well; this misalignment is due to the use of subtly inaccurate metaphors and generalizations, e.g. classical mechanics.

Taking their simple answer and methodically explaining why it’s incorrect efficiently develops their knowledge.

So this hubris is adaptive — it allows them to build their knowledge in a domain quickly.

Some might even do it intentionally, since they know the Internet can’t bear to leave an error uncorrected. ;-)