In relativity, such an extended distribution of matter is called a fluid.

mechanics; in other words, phase space is the set of all possible states the system could be in.

Finding geodesics is precisely analogous, except we’re minimizing the length of a curve rather than the action of a particle trajectory.

An exciting modern idea is that space emerges out of quantum entanglement, rather than being a substance in its own right, so maybe there’s a sense in which relationalism will triumph in the end.

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Today, most physicists would come down on the side of Newton, treating space as a thing in itself, for a couple of reasons. First, the space in between objects is not empty; it is filled with fields of various sorts. Second, space (as part of spacetime) has a life of its own; Einstein showed that the geometry of space responds to energy and can

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The important thing is that distance in space is what determines the strength with which things interact.

the momentum is pushed around by changes in the potential energy, and the position is pushed around by changes in the kinetic energy.