Indeterminism in Man
SUMMARY: The last several chapters have shown that microscopicsized phenomena, as described by Quantum Mechanics in terms of the customary mechanical observables--position, momentum, energy, time, etc.--are indeterministic for individual events. However when large numbers of micro-entities combine to produce some effect, this quantum indeterminism is swallowed up in a statistically predictable behaviour; and, at the macroscopic level, Classical Mechanics, an entirely deterministic theory, has proven itself to be the most successful universal theory of historical time judged by its ability to make verifiable predictions.
As an example of this, take the familiar phenomenon of a cube of sugar dissolving and diffusing throughout a cup of hot coffee. If one wanted to study this event in detail it would be necessary to follow the behaviour of each molecule as it moved through the potential field set up by all the other molecules. The complete analysis of this would require the solution of a set of simultaneous Quantum Mechanical equations, and, in consequence, each of the individual motions would be subject to the usual quantum uncertainty, and only a probabilistic description would be possible. Finally, the macroscopic density of the sugar would be calculated by a complicated statistical summation over all the molecules and all their individual possible locations. Now in fact no one would ever attempt, or need, to handle the problem in this way. The motion of individual molecules is ignored, and the diffusion is described by working directly with the solute density 'ρ'. (This is defined as the number of grams of solute per unit volume of solvent, in this case grams of sugar per cubic centimetre of coffee.) To find 'ρ' as a function of position and time we solve the diffusion equation of classical physics (7.1). In non-mathematical terms this equation states that the rate at which the amount of substance inside a given boundary is changing is equal to the rate of diffusion of outside substance over the boundary