Part B
What is Human Life? A Classical Viewpoint with
a Verifiable Scientific Hypothesis
Contents
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
References
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
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
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
agriculture
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
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.
References
1. Schrödinger, Irwin. What is Life?
2. Nagel, Thomas Mind and Cosmos: : Why the Materialist Neo-Darwinian
Conception of Nature is Almost Certainly False (Oxford U. Press,
3. Catechism
of the Catholic Church: Section 365.
Publications
Service, Canadian Conference of Catholic
Bishops,
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,
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
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 State.
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
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).
B. HYPIOTHETICAL GASES
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,
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
3.7 THE CLASSICAL WAVE
EQUATION :
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/c2 ∂2ψ/∂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.
3.8. 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 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.
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
+ V2 −2cV.
[
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 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,
2. Courant, R., and K. O. Friedrichs, Supersonic
Flow and Shock Waves. nterscience ,
3. Tsien, H,S., “Two-Dimensional Subsonic Flow of Compressible Fluids,” J. Aeron. Sci. 6, 39, 1939.
4. Chaplygin,
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.
End of Appendix B
.
Copyright, Bernard A. Power, June 2016
Compressibility
and Quantum Mechanics
Subjects
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
But
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
But,
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.
6.6 MASS RATIOS OF ELEMENTARY PARTICLES
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
1
2 3 1.73 eta (η) 548.8 1.73
3
4
5 6
2.45 rho (ρ) 776 2.45
6
7
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%.
Note:
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
Electron
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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3.-----------------------,
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Date:,
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Association for the Advancement of
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Copyright
2005 Bernard A. Power [Consulting meteorologist (ret.)]