Okay...I have heard about this thought experiment a while ago, but today I got reminded of it, so I'm trying to see if I'm missing anything. First, take a look at this link. Basically, the experiment says that when a mass of water rotates inside a vessel, like a bucket, it creates a 'concave' shape, like most of us have seen. The question newton posed is "rotates relative to what?' From that he concluded their is some absolute frame of reference that the water rotates. Long story short, Mach disagreed with newton, and said that the correct answer is that water rotates relative to celestial bodies, or 'fixed stars'. He says that if there were no celestial bodies, only the bucket and water, 'rotation' wouldn't have a meaning and so the concave shape of the water wouldn't be seen. And now comes the weird(for me) part: Einstein agreed with Mach, and even coined the term 'Mach's principle'. And he wrote:

Quote: it... turns out that inertia originates in a kind of interaction between bodies, quite in the sense of your considerations on Newton's pail experiment... If one rotates [a heavy shell of matter] relative to the fixed stars about an axis going through its center, a Coriolis force arises in the interior of the shell; that is, the plane of a Foucault pendulum is dragged around (with a practically unmeasurably small angular velocity).

Now, this is what I don't understand. Einstein's SR and GR makes heavy use of 'inertial frames'. So I don't understand why he dragged 'fixed stars' to the issue, and also I find it highly unintuitive the thought that somehow, if fixed stars didn't exist, they would change the way phenomena carry on here. To me, the answer is simple: The water is rotating in respect to,well, any inertial frame. That's it. Any inertial frame will do. No need for 'fixed' stars or anything. Are you,say, on empty deep space, and there are no fixed stars around, just you and the bucket? And you want to find out if you're rotating or not around your axis? You don't need the stars. Just spit. And watch your spit. If it travels in linear fashion, then you're not rotating. If it's not, then you are accelerating, or rotating, depends on the nature of the trajectory. Either way, it's very easy to determine if your frame of reference is inertial or not. So, is there something I'm not getting? What I said makes sense to me, but if Einstein needs the presence of 'fixed stars' to explain the phenom, I must be missing something. What's your take on this?

I always thought of the phenomenon as a combination of the centrifugal force and gravity acting on the water. So if you were to try this experiment is zero-gravity, you would get different results, namely spinning water but no concave shape.

However I don't have a zero-gravity environment handy in which I could test this theory [grin]

An inertial frame is distinguished from a non-inertial frame by the fact that the non-inertial frame is accelerating relative to the inertial frame. Problem is, how do you know which frame is inertial and which is non-inertial? You can tell you're in a non-inertial frame by the pseudo forces you can observe. How does the non-inertial frame 'know' that it's the one accelerating and not the inertial frame though? General relativity says it 'knows' due to the presence of all the other matter in the universe (the 'fixed stars'). You don't need to specify a privileged frame of reference relative to which the object is accelerating, it's determined by the aggregate of all other matter in the universe.

That's my incomplete understanding of what he meant anyway.

well, one could say there is exactly one fixed star in the universe. It's just impossible to determine which one it is.

isnt the water pushing against the side of the bucket, and therefore squishes against the side and moves up it slightly.

They have these are faregrounds, you go into a big cylinder, stand against the wall and it rotates. You suddenly feel like your lying down because of the force pushing you against the wall. If I was water i would spread out, in the case of a bucket this is up because the bottom is solid/flat.

I think it's a case of Newton's first law of motion combined with friction between the water molecules and the bucket and water molecules with each other. The bucket moves and this causes the water to move. The water molecule wants to continue moving in the same direction as the wall of the bucket the molecule rubbed against. Then the bucket begins to push against the water molecule preventing the molecule from continuing in a straight line.

As more molecules interact with the other rotating molecules more molecules begin to move straight. But straight is toward the outside of the bucket and the accumulation of this combined motion means that less molecules will be in the center of the bucket.

Summary: the water doesn't spin because of its relationship to anything, it spins because the bucket is physically keeping the molecules from escaping from their trajectory of induced motion.

That's my explanation at least.

This is a little deeper than a centripetal force being needed in a rotation. This is explained by inertia, things like to go at constant velocity when there is no force, or more generally Force =mass x acceleration ( or more accurately F = dp/dt, the instantaneous change of momentum over time.)

The question posed by Mach's principle is; If there is only one particle, there isn't anything else in the universe to compare to, how do you know if it is accelerating? Or another way of looking at it, is inertia a property that emerges from the fact that when you have more than one object you can make a comparison between them.

Personally I think the equivalence principle in general relativity explains it, gravity and inertia are linked.

I haven't gotten to the expertise in general relativity to check, but I have thought that perhaps the work required to accelerate an object is equal to the amount of potential 'radiated away' in the gravitational force, much like how it takes work to accelerate a charge in an electromagnetic field.

It occurs to me know the this discussion was about inertial frames of reference and not mechanics of rotation! As to that, I (think I) agree with capn_midnight.

edit: on second thought, Platinum314 makes more sense. I will blame lack of caffeine.