Energy Transformation and Flow; A Theory of Evolution

Scientific Paper
Title	Energy Transformation and Flow; A Theory of Evolution
Read in full	Link to paper
Author(s)	Richard Oldani
Keywords	thermodynamics, evolution, spontaneous emission
Published	2006
Journal	Physics Essays
Volume	19
Number	4
No. of pages	11

Read the full paper here

Abstract

Spontaneous emission by an atomic oscillator is defined in terms of energy transformation and flow. The description is expanded to include dissipative systems by introducing energy equipartition as a property of the flow. The Feigenbaum constant is derived quantum mechanically. A law of flow equivalent to the laws of thermodynamics is formulated for bounded systems and is then applied to living organisms. The common genetic structure of cells is seen as fulfilling the structural requirement of equipartition while the tendency of the organism towards an equilibrium state, or homeostasis, describes the equipartitioned flow. Since energy flow increases by superposition evolution may be interpreted as an extended series of spontaneous energy transformations from external to internal modes. Finally evolutionary theory is used heuristically to define a universal law of energy flow and to introduce time as a quantum mechanical variable. Two experimental tests are proposed.

Overview

Richard Oldani's paper is an attempt to run a single explanatory scheme from the atom to the fossil record. Its organising move is a change of coordinates: instead of describing physical systems in the canonical position–momentum pair (q,p), Oldani proposes to describe them in the energy–time pair (E,t), on the ground that "energy flow" is a variable common to an atomic oscillator, a convecting fluid, a neuron and a species. Once that substitution is made, he argues, the material structures supporting the flow "can for practical purposes be ignored", and phenomena that look unrelated turn out to have the same shape.

The paper's claim to novelty is that this shape is the shape of spontaneous emission as Oldani had earlier described it (Physics Essays 18, 3, 2005): a slow, continuous, reversible build-up of field energy on a bound electron, terminated by an abrupt, irreversible quantization in which a photon is released. Applied to biology, this becomes long stasis punctuated by sudden saltation. The departure from the mainstream is therefore twofold — against kinetic theory as the right description of energy flow in complex systems, and against Darwinian natural selection as the driver of evolutionary change, which Oldani demotes to "observables that reflect the presence of a simpler force operating at a deeper level."

The argument

Spontaneous emission as the template

Oldani's emission model differs from both the quantum and the semiclassical accounts. Excitation is a continuous classical process in which n independently oscillating wave trains superpose randomly at the bound electron; if sufficient field intensity is reached the electron rises to a higher state along a continuous trajectory, and a photon is then released. Excitation is conservative, reversible and exact; quantization is abrupt, irreversible and governed by the uncertainty principle, here written as ΔE·Δt ≥ h. Because the fields give an exact description, Oldani reinterprets the uncertainty relation: ΔE is not a spectral line width but the energy of the emitted photon, and Δt is its period.

A second uncertainty relation for flow

For dissipative systems Oldani posits a relation of the same form, his equation 2), Ė·τ = H, where Ė is the equipartitioned flow, τ the periodicity of the flow, and H "a universal constant relating flow and periodicity similar to the way Planck's constant relates energy and oscillatory period."

Alongside it he sets a "law of equipartitioned flow": as energy flows through a system it distributes itself uniformly over all available states, beginning with the lowest, "the way a liquid fills a container." He concedes at once that this law "cannot be expressed mathematically in any useful way because energy is both diffuse and indeterminate", but claims it as superior to kinetic theory because it packages the second law, equipartition and ergodicity in one statement, and because it does not distinguish discrete from continuous states.

The Feigenbaum constant

The worked illustration is Rayleigh–Bénard convection in liquid helium (Libchaber): a temperature difference of 0.001 °C across a box produces cylindrical convection rolls; increasing the flow produces a wobble, then period doubling, with the bifurcation sequence governed by the Feigenbaum constant. Oldani "decretizes" the flow by dividing total flow by the flow per period, ΣĖ/Ė_τ with Ė_τ = Ė/τ, calls the result Q (a footnote identifies it with the "quality factor"), and writes for three successive bifurcations his equation 3):

F(Ė_n) = (Q_n−1 − Q_n−2) / (Q_n − Q_n−1)

which he offers as "the quantum mechanical interpretation of Feigenbaum's universal constant" — the quantization of a rate being itself a rate, "the rate of the system's degeneration into chaos."

From flow to organisms

Life forms are treated as bounded, open flows in dynamic equilibrium with the environment, and their internal organs "assumed not to have independent influence on energy flow." Neurons are held to follow the emission pattern closely — a building flow ending in sudden discharge — and their slow signalling (a maximum of 120 m/s, poor compared with electrical conduction) is read as evidence that the cell, not the organism, is the fundamental unit of energy production. From this Oldani infers that equipartition requires all cells to have the same energy-producing capacity, and hence that the shared genome exists to permit equipartition: genes are "not templates or patterns, but conduits", while homeostasis maintains and restores the equipartitioned flow.

Evolution, the Cambrian and punctuated equilibrium

Evolution is then "a transformation of energy from external to internal modes." Internal energy rises generation on generation until structure can no longer support it; an irreversible discharge in the germ cells changes genetic content, producing saltation. Cell division is treated as the biological analogue of period doubling, both doubling the flow. The Cambrian explosion is explained by the acquisition of axial or bilateral symmetry, taken as the external sign of an internal energy gradient driven by an external source; the Ediacaran rangeomorphs, with their asymmetric, fractal, modular growth, are read as linear rather than global flow, lacking homeostatic regulation.

Punctuated equilibrium follows from equation 1). Because absorbed and discharged energy are equal, a long stasis implies a large ΔE and hence a short transition Δt — so Cambrian transitional fossils "are necessarily missing", whereas the well-populated Archaeopteryx series implies a small ΔE, since flight involves structural change "that ha[s] little to do with internal energy flow." Extended to cosmology, galaxies become dissipative structures and the universe escapes heat death through increases of the integrated flow. Three tests are proposed, including that complex systems release energy more slowly than they absorb it, and that play and cultural activity correlate positively with birth rate.

Assessment

What is genuinely attractive here is the diagnosis rather than the theory. Oldani is right that kinetic theory, built on elastic collisions of structureless spheres under large temperature gradients, is a poor tool for systems conducting small flows through asymmetric molecules with rotational and vibrational modes; right that the atomic oscillator is locally anti-entropic, converting diffuse field energy into a localised quantum; and right that the stasis–saltation pattern in the fossil record is formally similar to that. Choosing (E,t) as the working pair is a legitimate and interesting framing, and the paper is unusually honest about its own limits, admitting that the flow law has no useful mathematical expression and that measuring a complex system's energy flow is the hardest part of every test he proposes.

The difficulties begin with the load-bearing equations, and they are checkable. Equation 2) is not dimensionally analogous to equation 1). Ė is a flow — energy per unit time — so Ė·τ has the dimensions of energy, whereas E·Δt in the uncertainty relation has the dimensions of action. The constant H is therefore an energy, not a second Planck constant, and the stated similarity "to the way Planck's constant relates energy and oscillatory period" does not survive a unit check. Equation 1) itself is written with h where the Heisenberg relation carries ħ/2 = h/4π; Oldani's own reading rescues it, because for a photon E·τ = hν·(1/ν) = h identically — but that is the point: on his interpretation the relation is an identity satisfied by construction, not a constraint that could be violated, and it cannot then be used to derive a prediction about anything.

The Feigenbaum claim is the paper's most conspicuous overstatement, and it does not hold up. Feigenbaum's δ is defined as the limit of exactly the ratio Oldani writes, taken over successive values of the bifurcation control parameter. Equation 3) substitutes Q for that parameter and takes no limit at all — indeed F is written as a function of Ė_n, so it is not a constant. The number 4.6692… never appears; nothing is computed; and the ratio reproduces δ only if Q happens to be an affine function of the control parameter, which is asserted nowhere. Feigenbaum universality is a theorem about the renormalisation of unimodal maps, proved independently of quantum mechanics; re-labelling its defining ratio does not make it a quantum mechanical result. The abstract's "the Feigenbaum constant is derived quantum mechanically" therefore claims considerably more than the text delivers.

Several biological steps are asserted rather than argued. That internal organs have no independent influence on energy flow, that all cells must have identical energy-producing capacity, that genes are conduits rather than templates, and that external symmetry reflects an internal energy gradient are each stated without derivation from equations 1)–3) and without supporting measurement. The one place where the framework does make a sharp prediction — the fossil record — is arranged so that it cannot fail: a long stasis explains missing transitional forms, and a well-documented transitional series explains a small energy change. Both outcomes confirm the same relation, which is the signature of an unfalsifiable scheme. The citation of Rohde and Muller (Nature 434, 208, 2005) also appears to misread its source: 36,380 is the number of marine genera in the compendium they analysed, not a count of documented saltation and extinction events.

Finally, the treatment of Darwin is weaker than it needs to be. The "which survive? the fittest / which are fittest? those that survive" objection is a nineteenth-century tautology charge that modern population genetics answers by defining fitness independently, as expected reproductive contribution measurable in advance of the outcome; and Oldani's own replacement — fitness as internal energy, indexed by play and cultural activity — is at present unmeasurable in exactly the way he complains natural selection is uninformative. Read not as a derivation but as a programme, the paper's real contribution is the proposal that energy flow be measured across levels of organisation; that measurement, not the equations, is what would decide it.

See also

• Richard Oldani
• Entropy
• Thermodynamics
• Uncertainty Principle
• Planck Constant
• Quantum mechanics
• Arrow of Time
• Energy