Physics Essays Vol. 23, pp. 242-247 (2010)
This essay is an attempted to address, from a modern perspective, the motion of a particle. Quantum mechanically, motion consists of a series of localizations due to repeated interactions that, taken close to the limit of the continuum, yields a world-line. If a force acts on the particle, its probability distribution is accordingly modified. This must also be true for macroscopic objects, although now the description is far more complicated by the structure of matter and associated surface physics.
Quantum Mechanics and Motion-A Modern Perspective
Emergent behavior that appears at a given level of organization may be characterized as arising from an organizationally lower level in such a way that it transcends a mere increase in the behavioral degree of complexity. It is therefore to be distinguished from systems exhibiting chaotic behavior, for example, which are deterministic but unpredictable because of an exponential dependence on initial conditions. In emergent phenomena, higher levels of organization are not determined by lowerlevels of organization; or, more colloquially, emergent behavior is often said to be “greater than the sum of the parts”. The concept plays an especially important but contentious role in the biological sciences. This essay is intended to demystify at least some aspects of the mystery of emergence.
(This is an updated and expanded version of the original post with some portions rewritten to enhance clarity.)