How Did Life Originate? The Role of Cell Waves and their Negative Entropy
What is Human Life?
Alternative Post-Modern Views on Ancient Questions
Part A: Origin of Life
About seventy years ago Irwin Schrodinger proposed that life originated when negative entropy or ‘negentropy’ permitted the necessary complex physical order of life to emerge. The lack of any physical mechanism to produce the supposed favorable entropy occurrences however, led to eventual neglect of his proposal.
It is proposed ,however, that a feasible physical process with the required entropy change characteristics does exist in stress- strain waves which occur in solid or semi-solid materials. Therefore, since the cytoplasm of the cell is a semi-solid to solid material, then stress – strain waves will occur in the cell and will furnish and maintain a favorable entropy environment allowing the complex bio-molecules and the orderly systems of life to emerge, as Schrodinger proposed. This biological wave proposal is readily testable in the laborstory.
Part B: Human Life (In Preparation)
Part A: How Did Life Originate ? The Role of Cell Waves and their Negative Entropy
Part B: What is Human Life? (In Preparation)
After food, drink and shelter, the most important need of every one is surely some personal, satisfying answer to the questions of Who am I? What am I? Where am I going? What is the meaning of my existence? How should I live, and Why? How do I fit into the world around me? What is reality? How do I know what is true? The answers to these questions shape the direction and quality of each individual life. In sum, they may frame a civilization.
Today, there appear to be two main classes of belief about these question in the western world: Many, perhaps still a majority, follow some variant of the classical view and believe that we humans are essentially intelligent or spiritual creatures. From Aristotle’s great definition of ‘Man the Rational Animal’, to the refined mediaeval synthesis of Aquinas and the Schoolmen, to the many splendid critiques of modern times, this view has produced the civilized west, including the origins and development of its physical science. Parallel beliefs have founded the other great world civilizations.
Recently, many in post- modern science have abandoned classical and mediaeval roots, and, instead, now assert a materialist, neo-Darwinian, naturalism, which is uncritically assumed by many to constitute a viable, general view.
The American philosopher, Thomas Nagel, in his Mind and Cosmos, (Oxford U. Press, 2012)  presents a critical counter view that this physical, neo-Darwinian conception of nature, including man and his consciousness, is almost certainly false. As an atheist philosopher, he looks forward to the emergence of some purely naturalistic, but non- material factor, to resolve both the origin of life and ma’s consciousness.
We shall in Part A present the argument for a physical factor to explain the origin of life, but, in Part B, we examine the classical view for an immaterial, spiritual factor for the man’s intellect and his consciousness,.
How Did Life Originate?
The Role of Orderly Cell Waves and their Negative Entropy
1 Some Current Theories
The current scientific answer to the question of how life originated on earth is most commonly a naturalistic, physical, neo- Darwinian, evolutionary reductionism. Physical matter acting through well understood probabilistic interaction laws gradually produces physical complexity. First, in what is called the chemical evolution, the atoms form the bio-molecules of life, the amino acids. Then the amino acids gradually assemble to form the proteins, or building blocks of life. The genetic molecules RNA and DNA follow. Lipid, spherical proto-cells emerge to enclose these bio-molecules.. The process is physical, naturalistic, random and very slow. The emergence of the order and complexity of the living cell is seen as a continuation of emerging probabilistic physical complexity, taking place probably in a quiet, ‘warm pond’ environment. [1,2,3].
Historically, a major obstacle to full acceptance of this model has been a thermodynamic one involving entropy. Non-living processes obey the 2nd law of thermodynamics, and so, physical changes are always accompanied by an increase in entropy, -- that is to say, changes in entropy in any non-living physical process are always net positive and lead to an increase in the amount of uniform randomness. This opposes the emergence of complexity and order. With living things, however, it quite obviously works in the reverse -- they produce locally an increase in order and complexity, which means there has locally been a decrease in entrop. . How can this local entropy decrease be physically explained? Or brought about in the laboratory?
The negative entropy concept was proposed by Schrodinger on theoretically speculative grounds and he offered no physical mechanism. Quite naturally an intricate and lengthy thermodynamic controversy has followed.
Some have dismissed this negative entropy change as being a problem at all, by arguing that, while the entropy does decrease within the restricted living organism, still, the overall entropy, including that in the organism’s environment, always experiences a net increase as required by established 2nd law thermodynamic theory. This has led to the term dissipative systems in which living organisms are seen as overall entropy producers with one of their requirements being the ability to dissipate the entropy produced. To many, however, this is still not really satisfactory, as it leaves unresolved the matter of the undoubted local reduction of entropy within the living, developing organism.
Here are some additional current facts and theory:
.1. Life emerges from the inorganic physical world, first by the gradual, probabilistic chemical evolution of the necessary organic constituents of life, the amino acids, complex bio-molecules, DNA/RNA. and proteins. Much of this chemical evolution proposition has been experimentally supported by the results of the Miller/Urey type laboratory experiments  and by Fox [5a] with his work on peptides.
2. Later, a protocell consisting of a cytoplasm, enclosed by a lipid cell membrane, emerged by the same probabilistic process. The attempt to duplicate this protocell step in the laboratory, however, is still currently a work in progress.
3.The first single-celled organisms emerged about 3.5 -4 billion years ago. This is confirmed by the fossil record.. Simple multi-cell organisms emerged about 3 billion years ago.
4. About 500 million years ago, a great proliferation of multi-cellular animal life emerged at the time of the so called Cambrian Explosion At that time, within a spell of only 25 million years or so, all the major ancestral forms for modern animal life emerged. This is well based on the vast fossil record, but an explanation for the quite sudden emergence and relatively brief duration of the proliferation of these complex living things is still a matter for debate.
5. Since then, neo-Darwinian evolution has produced the immense variety of our modern living plants and animals. This is supported by the fossil record and other evidence.
The above theoretical structure for the origin of life, while very incomplete, is supported by the preponderance of the available evidence.
Two present day active research approaches are (1) the ‘genetic approach’ in which the evolution of genetic processes and RNA/DNA is proposed to have happened first, and (2) the ‘metabolic’ approach according to which the proteins emerged first.
Another research approach is the Clay Hypothesis, which involves a catalysis furnished by certain clay minerals. It has been shown to increase the rate of production of some biochemical species 100-fold.
Major unsolved problems are (1) a reason for the local entropy decrease with life in general, (2) the reason for the long delay between the first single-celled organism and multi-cellular life, and (3) the lack of laboratory replication of a living cell.
2. A New Solution: Negative Entropy Flow Produced by Stress Waves in Cell Cytoplasm
A proposal that would produce the required local entropy decrease in the cell is that stress-strain waves occur in the cell cytoplasm, and their favourable neutral or negative entropy change characteristics encourage and sustain the complex order needed for life.
This would supply the original Schrodinger negative entropy proposal  with the physical process needed to ground it as a probable mechanism in the emergence of life.
This wave proposal is also open to experimental testing. If experimentally verified, such a physical, cytoplasm wave process would overcome a major flaw in the present purely probabilistic theories.
Stress-strain waves do not occur in gases or liquids. Therefore, our proposal requires that the cell cytoplasm have a solid, or at least a semi- solid, nature. This is in fact the case, which is rather remarkable since the cytoplasm is about 80% water. However, the cytoplasm has many dissolved substances, and solid inclusions called organelles, and, when probed experimentally it is found, in fact, to behave variously as a gel, a visco-elastic solid, a glass- like solid, and so on. Thus, the cytoplasm does behave as a stress-strain medium and can support stress-strain waves. This cytoplasmic wave support accounts, for example, for the successful ultrasonic acoustic medical imaging of living tissues.
O course, the living cell is a very complex entity, and enormous amount is know about it. Here, we are simply going to look at the one physical factor of negative entropy -- already studied for generations -- but now based on a physical source of entropy changes, namely cellular wave action; this proposal with its physically based negative entropy change opens up a pathway for the orderly emergence of the complexity and biological order at the single cell level, and so is a key factor in the problem of the origin of life. The details of how this proposed favorable factor of cell wave action night act in the emergence of the other extraordinary complexities of living cell life is then a matter for cell biologists.
3. Cytoplasm Wave Types and Negative Entropy Change
Waves can occur in gases, liquids and in solids. In gases and liquids [6,7,8,9,10] these waves tend to be longitudinal compression waves, which are generally unstable, and which then grow to become shock waves. A stable exception is with the very low amplitude compressions, called sound waves or acoustic waves.
Currently, the cell cytoplasm is seen as being a gel-like material having sometimes the characteristics of a liquid crystal and sometime as behaving as a semi- solid or even as a glass- like solid. For another example, it is found to act as a solid when probed by force spectrum microscope.
Solid-like materials support stress-strain waves . [Kolsky: ‘Stress Waves in Solids’, 11] and so it is stress-strain waves of various types that will occur in the cytoplasm.
These waves are no longer only longitudinal compression waves, as in liquids and gases, but they are much more varied. They can be:
(1) Stable longitudinal compressive waves of both low amplitude ( i.e. acoustic, sonic and ultrasonic) and of large amplitude ;
(2) Stable rarefaction, expansion or dilatational waves, also of either low or large amplitude;
(3) Distortional , lateral or transverse waves;
(4) Standing waves;
(5) Surface stable waves, called Rayleigh waves, can also occur on a free surface of a solid;
(6) If the stress is not linearly proportional to the strain, then the wave motion is more difficult. For example in plastic materials, shock waves can then occur, of both rarefaction and compression. Hysteresis effects also occur.
This list is not exhaustive, but it will serve to show the wide variety of possibilities for orderly wave motions that will exist in a quasi-solid cytoplasm, and, consequently, the possibilities for the desirable negative or neutral entropy change conditions that these cytoplasm waves may support.
A general wave equation, known as the classical wave equation, is as follows:
∂2Ψ/∂ x2 = 1/ c2 ∂2Ψ/∂t2
This equation describes stable waves which, in gases and in most liquids, are limited to infinitely low amplitude waves, called acoustic or sound waves, such as those in air. In these stable, low amplitude waves, the motion is adiabatic so that no entropy changes occur. [6,7,8,9,10].
In a solid-like cytoplasm, however, most waves, whether of low or large amplitude, of compression or of rarefaction are stable.. The wave motion in solids can be either (1) adiabatic with no entropy change, or (2) isothermal with either increase or decrease in entropy. Thus, in the stress- strain waves in solids, for a majority of the time, the entropy changes dS will be either (1), zero, i.e. neutral or not opposing the order of life to emerge or (2) it will be negative [ dS = -ve] and so will positively favor order to emerge. Stress –strain waves in the cytoplasm will therefore provide the missing physical basis for Schrodinger’s negative entropy hypothesis.
Entropy Changes in These Cytoplasm Stess-Strain Waves [12,13,14]
Entropy and its changes are subjects in thermodynamics and physical chemistry [12,13,14].
Entropy (S) is a thermodynamic entity related to random kinetic energy, i.e. to heat and temperature. It is defined as:
dS = dQ/T
where dS is entropy change, dQ is heat change and T is the absolute temperature.
Entropy can be interpreted as a measure of the randomness of arrangement of a system. Thus an ordered system has lower entropy than a random one. A positive entropy change ( +ΔS) indicates the system has become more random or chaotic. A negative entropy change process ( −ΔS) is one that is becoming more ordered, more complex, less random.
Living systems are ordered and require negative entropy processes(-ΔS.). The emergence of new order is opposed by and existing order is broken up by the addition of random kinetic energy ( such as heat), i.e. by a positive entropy change (+ΔS).
In a wave train the local heating and cooling accompanying the pulsations of compression and rarefaction are related to entropy changes according to whether the change goes on adiabatically with no external heat flow into or out of the system, or isothermally, where the temperature is kept constant, and compensating for the heating and cooling pulsations of the wave train is by external heat flowing in and out..
If the wave pulsations are so rapid that the expansions and contractions are faster than the rate of heat diffusion, then the wave is said to be adiabatic and the heating and cooling energy of the wave pulses comes from the wave medium’s internal energy. The external heat flow dQ is then zero and the entropy change dS becomes zero. Adiabatic waves are therefore neutral with respect to the emergence of order and complexity.
If the wave motion is isothermal, as is especially the case with low frequency disturbances, then heat flows into the system upon expansion and out upon compression. The accompanying entropy change is then positive (+ΔS) for expansion cycles and is negative (-ΔS) for isothermal compressions. Thus, isothermal compression waves or wave segments with their negative entropy change are favorable for the order and complexity of life to emerge and function.
However, conditions for isothermal waves are less frequent than for adiabatic waves; the latter are the general l rule for cell waves.
The case for an ideal gas is simplest and most illustrative. There, the entropy change is related to tempersture and volume change as follow:.
ΔS = SB – SA = Cp lnTB/TA –R ln pB/ pA
ΔS = SB – SA = Cp lnTB/TA – R ln vA / vB
(a) For an isothermal wave , TA and TB are equal and so the equation reduces to:
ΔS = R ln vB /vA = R ln pA/ pB
Then in an isothermal expansion vB is greater than vA , and pA is greater than pB so that the entropy change ΔS is positive.
Bur, conversely, for an isothermal compression, the entropy change ΔS will be negative.
(b) For an adiabatic wave: The vibrations are so fast that all heat flow is from the internal energy of the wave medium . No heat enters or leaves the system from outside by diffusion and so the net entropy change is zero, ΔS=0 ( i.e. the wave changes are isentropic).
While the above analysis is for the ideal gas, the principles also apply to waves in solids. In sum, we see that stress-strain waves in the cytoplasm will be predominately either entropy neutral ( adiabatic waves) or entropy negative (isothermal compressions). Clearly cytoplasm waves should be carefully explored with respect to their providing the required favorable thermodynamic conditions for the emergence of the complex order of life and its continuation.
To sum up:
Entropy Changes in Wave Trains
Adiabatic waves in the cytoplasm will be entropy neutral ( ΔS = 0), since there is no net heat change, i.e. ΔQ is zero. .
Also, in the cytoplasm, large amplitude compression waves, if isothermal, would have negative entropy changes.
[ΔS = −-ve].
On the other hand, large amplitude rarefaction waves acting isothermally would have positive entropy change [ΔS = + ve].
In general then, the semi-solid cytoplasm should be on balance a medium of neutral to negative entropy change, and so would be positively favorable for the emergence and maintenance of life.
We should note here that in the solid-like cytoplasm the adiabatic wave motion with its order- neutral, zero entropy change will probably predominate. The compression mode will certainly also be common, but the desirable isothermal compression mode is intrinsically less likely to occur. Isothermal waves can readily be set up in the laboratory, but in nature their special conditions would be much more unlikely to occur. Thus, while the negative entropy of these isothermal compression waves is certain1y desirable for cell order to emerge, the majority of the time it would seem that the cell prioresses would have to operate on just the entropy neutral environment of the adiabatic waves. This may be part of the reason for the great time gap between the origin of single celled life and the sudden complexity of the Cambrian Radiation.
Entropy Changes in Individual Wave Pulses
For a single adiabatic wave cycle, the compression half of the complete wave cycle will have negative entropy change while for the rarefaction half cycle the change will bepositive. e. Thus, the effect of an adiabatic wave on the emergence of new order in the cell will depend on the relative speeds between the orderly structural change and the wave pulse speed ( i.e. the wave pulse frequency). Rapid atomic changes, for example, could take place even with short duration ( high frequency) adiabatic compression waves. But slow molecular ( longer duration) changes in structure, let us say, would require longer duration ( i.e. lower frequency) adiabatic waves in order to take advantage of the negative entropy occurring in the compression half of the adiabatic wave.
Fir an isothermal wave train and its pulse cycles, similar careful analysis is required. In general, though, it would seem that isothermal wave conditions in the cell will be rather rare or unusual, so that isothermal waves in the cell may be of overall much less consequence for orderly structural emergence than the more commonly occurring adiabatic waves.
For complete treatment of the thermodynamics and entropy of gels, semi-solids, glasses, solids etc. see textbooks on physical chemistry e.g. [12,13,14]
Standing Stress Waves in Cytiplasm
If standing adiabatic waves occur in the cell then the entropy positive and entropy negative actions of the standing wave have durations and stationary conditions as long as the wave persists. Thus the compression portion of a standing wave could have long lasting favorable negative entropy and order- producing conditions.
The possibility of standing waves forming will depend on the cell width and the stress-wave speed c. A typical cell width would be of the order of 10-5 m, while cell tissue wave speeds are around 1500 m/s. Thus, the frequency of the stress for the width of a single sell would be around 1.5 x 108 cycles per sec. Lower frequency standing eaves would seem to require standing waves extending over assemblages of many cells.
4.0 The Role of Amino Acids in Cytoplasm Structure
The semi-solid to solid behaviour of the cytoplasm, which is 80% water, requires explanation.
Several general physical effects such as sol gel , glass transitions etc can be cited to explain the observed behaviour of the cytoplasm. Possibly the cytoplasm inclusions are also of importance here.
Amino acids are prominent inclusions in the cytoplasm and they will have strong organizing properties on the water because of their hydrogen bonding properties [15.16.17]. Therefore, they may be central to the remarkable semi-solid nature of the cytoplasm which makes possible the existence of cell stress waves and their desirable neutral to negative entropy change property.
5. Further Discussion of The Proposed Role for Wave Action in the Cytoplasm of the Cell Promoting the Emergence of Organic Complexity and Life
We are proposing that the entropy changes in stable compression/expansion waves of both small and large amplitude that can occur in the semi-solid cytoplasm of the cell are of key importance to the emergence and development of organic life .
We have pointed out that stress-strain waves have some regions of neutral entropy change and some of negative, entropy change, and , therefore, cytoplasm wave environments in the main should be positively encouraging for life to emerge and develop. This proposed mechanism is open to experimental verification.
To repeat the conclusions of Section 2 above (1) in the cytoplasm all waves that travel adiabatically would be entropy neutral ( ΔS = 0), (because their expansion and dilation temperature changes ± ΔT can come from internal energy and so do not require heat flow ± ΔQ into or out of the wave train volume. ). Since, in this case, the heat changes are zero, then the entropy changes are also zero and the orderly emergence and rearrangement of biological molecules that life requires will not be hindered by chaotic heat bombardment that ordinarily prevents any orderly biological emergence outside the cell.
(2) Waves in the cytoplasm may also travel isothermally. In gases, the thermodynamic differences between adiabatic and isothermal motions can be large. But in solids these differences are usually small. With isothermal rarefaction waves the entropy change is positive so that small hindrance to orderly life building processes occurs. With isothermal compression, however, the entropy changes are negative ( ΔS = −ve) so that a positive drive towards order and complexity occurs.
In summary then, the waves in the cytoplasm, on average, either do not interfere strongly with emergence of biological order or they positivrely favour and encourage its emergence. This, we propose, is a dynamic drive that renders the emergence of life not only possible, but ensures that it does occur.
In our model then, a key to life’s emergence is a physical wave process occurring in a properly structured cytoplasm, rather than just a probabilistic result of random chemical process.
In principle, this cytoplasmic wave hypothesis can be tested in the laboratory. A lipid/cytoplasm synthesis experiment ,which includes it being subjected to such waves, should, if the wave entropy process is valid, produce complex biological chemicals faster and in greater variety. It may also produce higher order biological complexity.
We have proposed theoretically that the stress-strain waves in the cytoplasm will –in general—be thermodynamically favorable to the emergence of cell order, structure and complexity. We also point out that the per wave duration of favorable entropy change conditions will be inversely proportion to the wave frequency . Certain structural assemblage problems will be more facilitated with low frequency and longer duration of favorable entropy conditions. Other assemblage problems, such as those on the molecular and larger scale, may well, however, require high frequency, short duration, entropy- negative, wave pulses.
6. Environmental Forces and Energy Sources for Initiating Acoustic Waves in Cells
We have shown that stress- strain waves ( i.e. stable, finite amplitude, compression/dilation waves) can exist in the cytoplasm of the cell and should aid the emergence of order and complexity.. But, waves require some stimulation or perturbation to start them off and sustain them.
Such perturbations can arise from the cell colliding with its physical environment, presumably in water. Other obvious suggestions are: The noise and vibration of running water in and the roar and rumble of waves breaking on a shore line are major likely perturbation sources. Cells existing in coastal salt water ponds or pools would be subjected to almost continual vibrations from these sources. Cells which exist in mats or surface colonies in water are subjected to continual jostling by wind generated waves, especially on windward shorelines. Other forces exist in the flows of hot springs both on the earth’s surface and beneath the sea . Breaking forms and bubbles also emit pulse forces.
Another source of wave pulses lies in the explosive-like rupture forces of the cell’s molecular water bonds, which must break to allow molecular rearrangements in all kinds of chemical and physical processes. The classical isothermal theory of the tensile strength of liquids and solids was long an anomaly since the actual homogeneous ruptures forces, especially in water, were orders of magnitude less than the isothermal rupture theory predicted. In 2008 Power proposed that the rupture process, at least in water, was in fact adiabatic instead of isothermal. This reconciled theory and experiment. ( See Appendix A: Adiabatic rupture as an explanation for the anomalous weak tensile strengths of liquids and solids) .
Now adiabatic processes, as we have seen above, have no net entropy change ( ds = 0). They are therefore neutral or non-hindering for orderly change and complexity emergence in the cell. Thus, with the breaking of the cytoplasm bonds by adiabatic rupture, powerful explosive pulse waves are emitted which, being adiabatic, do not hinder atomic and molecular rearrangements in the cell. This obviously could be an important factor in the emergence and energetic functioning of life in the cell.
7. Verifying the ‘ Wave/entropy/Origin of Life’ theory: A ‘wave energized’ Miller-Urey type Experiment
One ot the most significant experiments in Origin of Life research is the Miler-Urey experiment  in which an aqueous mixture of inorganic chemicals is agitated by electric discharges for long periods of time and then, upon chemical analysis, exhibits a wide variety of amino acids and other organic precursors of life that have spontaneously been synthesised by this purely physical process.
More advanced experiments, with lipids for example, have successfully generated more complex biochemical molecules and structures such as peptides. None has yet succeeded in actually producing life.
We now suggest that the Miller-Urey and lipid type experiments could be carried on with the addition of various simulated cytoplasm media which are energized by wave action characterized by negative entropy generation. At a minimum , if the wave hypothesis is valid, the result should be to shorten the laboratory treatment time needed for complex order to emerge in a proto-cytoplasm test cell. .
Finding either a significant speed-up in the emergence of complex bio-chemicals, or the emergence of new bio-chemicals, organelles, or proto-cells would be verification of the proposed role of entropy- reducing wave forms in the emergence of life on earth.
A final caveat. While the above cell wave hypothesis will be a major step foreword, if experimentally verified as seems very probable, we would point out that the great complexities and subtleties of the life process makes it highly probable that other major steps may be needed for a full and final explanatory theory.
8. Another Source of Cell Waves: The Cell Membrane as A Surface Active Film Supporing Waves Which Could Also Lower the Entropy of Change At the Cell Surface
For completeness we note that two-dimensional linear waves also occur in surfsace active films on liquids and solids. [ ,20,21, 22]. The cell membrane has characteristics of a surface active film. , A surface-active membrane on a liquid droplet obeys the linear equation of state:
π = −aσ + b
re π is a surface pressure per unit area and σ is thee film density per unit surface ares and a and b are constants pertaining to the line slope and intercept.
Comparing this with the linear Tangent Gas equation of state
p = −av + b
we see that the two linear equations of state both relate to a pressure and a space dimension function, with the interfacial one referring to area while the Tangent gas equation refers to volume. Physically, however, with respect to wave behavior and entropy change , the interfacial film of a wave support entity in two dimensional motion should behave substantially the same as the tangent gas in three-dimensional ( volume ) motion, that is to say it should be linear in flow and in expansion or contraction.. In general , surface films can be solid, liquid or expanded [20, 21, 22].
The solid film case would have waves similar to those described for the semi-solid cytoplasm. Therefore, the orderly complexity of life would be favoured by certain types of waves in such a thin film. How these would act in concert with those in the cytoplasm in the cell interior is a matter for study.
We have proposed that a major development towards the emergence of life took place when the protocell first developed a solid- like cytoplasm capable of supporting stress –strain waves. Once this occurred, the cell wave environment would have become entropy favorable for the emergence and support of order and complexity, and the development of the complex living cell could then proceed to successful completion.
It should perhaps be noted that introducing an entropy neutral, or entropy negative, wave system into the cell does not logically affect the current abiogenesis nature of the theory of the natural emergence of life from the non-living physical world.
The change here is not some new non-physical effect, but rather that the current, purely random, physical evolution process in the warm pond environment, is now replaced by, or supplemented by, a suitably structured cytoplasm having new linear wave properties. This new physical element brings with it a new physical, order- favorable wave process, one with the property of having negative entropy change which favors emergence of the complex chemical and biological structures of life.
The order- favorable entropy change environment that occurs with cytoplasm waves seems theoretically solid. If it is also confirmed experimentally, then we will face a substantial new factor in origin of life theory. Its factual reality would mean that there would exist a positive order and complexity mechanism acting in a semi-solid cytoplasm cell.. What further questions does it then give rise to.?
We will clearly have some conceptual revision to do. The current theory is a probabilistic, Darwinian model where random order emerges occasionally and probabilistically in an immensely slow process from the chaotic heat environment by working against the restraints of positive entropy change. In this theory, any new order emerges accidentally and is then tested for suitability by Darwinian natural selection.
The new theory -- one of waves within the solid-like cytoplasm in the cell --is the reverse in that it is one of negative entropy change working for the natural emergence of order and complexity. In the new system, the new order emerges naturally, and is then tested for suitability by Darwinian natural selection.
One new possibility is that probabilistically emergent chemical entities, namely the amino acids, when incorporated into the water of the protocell, may, because of their property of organizing water structure, also assist in altering the cytoplasm structure to its semi-solid state. and enabling the occurrence of the necessary stress-strain waves and negative entropy for further emergent biological order, including the formation of more amino acids and the assemblage of these amino acids into proteins. This seems a bit more than the current random emergent life model can handle. What would emerge here would be not just component ‘things’ but a complex, self promoting system’.
Our viewpoint so far has been scientific. However, the philosophic aspects have their place, and so we might wonder if our new hypothesis should be seen and expressed philosophically, not just as an evolution of biological structures, or of biological ‘things’, but instead in terms of an evolution of emergent recurrent biological systems. [ 22].
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Copyright, Bernard A. Power, June 2016
Adiabatic rupture as an explanation for the anomalous weak tensile strengths of liquids and solids
Bernard A. Power
Reviewed Aug. _ Sept. 2007: Revised Oct. 2007
The observed tensile strengths of liquids and solids are orders of magnitude lower than the theoretical isothermal rupture values. The discrepancy is currently explained by heterogeneous nucleation of the ruptures in the theory of nucleation rates. Still, the observations for water do not agree with current theory. However, an adiabatic rupture producing of voids or bubbles ( Equation of state pvk = const.) would give much lower theoretical tensile strengths in agreement with the observations.. The concept should be of interest to materials science, to chemical reaction kinetics in aqueous solution, and so to cell biology and genetics.
Theoretical estimates of the tensile strength of solids and liquids give values of around 3 x 104 to 3 x 105 atm.. However, for solids, the experimental values are around 100 times smaller than that, while for liquids, the observed values are 600 to 1500 times smaller at 50 to 200 atmospheres (Kittell, 1968; Brennan ,1995), with water being among the very lowest.
A simple classical derivation (Frenkel, 1955; Brennan 1995) of the theoretical tensile strengths of solids or liquids considers the fractional volumetric expansion ratio ∆V/Vo needed to form the rupturing void, and this then is equated to an average numerical value of about 1/3 . Then, since liquids and solids have compressibility moduli K which are about. 105 to 106 atmospheres, we have a rupture pressure p(max) = −K(∆V/Vo). Taking the average 1/3 value for ∆V/Vo , the rupture pressure p(max) then becomes the theoretical 3 x 104 and 3 x 105 atmospheres just mentioned, far higher than actually observed.
For solids, the discrepancy in tensile strength is usually ascribed to heterogeneous nucleation of rupture at defects such as cracks or dislocations in the lattice (Kittell, 1968). In the case of liquids, the even larger discrepancy is usually explained by invoking the presence of irremovable tiny gas or solid nuclei within the liquid, which act to lower the pressures and tensions needed for mechanical rupture. Still, there remain discrepancies, and the foreign nuclei explanation, or heterogeneous nucleation process acting alone, has appeared somewhat artificial, especially since the thermal rupture ( boiling) values do agree more with the theory.
2. Adiabatic cavitation
The basic mechanical equilibrium equation for the production of a spherical void, or vapour-filled bubble, in a liquid by rupture is usually expressed as a balance of forces inside and outside the spherical incipient void :
pB − pL = ∆pmax = 2 σ /RC (1)
which gives the relationship between the (negative) rupture pressure ∆p(max), the interfacial surface tension σ, and the rupture radius r. This process is also assumed to take place at the temperature of the bulk liquid, that is to say isothermally.
The formation of a bubble by rupture thus requires a negative pressure ∆p(max) exceeding the tensile strength 2 σ/r in order to create the spherical void. However, instead of the isothermal process ( with general form of its equation of state pv+1 = const.) which gives those unobserved high tensile strengths and rupture predictions, we could conceivably have an adiabatic rupture with pvk = const. A, where k > 1. With k greater than unity, the adiabatic rupture pressure ∆p(max., adiabatic) will always be less than the presently assumed isothermal rupture pressure.
To see this more clearly consider the following:
The isothernmal bulk modulus or modulus of elasticity for a liquid K is given by
Kis = − v ∂p/∂v
And the adiabatic modulus is
Kad = − v ∂p/∂v= k p where k is the adiabatic exponent or ratio of specific heats cp /cv
For liquids ( e.g. water )the two moduli have nearly the same numerical value.
The pressure at the critical point is then
p(max.) = −Kis (∆V/Vo) and
p(mac.) = − Kad. (∆V/Vo)
The adiabatic bulk modulus Kad. for water has the value 2.2 x 104 atms. Table 1 then shows the effect of taking the adiabatic rupture/cavitation mechanism in water over a range of values of (∆V/Vo) i.e. (ρ/ ∆ ρ ) and for various values of the adiabatic exponent k from >1 to 7.. We point out first that V is the reciprocal of the density ρ, and so we can put . (∆V/Vo)k = (ρ/ ∆ ρ)k which is more convenient., that is
P(max.) = − Kad. (∆V/Vo)k = − Kad(ρ/ ∆ ρ)k
The first step is the conversion of the liquid water in a small volume V to a “gas-like” structure at the critical point, which means a fractional volume expansion of about 0.333 (i.e. the density of water at the critical point drops from 1 to about 0.3333). This initial step obviously requires the injection of a sufficient energy. The rupture pressure in the new gas-like volume at this critical stage is now p(mac.) = − Kad. (∆V/Vo) = 2.2 x 104 (0.333) = 7326 atm.
The second step is the adiabatic expansion of the same ‘gas-like’ volume to a larger bubble volume with consequent decrease of the pressure. Clearly, for any given expansion ratio, the adiabatic expansion yields a much smaller final rupture pressure than the usual isothermal rupture model. For example, in Table 1, a volume expansion of 1/3 (density ratio ρ/ ∆ ρ of 0.333) yields an isothermal rupture pressure of 7326 atmospheres, while the adiabatic expansion at k = 7 has a rupture pressure of only 10.1 atmospheres .(The experimental data also show a definite effect of temperature on the final rupture pressure; this does not affect the conclusions reached here, since they are based on comparative values of the isothermal and adiabatic processes at any given initial temperature).
Adiabatic rupture pressure p ( max.) for water ( Kad. = 2.2x104 ) for various assumed values of density change ratio (ρ/ ∆ ρ)
Rupture pressure (p ( max.) ( p = KAd. (ρ/ ∆ ρ)k)
(ρ/ ∆ ρ)
k = 1** k = 2 k = 3 k = 4 k = 5 k = 6 k = 7
0.1 3300 atms. 220 22 2.2 0.22 0.022 2.2x10-3
0.20 4400 880 176 35.2 7.04 1.41 0.28
0.30 6600 1980 594 178 53.5 16.0 4.81
0.3333* 7326 2444 815 272 90.5 30.2 10.1
0.40 8800 3520 1408 563 225 90.1 36
0.5 11000 5500 2750 1375 688 344 172
0.6 13200 7920 4752 2851 1711 1026 616
1 2.2x104 2.2x104 2.2x104 2.2x104 2.2x104 2.2x104 2.2x104
*. Density ratio (ρ/ ∆ ρ) at the critical temperature TC for water is approximately this value of 0.33, the same value assumed by Frenkel
Clearly, the isothermal hypothesis fails to yield the observed rupture pressures of around 50 -250 atmospheres for water at any assumed density ratio. The adiabatic expansion hypothesis, however, does let the pressure reach the experimentally observed low values.
What value for k are we then to adopt for pure water ? At the critical density expansion ratio of 0.333, any value of k from k = 4 to k = 6 would encompass the observed ed rupture pressures of about 250 to 50 atms. However, it may also be valuable to revisit the value of k = 7 obtained by Courant and Friedrichs (1948) who discussed the expansion and contraction of spherical blast waves in water, and fitted the experimental data to a quasi-equation of state for water under a pressure of around 3000 atm., which is pv7 = const or p =A ρ7 + B. They also derived this same value of the adiabatic exponent k = 7 theoretically as a solution to their non-linear flow equations for purely spherical ( i.e. radial) shock expansions in fluids. Their evidence that water rupture, at least in explosions, is spherical and adiabatic would also seem to be generally applicable, since all ruptures, even non- explosive ruptures, are quasi-sudden, and so, at least initially, they all could be adiabatic as well.
As to the proper value of the density ratio (ρ/ ∆ ρ) to accept, if the rupture process for water were envisaged as taking place by a transformation from its usual density of 1 by one of the usual cavitation mechanisms, such as a burst of electromagnetic or acoustic radiation into a small liquid volume ( the radiation being energetic enough to break all the liquid water bonds in that volume quasi-simultaneously), we would have a “ gas-like” liquid suddenly emerging with an expansion ratio of 0.333. Once the ‘gas-like volume has emerged, we see that it must at once expand from an initial gas-like density ρ, again taken as unity, to some smaller gas-like density ∆ ρ. by either the isothermal route p = K ((ρ/ ∆ ρ) or the adiabatic route p = K (ρ/ ∆ ρ)k where k is now greater than unity. The density ratio must then fall from unity to some value consistent with the usual equation for pressure equilibrium, p(max) = 2σ/r., where r is the radius of the critical bubble size.
Clearly the isothermal hypothesis cannot reach the observed low rupture pressures of 250 atmospheres or less,, while the adiabatic process can. From Table 1 we again see that a k value of 7, over the range of density expansion ratios (ρ/ ∆ ρ)k .from 0.4 to 0.6, would more than encompass the observed range of rupture tensions of 50 to about 250 atmospheres at normal temperatures.
The proposed model would l require simultaneous radial rupture over a sufficient number of adjacent bonds, and therefore the theory of nucleation rate analysis would still appear to apply. The radial rupture might also of course be heterogeneous, and then all the various heterogeneous mechanisms of bubble formation presently considered may still be in play.
The proper value to be used for k in aqueous solutions, where the densities are different from those of pure water, would appear to be a matter for further study.
The third step: the attainment of a critical radius rc for rupture
I must be noted that Step 2 above is based solely on the density ratio ρ/ ∆ ρ and has not specified any actual initial or final density or ( specific volume. ) However as the “gas-like’ liquid bubble expands, it eventually must physically become an ordinary vapour –filled bubble of homogeneous nucleaton theory, and the latter theory requires that, for the bubble to persist, it must meet the critical stability condition:
pB − pL = ∆pmax = 2 σ /RC
Table 2 shows this final stability condition over a range of sizes , rc
Critical ( stable) radius rc for various rupture pressures in water
Critical radius of bubble, rc Rupture pressure, p(max) = 2 σ /r
(cm) (m) (σ = 75 dynes/cm)
a) (dynes/cm2) b) atmospheres (dynes/cm2 x 10-6 )
1 cm 0.01 m 140 1.4 x10-4
10-1 0.001 1.4 x 103 1.4 x 10-3
10-2 10-4 1.4 x 104 1.4 x 10-2
10-3 10-5 1.4 x 105 1.4 x 10-1
10-4 10-6 1.4 x 106 1.4
10-5 10-7 1.4 x 107 14
10-6 10-8 1.4 x 108 140
10-7 10-9 1.4 x 109 1400
10-8 10-10 1.4 x 1010 14,000
1. The ratio between the critical state liquid pressure ( 1.4 x 104 atms).and the observed average rupture pressure for water ( say 150 atms) is about 100/1.
2. On the isothermal expansion hypothesis with p1/p2 = V2/V1 , the volume ratio at critical rupture must be the same i.e. about 100, .so that the radius ratio is r2/r1 = 1001/3 = 4.64.
On the adiabatic expansion hypothesis ( with k =7), it becomes p1/p2 = (V2/V1 )7 , so thatV2/V1 = (p1/p2)1/7 = 1.93. and r2/r1 = (1.93)1/3 = 1.25
3. If a bubble is to reach the critical rupture size of 10-8m at 140 atmospheres rupture pressure, then the initial radius size rc for an adiabatic expansion at k = 7 would have to have been rc = 10-8/ 1.25 = 8 x 10-9 m; moreover, an input of energy sufficient to bring a volume 4/3 π (8 x 10-8)3 to the critical “gas-like” state must have been supplied to the liquid to bring about the rupture. Any initial excited volume smaller than that may indeed form a tiny gas bubble but will immediately thereafter collapse because it is below the critical size required.
4. It may be noted that incipient bubbles, smaller than those having sufficient excited volume to become critical and bring about macro rupture of the liquid, may still cause important transient rupture effects on the molecular scale. These, while never reaching the critical radius leading to macro liquid rupture, may still be of great importance on the molecular scale in locally removing a water film barrier between chemical reactant molecules in solution or suspension. This solvent film barrier phenomenon may therefore also be important in the kinetics of so-called “slow” chemical reactions in solution.
Solutions, Solids, Reaction Kinetics
In simple cases, the relationship of k to n, the number of ways the energy of the system is divided, is given by k = (n +2)/n. With k = 7, the formula would require n to be fractional at n = 1/3, and we would have to then interpret this physically as indicative of the spherical or radial expansion.
For solids, because of structural and steric hindrance, the flow orientation in a rupture flow may conceivably be only quasi- radial, and so a value of k between 4 and 6 might. then be appropriate, giving tensile strengths higher than for liquids but below the classical theoretical estimates. It t would appear that the new model may be of interest to materials science.
Again, the “slow” chemical reactions mentioned in Note 4 above, occur more often in liquid solution than in gases, and they are also the most sensitive to pressure, just as is the case with liquid rupture; furthermore, the reaction rates are slowest when water is the solvent ( Laidler, 1965). This all suggests that the phenomenon of rupture in liquid water may be important in chemical reaction kinetics. In gases, of course, adsorbed molecular films can also be present, and their removal in collision reactions would enter in the same general way as for chemical reaction rates in solution.
Finally, we may note that all the chemical and genetic reactions of life take place in the aqueous medium of the cell. Therefore, the kinetics and probabilities of the reactions of life and its evolution should be subject to the probability laws that govern the aqueous rupture barrier which must be overcome on the molecular scale if the various biochemical reactions and interactions of life are to proceed.
Brennen, Christopher E. (1995) Cavitation and Bubble Dynamics. Oxford Univ. Press.
Courant, R. and Friedrichs, K. O. (1948). Supersonic Flow and Shock Waves. Interscience, New York.
Frenkel, J. (1955). Kinetic Theory
Kittell, Charles. (1968) Introduction to