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I Thoughts on Newton's Bucket and the relativity of rotation

  1. Jan 21, 2017 #1
    Isaac Newton imagined a bucket of water suspended on a fine (ideally torsionless) rope, set spinning. Friction eventually causes the water to rotate along with the bucket. The surface develops a dip in the middle and rises at the edges owing to the water's inertia. (You see this effect every time you stir a cup of tea.)

    Einstein considered this 'thought experiment' too, and asked what this rotation might be relative to. Was it relative to nearby masses, or to the entire mass of the universe surrounding the bucket? Or to an absolute 'stationary' ether (as Newton did)? And he wondered whether this inertia effect would occur if the bucket of water were spinning in an otherwise empty universe devoid of any other masses.

    My own 'Newtonian/relativistic' thoughts on this are as follows. The situation can be regarded as equivalent to a 'stationary' bucket with the rest of the universe spinning round it at the same rotational speed but in the opposite direction. The fact that the mass of the universe is orbiting the bucket of water implies that it is accelerating towards it (like the Moon accelerating in its orbit towards Earth). This implies that the bucket is exerting a force on the 'rotating' universe. But this in turn implies that the rotating universe is exerting an equal and opposite force on the bucket and the water within it. It is this force that causes the water to pile up at the edges and dip in the middle, and give the impression of possessing 'inertia'.

    It follows from this, that in an otherwise empty universe the inertia effect would not occur. That is to say, the spinning water would not develop a dip in the middle and rise at the edges, unless empty space has mass.

    I cannot believe for an instant that these thoughts are new. Would more knowledgable forum members please refer me to where in the literature my thought experiment has been described. And also, I'd be very interested to hear what YOUR thoughts are on this?
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  3. Jan 21, 2017 #2
    I've often thought about this too .....

    Imagine a planet in space not in orbit around a star ... far from anything .... we want to know if it's rotating about any axis ...
    We measure the gravity where we are on the surface ... then fire a rocket engine tangentially to the surface to change it's angular rotation about an axis ... we measure gravity again , if it decreased then we know we have indeed given it a real rotation ... if it increases then we know it had a rotation before , but in the opposite direction (the apparent 'gravity' we are measuring is really the the true force from gravity minus the centrifugal force)
    So we do this many times , different axis, until the gravity measured is a maximum everywhere on the surface , then we know this planet has zero spin.
  4. Jan 21, 2017 #3


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  5. Jan 21, 2017 #4


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    This idea is usually known as Mach's principle. My thoughts on it are that it is philosophically appealing, but very hard to formulate in terms of an actual testable theory. There was one theory, Brans Dicke gravity, that attempted to do so. However, insofar as BD gravity does embody Mach's principle the experimental evidence shows that the universe does not follow it.
  6. Jan 24, 2017 #5
    It's not a new idea, as you can see. I seem to recall there are some particular solutions to Einstein's equations for gravity in a rotating cylinder which mimics the centrifugal and coriolis forces on a bucket, but I think the general consensus is that the universe is not Machian. The reason is that these solutions require some very special parameter settings, while the calculation of the bucket in Newtonian physics is very straightforward and doesn't require any special parameter settings.
  7. Jan 28, 2017 #6
    Suppose you have a craft traveling in open space (far from any source of gravity). Does it have momentum and inertia? Yes. Can you change its direction without using any force? No. So a spinning bucket of water out in free space will show the same depression in the center and rising on the edges of its surface.

    The "relative" question is not so complex. You can calculate the rate of spin based on the slope of the water's surface from edge to center. That will tell you what the relative spin is compared to other objects.
  8. Jan 31, 2017 #7


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    Just a comment: some years ago, I tried to read about the history of the 19th and 20th century research on the problem of inertia. There was a document, a book, by Immanuel and Benedikt Friedländer that seemed to be interesting, but in spite of my efforts, I wasn't able to find it in the internet ('Absolute oder relative Bewegung?'). I have tried now again, and here it is...


    It seems that the internet gets better and richer by the day...
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