Toward a General Theory of Process

Would the Planck length and the cosmological limit be fixed measurables, be single-valued, that is, if they were to be measured on a Koch curve? John A. Wheeler’s superspace is something of a modular concept, in that it is composed of 3-geometries. A. D. Sakharov’s model of the universe is something of a modular concept, in that it is composed of 4-dimensional spaces joined in mirrored pairs of collapse/anti-collapse sheets. Neither of these two theories have explicitly challenged single-valuedness of Planck length or cosmological limit. Perhaps this is because they are not built on the notion of fractal dimensions.

Strangely enough, it was not in high energy particle physics or cosmology that single-valuedness of Planck’s constant (related to the Planck length) was first called into question, but in molecular biology. In 1969, James Isaacs and John Lamb found themselves arguing molecular indeterminacy on the basis of research undertaken at Johns Hopkins University School of Medicine (Complementarity in Biology: Quantization of Molecular Motion, The Johns Hopkins Press). The primary thesis of this unjustly neglected monograph is that Heisenberg’s indeterminacy principle applies to the variables describing molecular motion in living systems at normal pressures and temperatures. This hypothesis is justified, in the main, by arguing that the actual conditions in biological organisms do not fulfill the minimum prerequisites for assuming applicability of the central limit theorem of probability theory or a Gaussian (normal) distribution of the variables of molecular dynamics involved in an indeterminacy relation. This challenge to the statistical thermodynamics of molecular biology necessitates recourse to quantum principles in explaining emergent phenomena of organisms. Many properties of living systems poorly explained with deterministic notions of molecular motion, it is argued, become elegantly comprehensible by following through the implications of molecular indeterminacy.

Notwithstanding the enormous amount of data Isaacs and Lamb marshal in support of their thesis, it appears they conflate two independent arguments in accounting for the origins of molecular indeterminacy. This does not negate the value of their analysis or conclusions, but does call for some clarification and expansion of theory. The two conflated arguments are given as follows.

(I) This argument is stated explicitly and clearly, thus:

[a] in physical systems at atomic spacetime scales, distribution of conjugate variables of motion involved in an uncertainty relation is Gaussian, thereby yielding an equality relation with the uncertainty product;

[b] in living systems at molecular spacetime scales, distribution of conjugate variables of motion involved in an uncertainty relation is non-Gaussian, thereby yielding an inequality relation with the uncertainty product;

[c] since the conjugate variables of motion involved in an uncertainty relation cannot, by definition, be handled in a deterministic fashion, and since in living systems such variables of molecular motion cannot be assumed to be in Gaussian distribution, the molecular motion in living systems must be an expression of an enlarged indeterminacy;

[d] to reestablish equality of the uncertainty relation under non-Gaussian conditions, the uncertainty product must be multiplied by a factor of Î;

[e] absent knowledge of the value of factor Î for living systems, a plausibility argument, based on the conditions in living systems, is made to the effect that the value of factor Î is large enough to encompass in uncertainty molecular motions of living systems.
(II) This argument is tacitly embedded in the first. The lack of infinite divisibility of spacetime (intimately involved with Cantor’s “continuum hypothesis” explored by Paul Cohen) is sufficiently all encompassing as to be significant for instrumental intervention at molecular spacetime scales, thus making measurements of conjugate variables of motion, involved in an uncertainty relation at those scales, indeterminate.

The second argument is not made with sufficient explicitness or clarity. It is partly hidden in the concluding “then-must” predicate of point [c], above, and partly hidden in the attempt of the plausibility argument of point [e], above, to establish a sense of the magnitude of factor Î. Argument (II) must be made fully explicit and completely independent of argument (I), because, after all, the raison d’ être of indeterminacy is instrumental intervention having effects of sufficient magnitude on the system being measured, such that the measured system is consequentially disturbed. Multiplying the uncertainty product by a factor of Î is equivalent to scaling Planck’s constant, h, to the spacetime scale of molecular motion. This is the reverse of seeking a classical analogy for Dirac’s spin coordinate by allowing h to tend to zero; here the value of h jumps by a step-function (determined by relativistic limits associated with each limited spacetime domain considered) to a maximal value. Justification of this scaling of h must be given independently in argument (II); then, and only then, can argument (I) validly be used to establish a theoretical context for experimental determination of the value of Î.

The breakaway notion of Planck’s radiation law for blackbodies was realization that prediction does not require a description of the spatial field; characterization of the properties of an elemental oscillator is sufficient. This shifts the emphasis decisively from analysis of spatial ordering to that of temporal ordering. Quantum mechanics is a theory of “clocks within clocks within clocks” (David Bohm, Wholeness and the Implicate Order, 1983). Isaacs and Lamb touch upon this notion in their discussion of what they call “retroversion”, the fact that temporal and spatial limitations occur in interconnections between units forming subassemblies of a process. The issue of modular spacetime, or the formation of limited spacetime domains, is intimately involved with that of subsystem-system-supersystem partitioning in dynamic systems. Cascade theory of tornado genesis and the Paine-Pensinger model of the quantum wave properties of the DNA molecule address this subject by allowing limiting values of dynamic variables (relativity theory) to dictate quantization (quantum mechanics). The three orders of active temporal operators (“clocks within clocks within clocks”) in the canonical equation of the superconductant DNA model operate only at limiting values established by the phase velocity (and phase acceleration and time rate of change of acceleration) of those waves accomplishing energy and momentum transfer with perfect efficiency. This phase velocity is a limiting velocity relative to its given limited spacetime domain (no waves within the given domain may exceed this speed limit), just as the much faster velocity of light is a limiting velocity relative to its much larger limited spacetime domain, the universe at large. The fundamental concepts of cascade theory, expounded in the present paper, constitute the independent argument (II) spoken of above as being required to fully justify the conclusions of Isaacs and Lamb.

The value of Î is derivable from the phase velocity of the coherent waves generated by DNA. This phase velocity is a limiting velocity scaled to the limited spacetime domain of the living unit. The similarly appropriately scaled value of Planck’s constant, h, can be deduced from this limiting velocity. In this manner, Î and similar factors will disappear from the equations descriptive of the system and be replaced by appropriately scaled values of (multivalued) fundamental constants. The phase velocities of the coherent waves emitted by various histological types of DNA molecules can be derived from experimental observations of changing transition temperatures in response to changing ambient electromagnetic field parameters, as given in the equations of Paine and Pensinger’s superconductant DNA model.

A. Yu Kasumov, of the Institute of Bio-organic Chemistry and the Institute of Microelectronics Technology and High Purity Materials, Russian Academy of Sciences, presented a paper at the Nanotubes and Nanostructures 2000 Conference (2-4 October, 2000) on “Proximity-Induced Superconductivity in DNA” (in press, Science, early 2001). The involved experiments grew out of Kasumov’s research on supercurrents in nanotubes of self-assembled carbon. This DNA superconductivity is very low-temperature BCS-type superconductivity, it seems, but still strong support for the notion that DNA is superconductant at physiological temperatures. The involved experiments appear a variation on pendant-type-electron-donor experiments on conductivity of DNA. In the Paine-Pensinger model of DNA superconductivity, the superconductant process is driven, not by an electron pump, but by radiation exchange and exquisite timing processes orchestrated by Relativity physics, which surely are short-circuited by the modified state of DNA in both metallic-pendant and metallic-intercalator style DNA-conductivity experiments. Both of these classes of experiments remain substantially predicated on the hard-little-ball hitting hard-little-ball type idea of charge transfer, which notion completely ignores implications of the Aspect Experiments on nonlocality. But still, demonstrating that DNA can be superconductant at some temperature, however low, is a very big step.