Part B


 What is Human Life? A Classical Viewpoint with a Verifiable Scientific Hypothesis 





1. The Classical,  Rational and Spiritual Viewpoint


2.  The neo-Darwinian,  Materialistic World View of Human Life.


3. The Thomas Nagel Critique of  neo-Darwinian Materialism  as a Universal Explanation of Life and Human Consciousness


4.  An ‘Animal Soul ‘?


5. Our Classical Soul-Body Definition for Man,  The Rational Animal


6. The Classical  Philosophic View and a  Scientific Timeline


7. A Real, Dynamic Union of Soul and Body,  in which  Dualism Objections are Negated


 8. The Possibility of Scientifically Identifying  Soul-Body Waves


9.  Some Philosophic Dimensions


10. Conclusions





 What is Human Life?  


At present, there are two main lines of opinion  as to Man’s nature: 1) Social, Intellectual, Philosophical, Theological (the ‘classical view’) and  2)  a Physical,  Scientific.( naturalistic, neo- Darwinian)  point of view.                                  



1.0 The Classical  Rational and Spiritual Viewpoint


For millennia, Man’s intellectuality or reason has been viewed and put forward as overwhelming  evidence that he is essentially separate and distinct from the rest of the animal kingdom. As Aristotle put it : ‘Man is the rational animal’. 


In this classical view, the evidence for the  uniqueness of man’s nature,  based on his astounding intellectual, scientific,  cultural and civilized achievements, is simply overwhelming. Civilizations have  emerged from this viewpoint of Man.


This traditional  view takes the position that with Man we are dealing with an animal whose mental activity relates to, not only basic intelligibility in physical data,  but also to the  higher levels of consciousness and thought, that is  to such things, for example,  as probability distributions of basic data forms, their standard deviations , their correlations, and with  the myriad higher intellectual human activities involved in the sciences, in engineering, in fine arts, the practical arts, academic studies, theories, philosophies  and so on. In a word, to  human intelligence  as opposed to the simple basic sensitive detection of the  intelligibility in  physical environmental data.


Philosophical analyses and refinements, extending  from the  mediaeval synthesis on down to modern times, have, in general, continued this tradition. Today, we can add  cognitive science and  the ‘hard fact of human consciousness’ as further evidence for an  essential  separation of Man from the rest of the Primates.


However,  two centuries of enormous progress in the physical sciences, together with  their great  explanatory success, and the  heuristic satisfactions they have brought, have led  gradually, if uncritically,  to a growing feeling of satisfaction with  the notion that  a purely scientific factual  outlook  provides, or will soon provide,  adequate naturalistic explanation for these central problems. Philosophy and  theology have gradually seemed diminished  --- certainly in popular attitudes.


We note in passing that the findings of paleontology and archaeology of a gradual development of human civilization from very simple prehistoric beginnings do not affect the essential argument for man’s unique rationality.  Human progress and  civilization show a unique  exponential timeline of development,  and  the meaning of the complexity at any later period is not negated by the relative simplicity of the earlier ones. 


The development of biophysics, biochemistry  molecular genetics, and, currently, of  neuroscience have  inevitably intensified  interest in the  central nature of man.


 This great  mass of scientific data has led many to a general uncritical  assumption that the materialistic neo-Darwinian synthesis applies to the whole of reality including Man, and that a satisfactory   explanation for the origin of life and the hard problems of intellectuality and human consciousness are  only minor matters left to be cleared up. This casual attitude, of course,  faces some  intractable difficulties. Even physical theories for the origin of life, for example, have been far from convincing, and  this area also still lacks essential experimental verification.


We have therefore examined  this origin of life problem critically. Now,  in Part A:The Origin of Life: The Role of Orderly Cell Waves and their Negative Entropy we have presented a new ‘cytoplasm stress- wave’ hypothesis that supplies a missing  physical basis for Schrödinger’s negative entropy  in  his origin of life theory [1].  This new approach  not only  overcomes the previous entropy difficulty, but  is in principle experimentally  verifiable.


The new origin of life theory  replaces the  random chance theory for  the emergence of life with a  physical, orderly   cellular wave environment. . Statistical aspects remain, but they are now probability based and compatible with  the physical wave theory. The negative entropy, wave environment is  intrinsically favorable to the  emergence and maintenance of  the  order that is necessary for life.


Logically, of course, any developments whatever in science of whatever viewpoint , i.e. per se,  simply provide more support for the classical viewpoint  that man’s astounding achievements,  including, of course, physical and biological science, establish, well beyond any reasonable doubt,  his uniqueness, and that he is essentially intellectual, rational,  and non-material,  i.e. spiritual as well as animal. 


The evidence for the uniqueness of  man’s nature, based on his unique behaviour and accomplishments, may be overwhelming, .  but, man is not simply rational,  and his  emotional, dramatic, artistic, social  and other aspects need to be satisfied.  Therefore, a  possible integration of scientific knowledge with the rational , logical or  classical viewpoint  should be of importance.   


To sum up to this point: The  philosophical  evidence and reasoning lead to the classical conclusion that man is essentially a unique  animal  because of his intellectual and spiritual essence. Man  is thus essentially distinct from the non-rational animals.


Moreover , in this classical view, the evidence for the  uniqueness of man’s nature and  intellectual faculty, based on his astounding intellectual, scientific, artistic, cultures and civilized works and achievements,  is simply overwhelming. 


There are of course  relevant further questions that arise to be faced and answered. These are related to the nature of  intellectuality, to the nature of the union of body and soul, and to the relation of his human  body to the rest of the animal kingdom:  How does a spiritual element function in the material human body?  How are they a single unity? What about the failure of Descartes’ soul- body dualism? Is it relevant?  None of these objections, in fact,  is at all critical to the classical view. One of these further relevant questions – that of union of body and soul – is dealt with below in Section 7.0.



2.0  The neo-Darwinian,  Materialistic World View of Human Life


 The rise of physics and chemistry came naturally from, and so was easily compatible with, the ancient classical,  the mediaeval scholastic and the various  Renaissance  philosophical and theological syntheses.


It was  with the rise of biology, with its enormous fund of new observational facts,  that the customary strains of new growth  led to the adoption of  radical new postures that  were opposed to  the traditional classical  western synthesis on the essential nature of man, and which then  inevitably opposed the roots of the civilization  which had originated and nourished western science itself.


The great success of the neo- Darwinian/Mendelian theory of evolution in providing  a rational grasp  of an enormous range of biological developmental information led to a view among some that all classical and  theological views  had now become somehow irrelevant.


Again, the more recent  factual knowledge on the human brain furnished by neuroscience has led to a new flood of biological facts to be assimilated  about  an  essential aspect of man.  Some  specialists  quickly became so immersed in this vast new scientific information that  they uncritically adopted speculative new formulations as to man’s inner nature, and treated  a materialist  neo-Darwinian viewpoint, namely  that intellectuality and reason  could arise from the purely physical, as being  solidly grounded in reality.


Let us now briefly examine a recent critique of the scope and validity of this materialistic neo- Darwinian  explanation  from the viewpoint of its inability to fundamentally address the  question that surround the nature  of  human consciousness, of intellectuality and of mind.  


The materialist alternative  view appeals to the  physical/scientific facts as evidence.  If taken alone, this  approach  usually leads to a conclusion that man is reducibly  physical and not essentially  distinct from other primates. The scientific disciplines  cited are primarily neuroscience and genetic biology.  The facts of man’s uniqueness are not denied, but are simply treated as non-essential differences.


Some, however, such as the atheist philosopher Thomas Nagel [2],  find  the purely naturalistic, neo-Darwinian approach  unconvincing, and unable to account for the existence of mind and of human consciousness. He looks for an eventual  mental,  non-material, but still naturalistic  explanation.


There is  solid scientific evidence for the evolutionary relationship of man’s physical body  to the rest of the animal kingdom, and especially to the other primates. The current physical/scientific  explanation for man’s undoubted uniqueness and for his mental, rational, creative, scientific, and spiritual aspects is, however,  radically deficient.  It is essentially relying on an ever increasing knowledge of the evolution of the complexity of the human brain and nervous system to eventually provide some solid evidence  that  man is  not essentially  unique.


How such  a descriptive  approach can negate the massive classical argument for man’s  essential uniqueness is never adequately addressed. Logically, in fact, this physical/scientific approach actually always intrinsically  supports the view that man is unique, since raising  the very possibility of man having a scientific view of his own  nature, can be cited as another  instance of his uniqueness.




3.0 The Thomas Nagel Critique of the Materialistic neo-Darwinian Concept of Nature as a Universal Explanation of Life and Human Consciousness


In 2012 the American philosopher, Thomas Nagel, published his Mind and Cosmos: : Why the Materialist Neo-Darwinian Conception of Nature is Almost Certainly False (Oxford U. Press, N. Y,  2012). [2].


We should, perhaps,  first state that Nagel writes from an atheistic position, and that he indeed looks forward to  some immaterial yet still  naturalistic, broader scientific principle,  as yet undiscovered, which will provide the philosophically satisfactory answers he maintains are  lacking in the  viewpoint currently  in vogue.


In his book, we find the following passages:


         I would like to defend the untutored reaction  of incredulity to the reductionist, neo-Darwinian account of the origin and nature of life. It is prima facie highly implausible that life as we know it is a result of a series of physical accidents  together with the mechanism of natural selection.   We are expected to abandon this naive response, not in favor of a fully worked out  physical/chemical explanation,  but in favor of an alternative that is really a schema for explanation, supported by some examples”.


          “Science is driven by the assumption that the world is intelligible  …Without the assumption of an underlying order, which long antedates the scientific revolution, these discoveries could not have been made.”


          “ If …………we want to pursue a world view, I believe we will have to leave  materialism behind.  Conscious subjects and their mental lives are inescapable component of reality not describable by the physical sciences”   


These short excerpts may serve  to illustrate the general nature of Nagel’s thesis.  His full views on the nature of mind and consciousness, and what will be  required to explain them naturalistically, are given in his book.


We outline in Section 5  a new version of the  classical view, one which attempts to  answer some of the relevant further questions mentioned above in Section 1.  But first,  for clarity we turn briefly for assistance  to an ancient philosophical concept , namely that of  the ‘Animal Soul’, in a search for more precise physical clarification from  biological data and insight.



4.0  An ‘Animal Soul ‘?


This concept of a material soul  applying to plants and animals is  a philosophical characterization.  Currently, it is not  widely   considered useful for, and certainly  not necessary for, the scientific description or characterization of the nature  of plants and animals.


The animal soul usage, however, has an ancient lineage. Aristotle refers to a vegetative soul for plants, a  sensitive soul for animals,  a rational  soul for man. He also says, famously, “to attain any assured knowledge  about the soul is one of the most  difficult things in the world”.


With such an illustrious caveat, we  may wonder why one would bother to introduce such a specialized  philosophical concept into the description of plants and animals, considering the enormous existing descriptive power of  modern biological science.  However, we may perhaps take from philosophy the  goal or possibility of formulating  an overall specification for the essence  or ‘soul’ of non-human living organisms, but now on purely scientific grounds.. And  so we shall explore a scientific physical concept that does appear to offer an overall specification of validity and usefulness.


As a start, surely we  can agree  that the biological animal/plant world is a proper  matter for scientific description  and definition. So let us start with science, and then see how philosophy can  fit into this particular matter.


A. Wave Function Description   Living things possess  material complex structure, complex functioning, and genetic continuity. Their atomic and molecular components  are concisely described by quantum wave functions,  Ψ.  The larger molecular assemblages of life, such as proteins, DNA and so on,  also have material wave functions, but their wavelengths become increasingly so tiny that they are  of no practical use as concise descriptors. So, at least at present, we cannot use wave functions as an overall descriptor for living systems.                 


B. Functional Description   The current concise,  scientific depiction of the genetic code in the genome  is surely astonishing. Therefore, the genome  must certainly be a solid descriptor of some central aspects of the living organism, such as its structure,  its functioning and its genetics. Let us accept then that  the genome is a   concise,  blueprint for both the structure and functioning  of the living organism , as well as the director for its genetic reproduction.


Surely then, if the philosophical definition of the animal material soul is “ The central form of the animal, “or the “ the substantial central form of the animal “ then, more factually,  we  can .today scientifically define the animal  as   “ A genomic  functioning material  system”, or as   “ A ,genomic  functioning and reproducing, organic system .


A  plant might then be defined as :“ A, genomic, metabolic,  functioning and reproducing, vegetative , organic system”.


And an animal : as: “ A   genomic, metabolic,  functioning and reproducing, sensitive, self -mobile, organic system”.


In the light of the new cell wave,  negative entropy, theory of cell life set out in Part A  above, we might also consider  the following definition, “A  genomic, metabolic,  functioning and reproducing, organic, stably  undulating,  cellular  system” .


What has this re-defining accomplished?  It has attempted  to more  precisely bridge  a gap in expression and terminology currently dividing classical  philosophy  and  science in the matter of defining the essence of plants and animals.   The classical philosophic technical  terms “ central form” and substantial central form” for example, ,  are  opaque to many or most scientists. The suggested scientifically expressed, corresponding definitions may thus represent a useful scientific translation, one  more precise and meaningful than the philosophical ones alone.  


It is in this manner that the’ animal soul’ concept may perhaps be useful,  namely, to clarify the terminology of both science and philosophy so that as we move on to the  more difficult discourse on the nature of the Rational Animal  we may avoid unnecessary misapprehension on both sides of the discourse. 


Note We must point out that the nature of life is far from a settled matter. Even although we can make major advances -- one such perhaps being our current reintroduction of Schrödinger’s negentropy via  the negative  entropy stress- waves in the cell’s cytoplasm-in Part A,-- still, we can not be sure that we have the full picture until we have succeeded in actually producing  a living organism from non-living elements in the laboratory.  There may still be much more  to  the complex functioning organism of life than is presently known from physics, chemistry and negentropy, such as, for example,  some form of   quantitative,  physical  energy, one  possessing  organizing action  different from our presently known physical laws.   Our Animal Soul definition  may, for example,  have to eventually include something  like : A genomic,  metabolic, functioning and reproducing, sensitive, self-mobile, organic,  stably undulating,  structurally energized, system.   



5.0 Our Classical Soul-Body Definition for Man, The Rational Animal


We  in this essay,  hold the classical view that Man has a spiritual essence,  and, that his  body and soul are so unified as to constitute a new single unity. A concise, standard, classical definition of this human entity is as follows:


     “The unity of soul and body is so profound that one has to consider the soul to be the ‘form” of  the body, that is, it is because of its spiritual soul that the body made of matter becomes a living human body; spirit and matter, in man, are not two natures united , but rather their union forms a single nature  [3].


This spiritual soul/human body definition, or other similar definitions, satisfy  the overwhelming evidence on man’s unique  nature offered by his social, intellectual, artistic  and civilized  accomplishments and behaviour,  compared with  other primates.  Furthermore, the above definition philosophically refutes the soul/body duality arguments such as those arising from the Descartes duality controversy. The above definition seems to correspond to   Moreland’s   “ Thomistic substance dualism” [4].


The above  definition of man may perhaps also be restated formally as:    an entity or being having an intelligent or spiritual, central, substantial form.


With our  new science based definition of animal as being  “ A genomic functioning and reproducing organic system”, we might then describe man precisely and understandably  to both scientists and  philosophers  as :


An intellectual, genomic, metabolic,   functioning, reproducing , sensitive, self mobile, organic system.  Or, equally as:: A spiritual,  genomic,  functioning, reproducing , sensitive, self mobile, stably undulating,  organic system.


Or as: ´ A spiritual,  genomic, metabolic,  functioning, reproducing , sensitive, self mobile, organic, systematic, stably undulating , being.


The  term needed to be added to the animal definition in order to extend it to Man  the Rational Animal is  just    “intellectual” or ‘spiritual”. The proposed new distinction  is hopefully simple and clear, both philosophically and scientifically, which would be  an advance.  This precise addition of ‘intelligent’ or ‘spiritual’  is needed, so classicists argue,  to account for  man’s indisputable intellectual and  dramatic, powers and civilized activities. The debate between philosophy and science on the matter may hopefully proceed with more precision, more clarity and with more common ground.



6.0 The Classical  Philosophic View and a  Scientific Timeline


(a)The philosophic approach:  For millennia, Man’s intellectuality or reason has been viewed and put forward as overwhelming  evidence that he is essentially separate and distinct from the rest of the animal kingdom. Aristotle called Man  ‘the Rational Animal’. 


In this classical view, the evidence for the  uniqueness of man’s nature,  based on his astounding intellectual, scientific,  cultural and civilized achievements, is simply overwhelming. Civilizations have emerged from this viewpoint of Man.


The philosophical analyses and refinements, extending  from the  mediaeval synthesis on down to modern times, have, in general, continued this tradition. Today, we can add  cognitive science and  the ‘hard fact of human consciousness’ as further evidence for an  essential  separation of Man from the rest of the Primates.


(b) The scientific approach In addition, we present a scientific viewpoint on the classical philosophic conclusions. To do this we examine the   timeline of human inventiveness and progress, from the advent of homo sapiens [5]  in the Middle Paleolithic era, currently put at around 200,000 years-BP, on up through the advent of  stone tools, simple domestic  utensils, domestic animals,  human settlements, countries, nations, empires, etc  to the present day. [Table 1].




Table I


Age                      Subdivision           Progress Details             Years Before Present (t)      Time interval (Δt)    ln (Δt)                                                                                                                                                                             


 Stone Age      


1                            Middle Paleolithic      Rudimentary stone tools           200,000- 50,000 BP           150,000           11.9                                                                                     


2                           Upper                  Advanced tools              

                                                           Human settlements                          50000 -21,000               19,000                9.9           


3.                           Mesolithic             Domestication of Animals,                20,000 – 10,000             10,000               9.2       



4.                           Neolithic                Agriculture, smelting,                        10,000 – 5500                4,500                8.4                                                                                                                                             .                                                          cities                                                                                                                                                     


5. Bronze Age                                                                                           5300-2300                      2000                  7.6       


6. Iron Age    3200-1800BP                                                                        3200- 1800                   1400                    7.3       


7. Age of Steam                                                                                         1600-1950                      350                    5.9


8. Age of Internal Combustion Engine                                                                                           100                    4.6


9.0 Age of Air Travel, Electronics, Space, Digital                                                                           50                     3.9                   



When we inspect the time intervals  ( Δt) for each period of human progress and development in Table 1,, we see that the relationship of progress to time involved  is probably logarithmic, with initial long periods for small developments and increasingly shorter intervals needed for more advanced developments and improvements.


Progress Data                                                                                                                


Interval (N)     Interval (yrs BP)    ln(Δt)


1                    150.000                11.9

2                      19,000                  9.9

3                      10,000                  9.2

4                        4,500                  8.4

5                        2,000                  7.6

6                        1,400                  7.3

7                           350                  5.9  

8                           100                  4.6

9                             50                  3.9 






          Logarithmic Plot of Human Progress Intervals  Over  Time [ y = ln(Δt)   versus  x = n)]   




The  logarithmic plot of the timeline  data [ ( y = ln(Δt)   and x = n] bears out the above conclusion. Moreover, the relationship is stable and is not at all sensitive to quite large adjustments  in the time dating or  intervals.


Finally, we note that such a time line of progress is unique to humans. There is no  progress  time line for the other primates. Thus, a scientific analysis of the human  progress data agrees with the classical, philosophical conclusions as to the essential uniqueness of man. 




7.0 A Real, Dynamic Union of Soul and Body. In Which  Dualism Objections are Negated


If one accepts the above classical definition of Human, then  a number of relevant further questions  naturally arise. These  relate mainly  to the nature of a union of body and soul.  For examples:  How does this spiritual element function when it is unsoiled in a human l body?  How can soul and body be a single unity? What about the widely claimed  objection of Descartes’ version of a soul- body dualism?  [4].


A trenchant  philosophic perspective which will help us on the question of the  interaction of soul/spirit  with the human body is from Lonergan’s “Insight” [  6,  p. 520].      


 “ A solution seems to result from a simple principle, namely, that material reality cannot perform the role or function of spiritual reality but spiritual reality can perform the role and function of material reality.  Were man’s central form  a material intelligibility, then it could not be intelligent and so could not be the centre and ground of man’s inquiry and insight, reflection and judgment. Inversely, though man’s central form were a spiritual intelligibility , it could be the ground and centre of  his physical, chemical, organic and sensitive conjugates; for the spiritual is comprehensive; what can embrace the whole universe through knowledge, can provide the centre and  unity in the material conjugates of a single man.’


One  question has been  whether a real soul-body interaction is possible at all. We shall next show that a soul/wave interaction is, on the level of wave energy, just such a real union.  


Wave Action of the Soul

While the nature of the human soul is philosophic and extra-scientific, still its action in an ensouled human being might entail   scientific aspects. For example, consider  an embodied  soul, and let us suppose  that  one of this  soul’s  actions in the ensouled  human body is wavelike or undulatory.  Then if we apply Lonergan’s general principle, in this postulated  wave action in the  human body the soul  could assume the role of, and  obey the known laws of, physical wave action. Some examples follow:


 A. Unified Interaction Energy.   In this approach  we postulate that the soul may possesses  wave action in its human embodiment,. Then  this postulated wave action will entail interaction  with the ensouled human body  to form, on the  level of wave energy, an intrinsic unity of  soul and body.


To show this, let us recall  that, in compressible flow physics, a wave  having a velocity c when superimposed on a basic flow of velocity u, to produce a wave pulse,  has a resultant kinetic energy E (per unit mass)  equal to the sum of the velocities all squared, so as to yield :


Etotal = (cs + u )2 = cs 2 + u2 + 2cs u.                                                                      (1)


Here then, if  cs is the postulated  embodied soul’s wave speed   and u is the relative speed of any pulse or flow movement  between soul and body, then in such a  wave pulse  the corresponding   energies are cs 2 , u2, and 2cs u.


Note  that Equation 1 states that the wave velocity c interacts or adds to the flow velocity u, so that the wave pulse then has a velocity equal to the velocity sum. (cs + u).  Then, as the  energy is related to  velocity as a quadratic,  the total kinetic energy of the wave pulse Etotal  is the ‘square of the sum’ of the relevant velocities, that is it is (cs + u )2...


We now  draw special  attention  to the composite  interaction energy term 2cu . in Equation 1. This composite interaction  energy undoubtedly express a unity of the most intimate kind on the energy level.  Amongst other things, its reality  would  appears to settle  the problem of the possibility of a real  union ever occurring between  two different entities, soul wave c and body flow u,  provided only that they can interact or add to produce a wave pulse with increased total speed.  We submit that the  above example definitively demonstrates this  possibility, and so it also demonstrates that any ‘dualism’ objection [ 4] to a real unity  now becomes  untenable on physical or scientific grounds.


We have presented the interaction energy 2cu as a proof that two interacting entities, wave speed and flow speed,  can interact to produce a separate new energetic entity,  one that is  unified in the most intimate and complete way.


It is also felt that  reflection will support the conclusion that this interaction also negates any dualism objection to the  classical claim of a real union of spirit  and body being possible.


[For further  background, it may also  be mentioned here that the 2cV wave pulse interaction energy term, cited for human soul-body interaction, is of the same mathematical form as a wave interaction term  which  is also at the heart of quantum mechanics. A 2cV term occurs in the derivations of  Planck’s constant, of the de Broglie wave-particle equation, the Lagrangian  function, the wave funcfion operators for the Hamiltonian function and the momentum operator, and of  the uncertainty principle .  Clearly then, our   present  proposal that the 2cV  wave interaction energy can be  important has ample  precedent in another major field of  physics. [Appendix A  Compressible Flow and Quantum Mechanics)].


We conclude that  the evidence for the classical view of human nature and man’s spiritual essence is not only overwhelmingly  preponderant  from the standpoint of philosophy and theology, but, arguably, may  now  include evidence from science as well.


B.  Flow  Energy   It could also be the case that the soul may instead  act to initiate the wave pulse of velocity   c + us. Then The energies  of Equation 1 have different meaning, but the soul body interaction energy or union  energy  2cu is just as much a unity  as was the case in Paragraph  A above,  when the soul action was postulated  to provide the wave speed c. We now have


E =  c2 + 2cus + us 2


 C. Alteration of Wave Medium Characteristics


A third way for soul/body action to happen in a human cell would be for the soul,  by Lonergan’s principle,  to alter  the elasticity of the cytoplasm of the cell; this would  reset the quality of and speed c of the cell stress-strain waves.  Technically, this would mean resetting the values for  λ  and   μ,  the Lame’  constants of elasticity, which determine  the cytoplasm wave type and speed, c, and  ρ   is the density of the  wave medium,  which in our present case is the cell cytoplasm. Thus we  have:


c = [ (λ + 2μ)/ρ ]1/                                                                                                                              (2)


Other unique wave/human body interactions , especially neurological ones, may of course also exist, and await investigation.


At this point we may point out that if we consider the cited civilized  achievements of man scientifically from standpoint of the   prehistoric and historical timelines we see that the progress is exponential or logarithmic  Furthermore, such an exponential growth timeline over a period of some 200,000 years is unique to man among the primates since they exhibit  no civilized progress timeline whatever. This uniqueness requires  an explanation. Currently, only  the classical view that man is a a unique intellectual /spiritual being  provides such an answer..


A corollary to this uniqueness is that legitimate and desirable comparisons between man and the other primates must respect the total evidence. In a legitimate scientific – say neurological or psychological-- study of facts which are either similar or different among or between primates, it would appear to be  illegitimate to expansively  go on and state that, because of the established similarities  or differences  in the experiment , it is also then established that  man and the other primates are essentially the same  or essentially different. The essences are a matter  for philosophy.


 In addition to theoretically demonstrating the logical and scientific  possibility of a real  unity of soul and body , one that   disposes of any dualistic objection,  we now ask the question:  Is it possible to  scientifically detect and verify such soul/body wave action?




 8.0 The Possibility of Scientifically Identifying  Soul-Body Waves


The above three examples of wave interaction energy raise  the possibility  that  the  soul/body  waves in humans man may  be of a different quality than the wave quality and wave speeds which occurs in other  primates.  Might such  differences in  wave qualities between man and other primates  be detectible?


In Part A, on the Origin of Life,   we considered the  various  types of waves that  exist in physical nature.   These include:  low amplitude compression waves in liquids and solids, commonly called ‘acoustic waves;  stress-strain compression and dilatational waves of finite amplitude in solids and solid-like materials;  transverse waves of shear in solids and so on. In particular we proposed  that  stress-strain wave types should occur in the living cell.


What do we look for here?  Ordinarily in physical nature  various variations in waves  occur as deviations from the pure mathematical simplicity of, say,  the  classical  wave equation [Appendix A: Wave Interactions, Compressible Flow and Equations of State ],  For example ,  wave amplitudes  in nature, if large, may led to wave growth and then to shock wave discontinuities. There may also be variations in wave speed or in wave  phase.  Complex wave speeds also occur which are associated with wave resonance.  It is suggested therefore  that these  wave stability  distinctions, wave types, wave speed differences, and so on,  between human and other primates  be looked for,  especially in Man’s neurological manifestations..


For background, it may also  be mentioned that this 2cV wave pulse interaction energy term, cited for human soul-body interaction, is of the same form as a 2cV wave interaction term  which  is also at the heart of quantum mechanics.  This term  occurs for example,  in the derivations of  Planck’s constant, of the de Broglie wave-particle equation, the Lagrangian  function, the wave funcfion operators for the Hamiltonian function and the momentum operator, and of  the uncertainty principle .  Clearly then, our   present theoretical proposal that the  2cv  wave interaction  may be centrally important to human life   has ample  precedent in its central importance in another major field and other applications.. .[ Appendix B:  Compressible Flow and Quantum Mechanics)


We would conclude that  the evidence for the classical view of human nature and man’s spiritual essence is not only overwhelmingly  preponderant  from the standpoint of philosophy and theology, but, arguably, now  looks to and can invoke   evidence from  science as well.


For more details on wave theory and equations of state see Appendix A: Wave Interactions, Compressible Flow and Equations of State ]




9.0  Some Philosophic Dimensions


The relationship of science to philosophy is an interesting and subtle matter. Here let us simply  say that for our purposes, if the cell wave theory  for the origin of life  is experimentally validated , then the concept of emerging physical  order is restored to the discussion and random chance is discarded . Probability, but not chance, still remains and the full understanding of life and its origins will likely involve the emergence of orderly systems  on a  probabilistic time scale.


The  view of the nature of man in the present Part B  naturally also has  philosophic aspects,  just as other scientific approach to the nature of physical reality  and of human nature have done  in the past.  Lonergan has a comprehensive and reasoned  review of many of these scientific  world views in  his Insight [7].


Aristotle for example  “failed to grasp the abstract laws of nature of the classical type, and he also  explicitly repudiated the possibility of a theory of probability. His science was one of necessity and  not of derivable verifiable  physical laws.


The Galilean world view arose out of the accomplishments of mechanics.  It gave rise to a philosophy that was a deterministic  essentially mechanistic one of imaginable concrete observable “things”  obeying fixed laws. Probability is rejected as  implying current ignorance.


The Darwinian world view of a process of  survival by  natural selection  from  chance molecular genetic variations pushed out mechanistic determinism but obscured the concepts  of  order and structure [8].


Quantum mechanics introduced probability and uncertainty into the atomic world on a fundamental basis,  and in a spectacularly  successful way. Some of its  philosophic extensions have resulted in an indeterminist world view.


Our own foray (Part A) into the origin of life would replace neo-Darwinian  chance variations  with an orderly, physical system of stress strain waves in a solid-like cytoplasm. Specifically, it would be based on  order-neutral or order- favorable entropy change laws. Random chance is replaced by orderly probability.


Of course, a complete theory of life will almost  certainly involve more complex, interacting  systems,  metabolism, genetics,  neurology and so on.


Finally, in the case of man, there arise  the facts of intellectuality, reason and consciousness. Our choice of the classical/spiritual solution entails a more comprehensive philosophic viewpoint. What we have attempted is an integration of  verified facts of science with this philosophy, one  which we maintain accommodates and demonstrates  the proposed interaction and real unification of  spirit and matter in the human being.


We have also attempted  to investigate this human interaction  and to suggest that human wave interaction energies and wave properties may be essentially and  observably  distinct from  those of non-human animals, such as the other primates.  This additional proposition should be  scientifically observable.


Lonergan’s  careful analysis of the nature of reality,  and his definition of it as : “That which  can be intelligently  grasped  and   reasonably affirmed” , when thoroughly understood, provides  positive impetus,  opportunity and progress   for scientific work as  well as for philosophy [7].



10.0  Conclusions


We have maintained that the preponderance of evidence strongly supports the classical view of Man as a Rational or Spiritual animal,  versus a naturalistic  view that man is not essentially distinct from other primates.


At present only this classical view can offer a convincing  explanation and evidence for Man’s intellect or mind and his consciousness, unique activities and achievements.


A scientific analysis of the time line of human progress reveals a logarithmic progress.  A progress time line is unique to man, agreeing with the classical philosophic conclusion.


In this present Part B, we  also propos that man’s spiritual essence,  when embodied, may  act to generate human bodily waves which,  on the level of energy, can set up a wave  interaction unity of the most intimate kind, one  which disposes of any possible dualism objection. Also, such waves in their nature and action in the ensouled human body may in principle also be observable scientifically,  that is to say  neurologically. These waves would have properties which would be unique to man and  not found in other primates. 


The new approach may  help eventually in the process of an  integration of  philosophy and  science, and may possibly also lead to  a revived natural theology.





1.  Schrödinger, Irwin. What is Life?  Cambridge University Press, 1944.


2. Nagel, Thomas Mind and Cosmos: : Why the Materialist Neo-Darwinian Conception of Nature is Almost Certainly False (Oxford U. Press, New York, 2012).


3. Catechism of the Catholic Church: Section 365.  Publications Service,  Canadian Conference of Catholic Bishops, Ottawa, (Ontario) 1994.


4. Moreland, J.P., The Soul : How we know it is real  and Why it matters. Moody Publishers, Chicago. 2014. In this unique work Moreland  discusses various philosophic versions of soul- body dualism in a comprehensive and particularly lucid way.  


5. We have chosen homo sapiens for convenience  and general illustration.  If a later date is chosen for the start of man, say, Cro- Magnon  man,  then the logarithmic progress curve is essentially  unchanged.


6. Lonergan, Bernard J. F.,  S.J. Insight: A Study of Human Understanding. Philosophic Library, New York. 1956.


7. In the case of Man, we take the position that we are dealing with a being  whose mental activity relates to, not only basic intelligibility in physical data as with other animals,  but also to the  higher levels of consciousness and thought, that is  to such things as philosophy, science , mathematics,, and to   the myriad higher intellectual human activities involved in the fine arts, the practical arts, academic studies, theories,  and so on. In a word, to  human intelligence  as opposed to the simple basic sensitive animal detection of the  raw  intelligibility in  physical, environmental data.


This distinction between man and animal, or between ability to grasp the intelligible versus the ability to be  intelligent about the  intelligible  is dealt with extensively by Lonergan in his Insight. [6]:  He writes, for example:


1) “ …. The distinction between the intelligible emergent probability of prehuman process and the intelligent emergent probability that arises, is the measure that man succeeds in understanding himself and in implementing that understanding.”


2) “ in man there occurs the transition from the intelligible to the intelligent.”                       


3) “ ……and so in the limiting case of man, the intelligible yields to the intelligent …”


For Lonergan, intelligibility is the characteristic mark of material, physical reality, while intelligence or understanding and insight are the characteristic mark of man.


His theory of emergent probability offers  a rational, inclusive  framework for a philosophically and scientifically  integrated global world  view.


[8]. The difficulties with chance or random events in molecular biology are in contrast to physics, where the intelligibility in random kinetic molecular motions is seen as heat and is  then  described so successfully by the orderly laws of thermodynamics.


Copyright,  Bernard A. Power,  October,  2016

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Appendix A


 Wave Interactions, Compressible Flow and Equations of State 


3.0 Introduction


Our proposed solution to the problem of Dualism in Part B above  involved a wave interaction energy 2cV. The waves we are interested in are compression pulses in a compressible fluid, i.e. in a fluid capable of experiencing density variations and having a finite and variable wave speed c, (as opposed to incompressible fluids where the wave speed is theoretically infinite).  Specifically, these compression  waves are called  acoustic or ‘sound’ waves and are described by what is called the Classical Wave Equation.


This equation will be derived below. It is the description of all stable propagating waves of compression or rarefaction and of any amplitude, large or small. In compressible flow physics, the two equations of state for theoretical gases that support exact classical waves are called the Tangent/Tsien/Chaplygin Gas and the Orthogonal Gas


3.1 Compressible Flow


The physics of compressible flow [1,2]  embraces many fields, such as, hydromechanics, aeronautics, meteorology, jet flow, rocket propulsion, astrophysics and cosmology. Compressible flow is intimately linked to fluid wave motions. 


Its equations of state,  describing known, physically  real gases, are usually plotted in Cartesian coordinates on a pressure- volume or pv-energy  diagram in Quadrant  I, where the thermodynamic variables of pressure p, density or specific volume ρ=1/v , temperature T and pv-energy are all positive quantities. With one exception, the equations of state of gases linking pressure and specific volume  ( i.e. of a volume of a unit mass of gas  v = 1/ρ ) are hyperbolic curves on the pressure-volume diagram, for example the  Ideal Gas, atmospheric air, oxygen etc.



The exception is a hypothetical, or exotic compressible fluid called the Tangent Gas [3].   Its linear equation of state (p =  −Av +B)  was formulated in 1939 by H.S. Tsien in Quadrant I on the Cartesian pressure-volume  energy diagram  for aeronauticPs and rocket propulsion, and, in a slightly different form ( p =  −Av ) had already been formulated in 1904  by S.A. Chaplygin [4] for application to aeronautical  problems of jet flow and lift.


Figure 1. Equations of


An  extension of this linear Tsien /Chaplygin gas equation [ p = −Av] was made in 2001 from Quadrant I into Quadrant IV  in order to  obtain a cosmic flow with the negative pressure needed  to explain  the  observed acceleration in the rate of expansion of the  Universe  [5,6,7] .   


This Part 3  will outline the pertinent background  physics of compressible fluid flow and its equations of state. 



3.2  Compressible Fluid Flow

Compressible fluids change their shape and their density more or less readily. Those which are very compressible are called gases. Since they are subject to density changes as their pressure varies, they exhibit pressure waves of various sorts.  Their  physics  [1,2] embraces compressible  fluid mechanics, aeronautics, meteorology, jet flow, rocket propulsion, astrophysics, shock waves, supersonic flow,  cosmology, etc.

The quality of compressibility makes possible a wide variety of behavior in gases. Because of it, pressure waves are possible;, for example,  acoustic or sound waves, shock waves , etc.. The same physical principles also extend to quantum waves.

In known, or real gases, only compression waves are persistent,  rarefaction waves simply attenuate and die out. However, no known real gases will support waves of a finite amplitude --- such waves grow to compression shocks instead.  Only  very low amplitude waves, known as acoustic or sound waves, can travel unchanged for any length of time in real gases. One theoretical gas, however, known as the Tsien/Chaplygin gas or Tangent gas, is unique in that it can support finite amplitude  waves of either compression or rarefaction which remain stable. Expressed another way, we say that ‘these two linear gases ( p = −Av +B) obey, or support, the classical wave equation’.

The equations of state of most real gases ( linking pressure, volume, density and temperature)  are hyperbolic, ( e.g. pv = RT) and are depicted on the Cartesian pv-energy diagram in Quadrant I.

 The two principal hypothetical or exotic gases--- Tsien’s Tangent Gas  and Chaplygin’s negative pressure, cosmological gas----  actually have the same linear equation of state,  [p = −Av +B].


2.3  Equations of State of Gases

 A.  REAL GASES  ( Compressible fluid systems)

1. The Ideal Gas: Isothermal expansion  pv =constant =  RT   (Hyperbolic curve)            

                       2. Adiabatic expansion:  pvk = constant  (Hyperbolic curves)




The p-v plots of both of these real gas types are hyperbolic curves.


Figure 2. Cartesian plot of pressure –volume equations of state

in Quadrant I for the real Ideal gas and its adiabatic expansion


In the adiabatic expansion equation,  pvk = constant,  k  is the  ratio of the specific heats [k = cp/cp.].   For ordinary  atmospheric air,  k has the value  of 1.4.

The equation of state  variables are pressure (p) and volume per unit mass ( v = 1/ρ, where ρ is the fluid  density).





1. Tangent Gas / Tsien’s Tangent Gas :            p = −Av +  B  ( Linear; wave  speed c is real and positive). k = −1


2. Chaplygin’s Gas :      p =  − Av+  B  (Linear; wave speed c is real and positive).  k = −1


3. Orthogonal Gas ( Isothermal):  p = +Av +B  (Linear; wave speed is complex ic). k = +1


As we shall see, the plots of the equations of state of these three  exotic or hypothetical gases, linking pressure  p and specific volume,  v= 1/ρ ,  are linear, i.e. are all  simple straight lines on the pv-energy diagram.


3.4  The Tangent Gas Equation of State;  Unique Linear Fit  to the Classical Wave Equation

This  relationship in aeronautics  was formulated  in 1939 by Prof.  H.S. Tsien, co-founder  of the  Jet Propulsion Laboratory at Cal Tech, who is  also  known today as the Father of Chinese Rocketry. His equation is  called the tangent  gas” [1] (Figure 2). 

This tangent gas describes the behavior  of  a  theoretical fluid  whose linear equation of state [ p = −Av + B]  is placed on the pv-energy diagram so as  to lie  tangent to an ideal gas equation of state , or to an  adiabatic expansion equation [Fig.2].

Since  hyperbolic curves are somewhat difficult for manual computation,  Tsien in 1939, in the age of slide rule calculation for engineering work, well before the general use of computers, introduced this  simple approximate method consisting of drawing a tangent  line [p = −Av + B] to the hyperbolic curves at any desired point.  At or near  such a  tangent point on the ideal gas or the adiabatic expansion  curve,  his ‘tangent gas’ straight line   gives results very close to those of the hyperbolic real gas curve.

 The Tangent gas  approximation is unique (1) in that its equation of state describes the only known fluid, real or theoretical,  which  supports stable compression waves of any  amplitude  [1,8],  that is to say, it will theoretically propagate finite amplitude waves of expansion and compression  without them becoming unstable and growing to shock waves.  This is in contrast to known or real  gases,  such as the ideal gas or the adiabatic expansion gas, in which  waves of finite amplitude either die out, or grow unstably to become  compression shocks.  The tangent gas  (Tsien/Chaplygin gas) is also  unique in (2) satisfying the classical wave equation exactly,  without the approximations required for real gases.


3.5 The Tangent Gas and Quantum Physics Wave Equations


Quantum physics describes the world of the very small, namely that of the atom and elementary particles of matter at a space  dimension of around 10-9 m.


Atoms and elementary particles are described, not as point particles of matter, but instead as wave packets having a finite dispersion in space. An atom for example is at once a particle and a wave.


The wave equations describing the nature and behavior of the atomic and sub-atomic quantum world  are  derived from  the classical wave equation as a base,

 nd her relevant questions rom Part 2, Section ctualitye geersted in and move through bulk animal tissue  rarefaction ans of any

In quantum physics, various wave/particle equations are then added to the classical wave equation to obtain probabilistic  wave/particle equations describing the probable location of the particle in space and its various quantized` energy levels. For example:


as shown above, the classical wave equation is ( for one dimension x):


2 Ψ/∂x2 = 1/c2 ( ∂2 Ψ/∂t2 )


The Klein-Gordon equation for a spin-less particle is:


1/c2 ( ∂2 Ψ/∂t2 ) =  2 Ψ/∂x2  −( mc2 /h2 ) Ψ,


so that,  if the mass m is set to zero, the Klein-Gordon wave/particle equation  reduces to the classical wave equation.


In a similar manner,  the other quantum wave/particle equations, such as the Schrödinger equation, are derived.


Our point here is that a basic, starting wave equation for quantum physics is the classical wave equation.


The wave interactions that go on in quantum physics lead to interaction energy terms 2cV in the energy equations of quantum physics. We have then used this quantum physics example of wave energy  unity 2cV emerging from an interaction duality,  to clarify and  focus the argument in the Dualism debate in the Philosophy of Mind.


3.5.1  Wave/ pulse Interaction Energy 2cV


In the case of the classical wave equation, the wave pulses travel at the sum of the wave speed  c plus the flow speed u ( or V)


(dx/dt)I, I = c + u 

where u is the component of V in the x-direction.


Therefore, the wave pulse energy in the x-direction is the square of this pulse velocity, that is 


EΨ =  (dx/dt)2 I, II = ( c+ u  )2 = c2 + u2 + 2cu


and 2cu is the interaction energy between wave and flow in the x direction.


In three dimensional flow we have then,  ( c + V)2 = c2 + V2  +2cV.




3.6  The Orthogonal Gas: (Isothermal):


This is a new formulation of a theoretical gas, orthogonal to the Tangent Gas and with much the same properties,  which has a complex wave speed (ic)  and may have special pertinence to the theory of the functioning of the human Mind, since it involves resonance.




Equation of State


P = +Av +B


Wave speed is complex, ic















Lamb [8]  gives a complete 1-dimensional derivation of the classical wave equation as follows:


If the pressure p is a function of the specific density ρ only we have, without approximation


2ψ/∂t2 = ( p2 / po2 ) dp/dp   2ψ/∂x2                                    (1)


On the isothermal hypothesis that p/po =  ρ/ ρo ,  this becomes

3∂2ψ/∂t2 = po / ρo  2ψ/∂x2   / [ 1  +∂ ψ/ ∂ x ]2  for isothermal expansions       (2)


On the adiabatic hypothesis  p/po = (ρ/ ρo ) k , Eqn.1 becomes

2ψ/∂t2 = k po / ρo  2ψ/∂x2   / [ 1 + +∂ ψ/ ∂ x] (k + 1)                 (3)


For k = cp/cv= − 1,  Eqn 3 becomes the classical wave equation

2ψ/∂t2 = k po / ρo  2ψ/∂x2   = c2  2ψ/∂x2    or

 2ψ/∂x2 = 1/c22ψ/∂t2                            (4)



which is uniquely satisfied by the Tangent gas,  whose equation   of state is p = − Av +B = − A/ ρ   +B.


The Orthogonal Gas equation at right angles to the  Tangent Gas on the pv-diagram , namely p = +Av +B, is also a solution to the classical wave equation.


If the constant intercept B in these two equations of state is zero, then  the equation lines pass through the origin of the pv coordinate system  (Fig 1)and reduce to


[ p =  ± Av].




Fig. 1. Equations of State for Tangent Gas [p = −Av ]and Orthogonal Gas (p  = + Av) passing through the origin  ( i.e. when the  intercept B is zero. ).





Space solutions in one direction ( say x) of   Eqn. 4.  are expressed as  u = f(ct – x) +F( ct + x)  which represent two sets of waves traveling in the positive x- direction and the reverse.


Since  solutions to  the classical wave equation are  linear, they obey the superposition principle.


2,7.1  To sum up: The linear tangent gas  whose equation of state is  p = − Av +B is unique  among gases, real or theoretical, in that its waves,  of either  rarefaction or compression  and of any amplitude large or small, are stable and  obey the classical wave equation (4) derived  above.


The equation which is orthogonal to the tangent gas also  exactly supports classical waves.


3.7.2 The wave speed c in the Tangent gas is positive:  The wave speed c in a compressible fluid is given by


 c2 = dp/dρ

 and, since for the Tangent [ p = −Av +B] we have:

dp =−A d ρ-1 = −A (−1)  ρ-2  d ρ  so


dp/dρ = +  A/ρ2  which is positive in .


Therefore the interaction term 2cV for the tangent gas  is real and not complex.


3.7.3   The wave speed c in the Orthogonal Gas is Complex



As before, the wave speed c is given by,

c2 = dp/dρ


and, for the orthogonal equation of state [p = +Av  + B] = [+Aρ-1 +B] ,we have


dp = A d ρ-1 =  A ( −1)  ρ-2  d ρ 


dp/dρ = −  A/ρ2  which is negative  in sign , and so


c2 = = −  A/ρ2  and


c = i [A/ρ2] ½


so  that in Quadrant I, the wave speed of the Orthogonal Gas is complex. The symbol i is   the imaginary number  or   square root of minus one,   [−1]1/2. 


Physically this complexity means that the wave behavior is oscillatory or resonant at a particular point in space. This last result may have  importance for the  functioning of the human mind.


3.7.4    Waves of Compression in a Compressible Fluid or Thin Film: i.e. Acoustic or Sound Waves


The usual waves in compressible fluids and in thin films are acoustic or ‘sound’ waves. They are described by the classical wave equation, but are approximations to it. For example sound waves in air must be of low amplitude, otherwise any finite amplitude waves will at once grow to shockwaves.


The equation describing these stable acoustic small amplitude waves is the classical wave equation. The thermodynamics of air for example is  described by  the ideal gas law [pv = RT ], but if sound waves in air are to be  described by the classical wave equation then the restriction to infinitely low amplitude waves must be applied.


Acoustic or ‘sound’ waves occur in liquids and in solids as well.  The acoustic wave speed or speed of sound c is considerably higher in liquids than in gases  and is higher still in  solids. In air this speed is about 334 m/s at sea level conditions. In water and watery bodily tissue it  is 1540 m/s.






Quantum physics describes the world of the very small, namely that of the atom and elementary particles of matter at a space  dimension of around 10-9 m.


Atoms and elementary particles are described, not as point particles of matter, but instead as wave packets having a finite dispersion in space. An atom for example is at once a particle and a wave.


The wave equations describing the nature and behavior of the atomic and sub-atomic world  are  derived from  the classical wave equation as a base.


In quantum physics various wave/particle equations are then added to the classical wave equation to obtain probabilistic  wave/particle equations, describing the probable location of the particle in space and its various quantized` energy levels. For example:


The classical wave equation is ( for one dimension x):


2 Ψ/∂x2 = 1/c2  2 Ψ/∂t2.


The Klein-Gordon equation for a spin-less particle is:


1/c2  2 Ψ/∂t2 =  2 Ψ/∂x2  −( mc2 /h2 ) Ψ,


so that  if the mass m is set to zero, the Klein-Gordon wave/particle equation  reduces to the classical wave equation.

 nd her relevant questions rom Part 2, Section ctualitye geersted in and move through bulk animal tissue  rarefaction ans of any

In a similar manner  the other quantum wave/particle equations such as the Schrödinger equation are derived.


Our point here is that a basic starting wave equation for quantum physics is the classical wave equation which has the Tangent/orthogonal Gas as its only exact pv solution.


The wave interactions that go on in quantum physics lead to interaction energy terms 2cV in the quantum pulse energy equations. We have then used this quantum physics example of wave unity 2cV, emerging from an interaction duality,  to clarify and  focus the argument in the Dualism debate in the Philosophy of Mind.


3.8.1  Wave/ pulse Interaction Energy 2cV


In the case of the classical wave equation, the wave pulses travel at


(dx/dt)I, I = c +u 

where u is the component of V in the x-direction.


Therefore the wave pulse energy in the x-direction is the square of the pulse velocity, that is 


(dx/dt)2 I, II = ( c+ u  )2 = c2 + u2 + 2cu


and 2cu is the interaction energy between wave and flow in the x direction.


In three dimensional flow, we then  have for the flow energy : ( c + V)2 = c2 + V2  +2cV, or (c − V)2 = c2 + V22cV.

             [ Check the following insert for useful phrases etc.


6.0 The Physical Setting: Waves and Equations of State


The introduction of soul/body wave interactions, which are in principle are  open to being  neurologically verified as unique to humans, brings in the  physics of waves. Waves in turn are a part of compressible flow physics and of  hydrodynamics [Shapiro, C & F, Lamb, Prandtl and Tjetiens 


Compression/expansion systems ( gases and liquids)  have   equations of state describing their thermodynamic variables, namely pressure p, specific volume v, density 1/v,  and tempersture T. These systems  are plotted as curves on  a pressure versus volume diagram.



Curve A.. Most known compressible systems, gases and liquids, have hyperbolic equations of state. .[ Fig. 1.  Curve A)]



These have waves which tend to grow to form compression shocks, except when  they are  of infinitely low amplitude, in which case they  are linear, stable and called ‘acoustic waves’.[ Fig. 1.  Curve B)]









B. Curve B: The acoustic systems are quasi- linear and are described by a linear equation of state known as the Tsien/ Chaplygin /Tangent  gas. ]Figure I., Curve B].










Figure 1. Equations of State of liquids and gases


Curve C:. Theoretical, rarefaction or expansion  waves in fluids would have reverse curvature on the pv-diagram [Fig. 1, Curve C] None are  known to exist.


Note: Systems in Quadrants II.III.IV would be  purely theoretical with negative values of pressure or specific  volume.  The properties of  Quadrant II have been investigated. ( Body and Soul Problem )


  In a second instance  of use, in connection with the problem raised by the recently observed acceleration  the expansion of the universe, the Tsien/Chaplygin Gas was extended down  into Quadrant IV and the  negative pressures theoretically available  there were  used to explain the  high expansion rates observed by astronomers.       


 Wave References


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


2. Courant, R.,  and K. O. Friedrichs,  Supersonic Flow and Shock Waves. nterscience , New York, 1948.


3. Tsien,  H,S.,  “Two-Dimensional Subsonic Flow of Compressible Fluids,” J. Aeron. Sci. 6, 39, 1939.


4. Chaplygin, S.A., “On Gas Jets”,   Sci. Mem. Moscow Univ. Math. Phys. 21, 1.  1904.


5. Bachall, N.A., J.P. Ostriker, S. Perlmutter and P.J. Steinhardt. “The Cosmic Triangle:    Revealing the State of the Universe,”   Science,  284, 1481 (1999).6..


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

7.  Bilic, N.,  G.B. Tupper and R.D.Viollier,  “Unification of Dark Matter and Dark Energy: The Inhomogeneous Chaplygin Gas,”  Astrophysicsatisfying


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



End of Appendix B



Copyright,  Bernard A. Power, June 2016

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Appendix B


Compressibility and Quantum Mechanics




Compressibility and Quantum Mechanics

Quantum Wave Function

Normalized Quantum Wave Function

The Extra Energy term 2cV and Fundamental Quantum Relationships

Mass Ratios of the Elementary Particles of Matter

Quantum Wave Speed, Entanglement and Collapse of the Wave Function Problem



While this subject has not yet been studied in great detail, there are some  aspects which already indicate that compressible flow and the UF Universal Field)  concept are intimately related  to quantum phenomena, just as has been shown above for electromagnetism and gravitation.

The standard model of quantum physics is one of the most remarkable achievements of science.  It explains an enormous range of nuclear and atomic phenomena to a very high degree of accuracy, and is logically quite consistent.  Yet, for all its success, it has some serious deficiencies.

For example, while it is very successful in describing many aspects of particle creations, annihilations and interactions, it still has no predictive power to specify the values of the observed masses, and the mass-ratios of the elementary particles – the experimentally determined values of these masses must still be put into the theory by hand.  Again, it requires the arbitrary introduction of various fundamental constants, such as the speed of light c, and the fine structure constant of the atom α, which are essential for its calculations, but for whose physical existence or numerical value it has no explanation whatsoever.  Again, quantum physics is still essentially unrelated to classical mechanics, and although it can be related to electromagnetic theory through quantum electrodynamics, this is so only for the cases of the electron – the phenomena of the nucleus of the atom are as yet still essentially unrelated to the rest of physical science in the standard model of quantum theory.  Perhaps most seriously it has no explanation for the physical nature of the basic quantum wave function, nor for the transfer through space of quantum information, nor for the famous problem of the ‘collapse of the wave function’, nor for the wave/particle duality of matter. Yet again, quantum physics has little relationship to relativity, gravitation and cosmology.

Here we shall touch on only a few key aspects  as an indication of the relevance of the compressible  field (UF)  theory to quantum physics.                

6.1 Compressibility and Quantum Mechanics

We shall take the position that all quantum phenomena are basically compressible energy flow manifestations. The basic energy form ( variously to be called a characteristic, ray, wave pulse, wavelet, etc.) is the quantum wave function ψ which refers to a single, compressible, enray pulse or wavelet.

More complex waves ( elementary particles, etc. ) are built up from the linear enray ψ by superposition in a irreversible  shockwave compression event.


1. The unsteady flow ( wave pulse) energy equation is, as shown above 


c2 = co2 – (1/n) V2 – 2cV/n                                                                   (6.1)


where the extra energy term 2cV/n is the result of the pulse or acceleration of relative motion. For the electromagnetic case tthis could refer to the energy of the acceleration or oscillation of a charge which generates the electromagnetic waves.  All the other basic quantum relations such as the  de Broglie wave /particle equation  p = h/λ, the  Heisenberg uncertainty relationship, the quantum operators for position and momentum and so on, can also be derived  from this 2cV or ‘extra energy “ term. ( see  below)

6.2 Basic Quantum Wave

The wave function  ψ is the linear, ‘characteristic’, or ‘ray’ solution, of the hyperbolic, linearised, approximate differential equation called the classical wave equation

Ñ2ψ = 1/c2  2ψ/∂t2 ;         2ψ/∂x2 = 1/c2  2ψ/∂t2                                                                             (6.2)

Therefore, the basic formula for the characteristic or ray is as follows:

Ψ = c ± V

This may also be complex, as                                              Ψ = c ± iV  


6.3 Quantum Wave Function

ψ = c ± V                                                                                     (6.3)

Here, V is the relative velocity and may be set to zero, making c = co in the ‘at rest’ coordinate system chosen. (cf. Sects. 2.8; 5.2). For an energy flow, co is 3 x 108m/s.

In general, ψ is complex, and we then have

ψ = c ± iV                                                                                      (6.4)

and                                                                                     ψ2 = c2 – 2icV  +V2

The physical nature of the quantum wave function is thus the relative flow velocity  V ( or particle  momentum, mV = p)  plus the wave velocity c (or wave momentum, mc).

This still leaves open the question of  the physical nature of the wave and the wave field, which however have been dealt with above where the classical waves of the Universal Field (UF) ( n and k both equal to –1) were  considered both for electromagnetism and for gravitation.

6.4 Normalized Quantum Wave Function

From the kinematic energy flow equation  (c/co)2 = 1 – 1/n (V/co)2,   we have the normalized wave function

  ΨN = c/co + i V/co;        ψ*N = c/co – i V/co                                                                                              (6.5) 

For small V, this reduces to ψN ≈ c/co.

This  wave speed ratio c/co relatesof course,  to  all the isentropic, thermodynamic ratios    p/po, ρ/ρo, T/To  as

c/co = [p/p­o­]1/(n+2) = [ρ/ρo]1/n = [T/To ]1/2


For the UF where k = – 1 = n, we have                  

c/co = p/po = ρo/ρ = [T/To]1/2                                                                      6.6)

The Fitzgerald/Lorentz contraction factor in the general case is now c/co = [ 1 – (1/n) (V/co)2 ]1/2 . For the UF where n itself is negative, this has the minus  sign reversed to become 

c/co = [ 1 + V2 /co2 ]1/2                                                                           (6.7)

a new Lorentz relationship which requires special study.


6.5 The ‘Extra Energy’ Term, 2cV yields the Following Fundamental Quantum Relationships:

The unsteady energy equation

c2 = co2 – (1/n) V2 – 2cV/n                                                                   (6.8)


contains a wave pulse energy term 2cv. Here we show that this then yields the fundamental quantum relationships as follows


a)  Planck’s Constant  h

For n = 1, if cV = constant energy for each  waves, then cV/υ = constant energy per cycle or pulse:

cV/υ = h

cV = hυ = hω/2π = ħω = ευ                                                                                                                (6.9)

For the complex case,

cV/υ = ħ/I = -iħ


b)   De Broglie Wave /Particle Equation

cV/υ = h

But c/υ =  λ;  V(m) = p (momentum), so

λp = h, or

p = h/λ                                                                                     (6.10)


c)   Lagrangian Function, L

L = 2cV 


d)   Quantum Wave Function Operators :

1) Hamiltonian Energy Operator

cV= hυ = -ħω = ε                                                                          (6.11)

icV = -iħω


iω = ∂../∂t, and so cV = h/I ∂../∂t = +iħ∂../∂t = Hop

which is the Hamiltonian energy operator.

( To ensure correct dimensions, it must be applied to the normalized quantum function ψN).

2) Momentum

cv = hυ = +hω = ε

V = (1/c))ħω, or (m)V = p = (m)(1/c)ħω

Multiplying by i, we have:         

 (m)iV = (m)(1/c) iħω

= (m)(1/c) ħ ∂../∂t

So, we have

(m) V = p = (m)(1/c) iħ ∂../∂t


I1/c) ∂../∂t = ∂../∂x, and so

(m)V = p = -iħ∂../∂x = pop                                                                                                                (6.12)

which is the quantum wave operator, ( to ensure correct dimensions, it must be applied to the normalized quantum function ψN).


e)   Heisenberg Uncertainty Principle             

cV = hυ;  cv/υ = h

λV = h

But λ = Δx and V(m) = Δp, so

Δx . Δp ≥ (m) h                                                                              (6.13)

which is the Heisenberg uncertainty principle.



It has been proposed that all elementary particles of matter (with the possible exception of the neutrino) are condensed energy forms. The forms are given in terms of a simple, integral number n ( n = degrees of freedom of the compressible energy flow):

Baryons and Heavy Mesons

For the baryons and heavy mesons the energy condensation that produces the mass is postulated to take place via the strong shock option [  ] and is proportional to the shock strength given by = [n+1]1/2

mb/mq = Vmax/c* = [n+1]1/2                                                                                                                       (6.14)


mb is the mass of any baryon particle, mq is a quark mass, Vmax = co n1/2 is the escape speed to a vacuum; that is, it is the maximum possible relative flow velocity in an energy flow for a given value of n, the number of degrees of freedom of the energy form,   This is a non-isentropic relationship, and it corresponds physically to the maximum possible strong shock.

Experimental evidence for this new baryon mass ratio formula is given in the following Table :


Experimental Verification of the Mass Ratio for Baryons and Heavy Mesons


n     n +1     [n+1]1/2    Particle         Mass (mb)        Ratio to

                                                      (MeV)            quark mass

0     1             1          quark (ud)         310 MeV          1

                                             (s)          505


2     3             1.73      eta (η)                548.8               1.73      



5     6             2.45       rho (ρ)               776                 2.45



8     9             3          proton (p)            938.28          3.03  (1)

                                  neutron (n)           939.57         3.03

                                   Λ  (uds)             1115.6          2.97  (2)  

                                    Ξo (uss)             1314.19        2.99  (3)

9   10           3.16          Σ+  (uus)            1189.36        3.17  (2)

10   11         3.32          Ω-  (sss)             1672.2         3.31  (4)

Note: Average quark mass is 310 MeV; (2) Average quark mass is (u + d+ s)/3 = 375 MeV  (B) Average quark mass is (u+s+s)/3 = 440 MeV; (4) Average quark mass is 505 Mev.

Therefore, Equation 21 is verified to within about 1%.


For the UF with k = − 1 = n,  shocks are impossible, since V can approach but never equal c [  ] and the Mach number M = V/c never reaches or exceeds unity, as required for condensation shock formation . Also, we see that in the UF   [ n + 1]1/2  becomes zero, again confirming that no mass condensation of flow energy can take place in the  UF. Thus, the origin of the energy condensation which is our  postulated origin for the emergence of mass takes place entirely in World A where n is positive.


Leptons, Pion and Kaon

We form  the ration of the  mass of each lepton mL to the mass of the electron me  as          

mL/me-  =  k/α2 = [(n+2)/n]/α2 = {(n+2)/n] x 137                                                 (6.15)

where α = 1/11.703 is the fine structure constant, and k is the adiabatic exponent or ratio of specific heats, k = cp/cv = [(n+2)/n]. Because of the presence of k, this formula for the mass of the leptons is a thermodynamic and quasi-isentropic one.

The leptons are formed via the weak shock option.

The experimental evidence for the lepton mass ratio formula is given in Table below.


Lepton Mass ratios

n     k = (n+2)/n       Particle                  Mass               Ratio        Ratio

                                                              (MeV)              to           x 1/137


1/3           7              Kaon  K±               493.67            966.32          7.05

2              2              Pion π±                  139.57            273.15          1.99

4              1.5           Muon μ                  105.66            206.77          1.51

-                -             Electron                 0.511              1


Clearly, k ≈ ml/me (1/137), supporting Equation (22).


6.7 Quantum Wave Speed, Entanglement and Quasi- instantaneous Collapse of the Wave Function Problem


A examination of these quantum subjects indicates that a quasi-instantaneous transfer of quantum information would  remove many of the difficulties and some so-called quantum weirdness, including action at a distance problems.  It is natural then to  propose some  connection between the  quasi-instantaneous secondary  wave pulses we have discussed at the p = 0 discontinuityand which arise witrh all UF waves  if we set po the static  pressure at 6.673 x 10-11 , that is to say so near to the zero pressure point that all quantum wave oscillations automatically must reach the zero pressure point and be reflected and quantized as we have described above.


The possibility of a secondary wave of quasi- instantaneous speed being generated then emerges. This secondary, quasi instantaneous wave is proposed as a quantum information wave. It appears suitable for the transfer  of information at superluminal but not quite instantaneous speeds, and so able to deal with the quantum theory problems such as those  associated with action at a distance, quantum entanglement  and collapse of the wave function. and others..  


SUMMARY:  We have been able to  related the  fundamental quantum relationships to a single energy pulse term 2cV/n. in compressible flow theory.

We have, in effect, quantized the various energy ‘fields’ represented by 2cV/n for various values of n, by equating them to the ‘time-like’ condition set by the frequency υ in the quantum equation hυ = 2cV/n.

(Note that these equations, as is usual in compressible flow theory, are for ‘specific’ energy, that is, for  unit mass flow. For a definite particle, the numerical value of the mass is to be inserted --  the dimensions of the equations being  not thereby changed, since in our system, mass (m) is dimensionless. Thus, for the photon, we have hυ = mγ cV, where mγ is the relativistic mass of the photon. In terms of the photon momentum, we have

             hυ = (m)cV = cp                                                                  6.16)

which is the de Broglie equation for the photon  Other fundamental difficulties with quantum  theory may also be removed by the introduction of the new  quasi-instantaneous speed for the transfer of quantum information through space..


7. Experimental Evidence for the Existence of the Universal Field


The above Sections have presented mostly theoretical evidence for the reality of the UF.


Naturally, verification of the theory will also require experimental evidence.  . The mass- ratio evidence in Section 6 is one  such set of experimental evidence. Another is the well established  optical shifts related to relative motion and accelerations of the Michelson-Morley, Fizeau and Sagnac type experiments Here, Lorentz himself was of the opinion that any optical effect whatever, such as a fringe shift  of any magnitude   constituted  disproof of special relativity and he quoted Einstein to back  up his opinion.


A new experimental approach emerges as a consequence of the new orthogonal isothermal equation of state. This isothermal state    requires a flow of heat  (∆Q) to accompany any UF wave activity. Some of this heat may possibly flow to the UF from  our  real physical world A, in which case temperature fluctuations should in principle be detectible. Preliminary, but quite extensive, experiments carried out nearly two decades ago did detect temperature fluctuations apparently linked to the inertial forces accompanying mass acceleration. These previously inexplicable findings are currently being re-examined in the light of the new UF wave theory.




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


3.-----------------------,  NASA Proposal: Control No. K- 2453;  Date:, 03-31-80. Implications of a Photon Shock Wave Effect for                                      the Fizeau Experiment on the Velocity of Light in a Moving Medium.

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  Copyright 2005 Bernard A. Power [Consulting meteorologist (ret.)]