Newton was not satisfied with mere definitions of absolute space. He concluded the Scholium with a virtuoso performance, and suggested experiments and arguments proving the existence of absolute space. These have had an extraordinary afterlife. They were a direct inspiration to Einstein as he struggled with his theory of gravitation. In different guises, they remain today at the centre of debates over space and time among philosophers. But students sometimes giggle when they read Newton’s proposals: they seem silly, almost crude and rustic. These first impressions are wrong. A satellite built by NASA and Stanford University (see Appendix D for their websites) is a hightech version of Newton’s proposals, as will be explained below.

Newton’s famous bucket argument is now considered a philosophical classic. As their studies progress, philosophers sometimes fall in love with arguments the way others might with a favourite novel, a breathtaking mountain or a moving symphony. As connoisseurs, philosophers hope for arguments with beauty, depth, simplicity – and a bit of mystery. When they find these together, they return again and again to the argument, hoping each time to learn a little more, to push it a bit farther. For all its simplicity, Newton’s bucket illuminates the deepest issues in relativity theory and few can resist its allure.

The strategy of Newton’s proof is to show that there are certain observable effects that could only be caused by absolute space. Newton begins disarmingly. Even though absolute space is not directly observable, he proposes to prove its existence with a bucket. Suppose, he says, that our wooden bucket is nearly full of water and is suspended by a good, flexible rope from the tree branch overhead. Suppose we rotate the bucket and twist the rope up as far as it will go without tangling. If we now gently release the bucket, the calm, flat waters will at first remain still within the rotating bucket. As the rope unwinds and the bucket begins to whirl more quickly, the water will gradually be affected by the movement of the bucket and start to spin. As it does, the surface of the water will become concave: it will be lower in the middle as the water crowds outwards towards the sides of the bucket.

All this is straightforward, but Newton’s genius now notices a subtlety. As the rope smoothly unwinds, the spinning concave water in the bucket will finally catch up with the rotating bucket. Soon they will rotate at the same speed. Newton saw here an argument for the existence of absolute space. (Do you?) The argument turns on two key facts: the surface of the rotating water is concave, and the bucket and water eventually rotate at the same speed. In this state, there is no relative motion between the water and the bucket – just as a child on a spinning merry-go-round is moving around along with the horses, and thus not moving relative to the horses. Newton’s argument can be interpreted as follows:
       Newton bucket argument
  •  The motion causes the concavity
  •  Motion is either relative or absolute
  •  Thus, either relative or absolute motion causes the concavity
  •  But relative motion does not cause the concavity
  •  So absolute motion causes the concavity
  •  If something is a cause, then it exists
  •  So absolute motion exists
  •  If absolute motion exists, then absolute space exists
  •  So absolute space exists
Several of the assumptions here are straightforward. For example, motion causes the concavity, A, because the surface of the water is flat before the bucket is released and begins to turn. Newton actually leaps from E to I, but later debates have shown that it is important to fill in these steps

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