If scale is a physical continuum, then shouldn’t there be situations we must use a cross-scale approach? What sorts of problems might require such a cross-scale approach?
Consider attempting to determine the combined velocity of a small object (on earth) in space. There is the velocity of our galaxy cluster (relative to other clusters), the velocity of our galaxy (relative to other galaxies in our cluster), the velocity of our spinning galaxy, the velocity of our sun relative to other local stars, the velocity of the earth around our sun, the velocity of the spinning earth. All these velocities are large scale and apply to all smaller objects on the earth. From here we need to add in ‘human local’ velocities, such as the train we are riding in, the velocity of us walking in the train, the velocity of the ball we are bouncing in the train. Then we would need to shift to the velocity of the surface of the tennis ball being bounced, the movement of the hair on the surface of the tennis ball. Then onto the ‘macromolecule’ that is part of the hair on the tennis ball, then on to the movement of atoms in the macromolecule, the movement of an electron in one atom of the macromolecule.
To address this problem:
- How can we determine all these velocities in a single 3-D model of space?
- How can we measure all these velocities using our current tools of scale-dependent units of measure?
- If, as current physics proclaims, all actions derive from the very small, how can all these velocities be derived from the actions of sub-atomic particles?
Note that we must break down this problem by the levels of scale. We need to start with the ‘most significant’ velocities first – the largest first. We are going to have difficulties adding the velocities across such a large expanse of units of scale.
How can this problem be addressed using our current 3-D model of space (which does not include scale as a position locator of objects within it)? How can we understand ‘time’ at all these different scale units of measure? How can we be sure it is the same ‘time’ at all levels of scale – and that it is not influenced by one or the other large (or small) scale velocities? Can this ‘time’ be captured by a single dimension of space-time?