Excerpt: Wholeness and the Implicit Order by David Bohm
Order, Measure and Structure in Classical Physics
As has already been indicated in general terms, classical physics implies a certain basic descriptive order and measure. This may be characterized as the use of certain Cartesian coordinates and by the notion of universal and absolute order of time, independent of that of space. This further implies the absolute character of what may be called Euclidean order and measure (i.e., that characteristic of Euclidean geometry). With this order and measure, certain structures are possible. In essence, these are based on the quasi-rigid body, considered as a constituent element. The general characteristic of classical structure is just the analysability of everything into separate parts, which are either small, quasirigid bodies, or their ultimate idealization as extensionless particles. As pointed out earlier, these parts are considered to be working together in interaction (as in a machine).
The laws of physics, then, express the reason or ratio in the movements of all the parts, in the sense that the law relates the movement of each part to the configuration of all the other parts. This law is deterministic in form, in that the only contingent features of a system are the initial positions and velocities of all its parts. It is also causal, in that any external disturbance can be treated as a cause, which produces a specifiable effect that can in principle be propagated to every part of the system.
With the discovery of Brownian motion, one obtained phenomena that at first sight seemed to call the whole classical scheme of order and measure into question, for movements were discovered which were what have been called here ‘order of unlimited degree’, not determined by a few steps (e.g., initial positions and velocities). However, this was explained by supposing that whenever we have Brownian motion this is due to very complex impacts from smaller particles or from randomly fluctuating fields. It is then further supposed that when these additional particles and fields are taken into account, the total law will be deterministic. In this way, classical notions of order and measure can be adapted, so as to accommodate Brownian motion, which would at least on the face of the matter seem to require description in terms of a very different order and measure.
The possibility of such adaptation evidently depends, however, on an assumption. Indeed, even if we can trace some kinds of Brownian motion (e.g. of smoke particles) back to impacts of smaller particles (atoms), this does not prove that the laws are ultimately of the classical, deterministic kind – for it is always possible to suppose that basically all movements are to be described from the very outset as Brownian motion (so that the apparently continuous orbits of large objects such as planets would only be approximations to an actually Brownian type of path). Indeed, mathematicians (notably Wiener) have both implicitly and explicitly worked in terms of Brownian motion as a basic description (not explained as a result of impacts of finer particles). Such an idea would in effect bring in a new kind of
order and measure. If it were pursued seriously, this would imply a change of possible structures that would perhaps be as great as that implied by the change from Ptolemaic epicycles to Newtonian equations of motion. Actually, this line was not seriously pursued in classical physics. Nevertheless, as we shall see later, it may be useful to give some attention to it, to obtain a new insight into the possible limits of relevance of the theory of relativity, as well as into the relationship between relativity and quantum theory.
