Part II


The Evolution of Physical and Biological Complexity

( January 2008)



Preface:    The remarkable ability of the Chaplygin/Tangent gas, seen as a universal field (UF), to unify the forces of physics and to offer an explanation for the observed accelerated expansion of the universe has prompted further exploration of its possible use in problems of cosmic and biological evolution.


In Part I, the evolution of the UF itself was explored before and after the Big Bang singularity. The unfolding of our atomic and molecular world of astronomy which originated at the Big Bang was left for this Part II. However, this area has two aspects, one is the expanding material cosmos of atoms and molecules since the Big Bang singularity in which it originated, and the other is the  development of the order and complex variety within this material world, which we call evolution.


The expansion phase of the atomic and molecular cosmos over the first 9 billion years or so has, until recently, been dealt with in cosmology by the general theory of relativity, which has had its difficulties.  These stem from the fact that general relativity (1) has as its basic equation a postulated geometrical space and time (x,y,z,t) field or continuum in which accelerations ( i.e. gravitational force) are the results of a geometrical curvature  of the postulated continuum, (2) its dynamical equation of force is a differential equation with no unique solution,  and (3) it  has no equation of state to physically account for the expansion of the cosmos which it is used to describe.


The UF on the contrary is a compressible physical field, whose basic equation is an integral equation of state with a unique solution, and whose expansion is naturally explained. Its force equation likewise stems from an integral  energy equation whose space gradients set up the forces, explains their existence in a physical, instead of a geometrical, way, and unifies them all for the first time.


The world of material molecules and atoms since the Big Bang can be envisaged as a quasi-compressible fluid of atoms and molecules with an equation of state relating pressure, specific volume and temperature. However, the observed cosmos with its galaxies, clusters and immense voids is certainly not a close approximation to an ideal expandable gas, so that this approach is a matter for experts who have a full range of the essential data at hand.  Consequently, for now, instead of treating the cosmology of the post-Big Bang expansion, we shall turn to the development of physical order and complexity and to biological evolution. 


Although progress in the formulation of a satisfactory theory of biological evolution has been punctuated by a series of radical revisions, the thesis that biological complexity has evolved appears to be well established.


Darwin’s original explanatory theory, that this evolution has occurred by a natural selection of chance biological variations passed from one generation to the next, suffered a check when Mendel’s laws of inheritance were re-discovered. Mendel’s obstacle was the fixed inheritance of genetic characteristics, which was further solidified with the discovery of the genes and their DNA/RNA mechanisms. After a considerable time, Darwinism was revived as neo-Darwinism when probabilistic laws of gene combination were introduced, and the proposed evolutionary mechanism became, in effect, gene emergence probability.


However, the basic physics or biophysics of the problem still remained fundamentally unresolved, because the emergence of complexity in nature, such as in the formation of genes, appears to be in opposition to the 2nd law of thermodynamics. In spite of this problem, plausible, but essentially incomplete, theories of automatic emergence of physical complexity skirting the 2nd law have been developed, extended to the emergence of the genes, and a near final solution to the problem of the evolutionary mechanism is now sometimes asserted to have been achieved.


Some serious attempts to reconcile the emergence of complexity with the obstacle of the 2nd law have been made, but these have not won general acceptance. In practice, the 2nd law problem is often just set aside as only a detail, destined to inevitably be resolved in some manner yet unknown.  Detailed analysis of the emergence of physical complexity and its connection with evolutionary biology has been undertaken, but these efforts have lacked any integration with the underlying orderly physical forces that are the dynamism of change. The present situation might, not too unkindly, be characterized as an optimistic expectation that all will eventually be well and that, notwithstanding the 2nd law, biological order will eventually somehow emerge from random physical disorder.


Now, in the last few years, the emergence of the concept of a universal wave and force field (UF), derived from the so-called   Chaplygin/Tangent gas of aeronautics and gas dynamics, has introduced a new level of basic physical order.  This approach has succeeded in unifying the fundamental forces of physics, and so reconciles gravitation, electromagnetism and quantum physics. Based on this standard dynamics and thermodynamics of a compressible fluid medium, orderly force fields pose a fundamental problem for the neo-Darwinian theoretical assertion of a purely probabilistic emergence of physical complexity. This source of basic order in both physics and biology, and its interaction with probability to produce the complex physical and biological reality evolving around us is the subject of this monograph.






1. Introduction


2. The Forces of Nature: A Universal Wave and Force Field (UF) Related to the Chaplygin/Tangent Gas -- a Universal Source of Physical Order


3.  The Emergence of Physical and Chemical Complexity:  A Critical Analysis of the Complexity Theory of  Nicolis and Prigogine

4.  A New Approach to the Emergence and Evolution of Biological Complexity in the Aqueous Environment of the Living Cell.

          4.1 Introduction

          4.2 The Living Cell: An Aqueous Medium

            4.3 The Adiabatic Rupture of Cell Water and the Effect of this Entropy Change on Biochemical and Genetic Reaction Rates

            4.4 Chemical Reactions in the Aqueous Environment of the Living Cell: An Entropy of Liquid Rupture

            4.5 Entropy Increase, the 2nd Law of Thermodynamics and Evolution.

5. Conclusions on Biological Complexity: Do Orderly Forces Acting on Random Kinetic Motions Result in the Emergence of Variety on  a Probabilistic Time Scale?




1. Introduction:   Early  theories of biological evolution, such as those of Buffon, and Lamarck, stressed the obvious morphological and functional adaptation that organisms have to their environment and asserted the inheritability  of acquired adaptations. The theory was descriptive and speculative, but provided no physical mechanism to bring about either the claimed adaptation or its inheritance.


Charles Darwin’s original theory of evolution stressed the role of chance variations in automatically fitting the organism to its environment, followed by the survival of the fittest, and the passing on of this random variation in fitness to the offspring. The theory was factually descriptive, and based on chance, but its simplicity was a better fit to the canon of parsimony than earlier theories.


Mendel’s experimentally-based genetics then emerged to assert the impossibility of inheriting anything other than the genetic endowment. Darwinian chance variations were not inheritable no matter how fit they were. With fixed genes, evolution could not take place.


Neo- Darwinism overcame the Mendelian obstacle by postulating the random or chance emergence of new genetic material, combined with the subsequent non-random probabilistic survival of the genetically most fit population or sub-population. Given a sufficiently large genome or pool of genetic potentialities, the probabilistic emergence of new species would be automatically assured. The theory is quantitative via probability theory once the necessary genome size is somehow generated. The physical origin of the large genome pool is not rigorously addressed; instead the automatic emergence of physical complexity is implied.


A serious attempt to explain the role of entropy and the 2nd law of thermodynamics in biological systems, where it appears to act in opposition to its role in non-living systems, has been made by Brooks and Wiley [1]. These studies have not been widely adopted, but they go directly to the heart of the problem in the search for a physical theory of evolution.


Recent studies by the Prigogine et al. school [2] have endeavored to properly ground the emergence of physical complexity in  physics and chemistry, by studying  the automatic emergence of  complexity from random physical and kinetic motions when the random physical system is thermally stressed or not at equilibrium. This approach properly addresses some of the physics, but fails to  include the role of the basic physical forces involved  – orderly, non-random forces  of gravitation fields, orderly non-random  inertial forces, orderly pressure field forces, etc, etc,  Thus, its assertion that the desired  complexity simply emerges automatically from random kinetic systems is invalid, since it leaves out the role of the  basic, non-random,  physical forces that also participate in bringing about  the new complex order on the observed probabilistic time scale.


In this present study, we shall (1) examine  the role of ordered physical forces arising from the UF  in bringing about physical complexity, (2) examine the physics of the rupture of water -- the aqueous environment of the living cell in which all biological reactions and processes take place, (3) introduce a new entropy of rupture into cell reaction kinetics, which in turn  appears  to be  reflected in the observed logarithmic time scale of evolutionary history, (4) and,  in addition to the role of the 2nd law in evolution, we shall  introduce the possibility of  two additional entropy regimes or entropy orders arising in the Universal Field,

 which appear related to the observed orderly and complex characteristics of  plant and animal life.



2. The Forces of Nature :  The Universal wave and force field (UF) which is related to the Chaplygin/Tangent Gas: a universal source of physical order, waves and forces




2.1. The Forces of Nature

    2.2. A Universal Wave and Force Field (UF) Related to the Chaplygin gas and Tangent  Gas

2.3. Wave Motion in the UF

2.4. The Universal Field (UF) and the Transmission of Transverse Electromagnetic Waves in Space

2.5. Maxwell’s Electromagnetic Waves and the UF

2.6. Gravitational Force and the UF

2.7  The Strong and Weak Nuclear Forces: Strong and Weak Shock Options.

2.8. Summary


2.1 The Forces of Nature:  The four fundamental forces of nature are gravitation, electromagnetic force, and the strong and weak nuclear forces. Other subsidiary or related forces are the intermolecular chemical forces among molecules such as the van der Waals and London forces, the force of surface tension, pressure gradient force  etc. 

The general definition of force is the space gradient of energy, or

F = dE/dx  ( in one dimension )

An equivalent formulation is the dynamic or Newtonian definition of force:

F =m (dv/dt) = ma  (in terms of particle mass m and acceleration a)


In any compressible fluid the force is given by the Euler equation which, for 1-dimensional flow is


∂u/∂t + u ∂u/∂x + v ∂u/∂y +w ∂u/∂z = −(1/ρ) ∂p/∂x                                              


where  p is the pressure, ρ is the specific density and the term on the right hand side is called  the pressure gradient force.


Until the emergence of the UF theory, the concept of force in physics has been compartmentalized. Electromagnetism and the nuclear forces are conceived of as involving some sort of “exchange of particles”. In the case of the electromagnetic force, the particle exchanged is the photon, for nuclear forces the particles are gluons or the Z particle, and so on. For gravity, a “graviton” force particle has been postulated but has never been experimentally detected. In short, attempts to unify the concept of force in physics have, until recently, essentially failed.


The energy gradient definition ( 1) requires a non-uniform region  in a field of energy where the force develops and acts on any material particle at that point.  The relevant point we make here is that a field of energy and its space gradients is an existing orderly physical element. The existing elements are not just the molecular and atomic particles, but also include this force field which acts jointly with them to produce a resulting complex motion. Complexity in such a system thus arises automatically from the physics, but not solely from random kinetic motions of particles; instead it arises from the interaction of the random kinetic motions of the particles and the action of the co-existing orderly force field.


The second or Newtonian definition of force is phenomenological. It accurately describes what happens but does not address the physical origin of the force. When the particle is not accelerating there is no force present, when it does accelerate the force emerges. Newton does not advance any hypothesis here to account for the full nature and origin  of the inertial force that his equation so well describes, any more than he does with his gravitational force  F=m1m2 G/r2 which travels across the cosmos to tie all matter together in orderly cosmic motions.


In addition to the four fundamental forces there are other derivative, well understood forces of nature such as the intermolecular forces which hold molecules together, the pressure gradient force in gases (Euler Equation), the surface tension forces on surfaces of liquids, vapour pressure forces. These are all ordered physical realities. They are not probabilistic in the sense that they sometimes have one value and sometimes another and that only their mean value is of physical significance -- they are always orderly and determinate.


The attempt to unify the various forces in terms of a grand unification theory has occupied physics for generations. While its accomplishment eluded physicists, there was no disagreement on the existence of forces as residing in quantitatively understandable orderly physical fields.  Consequently, any attempt to understand the obvious emergence of physical complexity should therefore take the orderly nature of forces into account and not just focus on the random kinetic aspects of the material world. The emergence of complexity or evolution is thus to be seen as a binary process of probabilistic kinetics plus order.


It has proved possible to unify the forces of nature by postulating a universal wave field (UF) encompassing the Chaplygin/ tangent gas and its unique wave properties. This universal wave field has emerged from cosmology, where the recent discovery of the acceleration in the rate of expansion of the universe has quickly led to the application of a compressible exotic or theoretical fluid called the Chaplygin gas as a universal cosmic energy field [3,4,5,6,7,8,9,10,11].


Subsequent analysis of this exotic cosmic fluid (especially in a version introduced by Tsien [4, 1939]   and von Karman [5, 1941] called the ‘Tangent gas’ in aeronautics ) plus the recent  formulation of an orthogonal, isothermal equation of state for the field  has led to the concept of a Universal Wave field (UF) [ 12 -22}  with its remarkable  wave and force properties.


Since this UF entity is compressible, it will yield a force identical to the Euler force equation already mentioned.



2.2 A Universal Wave and Force Field(UF) Related to the Chaplygin gas and Tangent  Gas


The UF has the following  Equation of state relating the thermodynamic variables p,v, ρ, and T


pρ = ART + B  ; p = −Av +B  


i.e. an adiabatic equation of state- corresponding to the Chaplygin/ tangent gas equation


  pvk  = pv-1 = const. with  k = cp/cv = − 1; n = 2/(k − 1)


and an isothermal equation of state ( which in the case of the  UF is uniquely orthogonal to the adiabatic equation)


p = +Av – B


The UF’s  highly  unusual properties include (1)  the  unique ability among known  fluids or gases to propagate stable waves of any strength, which also (2) uniquely  obey the simple classical  wave equation, (3) a unique ability to support transverse waves, which is something impossible for any other known or theoretical fluid, and which thus provides for the first time a physical basis for the existence of the electromagnetic field and of  electromagnetic waves, and  for the  transfer of radiation through space at the speed of light, (4) the unique ability to carry purely attractive gravitational waves which transfer gravitational force through space, and finally, (5) a unique linear wave field that  may also serves as the  basis for the transfer of quantum information through space at quasi-instantaneous  speeds ( 1023 m/s). .  



Fig. 1. Equations of State in the UF




2.3  Wave Motion in the UF


For simple compressive waves  the exact wave equation [8], expressed in terms of the wave function ψ for amplitude, is


Ñ2 ψ  =( 1/c2) ∂2ψ/∂t2 / [ 1 + Ñψ ](k + 1)                                                           (1 )


or, for one dimensional motion in the x-direction


2ψ //∂x2  = (1/c2) ∂2ψ /∂t2 / [ 1 +    ψ /∂x ](k +1)                                            (1a)


This exact equation means that for material gases ( k > 0) compressive waves are always unstable and grow with time. For very small amplitude waves, however, the term in the denominator of Eqs. 1 and 1a involving ψ /∂x  is approximately unity, and the equation simplifies to becomes the classical wave equation [8]


Ñ2 ψ = (1/c2 )∂2ψ/∂t2                                                                                                                (2)


 which has the general linear solution

ψ = ψ1(x – ct) + ψ2 ( x – ct)                                                            (2a)


In the case of the  UF, however we see that, since k = – 1, the exponent  ( k + 1) in the denominator of Eqs. 1 and 1a  becomes  zero, thereby automatically  reducing them to the simple classical wave equation, but without  the restriction to small amplitudes necessary for molecular gases such as air.


The UF is therefore  truly  unique in that it is automatically exact for waves of any wave amplitude, large or small  and is not limited to infinitesimal waves as is the case with  real gases. The UF is  therefore unique among gases since  it is the only field in which the Classical Wave Equation is strictly valid and which therefore can transmit stable waves, of either condensation or rarefaction, of any amplitude.


So far we have not distinguished between longitudinal and transverse wave motions in the UF. Clearly there is no problem with stable longitudinal waves; they are uniquely supported in the UF, and, moreover, they are not restricted to low amplitude acoustic type waves as in real gases where  k is positive.


We shall now present evidence that transverse waves are also uniquely supported in the UF and that they in fact correspond to Maxwell’s electromagnetic waves.



2.4  The  Universal Field (UF)  and   the Transmission of  Transverse Electromagnetic Waves in Space


We should point out that this is an entirely new concept which emerged only in 2005 after an analysis of the isothermal properties of the exotic cosmic UF.  It has been known for over a century that real gases can only support longitudinal waves, that is waves in which the density variations ±∆ρ are along the direction of wave propagation. Real gases cannot support transverse waves in which the density variations would be transverse to the direction of wave propagation. It was this inability to transmit the transverse waves of light which led to the demise of the old luminiferous ether concept.  We now ask:  What is the evidence for transverse fluid waves  in  the Universal Wave Field (UF ) with its orthogonal adiabatics and isotherms?


We consider a simple pressure pulse ( ±∆p) in the UF as in Fig.6 below:



Figure 6.  A pressure pulse ( ±∆p) in the Orthogonal  Environment of the UF




The initial or static state is designated as po. When the pressure pulse ( +∆p) is imposed from outside in some way, the UF must respond thermodynamically in two completely orthogonal and hence two completely isolated ways, namely, by (1) an adiabatic stable wave along the adiabatic ( TG) and (2) by an isothermal stable pulse along the isotherm (OG).


Spatially, the pressure disturbance ( +∆p)  must propagate in the direction of the initial impulse. But, since the two components of the pulse are orthogonal, they must still remain completely independent and physically  isolated.


 The only way possible for this to take place is for the two mutually orthogonal components to also be transverse to the direction of propagation of the two pressure pulses.  Vectorially, this requires an axial wave vector  V in the direction of propagation ( say z)  with the two pulses orthogonally disposed  in the x-y plane. i.e. TG X  OG = V, which is evocative of the Poynting energy vector  S  = E x B in an electromagnetic wave.







A wave of amplitude ψ traveling in one direction (say along the axis x)  is represented by the unidirectional  wave equation


dψ/dx = 1/c dψ/dt


2.5  Maxwell’s Transverse Electromagnetic Waves and the U.F.


Here, however, in the case of our adiabatic and isothermal pressure pulses,  we have two coupled yet isolated unidirectional waves, and this reminds us of Maxwell’s coupled electromagnetic waves for E and B, as follows


dEy/dx  = (1/c) dB/dt and dBy/dx = (1/c) dH/dt


where c is the speed of light, E is the Electric intensity and B is the coupled magnetic intensity.


Maxwell’s  E and B vectors are also orthogonal to each another and transverse to the direction of positive energy propagation.


Therefore, we have established in outline an orthogonal  two component wave system in the Universal Field (k = −1) which formally corresponds to the E and B, two component, orthogonal system of Maxwell for the  propagation of electromagnetic waves through space in a continuous medium. His equations for E and B are


Curl E  = ∂Ey/∂x = −(1/c) ∂B/∂t                                                                     (3)


Curl B = ∂By/∂x = − (1/c) ∂E/∂t                                                                     (3a)


If we now designate our Tangent gas as A ( for Adiabatic) and our Orthogonal gas as I ( for Isothermal) then our analogous wave equations would be


Curl A = ∂Ay/∂x = − (1/c) ∂I/∂t                                                                    (4)


Curl I = ∂Iy/∂x =  − (1/c) ∂A/∂t                                                                   (4a)


The two systems are formally identical. Therefore, we propose that the medium in which Maxwell’s transverse electromagnetic waves travel through space  is physically identified with a Universal  Compressible Field  (UF) having the above described thermodynamic properties for adiabatic and isothermal motions initiated in the UF by imposed pressure pulses ( presumably by accelerated motions of electric charges.) The compressibility property of the UF now properly accounts on physical grounds for the observed finite wave speed (speed of light c = 3x108 m/s)); moreover, wave motions in this fluid medium are transverse as required by the electromagnetic observations.


It is possible to reduce Maxwell’s two equations UF equations to a symmetrical single wave equation


 2E/∂x2  = (1/c2) ∂2E/∂t2                                                                                                                          (5)


2B/∂x2  = (1/c2) ∂2B/∂t2                                                                        (5a)


and similarly with A and I  for our Adiabatic/Isothermal coupled wave in the UF:


2A/∂x2  = (1/c2) ∂2A/∂t2                                                                         (6)


2I/∂x2  = (1/c2) ∂2I/∂t2                                                                          (6a)



This is not surprising since the UF, with its k = −1 thermodynamic property, is the only compressible fluid which automatically generates the classical wave equation ( Eqn. 2) with its stable, plane waves. The formal agreement of the UF theory with Maxwell is again striking.


Instead of taking our initial external perturbation  as a pressure pulse ( +∆p)   we should  more realistically from the physical standpoint take it to be a density condensation (s = ( ρ – ρo ) / ρo =  +∆ρ/ ρo). This will now result in a positive pressure pulse   (+∆p) appearing in the adiabatic  (TG) phase of the UF but a negative  pressure pulse ( −∆p) in the isothermal or orthogonal perturbation component (OG) . This perturbation is represented by the two orthogonal sets of arrows on the pv diagram, one corresponding to +∆p and the other set corresponding to − ∆p. As the wave progresses the two orthogonal vectors also rotate.





Figure 5. The physical ambiguity which results from a pressure/density perturbation in the Tangent/Orthogonal UF


An oscillating density perturbation ( ±∆ρ) then results in an axial wave vector having two mutually orthogonal components  of a density perturbation wave.   This appears to correspond formally to the Maxwell electromagnetic wave system with its two mutually orthogonal vectors for electric field intensity E and magnetic field intensity B.


We have thus established a case for the compressible UF being a cosmic reality which generates and transmits transverse electromagnetic waves through space.   


These waves with their oscillating space gradient of energy ( i.e. of force) generate the electromagnetic force.


2.6  Gravitational Force and the UF


Here we shall not go into details, but the analysis of the UF waves also provides for the first time a system of exclusively attractive gravitational force as required by Newton’s force equation.


Briefly, in any compressible fluid, force is given by the Euler equation , which for  1-dimensional flow is

F = ∂u/∂t + u ∂u/∂x + v ∂u/∂y +w ∂u/∂z = −(1/ρ) ∂p/∂x

where the term on the right hand side is called  the pressure gradient force.



In any compressible fluid medium, waves set up local transient  pressure forces. Most waves in real gases and fluids are pressure oscillations (±∆p) and so they  do not exert any net directional force on a material object they encounter.  However, in the UF special types of waves can occur which can be either exclusively pressure compressions (+∆p) thereby exerting a net repulsive force on any material body in their path,  or they can be exclusively pressure rarefactions (−∆p)  which would then exert exclusively attractive force.

Consider Figure 6 where a condensation pressure pulse (+∆ρ; +∆ρ)  imposed on the initial static pressure po  in the UF will produce a rarefaction pressure pulse  (−∆ρ)  in the isothermal mode of response. Consequently, a source of pressure condensations will produce a train of isothermal pressure pulses as a response in the UF, and these pulse will travel spherically outwards through space.

When these rarefaction waves eventually impact a material body (mass)  they will exert a net attractive force on it. This mechanism therefore in simple outline is formally equivalent to the force of gravity being produced by a rarefaction pressure gradient force.




Figure 7.  Positive density pulse ( +∆ρ)  of any magnitude produces a quantized gravitational rarefaction pulse (−∆pg )  of constant magnitude pg =6.67 x 10-11 kilopascals


2.7 Strong and Weak Nuclear Forces : Strong and Weak Obligue Shock Options.


We are  not  concerned with nuclear force in this monograph. However, for completeness, we note here that they also are explainable theoretically in compressible fluid flow theory via energy gradients which give rise to the forces ( F = dE/dx ).


There is another interesting compressible flow phenomena, that of shock discontinuities. In strong shocks, the energy gradient in the shock discontinuity is very large, and so the resulting associated force is also very large, and vice versa for the weak shock phenomenon.  Furthermore, in oblique flow past an obstacle, the option may occur for either one or the other shock to occur.  This is depicted in the so called “shock polar” which is  a representation  of these two options in a  two-dimensional flow situation ( in velocity coordinates u and v):




Weak intersection  W




For each inlet Mach number M1 ( = VN1/c), and turning angle of the flow θ, there are two physical  options:

1) the strong shock ( intersection S) with strong compression ratio and large flow  velocity reduction (p2 >> p1;  V2 << V1,  and large spatial energy gradient and strong force (Fs = dE/dx ) , or

2) the weak shock (intersection W, with small pressure rise, small velocity reduction,  small spastial  energy gradient and weak force

Which of the two options occurs depends on the boundary conditions: low back, or downstream, pressure favours the weak shock occurrence; high downstream pressure favours the strong shock.


It is natural to consider whether these two shock options do not also correspond to the strong and weak nuclear forces.  We point out, however, that  the shock discontinuities  in energy gradient ( dE/dx)  which give rise to forces (F = dE/dx ) may  actually have to  reside in condensations of matter/energy  and not in the UF itself.  This is because in the UF the flow Mach number M = v/c may approach, but never reach or exceed unity, and therefore  shock  discontinuities or instabilities cannot occur in it;  the UF  supports only stable wave forms, although they may be of any strength, strong or weak  The details of the nuclear forces do not concern us here.


2.8. Summary


Other minor forces exist, such as those of surface tension, intermolecular force and so on, but they are all variants of the fundamental forces set up by spatial energy gradients or by accelerations in the UF.

It may be worth restating here that this remarkable ability of the UF to unify all the forces of nature arises from its property that changes the sign of k in the equation of state pv k = const. from k = +1 ( ideal isothermal gas)  to k = – 1 ( UF ).  That gives us the UF orthogonal  and tangent  gas equations of state p = +A  +B  and p = −A +B, while the wave equation simply becomes the linear classical wave equation ∆2 ψ = ( 1/c2 )  d2ψ/dt2. from which the forces emerge.  All thus unification and simplification arising from a simple change of sign in the ratio of the specific heats k from positive to negative is truly astonishing.


This then completes our survey of the orderly wave and force field.  We now return to the emergence of complexity in physical systems and then to applications to biological evolution.




3.  The Emergence of Physical and Chemical  Complexity.  A critical analysis of the complexity examples of Nicolis and Prigogine



In their book Exploring Complexity,  Nicolis and Prigogine [2] examine in detail the emergence of physical and chemical complexity from previously  random kinetic systems such as gases and liquids when some source of additional energy is applied to the system in a non-equilibrium  process which they term  stressing of the system.


Various physical forces that are involved are mentioned, intermolecular forces and gravitation in particular, but they are treated by Nicolis and Prigogine simply as “givens” or adjuncts to the random kinetic motions of the atoms and molecules involved. This limited approach to the nature of the forces that cause the ordered motions and interactions leads to overlooking the orderly nature of the ever- present force fields that exist in each of the examples of complexity they present, and so to their faulty conclusion that biological complexity arises solely from random or kinetic physical events.

3.1.  Their first physical example is the ‘ production of an ice crystal’ ( e.g. a dendritic snowflake ) from bulk water. They state that when the water is cooled below the freezing point the snowflake appears and grows.  This, they argue is a simple example of the emergence of a highly ordered state from a disordered state, i. e. complexity emerges automatically upon cooling a liquid below its phase change temperature

Comment: Their first example is presented simply and makes no claim to exactness. However, we should point out that the process of snow flake production from water involves, not bulk water, but disordered water vapour.  At most temperatures, the formation of  crystalline ice from either bulk water or water vapour requires the presence of  a suitable substrate or foreign ice nucleus whose preexisting orderly structure is essential to the initiation of the ice formation. Once nucleated, the type of crystal produced from water vapour is, moreover, not typically a dendrite, but depends instead upon the ambient temperature and pressure of the water vapour field surrounding the growing crystal. The crystal forms may range from needles to plates, to columns, to columns with plates attached to their ends, to  dendrites and to other composite shapes  depending on the ambient temperature and vapour pressure  [24,25,26,27 ].   In addition, heat of sublimation is released in the change of state from vapour to solid ice and this evolved heat must be taken up by the total system as an entropy increase ( i.e a disorder increase).  The vapour flows are governed by the vapour pressure gradient forces arising from the gas density gradients at the points where the water vapour interacts with the emerging crystal shape. The forces are not random and kinetic, but are orderly and determined by the gas law. Thus the resulting ice crystal shapes, once initiated by the pre-structured ice nuclei, are jointly determined by random or kinetic behaviour, by the orderly pressure gradient forces of an ideal gas, by the ambient temperature, and by the crystal energy requirements of the solid state that emerges. (Homogeneous ice nucleation can take place at around -40C but the argument is not essentially altered).

Clearly, the complexity which emerges upon ice crystal formation does not arise automatically from a purely kinetic state, but instead involves both a random kinetic component in the vapour and an orderly field of short range vapour pressure gradient forces around the growing ice crystal.  (The force of gravity in this case acts only indirectly. But it should be remembered that it does produce the orderly ambient pressure field of the atmosphere, including its partial water vapour pressure component at the particular height above ground involved) .


Hence, in this case, complexity emerges, not automatically from kinetic disorder by self-organization as Nicolis and Prigogine concluded, but instead from an interaction of disorder and order. The orderly gravitational force produce an ideal gas field; the orderly vapor pressure gradients surrounding  the random nucleating event produces an orderly snow crystal; the orderly crystal has a random element  or sub-structure which manifests itself in a great variety of  individual variations within the general crystal type  dictated by the prevailing temperature and humidity of the vaporous environment ( 24,25 ].

3.2.’ Convection patterns in thermally disturbed  fluids:  Bénard cells’ 

This case is called by Nicolis and Prigogine  a prototype  of self-organizational  phenomena in physics” and so it will bear our careful analysis.

They discuss a shallow layer of water between two extended top and bottom plates. Left to itself the water rapidly assumes an equilibrium state of uniform temperature or uniform internal kinetic molecular disorder. If the system is now heated from below by a small amount, the injected heat is transferred upward by thermal diffusion, that is by the kinetic molecular motions under the action of the physics of a diffusion wave.  Next, when more strongly heated by a certain critical amount, the temperature stress ∆T from bottom to top will set up a regular pattern of convection (Bénard) cells consisting of rising and descending fluid streams which organize into rotating cells. The direction of rotation seems to be random. This complexity or pattern has thus emerged automatically when the uniform state is stressed thermally and an energy flow is set up. The rising and falling motions are the result of density (buoyancy) differences in the various parcels of water, i.e. from assemblages of molecules large compared with the size of the individual molecules which are still undergoing only random motions. The fluid motions arise from the instability of dense and less dense water parcels side by side at a given level resulting in a descent of the more dense and the rise of the hotter ( less dense) parcels.

Various patterns of convection cells result depending on the boundary conditions and the vertical gradient of teméperature stress. For a sufficiently large heating, turbulent or disordered motions on the macroscopic scale set in.

This type of convective motion is treated in detail in texts on dynamical meteorology under the topics of potential instability and  cumulus dynamics, where  the density differences of perturbed air parcels under a uniform gravitational force  field, combined with differential wind shear variation with height, explain the resulting cloud patterns and motions.

Nicolis and Prigogine conclude from their analysis that:

“ To summarize, we have seen that non-equilibrium ( heating) has enabled the system to avoid the thermal disorder and to transform part of the energy  communicated from the environment into an ordered behavior. We can therefore cay that we have witnessed the birth of complexity. Our complexity achieved is rather modest, nevertheless, it presents characteristics that usually have been ascribed exclusively to biological systems.  More important, far from challenging the laws of physics, complexity appears as an inevitable consequence of these laws when suitable conditions are fulfilled.”

Since the direction of rotation in the cells can be right handed or left handed and is apparently random, they also introduce the notion of chance at this point  and draw a comparison between this and the randomness or chance asserted to exist in biological evolution where mutation is asserted by them to be controlled by chance and natural selection operates.  No physical  mechanism for this connection between physics and biology is offered.

On thermal convection phenomena they postulate (1) an initial uniform , kinetically disordered layer of fluid,  plus (2) a thermal stress imposed on a   boundary which sets up a gravitationally unstable stratification, and then at some critical value this results in ordered convection cells forming;  this they interpret as being the automatic emergence of physical complexity from disorder.

Comment: We have several physical elements here: (1)  a compressible fluid initially uniform and then (2) stressed or disturbed thermally to bring about an unstable stratification when (3)  a suitable gravitational field also exists.  Nicolis and Prigogine miss the importance of the presence and strength of the gravitational field.   It is crucial to the emergence of the particular convection they cite. For example, if the gravitational field is absent, say in a space ship in outer space, no potential motion can exist and no cells can form. Again if the field is too weak, the cells can never reach the critical stress value. Again if the field is not uniformly vertical , but is  converging or diverging, an entirely different complexity pattern and motion emerges. This specifically orderly gravitational field element is central to the existence and nature of the convection cell phenomenon, The phenomenon is therefore the physical result of the interplay of random kinetic molecular motions, ordered by gravity into an orderly pressure field (pressure of the fluid) plus the introduction of an asymmetrical temperature pulse, plus the action of an orderly gravitational buoyancy force field. The resulting complex behaviour then emerges, not from chance as they assert , but from the interplay of random or chance, probability laws, induced asymmetry and an ordered force field.

Thus, the Benard and convection cell phenomenon in their example is not one of emergence of complexity and order from physical randomness alone;  instead, it is a complex physical interaction of factors, a stressed physical disorder plus an orderly physical force field. Physical complexity does not arise solely from disorder  but from an interaction of disorder and imposed order. The  Nicolis and Prigogine “prototype of self organization phenomena in physics”  example is fundamentally flawed and incomplete  as a foundation for their emergence of physical complexity thesis.

(Properly formulated, however, the Bénard cell  example does show central  features of the emergence of physical  complexity in the physical world. Thus, they have chosen the proper example, even although it does not support their conclusions) .

3. Self Organization Phenomena in Chemistry:  The Belousov-Zhabotinski  (BZ) Reaction’

Nicolis and Prigogine consider  the state of equilibrium of any chemical reaction  reached when  two reactants produce a third chemical  substance, or more typically two more substances

A + B →  C + D and the reverse reaction

C  + D → A + B

They then point out that, when certain of these reactions are disturbed or suddenly  moved far from equilibrium, quite unexpected results are obtained

They then  cite  the BZ ( Belousov- Zhabotinski)  reaction. For example, a solution of cerium sulfite Ce2SO4, malonic acid CH2(COOH)2 and potassium bromate KBrO3 , in sulfuric acid, with  an excess of Ce4+ ions gives a pale yellow colour, while an excess of Ce3+m ions gives no colour  at all.

If now the reaction is carried out with stirring, several quite different types of behaviour are observed, namely oscillatory or clock-like behaviour of alternate colour and absence of colour, and chaos or turbulence.  

If the reaction is carried out without stirring, orderly propagating wave fronts bring about the formation of spatial coloured spirals and spatial target patterns.

They then cite this behaviour as exemplifying the emergence of complexity from purely random or chance motions.


In their analysis of the B-Z chemical reaction  Nicolis and Prigogine fail to discuss the  actual forces involved.  In chemical combination processes such as chemical reactions  the relevant forces are intermolecular.  These are Van der Waals forces arising from chemical dipoles existing in the asymmetrical  atoms and molecules.  It is these intermolecular forces which act to hold the various reacting  chemical species or molecules  together to form new chemical reaction products once they succeed in colliding with sufficient energy  and entropy of activation.  Without these forces of attraction, the molecules would simply collide and rebound kinetically and randomly  as in a gas or liquid without combining at all.

However we have shown that all forces are orderly and arise from ordered deterministic force (linear and  non-linear) and so  their thesis that complexity is the automatic emergence of order, and pattern  from random or chance subsystems alone is incorrect.

[Note. Later in Section 4.3 we discuss  the entropy change in liquid ruptures that  occur during reactions in solution and which are intimately connected with chemical reaction kinetics. They arise from ordered forces in a compressible medium, and have a key role  in determining the rates of the chemical reactions; they are not described here as they are  not essential to the present example].   

3.4.Surface Tension Induced Phenomena in Materials Science’

Here they mention interfacial phenomena such as droplet formation and  interfacial flows as examples of complexity emerging spontaneously from physical uniformity, but give no analysis and do not discuss the force of surface tension which again is ordered and not random..

3,5. ‘Cooperative phenomena induced by electromagnetic fields: electrical circuits, lasers, optical bi-stability’

The example offered here is the action of a coherent electromagnetic field ( a laser beam) injected into a resonant cavity  filled with a suitable light absorbing medium. Under certain conditions the behaviour becomes bistable and can act as on optical switch. The behaviour is complex and non linear.

Comment:  While the behaviour is complex, it is not the result of any spontaneous emergence of complexity from a non-complex or random predecessor state. Rather it is the result of a random (uniform) medium being acted upon by a highly-ordered electromagnetic field force.

The motions and forces in the e/m field are highly ordered. They are given by the Maxwell electromagnetic wave equations


Curl E  = ∂Ey/∂x = −(1/c) ∂B/∂t

Curl B = ∂By/∂x = − (1/c) ∂E/∂t                                                                    

Consequently, complexity arising in these systems must also reflect these highly ordered waves and their forces. It can still properly  be called self-organization, because it is an entirely  physical process, but it is not a chance mechanism. As we have seen in Section 2, the electromagnetic force arises from the occurrence of transverse waves in the UF, the fundamental  field of physical order.

3.6. ‘Complexity in  Biological Systems’

Here they state, “ Being convinced by now that ordinary physico-chemical systems can show complex behaviour presenting many of the characteristics usually ascribed to life …” They then describe in very general terms a few examples of biological systems.

This appears to be a greatly simplified claim. It might be more accurate to say “presenting some of the most elementary complex characteristics of living systems.”

Of course since biological systems undergo the same physical and chemical processes as do non-living systems, it is only natural to suspect that they also exhibit  the same rudimentary complex characteristics that arise in non-living systems. The problem is not that biological systems are not as  physical  as non-living systems,  but that they are so outwardly different from physical systems, and that we cannot presently explain why this  is so in the necessary detail.  In particular, so far as entropy flow is concerned, biological systems appear to violate the 2nd law. 

3.7.  Complexity at the Planetary and Cosmic Scale’

This is an interesting listing of complexity of physical  events but the discussion is never at the level of the physical processes that occur. While it is open to an analysis that would include the  details of the forces involved, it is not essential for our purposes and  is set aside for some possible future exploration.

3.8. ‘The mathematical theory of complexity’. The bulk of the Nicolis and Prigogine analysis goes on to deal in some depth, with the mathematical theory of complexity, chaos and randomness. This will be very useful once the necessary clarification of the role of orderly forces that we are recommending is completed, so as to provide a formulation of a more complete theory of complexity, both physical and biological.

3.9 Conclusions on Physical Complexity

The general process under study is the action of fields of force on material particles (atoms and molecules) and on material assemblages of matter (gases, liquids and solids). In the absence of external force fields, the particles undergo random or purely kinetic motions.  When orderly field forces are present they interact with the kinetic field and a composite pattern of order or complexity then emerges from the random chaos. It is our thesis that this binary, composite character of complexity must be considered in any account of the evolution of the physical universe and the biological world.

It should perhaps be noted in addition, that, with all physical force apparently arising from as universal field UF, this same field  is  uniquely orderly:   (1) It is the only  wave field that obeys the linear classical wave equation;  (2) it alone supports and transfers stable waves of any amplitude; (3) it alone supports waves of both compression and rarefaction;  (4) it alone accounts for the forces of nature and uniquely unifies them; (5) it alone supports transverse electromagnetic waves in space.  Those unfamiliar with gas dynamics, acoustics and compressible flow may not fully realize how astonishing this all really is, but in fact, apart from the UF ( i.e. the Chaplygin/Tangent gas)  in  the physical world no kinetic molecular gas or compressible fluid can support  stable linear waves of any finite amplitude whatever. All gases or compressible fields other than the UF are non-linear, unstable and tend towards shock discontinuities.   If then, a unique orderly, stable, linear UF wave and force field underlies all the molecular physical world, and is the source of all its forces, then  the proposition that complexity arises automatically and solely from molecular disorder and stress energy is untenable.

Many other physical interactions of force and kinetic interaction are of interest and remain to be studied.  In the meantime we turn to biological complexity.


4.  A New Approach to the Emergence and Evolution of Biological Complexity in the Aqueous Environment  of the Living Cell  Involving an Entropy Rate  Factor  7N


4.1 Introduction   Up to this point, we have argued that complexity in the physical world results from an interplay of two  elements, namely, random or kinetic elements on the one hand, and orderly forces on the other. Complexity is thus a binary physical process. In the following approach to explaining complexity in the biological world of living organisms, we shall cite  these same two physical elements and their interaction as agents in bringing about the observed complexity.


We examine biological processes and evolution within the basic living cell.  We concentrate on the physical forces that must be present to operate the metabolism of the living cell, to operate on the proteins and genes in the body cells so as to enable cell growth, the transmission of the organizing instructions to the cell component parts, and to operate on and occasionally to mutate or change the genes so as to transmit the biological integral forms from one generation to the next while still allowing for emergent change or evolution.. 


Clearly this approach is different from that of neo-Darwinian population genetics, which offers little on the physical processes underlying the emergence of the gene forms themselves and focuses mainly on the results of various probabilistic combinations within the given, already existing, very large gene pool. Physical process involved in conformational protein alteration and gene mutation, while involving probabilistic process, cannot be essentially or exclusively random since they involve orderly forces.


Our new physical approach  also involves a closer look at the aqueous  environment of the living cell.  We look at biological interactions and reactions as taking  place in an aqueous  medium,  that is, as chemical  reactions occurring in suspension or in solution in the cell aqueous medium.


We shall first look at a neglected necessary physical step in any reaction in water, namely the local rupture and removal  of the water films between  reactant molecules in the living cell  so that any collision between molecules can come to completion and allow the reaction to proceed. This new element of cell water rupture is then included in the energy of activation in standard collision theory of chemical reaction kinetics, or in the entropy of activation in the statistical mechanics approach to chemical reaction kinetics.[28]. 


4.2. The Living  Cell: An Aqueous Medium


The living cell is typically quasi-spherical in shape and from 10 to 30 micrometers ( 10-5  to 3 x 10-5 m) in diameter. The cell is surrounded by a cell wall or semi-permeable membrane of lipids about 90 angstroms thick, which serves to isolate the cell from its environment so as to maintain its identity or homoeostatic nature. The cell membrane is reminiscent of the physical prototype of a lipid envelope in water- oil emulsions, or of the monomolecular films of various terpeneoid and essential oils from vegetation that coat atmospheric cloud droplets in most areas of the world.

The aqueous cell medium.  The typical living cell is essentially a water globule, surrounded by a semi-permeable cell wall or membrane, and having in solution or suspension various organic structures, and with a central core of genetic material which directs the cell life, growth and reproduction.  The essentials of life therefore take place in water, so that we must consider the physical properties of water in any biological process or function; it is not simply an inert physical medium.


Furthermore, at the basic physical level, any reaction or interaction in a liquid  must involve the usual elements of (1)  collision energy of activation ∆E and (2) the entropy of activation ∆S , both of which quantities are standard in chemical reaction theory [28].  It is suggested here that this entropy of activation also must include the energy involved in the rupture of the water film around or between the various suspended or dissolved chemical reaction species. That is to say, any liquid film that separates two reactant molecules must first be ruptured and removed before actual collision and subsequent reaction can occur. Only after this rupture has taken place and a ‘void’ has opened up can the chemical /molecular  constituents collide, interact or  reassemble.


The cell must obey the thermodynamics of the physical fields it encloses, in particular this means for biology that the entropy changes in the cell and in particular the direction of such changes must be considered. These may conveniently be summarized on the usual pressure volume diagram of thermodynamics as follows:


(1). Micell or Lipid-covered  Water Droplet ( A Physical Analogue of the Living Cell




Simple ‘cell’ wall

Aqueous with random mineral species in solution

No fixed size. Size is determined by relative humidity of ambient vapour  and surface tension

Minimum interior complexity

Non-living, non-reproducing, i.e. a simple kinetic physical system


Equation of state  has form pvk = const.  (Quadrant I )

Internal de Broglie waves in aqueous fluid

Pressure, specific volume, density, temperature and pressure energy are all positive

Entropy change dS = dQ/T is always positive and the 2nd Law of Thermodynamics holds


This order of entropy change( i.e. the 2nd Law of thermodynamics)  governs  gas dynamics as it impacts on cosmic evolution




(2)  Animal (plant) Cell




 Complex cell wall

          Aqueous with complex inclusions (Nucleus, orgnelles,

          DNA/RNA etc)     

          Cell size 20-30 micrometers

          Great interior complexity

                                             Living and reproducing





 Supports enclosed UFI standing wave forms in Tangent gas and Orthogonal (isothermal) gas

                                                          Eqn. of state: Tangent gas p = −Av +B          (Quadrant I)


 Eqn. of state:  Isothermal (Orthogonal) gas p = +Av −B  


 Entropy change in the Tangent gas,  ds = dQ/T is positive, and 2nd Law holds( i.e. “uniform disorder seeking”)  

 Entropy change in the Isothermal (Orthogonal)  gas is zero, ds = 0/T = 0, ( i.e. “ stability seeking” )  

Pressure positive  (+p)

Specific volume positive (+v)

Specific density positive  (+ρ)  ( i.e.Wave forms are compressive)

Pressure energy is positive ( +pv)




It appears that the entropy change laws in Quadrant I of the p-v thermodynamic diagram would then enter into the nature and direction of plant and  animal evolution as follows:

Quadrant I:   (a) Tangent Gas:  dS = dQ/T is positive ( 2nd law of thermodynamics holds ( “disorder seeking”)

                    (b)  Orthogonal ( Isothermal) Gas: dS = dQ/T = 0 ( “stability seeking” )



Note: There is another entropy condition in the UF , namely that in Quadrant II  dS = − dQ/T, which has very unusual properties apparently matching the human condition.  This is discussed briefly in Section 5 below, and in detail in  Science and the Soul/Body Problem: An Exploratory Reassessment.


4.3 The Adiabatic Rupture of Cell Water and the Effect of this Entropy Change  on the Rate of Biochemical and Genetic Reactions


The process of the formation of microscopic voids or micro- bubbles in a fluid which may lead to its rupture has been intensively studied in the phenomenon of cavitation and bubble formation, and in the reverse process of the homogeneous and heterogeneous nucleation of condensation of  liquid from the vapour [28].


However, with respect to liquid rupture, we must take note of the fact that there is a long-standing major discrepancy between the theoretical and the experimentally observed tensile strengths for all liquids, and especially for the case of water. Recent work has offered a possible solution to this long standing problem by postulating an adiabatic rupture process instead of the usual isothermal one; this new approach has succeeded in a  reconciliation of theory with observation. The new theory is as follows:



Adiabatic rupture as an explanation for the anomalous weak tensile strengths of liquids and solids

Bernard A. Power

 Reviewed Aug. _ Sept. 2007: Revised Oct. 2007

The observed  tensile strengths of liquids and solids are orders of magnitude lower than the theoretical isothermal rupture values. The discrepancy is currently   explained by heterogeneous nucleation of the ruptures in the theory of  nucleation rates. Still, the observations  for water do not agree with current theory.   However, an adiabatic  rupture producing  of voids or bubbles  ( Equation of state pvk = const.) would  give much lower theoretical tensile strengths in agreement with the observations.. The concept should be of interest to materials science, to chemical reaction kinetics in aqueous solution, and so to cell biology and genetics.


1. Introduction

  Theoretical estimates of the  tensile strength of solids and liquids give values of around  3 x 104  to 3 x 105 atm..  However, for  solids, the  experimental values are around 100 times smaller than that, while for  liquids, the observed values are 600 to 1500 times  smaller at  50 to 200 atmospheres (Kittell, 1968; Brennan ,1995), with water being among the very lowest.


 A simple classical derivation (Frenkel, 1955; Brennan 1995)  of the theoretical tensile strengths of solids or liquids considers the fractional volumetric expansion  ratio ∆V/Vo   needed to form the rupturing void, and this then is equated to an average  numerical value of  about 1/3 . Then, since liquids and solids have compressibility moduli K which are about. 105 to 106 atmospheres, we have a  rupture pressure  p(max) = −K(∆V/Vo).  Taking the average 1/3  value for ∆V/Vo ,  the rupture pressure p(max)   then becomes the theoretical 3 x 104  and  3 x 105 atmospheres just mentioned,  far higher than actually observed.


For solids, the discrepancy in tensile strength is usually ascribed to heterogeneous nucleation of rupture at defects such as cracks or dislocations in the lattice (Kittell, 1968).  In the case of liquids, the even larger  discrepancy is  usually explained by invoking the presence of irremovable tiny gas or solid  nuclei within  the liquid,  which act to lower the pressures and tensions needed for mechanical  rupture. Still, there remain discrepancies, and the foreign nuclei explanation, or heterogeneous nucleation process  acting alone, has  appeared somewhat  artificial, especially since the thermal rupture ( boiling)  values do agree more with the theory.



2. Adiabatic cavitation


 The basic mechanical equilibrium equation for the production of a spherical void, or vapour-filled bubble, in a liquid by rupture is usually expressed as a balance of forces inside and outside the spherical incipient void :

      pB  pL  =  ∆pmax  = 2 σ /RC                                                      (1)

 which gives the relationship between  the (negative) rupture pressure ∆p(max), the interfacial surface tension σ, and the rupture radius r. This process is also assumed to take place at the temperature of the bulk liquid, that is to say isothermally.


 The formation of  a bubble  by rupture thus requires a negative pressure ∆p(max)  exceeding  the  tensile strength 2 σ/r  in order to create the spherical void.     However, instead of the isothermal process ( with general form of its  equation of state pv+1 = const.)   which gives those unobserved  high tensile strengths and rupture predictions,  we could conceivably have an adiabatic rupture with pvk = const. A, where k > 1.   With k greater than unity, the adiabatic rupture pressure ∆p(max., adiabatic)  will  always be less than the presently assumed  isothermal rupture pressure.


To see this more clearly consider the following:


The isothernmal bulk modulus or modulus of elasticity for a liquid K is given by

Kis = − v  ∂p/∂v

And the adiabatic modulus is

Kad = − v  ∂p/∂v= k p  where k is the adiabatic exponent or ratio of specific heats cp  /cv


For liquids ( e.g. water )the two moduli have nearly  the same numerical value.


The pressure at the critical point is then  

p(max.) = −Kis (∆V/Vo) and



p(mac.) =  − Kad. (∆V/Vo)


The adiabatic bulk modulus Kad. for water has the value 2.2 x 104 atms.  Table 1 then shows the effect of taking the adiabatic rupture/cavitation mechanism in  water over a range of values of (∆V/Vo) i.e.  (ρ/ ∆ ρ )  and for various values  of the adiabatic exponent k from >1 to 7.. We point out first that V is the reciprocal of the density ρ, and  so we can put . (∆V/Vo)k =  (ρ/ ∆ ρ)k which is more convenient., that is


P(max.) =  − Kad. (∆V/Vo)k = − Kad(ρ/ ∆ ρ)k



The first step   is the conversion of the liquid water in a small volume V to a “gas-like” structure at the critical point, which means a fractional volume expansion of about 0.333 (i.e. the density of water at the critical point drops from 1 to about 0.3333). This initial step obviously requires the injection of a sufficient energy. The rupture pressure  in the new gas-like volume at this critical stage is now  p(mac.) =  − Kad. (∆V/Vo)  = 2.2 x 104 (0.333) = 7326  atm.


The second  step is the adiabatic expansion of the same ‘gas-like’ volume to a larger bubble  volume with  consequent decrease of the pressure. Clearly, for any given expansion ratio, the adiabatic expansion yields a much smaller final rupture pressure than the usual  isothermal rupture model.  For example, in Table 1,  a volume expansion of 1/3   (density ratio  ρ/ ∆ ρ  of  0.333)  yields an isothermal rupture pressure of  7326 atmospheres,  while the adiabatic  expansion at k = 7 has a rupture pressure of only  10.1 atmospheres .(The experimental data also show a definite effect of temperature on the final rupture pressure;  this does not affect the  conclusions reached here, since they are based on comparative values of the isothermal and adiabatic processes at any given initial temperature).



Table 1


Adiabatic rupture pressure  p ( max.)  for water ( Kad. = 2.2x104 )  for various assumed values of density change ratio (ρ/ ∆ ρ)



Rupture pressure  (p ( max.)  ( p = KAd. (ρ/ ∆ ρ)k) 




(ρ/ ∆ ρ)

                        k = 1**            k = 2        k = 3            k = 4         k = 5           k = 6                k = 7


0.1                   3300 atms.       220           22               2.2            0.22            0.022               2.2x10-3

0.20                 4400                880           176             35.2          7.04            1.41                 0.28

0.30                 6600                1980         594             178           53.5            16.0                 4.81

0.3333*           7326                2444         815             272           90.5            30.2                 10.1

0.40                 8800                3520         1408           563            225            90.1                 36

0.5                   11000              5500         2750           1375          688            344                  172

0.6                   13200              7920         4752           2851          1711          1026                616

1                      2.2x104            2.2x104      2.2x104          2.2x104        2.2x104      2.2x104            2.2x104           


*. Density  ratio (ρ/ ∆ ρ) at the critical temperature TC for  water is approximately this value of 0.33, the same value assumed by Frenkel


** Quasi-isothermal


Clearly, the isothermal hypothesis fails to yield  the observed rupture pressures of around 50 -250 atmospheres for water at any assumed density ratio. The adiabatic expansion hypothesis, however, does let the pressure reach the experimentally observed low values. 


What value for k are we then to adopt for pure water ?  At  the critical density expansion ratio  of  0.333, any value of k from k = 4 to k = 6 would encompass the observed ed rupture pressures of  about 250 to 50 atms. However,  it may also be  valuable to revisit the value of k = 7 obtained by  Courant and Friedrichs (1948) who discussed the expansion and contraction of spherical blast waves in water, and fitted the experimental data  to a quasi-equation of state for water under a pressure of around 3000 atm., which is pv7 = const or   p  =A ρ7  + B. They also derived this same  value of the adiabatic exponent k = 7  theoretically as a solution to their non-linear flow  equations for purely spherical ( i.e. radial) shock expansions in fluids. Their evidence that water rupture, at least in explosions,  is spherical and adiabatic would also seem to be generally applicable, since  all ruptures, even non- explosive ruptures, are quasi-sudden,  and so, at least initially, they all could be adiabatic as well.

As to the proper value of the density ratio (ρ/ ∆ ρ) to accept, if the rupture process for water  were envisaged as taking  place  by a transformation  from its usual density of  1 by one of the  usual cavitation  mechanisms, such as  a burst of electromagnetic or acoustic radiation into a small liquid volume ( the radiation being energetic enough  to break all the liquid water bonds in that volume quasi-simultaneously),  we would have a “ gas-like” liquid suddenly emerging with an expansion ratio of 0.333. Once the ‘gas-like  volume has emerged, we see that it must at once  expand  from an initial gas-like density ρ, again taken as unity,  to some smaller gas-like  density  ∆ ρ. by either the isothermal route p = K ((ρ/ ∆ ρ)  or the adiabatic route p = K (ρ/ ∆ ρ)k  where k is now greater than unity. The density ratio must then fall from unity  to some value consistent with the  usual  equation for pressure equilibrium,   p(max) = 2σ/r., where r is the radius of the critical bubble size.

Clearly the isothermal hypothesis cannot reach the observed low rupture pressures of 250 atmospheres or less,, while the adiabatic process can.  From Table 1 we again see that a k value of 7, over the  range of density expansion  ratios   (ρ/ ∆ ρ)k  .from 0.4 to 0.6, would more than encompass the observed range of rupture tensions of  50 to about 250 atmospheres at normal temperatures.


The proposed model would l require simultaneous  radial  rupture over a sufficient number of adjacent  bonds,  and therefore the theory of nucleation rate analysis would still appear to apply. The radial rupture might also of course be heterogeneous, and then all the various heterogeneous mechanisms of bubble formation presently considered may still be in play.


The proper value to be used for k in aqueous solutions, where the densities are different from those of pure water, would appear to be a matter for further study.


The third step: the attainment of a critical radius rc for rupture


I must be noted that Step  2 above is based solely on the density   ratio ρ/ ∆ ρ and has not specified any actual initial or final density or ( specific volume. ) However as the “gas-like’ liquid  bubble expands, it eventually  must physically become an ordinary vapour –filled bubble of homogeneous nucleaton theory, and the latter theory  requires that, for the bubble  to persist,  it must meet  the critical stability condition:


pB  pL  =  ∆pmax  = 2 σ /RC                                                         


Table 2 shows this final stability  condition over a range of sizes , rc


Table 2


Critical ( stable) radius rc for various rupture pressures in water


Critical radius of bubble, rc                                Rupture pressure,  p(max)  = 2 σ /r 

        (cm) (m)                                                   (σ = 75 dynes/cm)


                                                            a) (dynes/cm2)              b) atmospheres (dynes/cm2 x 10-6  )     

 1 cm                0.01 m                         140                                                      1.4 x10-4

10-1                  0.001                           1.4 x 103                                                             1.4 x 10-3

10-2                  10-4                              1.4 x 104                                                             1.4 x 10-2

10-3                  10-5                              1.4 x 105                                                             1.4 x 10-1

10-4                  10-6                              1.4 x 106                                              1.4

10-5                      10-7                              1.4 x 107                                              14

10-6                  10-8                              1.4 x 108                                              140

10-7                  10-9                              1.4 x 109                                              1400

10-8                  10-10                             1.4 x 1010                                             14,000




1.  The ratio between the  critical state liquid pressure ( 1.4 x  104 atms).and the observed   average rupture pressure for water  ( say 150  atms)   is  about 100/1.


2. On the isothermal expansion hypothesis with p1/p2  = V2/V1 , the volume ratio at critical rupture must be the same i.e.  about 100, .so that the radius ratio is  r2/r1 = 1001/3 = 4.64.


 On the adiabatic expansion hypothesis ( with k =7), it becomes p1/p2 = (V2/V1 )7 , so  thatV2/V1 = (p1/p2)1/7 = 1.93. and  r2/r1 = (1.93)1/3  = 1.25


3. If a bubble is to reach the critical rupture size of 10-8m at 140 atmospheres rupture pressure,  then the initial  radius size rc  for an adiabatic expansion at k = 7 would have to have been rc = 10-8/ 1.25 = 8 x 10-9  m;  moreover,   an input of energy sufficient to bring a volume  4/3 π (8 x  10-8)3  to the critical  “gas-like”  state must have been supplied to the liquid to bring about the rupture.  Any initial excited volume smaller than that may indeed   form a tiny gas bubble but  will immediately thereafter collapse because it is below the critical size required.


4. It may be noted that incipient bubbles, smaller than those having sufficient excited volume to become critical and bring about macro rupture of the liquid,  may still cause important  transient rupture effects on the molecular scale.  These, while never reaching the critical radius  leading to macro liquid rupture,  may still be of great importance on the molecular scale in locally removing a water film barrier between chemical reactant molecules in solution or suspension. This solvent film barrier phenomenon may therefore also be important in  the  kinetics of  so-called “slow” chemical reactions in solution.    



Solutions, Solids, Reaction Kinetics 


In simple cases, the relationship of k to n, the number of ways the energy of the system is divided, is given by k = (n +2)/n. With k = 7, the formula would require n to be  fractional at n = 1/3, and we would have to then interpret this physically as indicative of the spherical or radial expansion.


For solids, because of structural and steric hindrance, the flow orientation in a rupture flow may conceivably be only quasi- radial, and so a value of k between 4 and 6 might. then be appropriate, giving tensile strengths higher than for  liquids but  below the classical theoretical estimates. It t would appear that the new model may  be of interest to materials science.


Again, the  “slow” chemical  reactions mentioned in Note 4 above,  occur more often in liquid solution than in gases, and they are also the most sensitive to pressure, just as is the case with liquid rupture;  furthermore, the reaction rates are slowest when water is the solvent ( Laidler, 1965).  This all suggests that  the phenomenon of  rupture in liquid  water  may be important in  chemical reaction kinetics.  In gases, of course, adsorbed molecular films can also be present, and their removal  in collision reactions would enter in the same general way as for chemical reaction rates in solution.


Finally, we  may note that all the chemical and genetic reactions of life take place in the aqueous medium of the cell. Therefore, the kinetics and probabilities of the reactions of life and its evolution should  be subject to the  probability laws  that govern the aqueous rupture barrier which must be overcome on the molecular scale if the various biochemical  reactions and  interactions of life are to proceed.   


Brennen, Christopher E. (1995) Cavitation and Bubble Dynamics. Oxford Univ. Press.

Courant, R. and Friedrichs, K. O. (1948). Supersonic Flow and Shock Waves.  Interscience, New York.

Frenkel, J. (1955). Kinetic Theory of Liquids. Dover, New York.

Kittell, Charles. (1968)  Introduction to Solid State Physics. , 6th. ed. John Wiley & Sons Inc.,  New York

Laidler, Keith, J., (1965). Chemical Kinetics. McGraw-Hill.



4.4 Chemical reactions in the aqueous environment of the Living Cell: An Entropy of Liquid Rupture


Following the above insight into the rupture of liquids we return to the living cell. It is well known that many chemical reactions especially those in solution do not take place at the theoretically predicted rates, but instead take place at rates that are much  too slow [29]. For example, there are many bimolecular reactions (both in gas phase and in solution) which are too slow by factors up to 10-9. ,so that the rate equation K = Z e –Ea/RT , (where Z is the collision number, Ea is the activation energy)   must be written as ka = PZ e –Ea/RT where P the probability factor is  inserted  to account for the disparity in reaction  rate,  and ka  is here the activation factor or rate [29].


When the collision theory is replaced by the statistical mechanics approach, the same result is obtained, but the arbitrary probability factor P is now explained as a steric hindrance factor which makes more theoretical sense. And since the logarithm of the probability is the Boltzmann definition of entropy ( d lnP = ∆S) , the rate equation then takes the  form


Krate = PZ e –Ea/RT, and  where PZ becomes


PZ =  e∆S/R (kbT/h)


and the entropy of activation  ∆S now appears., with kb being the Boltzmann constant.


The entropy of activation in chemical reaction kinetics can easily be related to the new

entropy of rupture  ∆SR  , in the following manner:


The pressure relationships across a non-isentropic discontinuity in a compressible fluid may be expressed as


p1/p2 = e-∆S/R where  ∆S is the entropy change across it.


Since  in any adiabatic process, we also have p1/p2 = (V2/V1)k = (ρ1/ ρ2)k , therefore we also have  p1/p2 = (V2/V1)k = (ρ1/ ρ2)k =      e-∆S/R;   and  finally

ln(ρ1/ ρ2)k) = k ln (ρ1/ ρ2 ) = − ∆S/R


Therefore, ∆S is proportional to k, and for spherical expansion of water, k = 7, so ∆S for this case is also proportional  to 7.    That is,  ∆S 7.


There are three main approaches to the relationship of entropy S  to probability P. First, in classical thermodynamics, as in the example above where   P = e-∆S/R  , we have  ln P =  − ∆S/R.  Here  P is physically and mathematically equal to or less than unity.

The second relationship is the  thermodynamic  probability of Boltzmann and of statistical mechanics where the entropy S is related to the logarithm of the number of accessible thermodynamic states of the system, called the thermodynamic probability P or W, which is a number greater than unity,  but which can  be  related to the  mathematical probability by a normalization if desired.  Here, ∆S = ln P ( or S = ln W).  Relating this to water rupture, we then have:


(a) From classical chemical kinetic theory,  ln P1  = − ∆S1,  where P = e−∆S  and so for rupture reactions in water  ln PN = − ∆S   7 , or log7 P = ln P / ln 7= − ∆S. 


(b) From Boltzman theory,  ln N = − ∆S  , where N is the  number of accessible states and so for  reactions involving water rupture  P and N are  related as log 7 P= 7N


 (c) A third entropy relationship is from information theory, where  P =  loga N, with   P  now being the number of bits of information. Consequently, for a system composed of N assemblages of a  bits of thermodynamic information, we have logaN =  P and for  a = 7  this becomes log7 PN = 7N.


If, finally, we make the assumption that in any time series of evolutionary rupture/ collision events (i.e. sequential assemblages each having 7 bits of thermodynamic information or entropy) the probability  P of a number of accessible states is  proportional to the time t available for the process, then  we can put


log7 t  = log7P and t = 7N . When P is normalized to unity this becomes  t = 7N + const.


Therefore,  since evolutionary change takes place by gene reaction  in  aqueous solution or suspension in the living cell, and if rupture of water film  is involved in all such genetic  interactions and mutations, and if water rupture involves an entropy change proportional to 7  and a probability relationship of log P log t = log7N ,   then the time series  of evolutionary events   may also show evidence of a frequency/probability or entropy  involving  the factor 7N where N is the number of collision/rupture events leading up to the emergence of the biological form.


This possibility has been investigated.  In  A Logarithmic Scaling of the Time Series of Cosmic Evolutionary Events to the Base Seven the results  do show a  7N factor. Therefore, this  physically based numerical  factor in evolutionary data  would seem to merit further investigation.  For convenient reference some data from the study are as follows:  




1.  The times of the events in years ( Nyrs) are  made dimensionless as required for logarithmically analysis by dividing each  time in years  by the first year in the series (No )which is taken as  being unity, i.e. as year one. Thus  N/No is dimensionless.


5.  Plot of Log 7 Data




Figure 1.  Logarithmic plot to base 7 of (A) all cosmic data,  and (B) biological data  only



For Curve A  the least squares regression equation is:

(a) negative slope:   y = − 0.994 x + 12.18      (b) positive slope:   y = +  0.994 x  + 5.22       (c) correlation coefficient:  0.998



For curve B the least squares regression equation is:

(a) negative slope:     y = − 1.02 x + 11.30     (b) positive slope:     y = + 1.02 x + 5.17          (c) correlation coefficient:  0.9988


This empirical evidence for the presence of a 7N factor in emerging complexity and evolution is of course  preliminary, but more examples can be found. However, considerably more effort  will be needed before it can be said to be fully established and its scientific implications understood.



4.5 Entropy increase, the 2nd Law of thermodynamics and evolution.


We have repeatedly mentioned the problem presented  to all  theories of evolution  by the 2nd  law of thermodynamics, which states that in natural processes  entropy must always increase  i.e.  dS = + dQ/dt.  Since the emergence of biological order in the living cell  represents a clear decrease in entropy,  this has always been a problem to explain.  Brooks and Wiley [ 1 ] have endeavored  to account for this contradiction or barrier by postulating  that, while total entropy does always  increase, still, locally, for example in a living cell, the  entropy may decreases if the  necessary increase in entropy somehow  gets exported to the cell ‘s exterior environment. Although this approach  has not met with general acceptance, it does go directly to the heart of the  problem.


We may summarize our ideas on the situation for material systems as  follows:


It appears that the entropy change laws in the UF in Quadrant I of the p-v thermodynamic diagram should enter into the basic nature and direction of  plant and  animal evolution as follows:

(a) Tangent Gas:    1. non-isentropic processes dS = dQ/T is positive ( 2nd law of thermodynamics holds ( “disorder seeking”)

                             2. isentropic stable waves : dS = 0

b)  Orthogonal ( Isothermal) Gas: 1. non-isentropic processes  dS = dQ/T = 0  ( “stability seeking” )

                                                    2. isentropic stable waves     dS = dQ/T = 0



The detailed interaction of ordinary physical processes  with the tangent gas and the isothermal gas entropy laws of the UF where the forces originate,  remains to be examined. 


The existence of stable waves in the UF provides for the orderly forces observed in physical processes and supplies the observed order which emerges in complexity.


The existence of a  quite separate “stability seeking” entropy in the UF’s isothermal gas raises the question of whether the emergence of biological complexity might not then be essentially different in nature from emerging complexity of non-living physical systems. If this is so, then, not only the existence of orderly forces must be considered, but also the existence of an essentially different entropy system , one that is intrinsically not only affected by order but actually seeks the stability of order instead of merely tolerating it. Physical complexity would then arise from the forces of the UF acting under the 2nd law. But living plant and animals would arise from the same orderly forces, plus the ‘stability- seeking’ flow of entropy in the isothermal UF gas. The emergence of complexity in biological systems would then have an essentially different ingredient from its emergence in non-living physical systems. 


[Note: There is another entropy condition in the UF , namely that in Quadrant II (dS = − dQ/T) ;  this implies  very unusual properties which appear to match the human condition. This is discussed briefly in Section 5 below, and in detail in Science and the Soul/Body Problem: An Exploratory Reassessment .


It is now time to sum up this survey.


5.0  Conclusions on Biological Complexity: Do Orderly Forces Acting on Random Kinetic Motions Resuslt in the Emergence of Variety on a Probabilistic Time Scale?

We started by examining the  proposition that evolution, defined as the emergence of complexity, both physical and biological,  arises in chaotic or kinetic systems which, when not at equilibrium,  receive an input of “stressing”  energy. The only elements considered in this system are suitable  material particles ( essentially molecules and gene pools) undergoing energetic, random (i.e. kinetic)  motions. 

Our analysis concluded that several physical elements were thereby ignored and must be included in any valid explanatory system. These include, the presence of  (1) orderly forces ( which we have argued are best explained by the existence of a universal wave and force field (UF)  (2) acting on random kinetic motions of molecular species in space and  over time, and  (3) in the case of the aqueous environment of the living cell, also involving  the entropy change  in the rupture of water barriers between reacting molecular assemblages, and (4)   the presence of two new orders for entropy change direction  governing force interactions with the UF, in addition to the long standing rule of the   2nd law of thermodynamics for kinetic processes among molecular species.  

If the orderly forces are, say, a UF wave passing through a kinetic motion field, then, because the wave is extended in space it will affect the kinetic field at one point only over  a certain interval of time set by the wave speed.  This will inevitably introduce further  quasi-ordered variation into the kinetic field over the space of the affected  field and over the elapsed  time at any one point in the field. The order of the UF wave  is therefore  not manifested in the physical field directly, but instead appears in a space- modified and  time- dependent manner at any one location. This would seem to mean the emergence of variety from the interaction of  UF wave order and random physical kinetic field. The process is deterministic  in that the UF imposes  order, but it is probabilistic in the time sequence in which  the realized ordered system emerges and in the variety of the realized order  that  interaction  makes possible. The various physical complexity examples discussed by Nicolis and Prigogine could be re-analysed from this point of view; e.g.  snowflakes  emerge from a super cooled cloud under the action of an orderly vapour force field in orderly types, but they emerge individually on a probabilistic time scale and are individually highly non- uniform in their fine scale structure.

Four obvious approaches to a better understanding of this new scheme  would seem to be : (1) a re-analysis of the emergence of physical complexity with the inclusion of orderly physical  force fields, and (2) a detailed quantitative analysis of molecular genetic and metabolic  interactions in the aqueous cell medium,  (3) a theoretical analysis of the interaction of order and probability in physical systems, (4) evaluation of the implications for biology of the two new orders of entropy change now theoretically available from the UF (namely “order stability”  and “order seeking”).

The suggested new approaches, if eventually validated, may not greatly affect much  of current  biological  investigation,  working theories, and progress,  for example in the marvelous structural complexities being revealed by molecular biology.  However, a new attention to the force fields involved in these processes should open up many new avenues for experimental exploration and verification. At the theoretical or conceptual level,  it should perhaps also be noted that the interpretation of the conclusions  extends well beyond the autonomy and methods of science into  the other two methods of the  rational investigation of reality, namely philosophy ( ontology, being ) and theology ( ultimate meaning).

In summary:

1.The neo-Darwinian proposition that biological evolution arises out of purely random physical processes alone, and then proceeds via probability laws, is untenable, since it ignores the orderly  physically  forces that are acting.

2. The proposition that evolution arises from a combination of kinetic disorder plus orderly forces is presently tenable for non-living physical systems, but it still does not account for the violation of the 2nd law in the emerging complexity of biological systems. 


3. The proposition that the UF is the source of physical force ( wave energy exchange ), structural and flow order (entropy minimization) is tenable, and therefore the UF’s  entropy change relationships must also be acting in any interaction with atomic and molecular material systems. These relationships appear now to  a) agree with the 2nd Law for the tangent gas in Quadrant I of the pressure-volume diagram, b) require zero entropy change in material  interactions with the UF’s orthogonal or isothermal gas,  c) require negative entropy change in interactions with the UF’s  dynamic entity in Quadrant II.


4. In addition to the presence of orderly forces, there are now three entropy change regimes, instead of only  the 2nd law, that must be considered in evolutionary change.


5. These new entropy orders or regimes appear to  point towards an essential entropic difference  between  non-living and living systems in the  case of the UF’s orthogonal/isothermal dynamic order in Quadrant I, where  non-living physical systems obey the 2nd Law and living systems obey the UF’s orthogonal/isothermal gas law.


6. In the case of the UF in  Quadrant II,  the entropy decrease law  (dS = −dQ/ T) appears to point  towards an essential  difference between plant/animal systems on the one hand and human beings on the other.  If this property of the UF is valid as interpreted here, then science may be at a frontier between itself and philosophy/ theology. Science is ordinarily thought of as being concerned with measurement and with the quantitative laws of the behaviour of matter. However, Quadrant II in the UF appears to present a dynamic, non-material substance, extrinsically rather than intrinsically  quantified, and  “ order seeking”  in its entropy law, i.e  tending towards the intellectual.


The new statement of entropy change appears to be  theoretically valid, although it may not be directly experimentally verifiable (or falsifiable). In short : the differential equation dS = + dQ/T  is a rational, mathematical, scientific, physical statement and a verified scientific  law describing the direction of flow of non-biological  ( the 2nd  Law of  thermodynamics) . What then is the nature of the statement made by the differential equation dS = −dQ/T , both  physically and metaphysically?  It also is rational, mathematically sound, makes a physical statement, and describes the flow of information and order seeking, or insight,  in human intellectual capabilities. 


Does it also raise a question as to whether the statement constitutes a frontier between, or a  bridge to,  philosophy/ theology,  which have rationally affirmed the reality of spirit for millennia?


It might then be tentatively restated, and rather loosely, that the new theory conceptually means that (1) the  quantitative interaction of the UF with material particles (condensed from it in Quadrant I [23]) and the subsequent cosmic and biological evolution is a concern of science,  (2) the interaction of the UF in  Quadrant II ( soul/spirit) with matter in Quadrant I constitutes human life whose evolution is  a subject of prehistory and then history,  (3) the meaning of the theory is a  concern of philosophy, and  (4) the origin of the UF, its purpose and destiny, and the purpose and destiny of humanity are the concerns of both philosophy and religion. 


7.  In the mid-1950’s, Lonergan [30] critically analyzed a wide variety of scientific theories as instances of human insight ( and oversight)  and of the nature of rationality or the act of human understanding which leads to the development of natural science, philosophy and theology. He then developed a philosophic world view which took  into account both the classical  deterministic physical laws and the statistical probabilities of experimental science in  a synthesis which he termed emergent probability.  It might  be of interest to now see how his emergent probability alters or survives when the UF and its laws are included.  The new orderly wave and force field would appear to relate to his classical deterministic laws so as to make them more concrete, while the new entropy laws  would appear to introduce discontinuities which separate distinct orders of existence, and  which must also fundamentally affect probabilities attached to the emergence of events.



1. Brooks, Daniel R., and E.O. Wiley. Evolution  as Entropy. University of Chicago Press, Chicago and London, 1986.

2. Nicolis, Gregoire and Ilya Prigogine.  Exploring Complexity, W. H. Freeman and Company, New York, 1989.


3.  S. A. Chaplygin,  On Gas Jets.  Sci. Mem. Moscow Univ. Math. Phys. 21, 1 (1904).


4.  H. S. Tsien,  Two-Dimensional Subsonic Flow of Compressible Fluids.  J. Aeron. Sci. 6, 399 (1939).


5. T. Von Karman, Compressibility Effects in Aerodynamics.  J. Aeron. Sci. 8, 337 (1941).


6. A. H. Shapiro, The Dynamics and Thermodynamics of Compressible Fluid Flow. 2 Vols.( John Wiley & Sons, New York, 1953).

7. R. Courant and K. O. Friedrichs,  Supersonic Flow and Shock Waves. (Interscience , New York, 1948).


8. Horace Lamb,  Hydrodynamics. 6th ed .  ( Dover Reprint, Dover Publications Inc.  New York, 1936 ).


9. N. A. Bachall, J.P. Ostriker, S Perlmutter and P.J. Steinhardt. The Cosmic Triangle:    Revealing the State of the Universe. Science,  284, 1481 (1999).

10. A. Kamenshchick, U. Moschella and V. Pasquier,  An alternative to quintessence. Phys Lett. B  511, 265 (2001).

11. N. Bilic, G.B. Tupper and R.D.Viollier,  Unification of Dark Matter and Dark Energy: The Inhomogeneous Chaplygin Gas. Astrophysics, astro-ph/0111325  ( 2002).


12. Power, Bernard A., Much of the work leading up to the present theory has appeared in connection with studies into  the scientific basis for the image formation on the Holy Shroud of Turin. Some of these are as follows:

13. ---------------, Il Meccanismo di Formazione dell’Immagine dela Sindon di Torino, Collegamento pro Sindone, Mgggio-Giugno,  pp. 13-28, 1997, Roma.

14.---------------, Caratterizzazione di una Lunghezza d’Onda per la Radiazione che Potrebe aver Creato I’Immagine Della Sindone di Torino. Collegamento pro Sindone, Roma. Novembre-Decembre, pp. 26-36, 1999.

15.---------------, An Unexpected Consequence of Radiation Theories of Image formation for the Shroud of Turin. Proc. Worldwide Congress Sindone 2000,  Orvieto, Italy, Aug. 27-29, 2000.

16.---------------, Image Formation on the Holy Shroud of Turin by Attenuation of Radiation in Air.  Collegamento pro Sindone website (   March 2002.


17.---------------, How Microwave Radiation Could Have Formed the Observed Images on The Holy Shroud of Turin. Collegamento [ro Sindone Website, Jan. 2003. (


18. --------------, Shock Waves in a Photon Gas. Contr. Paper No. 203, American Association for the Advancement of Science, Ann. Meeting, Toronto, Jan. 1981.

19.---------------. Unification of Forces and Particle Production at an Oblique Radiation Shock Front. Contr. Paper N0. 462. American Association  for the Advancement of Science, Ann. Meeting,  Washington, D.C., Jan 1982.

20.---------------, Baryon Mass-ratios and Degrees of Freedom in a Compressible Radiation Flow.  Contr. Paper No. 505. American Association for the Advancement of Science, Annual Meeting, Detroit, May 1983.

21.---------------, Summary of a Universal Physics. Monograph (Private distribution) pp 92. Tempress, Dorval, Quebec, 1992.


22. ……………, Properties of a Universal Wave Field (UF). November, 2005.


23. ……………, Cosmology of a Binary Universe, Part 1: The Origin, Properties and Thermodynamic Evolution of a Universal Wave and Force Field. April 2007.


24. L. W. Gold and B. A. Power. Dependence of the forms of natural snow crystals on meteorological conditions. J. Meteorology  S9, 447 (1952).


25. Nakaya, Ukichiro.  Snow Crystals: Natural and Artificial. Harvard University Press, Cambridge, Mass.  1954.

26. B. A. Power and R.F. Power. Some Amino Acids  as Ice Nucleators.  Nature, Vol. 184, 1170. 1962.

27. -------------------------------------  Vanillin, cis- Terpin and cis- Terpin Hydrate as Ice Nucleators.  Science. Vol. 148, 1088, 21 May, 1965.

28.  Brennen, Christopher, E. Cavitation and Bubble Dynamics. Oxford Univ. Press. 1995.      

29. Laidler, Keith, J.,  Chemical Kinetics. McGraw-Hill. 1965.

30. Lonergan, Bernard , S.J., Insight: A Study of Human Understanding.  Philosophical Library, New York. 1956.




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