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Ecological Modelling 222 (2011) 2869– 2877

Contents lists available at ScienceDirect

Ecological Modelling

jo ur n al homep ag e: www.elsev ier .com/ locate /eco lmodel

he role of water in the information exchange between the components of ancosystem

arissa S. Brizhika,b, Emilio Del Giudiceb,∗, Alberto Tedeschic, Vladimir L. Voeikovb,d

Bogolyubov Institute for Theoretical Physics, 03680 Kyiv, UkraineIIB, Neuss, GermanyWHITE HB, Milano, ItalyMoscow State University Moscow, Russia

r t i c l e i n f o

rticle history:vailable online 9 June 2011

eywords:cosystemslectromagnetic field

a b s t r a c t

Living organisms and ecosystems have been shown to be sensitive to very weak signals originating very faraway. The dynamics governing these phenomena is discussed in the framework of Quantum Field Theory.This phenomenon gives an indication on the dynamics responsible for the exchange of information inecosystems. The peculiar role of coherent water is stressed. It is shown that energy is able to travel in acoherent medium in form of solitons, without any losses.

© 2011 Elsevier B.V. All rights reserved.

hase interactionoherenceater

harge transportolitonatchet phenomenon

iological information

. Introduction

We wish to address in the present paper the problem of themergence of organization within complex systems, such as liv-ng organisms and ecosystems. The organization of those systemshould account for the well known fact that they are not pas-ive systems, able to move only if acted upon from outside; theseystems are also active in the sense that they are able to trans-orm the energy received from the environment in form of heat,hich has no internal direction, into a purposeful energy, able to doork on themselves and on the environment. Moreover it has been

hown (Piccardi, 1962) that such systems are able to be triggered byery subtle actions at a distance where presumably no significantow of energy has occurred. The conceptual framework of classicalhysics, which is usually adopted in biology and ecology, appearso be unable to provide a rationale for the effects of these subtle sig-als. As a matter of fact, how is it possible to account for the Piccardi

bservation that the cycles of sunspots could affect the physical andhemical properties of a colloidal suspension on Earth? Should thisbservation of Piccardi be correct, one should accept the possibility

∗ Corresponding author.E-mail addresses: brizhik@bitp.kiev.ua (L.S. Brizhik),

milio.delgiudice@mi.infn.it (E. Del Giudice), gowhite@usa.net (A. Tedeschi),.l.voeikov@gmail.com (V.L. Voeikov).

304-3800/$ – see front matter © 2011 Elsevier B.V. All rights reserved.oi:10.1016/j.ecolmodel.2011.05.017

that those cycles, and moreover other cosmic events, could affectthe behavior of systems more complex than colloidal suspensions,such as living organisms and ecosystems.

We assume the point of view of using this feature of sensitivityto subtle signals as a key for understanding the kind of organiza-tion existing in living organisms and ecosystems. The starting pointis obviously the verification that such actions at a distance are areal phenomenon and not a fake. As a matter of fact the work ofPiccardi is quite impressive but we have done some more verifica-tions. One of us (V.V) has detected that some physical properties ofaqueous bicarbonate solutions change in coincidence with cosmicevents, in agreement with Piccardi. We will describe these exper-iments in Section 2. Since liquid water is an essential componentof living organisms and ecosystems, we feel authorized to assumethat the same sensitivity should be shown by them. Furthermorewe propose a theoretical scheme able to justify such phenomena.The main property of an organism or an ecosystem is its ability ofperforming as a unitary system, made up of a plurality of differ-ent components, each one having an individual dynamics; in otherwords the complex system emerges from the onset of an array ofcorrelations among different individuals. In order to establish thisarray a system of communications should appear; moreover these

communications should connect individuals quite far among them,so that a long-range messenger is needed. Nature offers a uniquecandidate for this task, the electromagnetic field (e.m.f.), which isthe only interaction field, known in present science, able to connect

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toms and molecules. The ability of the e.m.f. to induce long-rangerganization in living organisms has been suggested by a num-er of researchers (Fröhlich, 1968, 1977, 1980; Del Giudice et al.,986, 2010; Del Giudice and Preparata, 1994; Freeman and Vitiello,001; Popp et al., 2002; Brizhik and Eremko, 2003; Tedeschi, 2010).oreover e.m.f. has been suggested, too, to be responsible of the

elf-organization of an ecosystem (Brizhik et al., 2009).Let us quote Piccardi (pp. 120–121 of the quoted book) on the

roblem of the interaction at a distance involving living organisms:Living organisms of necessity take part in the events of the environ-ent in which they exist. Very often they participate by means of

pecialized organs in accordance with their degree of evolution andomplexity. But it is not important for us to know whether the beingsn question possess them, whether in greater or lesser number.”. . .“Allf this is of no use to us so we will concern ourselves with the possibili-ies offered to living beings directly aware of particular environmentalhenomena. The events which take place in space act upon livingrganisms either by “contact” or at a “distance”. . .“But the study ofction by contact, which is accessible to direct experimental inves-igation, is, as I see it, related more to physiology than to medicallimatology.”. . .“On the other hand, certain phenomena which takelace in geophysical space and all the phenomena which take place inolar space and astrophysical space act at a distance. No matter whathe nature of far-off spacial phenomena, their action is exercised byeans of radiations of an electromagnetic or corpuscular nature, or

y means of variations in the general field, electrical, magnetic, elec-romagnetic or gravitational. All of this may today be listed as beingistant actions.” A few pages later (p. 126) Piccardi states: “Definitely,ll living matter reacts to far-off spacial actions, both electromagneticnd field”.

The e.m.f. acts as a messenger able to involve simultaneously large number of molecular components, affecting therefore aacroscopic being; e.m.f. interacts with all the molecules presentithin its own wavelength. Moreover, liquid water, which accounts

or the huge majority of molecular components of living organisms,hould play an essential role in this process, as realized by Piccardi.t has been shown that biological dynamics works only when waterxceeds a threshold (Clegg et al., 1978; Marchettini et al., 2010).

In the conceptual framework of physics, there is a phenomenonble to convert small stimuli into large responses, namely the phe-omenon of resonance. When a stimulus having a well defined

requency is applied to a system able to oscillate on the same fre-uency, the response of the system grows with time until reachingery large amplitudes. Consequently the sensitivity of very com-lex systems to very subtle external stimuli, having a well definedhythm of oscillation, such as the cosmic events investigated byiccardi and Voeikov, implies that such systems should have a wellefined spectrum of oscillations, namely they should be made upf ensembles of oscillators fluctuating in unison at well definedrequencies. These systems are termed coherent in the jargon ofhysicists. An example of a coherent system is a laser.

According to the above argument, we adopt the point of view,ntroduced for the first time by Herbert Fröhlich (Fröhlich, 1968),hat living organisms, and ecosystems too, should be coherentystems. This point of view has found in the last years some cor-oboration in the investigations (Scholes et al., 2007; Collini, 2010)hich prove that molecules involved in the photosynthetic pro-

esses in chloroplasts are coherent among them for quite a longime. In the last decades, by using the concepts of Quantum Fieldheory (QFT), it has been shown (Preparata, 1995) that waterolecules are able to tune together their fluctuations, dictated by

he principles of Quantum Physics, and give rise to large aggre-

ates (Coherence Domains) of mesoscopic size where all moleculesscillate in phase with a self-trapped electromagnetic field. Suchoherence Domains are the natural receptors of the extra weakignals coming from afar. Water, therefore, becomes the struc-

lling 222 (2011) 2869– 2877

ture around which other molecules get organized according toa tight interplay between electrodynamics and chemistry. At agiven time Coherence Domains (CDs) oscillate at a given frequency,attracting the molecules able to resonate with the same frequency;the attracted molecules react chemically among them and releaseenergy, which is absorbed by the e.m. fields trapped in the CDand changes in turn its oscillation frequency and consequentlythe attracted molecular species. In this way a time-dependentbiochemical scheme is developed according to a non diffusivedynamics. The fact that molecules are not moving by diffusion, butby the attraction of the e.m. fields increases very much the rateof the chemical reactions. Diffusive regimes, such as those givingrise to Turing patterns (Turing, 1952), could play also a role butthe electrodynamic mechanism gives to the system its stability. Itwould be interesting to rephrase the Turing approach by replacingthe diffusive motion with a motion induced by the e.m.f.

We observe that the onset of coherence and the consequentphase agreement among the oscillations of a large number ofmolecules imply a sharp decrease of the entropy of the system,which therefore becomes able to behave as a dissipative structurein the sense of Prigogine (Prigogine and Nicolis, 1977).

In the present paper we will discuss the response of coherentsystems, such as living organisms and ecosystems, to very weakexternal stimuli and moreover we will show that within a coherentsystem energy is able to travel in a very effective way, withoutlosses in form of solitons, which are coherent structures able tokeep their form for a long time.

The article is organized as follows. In Section 2 we will reportand discuss the experiments performed by one of us (V.V.) on thesensitivity of aqueous systems to cosmic events occurring quitefar away. In the following Section 3, we will discuss the possibletheoretical dynamics underlying these phenomena, based on theproperties of water. The electromagnetic properties and the ratchetbehavior of those self-trapped charge carriers in coherent watersystems, that are the solitons, are summarized in Section 4.

2. Sensitivity of aqueous systems to ultra-weak externalfactors

In this section we report some experiments meant to showthe sensitivity of artificial systems, namely aqueous solutions ofinorganic carbonates, to externally supplied weak signals. Thoseartificial systems are studied as simplified organic systems, so thatthe outcome of the experiment could provide some suggestions onthe behavior of the real living systems, which may be provisionallydefined as organic (carbonaceous) aqueous systems being in a per-sistent state of energy transformation. In the simplest case “real”(natural) aqueous systems represent solutions of inorganic carbon-ates. Carbonates are a family of inorganic compounds with differentphysical and chemical properties inter-converting into each otherin aqueous solutions, depending on different factors, in the firstplace pH:

(CO2)aq + H2O ↔ H2CO3 ↔ HCO3− + H+ ↔ CO3

2− + 2H+ (1)

CO2 is the major product of respiration, so biological liquidsincluding cytoplasm and intracellular liquids always contain car-bonates. Practically all natural waters also contain carbonateswhere they represent the main buffering system and also partic-ipate in the cleansing of natural water.

Carbonates and, in particular, bicarbonates play an importantfunctional role in a variety of biochemical reactions and in the pro-

cesses going on in natural waters. Until recently the major role ofcarbonates was ascribed to their ability to work as major buffersmaintaining proper pH values in biological liquids; however moreand more data accumulate indicating that they actively participate

Modelling 222 (2011) 2869– 2877 2871

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L.S. Brizhik et al. / Ecological

n red/ox processes responsible, in particular, for energy trans-ormation in biological systems. The majority of living organismseceive energy for the performance of all their vital functions fromerobic respiration – “burning” of organic fuels with oxygen. It washown long ago that, even when fuels and oxygen are not limiting,espiration may be halted if the living system is severely deficient inarbonates (Henderson, 1938). Carbonates play an important rolen the regulation of many other biological processes and their bio-ogical effects are so versatile that they may be considered universalegulators of metabolism.

We suggested earlier that if the process of aerobic respi-ation may be envisaged as full reduction of oxygen to waterO2 + 4(e− + H+) → 2H2O + Energy] water itself may serve as a poten-ial electron donor for oxygen reduction (Voeikov and Del Giudice,009). This idea is based on the Quantum Electrodynamics the-ry of water (see the next section) according to which Coherenceomains having high reducing potential are always present in liq-id water. However, this process cannot go without a catalyst,romoting transfer of electrons from CDs to oxygen. Our studiesf bicarbonate aqueous solutions suggest that carbonates may playhe role of such catalysts.

We found that addition of 5–10 mM of Fe(II) salts (FeSO4 oreCl2) to bicarbonate artesian waters or aqueous bicarbonate solu-ions induces a wave of photon emission (PE) from them. Intensityf the wave was boosted in the presence of luminol, the probe foreactive oxygen species (ROS). PE-waves in bicarbonate aqueousolutions could be induced in them by addition of Fe(II) in the pres-nce of luminol at any time after their preparation (Voeikov et al.,003). This means that an electron transport chain is operating inicarbonate solution, and electrons are permanently transferredrom an electron donor to an electron acceptor. Recently we foundhat superoxide radical and hydrogen peroxide are present at lowtationary levels in bicarbonate solutions (data not yet published)ndicating that oxygen reduction in bicarbonate solutions indeedroceeds.

This process turned out to be sensitive to some cosmic events.uring day-long monitoring of the “activity” of bicarbonate solu-

ion, (we define “activity” the amplitude of photon emission waven response to Fe(II) addition to it) this parameter persisted for

any days at a quasi-stationary level displaying circadian vari-tions in the range of about 10% of the mean. However, severalays after the beginning of the experiment 70–80% decline in themplitude of Fe(II)-induced photon emission wave was observed.t persisted at low values for about one day and then graduallyeturned to the original high level (Voeikov et al., 2010a, Figure 2).ee Fig. 1.

The minimal amplitude of the photon emission-wave (“activ-ty” of bicarbonate solutions) coincided with the period of the New

oon.Interesting results were obtained in the experiments with bicar-

onate solutions activated by addition of hydrogen peroxide inillimolar and sub-millimolar concentrations. Addition of H2O2 to

icarbonate solutions initiates a process accompanied by sponta-eous low-level photon emission amplified by luminol. The processccompanied by photon emission may proceed for many monthsn hermetically closed test-tubes containing activated bicarbonateolutions. Some samples keep on emitting light for more than 1.5ears after their preparation. Samples with activated bicarbonateolutions placed in a chamber of photon detector continued to emithotons at a quasi-stationary level with some circadian variationsor several weeks. Thus neither exchange of substances with thenvironment nor illumination with external light is needed for con-

inuous generation of high density energy of electronic excitationn these aqueous systems.

Drastic changes of photon emission from activated bicarbonateolutions coincided with Moon and Sun eclipses. In particular on

This figure is taken from Voeikov et al. (2010a, Figure 2).

February 9, 2009 at 17:34 (Moscow local time) photon emissionintensity started to increase and within 2 h it nearly doubled. At19:38 a spike on the kinetic curve was observed. This pattern coin-cided exactly with the time-table of the full Moon eclipse that tookplace during this day. At 17:34 an eclipse started and at 19:38 theMoon’s eclipse was full. After the end of the Moon eclipse pho-ton emission intensity did not decrease to its initial value, butoscillated with a pronounced circadian pattern where the intensityexceeded the previous one by a factor 2–3. Two days after the startof the Moon’s eclipse PE dropped to the level preceding the Moon’seclipse. It is notable that exactly 48 h after the full Moon’s eclipse,at 19:38 on February 11, a spike similar to that one observed at themoment of full Moon’s eclipse appeared again on the curve. Dur-ing the next 3 days occasional spikes were observed in the kineticcurve (for more details, see Voeikov et al., 2010b).

Dramatic changes of photon emission from an activated bicar-bonate solution coincided also with the Sun eclipse that took placeon January 15, 2010. It was an annular Sun eclipse in the equatorialregion of the Earth, and it was not observed in Moscow. Never-theless the pattern of photon emission from the sample changedsuddenly at 08:30 on January 15 and continued to be “excited” forthe next two days (for more details, see Voeikov et al., 2010a andillustrations ibidem). It is interesting to note here that increase of PEintensity from the active bicarbonate solution also lasted for about2 days after the Moon’s eclipse.

Our data indicate that plain bicarbonate solutions display stablenon-equilibrium properties, which can be revealed by the appear-ance of a wave of photon emission from them in response to theaddition of a small quantity of an electron donor, Fe(II). Bicarbon-ate solutions activated by small quantities of H2O2 demonstratestable non-equilibrium much more impressively. Activated bicar-bonate solutions preserve ability for spontaneous photon emissionfor many months in complete darkness and under the conditionswhen exchange of matter (oxygen, water vapor, volatile reactionproducts) with the environment does not occur. This means thatprocesses accompanied by generation of energy of electronic exci-tation go on in these systems permanently without irreversibleconsumption of reagents. The system can accumulate high den-sity energy since it can react to subtle irritations by strong andprolonged rising up of PE intensity.

It is premature to suggest a detailed mechanistic model ofprocesses responsible for permanently excited states of activatedbicarbonate solutions. However, some preconditions which should

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e taken into account for the elaboration of such a model should beentioned.We will see in next section that aqueous systems can be

egarded in the first approximation as two-phase systems. One ofhe phases is represented by dynamically organized water (“Coher-nce Domains”), the other phase by a more “gas-like” water. Oxygennd other solvents are present in the latter phase. According to theheory Coherence Domains have reducing properties – they containuasi-free electrons. Indeed the existence of a charge separationetween two aqueous phases coexisting in water has been exper-

mentally demonstrated. For example interfacial water (Exclusionone water, EZ-water) studied by the G. Pollack group is chargedegatively with respect to “bulk” water, and an electric currentows in a conductor connecting two electrodes one of which islaced in EZ-water, and the other in bulk water (Ovchinnikova andollack, 2009). As it has been demonstrated by (Lo et al., 2009),table water clusters could be isolated from highly diluted saltolutions. They bear negative charge and the electric potentialifference between their periphery and surrounding water mayxceed 100 mV.

A lot of data indicates that under mild conditions oxygen presentn water may be reduced by electrons donated by water (Voeikov,005 and references therein). A paradoxical feature of this process

s that the products of “water burning” coincide with the reagents water and oxygen:

H2O (CD–water) + O2 → O2 + 2H2O (non-coherentwater),

+ n ∗ h�(Energy)

No substances are consumed in this process though it may be theource of free energy (for instance, photons). The ultimate sourcef free energy in such system is destruction of low entropy waterccompanied by an overall increase of entropy in the aqueous sys-em containing two water phases. If the conditions for coherentater regeneration exist, water may keep on “burning” for a long

ime. However direct oxidation of water by oxygen (from anothererspective – oxygen reduction by electrons donated by water)eeds either continuous supply of energy of activation (for examplehotolysis), or the presence of catalysts.

Carbonates are good candidates for being such catalysts. If suit-ble electron donors are present one-electron reduction of CO2 toarbon dioxide anion radical (CO2

−•) becomes thermodynamicallyeasible (Halmann, 1993). This radical is a strong reducer and it

ay reduce oxygen playing the role of a “shuttle” between lowntropy water and oxygen. On the other hand one of the productsf one-electron water oxidation, hydroxyl radical (HO•) easily oxi-izes HCO3

− to carbonate anion radical (CO3−•). The latter may

articipate in multiple free radical reactions developing in bicar-onate solutions. These reactions are accompanied by generationf energy of electronic excitation providing the oxygen activationeeded for its further reduction. A network of coupled and mutuallytabilizing cyclic red-ox reactions develops. In the course of theseeactions carbonate radicals regenerate back into carbonates. Theeagents – water, oxygen and carbonates – are not consumed.

Whatever the mechanism providing for stable non-equilibriumtate of bicarbonate aqueous systems, its capability for permanenthoton emission demands a permanent energy supply from thenvironment. A natural source of this energy is the thermal bathhere the system resides. Pollack and associates had shown that

tructural temperature of EZ-water is lower than that of less orga-ized water with which it is in contact (Zheng et al., 2006). As far as

temperature gradient between two water phases exist, EZ-wateran draw heat energy (IR-radiation) from the environment andransform it into energy of much higher grade – energy of electronicxcitation (radiation in the visible and UV-range of the spectrum).

lling 222 (2011) 2869– 2877

From this it follows that bicarbonate solutions represent step-upenergy transformers rather than energy generators.

Exact temporal coincidences between the changes in the pat-terns of photon emission from bicarbonate solutions with cosmicevents can hardly be explained by chance coincidences. In fact thedependence of the processes in aqueous systems on cosmic eventswas first conclusively demonstrated by Professor Giorgio Piccardiwho discovered the effect of solar activity upon the behavior of col-loid solutions. Basing on his experiments he made the followingdeduction: “. . .it must be taken into account from an ecological-climatic point of view because everything is made up of water or whichcontains water, solutions, colloidal solutions, suspensions, is subject tothe same spacial actions [in particular – the action of the solar activ-ity] as are living organisms, and is modified as a result. Thus the waterof rivers, lakes seas, marshes and ponds, their inorganic, organic andbiological colloids, clay sediment, mud, in short what is found in dis-persed state and which has not yet attained a state of thermodynamicequilibrium” (Piccardi, 1962, p. 127). The mechanism of long-lastingeffects of Sun and Moon eclipses on photon emission from aque-ous systems can be considered only hypothetically at this point.Both events represent special cases of cosmic influence upon theEarth. It is clear that the direct effect of the variations of the posi-tion of celestial bodies upon water samples is practically negligible.Therefore the effect of such changes should be the variation of theelectromagnetic potential at the particular Earth spots, producedby its modulation induced by the physical events (Brizhik et al.,2009). It should be noted that the cosmic events may influence thebehavior of practically all non-equilibrium aqueous systems on theEarth including water in living organisms producing long-lastingeffects.

In conclusion, aqueous systems where a stable non-equilibriumphase of organized water and a much less organized phase of bulkwater coexist, are able to give rise to a proto-respiration catalyzedby carbonates provided that oxygen, its active species and protons(hydroxonium ions) are present. If the system has access to nitro-gen and other non-organic compounds it may grow and develop(evolve) turning into a proto-organism at a certain stage of its devel-opment. It should be stressed that such systems evolve due to theirintrinsic activity provided by the inherent properties of water andcarbonates rather than under the action of external forces uponthem. However, their behavior is modified by the external infor-mational influences to which they are always open. This behaviorrepresents the phenomenon of true self-organization that gives riseto the emergence of more and more complex systems that are basi-cally similar to each other but possess individuality providing forthe emergence of diversity, bio-diversity in particular.

3. The role of water

The reported experiments together with the results of Piccardipoint to water as the essential matrix allowing the dissipativedynamics underlying life to go on.

What is water? According to the conventional point of view liq-uid water is seen as an ensemble of molecules kept together bystatic interactions, and in this context hydrogen bonds are pro-posed as the best candidate (Franks, 1972–1982; Teixeira and Luzar,1999). However, statistical investigations of liquid water (Stanleyand Teixeira, 1980; Bertolini et al., 1989) reveal that lifetime ofhydrogen bonds is quite short, in the order of picoseconds. Thisduration of the fluctuations of bindings, which involve the electronclouds of molecules, would imply the appearance of e.m.f. modeswith the corresponding frequencies as co-factors of the dynam-

ics. Consequently the general problem of the interaction amongwater molecules cannot get rid of the unavoidable presence of thetime-dependent electromagnetic field; the use of the static approx-imation would necessarily give rise to inconsistencies.

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The problem of the interaction of water molecules and the e.m.f.as been addressed in recent years in the conceptual frameworkf Quantum Electrodynamics (QED) (Preparata, 1995; Arani et al.,995; Del Giudice and Tedeschi, 2009; Marchettini et al., 2010; Deliudice et al., 2010). The results can be summarized as follows.

1. According to Quantum Field Theory (Umezawa, 1993; Blasoneet al., 2011), photons are able to come out from the quantumfluctuations of the vacuum; the interaction of these photonswith matter produces detectable experimental consequences,such as the Lamb-shift of the hydrogen atom levels or theCasimir effect;

2. Each of these photons could resonate with water moleculespresent in its volume. This volume is the cube whose side isjust the wavelength � of the mode corresponding to the energyjump E between two levels of the molecule: � = hc/E, where h isthe Planck constant and c is the speed of light; therefore the vol-ume has a value �3. In the case of water it has been shown (Araniet al., 1995) that E = 12.06 eV (electron volts), so that � = 0.1 �m,which is one thousand times larger than the size of the singlewater molecule (slightly more than 1 A). As a consequence aphoton would include within its own volume many molecules;in the case of water at the boiling point, about 20,000 molecules.

3. Let us call P the probability of interaction of 1 photon with 1molecule, which can be estimated by the Lamb-shift to be in theorder of 10−4 to 10−5; when the quantity P �3 N/V (where N/Vis the molecule density) becomes equal to 1, the photon can-not escape any longer from the region occupied by moleculesand is compelled to bounce continuously among the differentmolecules getting trapped by their ensemble.

4. All photons coming out from the e.m.f. background (whichincludes the vacuum) undergo the same fate, so that a pile upof photons occurs within the volume �3 (which from now onwill be termed Coherence Domain (CD)) giving rise to a sizeablee.m.f. able to attract by resonance the surrounding moleculesand therefore producing a sharp increase of density. This fitsexactly what happens in the real vapour–liquid transition!

5. The frequency of the photons trapped in the CD gets renormal-ized to a smaller value, since the time T of the single oscillation,whose inverse is just the frequency � = 1/T, is increased bythe time spent in the molecule excitations. Consequently �becomes smaller and according to Quantum Optics (Preparata,1995) photons become unable to be irradiated by the CD andget permanently trapped within the CD.

6. As a consequence of the above dynamics all molecules belong-ing to the CD oscillate in unison between the two individualmolecule levels in tune with the trapped co-resonating e.m.f.which has lost its independence; its energy gives rise now tothe cohesion of the system. The phase agreement of moleculesand field is named Coherence. In a coherent state it is possibleto give a definite value Ф to the phase, which denotes in thephysical jargon the rhythm of oscillation of the system.

7. In the particular case of water, the coherent oscillation of thewater molecules occurs between a ground state where all elec-trons are tightly bound to the molecule, so that none of themcould be easily released, and an excited level where one elec-tron becomes so loosely bound to be easily released, either bya quantum tunnel effect or by a mild external energy supply.Consequently CDs become electron donors providing an expla-nation for the electron transfer processes observed in aqueoussystems.

8. The existence of a trapped e.m.f. within the CDs gives rise to the

appearance of a difference of electric potential on its boundary(Marchettini et al., 2010).

9. The above electromagnetic attraction is counteracted at a nonvanishing temperature T by thermal noises, which include

lling 222 (2011) 2869– 2877 2873

Brownian motions and diffusive processes. As discussed inArani et al. (1995) the interplay between the thermal dynamicsand the electromagnetic attraction gives rise to a dynamicalequilibrium whose consequence is, like in liquid helium (Tisza,1947), the formation of a two phase fluid, the first phasebeing the ensemble of coherent molecules assembled in theCDs, whereas the second phase is the gas-like ensemble ofmolecules pushed out of tune by the collisions produced by thethermal noise. Coherent and non coherent fractions have welldefined values for each set of thermodynamic values. Coher-ent fraction excludes all solutes from inside; solutes could behosted in the non coherent fraction only. This result reproducesthe old fashioned model developed by Rontgen (1892).

10. Near a surface the disruptive effect of thermal noise oncoherence could be compensated by the attraction of watermolecules to the wall. As a consequence the coherent fractionassumes a much larger value near a surface than in the bulk.Properties of interfacial water (and water in living organismscan be assumed to be almost totally interfacial) should beconsidered almost coincident with the properties of purelycoherent water (or the water at very low temperature) andtherefore quite different from the properties of usual bulkwater. We are now in the position to give a rationale to theobserved difference between normal bulk water and the waterpresent in living organisms (Pagnotta and Bruni, 2007; Zhouet al., 2009). In recent times the existence of peculiar propertiesof the water close to surfaces has been reported (Pollack, 2010,and references therein).

11. The ensemble of almost free electrons present in the water CDscould be further excited by external supplies of energy, givingrise to the possibility of oscillations of the CD between itsground state and one of its many excited states. Repeating thesame process described above for water molecules, water CDscould become in turn coherent among them giving rise to anextended coherence (coherence among Coherence Domains)which, as has been discussed elsewhere (Del Giudice andTedeschi, 2009; Del Giudice et al., 2009), is able to imple-ment the dynamics predicted on thermodynamic grounds byPrigogine (Prigogine and Nicolis, 1977).

Taking into account the features of liquid water described above,as predicted by Quantum Field Theory, we are now in a positionto discuss the reported experiments and also the Piccardi results.On the basis of the QED theory of water summarized above, liv-ing organisms and the aqueous systems have a definite phase Ф.Such systems are subjected in Quantum Physics to the so calledAharonov–Bohm effect (Aharonov and Bohm, 1959, 1961), whichprescribes that the externally applied e.m. potential adds up tothe phase, changing consequently the internal dynamics of thecoherent system. Quantum systems therefore exhibit an additionalpossibility of electromagnetic interaction with respect to the classi-cal systems. In classical systems the only possible interaction is theone mediated by an exchange of energy and/or momentum, namelyby an externally applied force. In quantum systems, thanks to theAharonov–Bohm effect, a new possibility appears: an interactionmediated by the potential, which in classical physics cannot exist,whose consequence is a change of the phase, namely a change of thedynamics governed by the internal rhythm of oscillation, which istypical of the living systems and of special aqueous systems. In thephase interaction the intensity of the e.m.f., which is connected tothe exchanged energy, plays no role, whereas the significant vari-able is the potential which, as described in Brizhik et al. (2009),

could be non vanishing also when the field is zero.

Let us introduce a metaphor: consider an orchestra and its direc-tor. The energetics of the orchestra is produced by the players,whereas the director interacts with the orchestra not exchanging

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nergy but tuning together the phases of different players, trans-orming therefore a noise into a music. The interaction betweenirector and players, which does not imply a significant exchangef energy, transforms the orchestra into a coherent system.

Consequently very weak fields can produce major effects onoherent systems through the impact of their associated poten-ials on the phase of the systems acted upon. The Aharonov–Bohmffect might therefore provide a rationale to the existence of sub-le influences on living organisms and ecosystems. In particulart is well known that all living organisms obey to the celebrated

eber–Fechner Law (see Chisholm and Hugh, 1911), which stateshat the response � of a living organism depends on the stimulus Shrough the relationship:

= C logS

S0(2)

here C is a constant and S0 is the value of the stimulus producingo response. The Weber–Fechner Law, which has been experimen-ally established by classical physiology in the XIX century, couldppear counterintuitive to a mechanistically minded reader, usedo think that the response of an organism should be proportionalo the stimulus. This could be the reason why conventional biologynd medicine usually neglect the importance of very weak stimuli,ike for instance the environmental e.m. fields.

It is interesting to observe that, according to the Weber–Fechneraw, when S is much smaller than S0, the amount of the responseecomes larger and larger; it is no longer out-bound, but in-bound,amely it is not directed outwards but produces an internal changef the system. Weber–Fechner Law cannot be understood in therame of conventional explanations based on the central role ofnergy but acquires a rationale within a dynamics where coher-nce, and consequently the phase, plays a pivotal role. As a matterf fact, non-coherent systems, such as inert bodies, are unable toeel subtle influences. We can realize that conventional thinking,hich assumes that all bodies in Nature are inert in the sense that

hey can be moved from outside only, is unable to understandhe existence of subtle influences in the Universe, like the cos-

ic events investigated by Piccardi and discussed in the presentaper.

An additional intriguing property of the phase is that it is ableo travel at a speed higher than light. Since correlations in coherentystems and among them are kept at phase velocity (Del Giudicend Vitiello, 2006), these subtle messages travelling in the Universe,n ecosystems and among them could violate the Einstein causalitynd give rise to synchronic phenomena, such as those predicted byung (1952).

Phase appears therefore to be the vehicle of the long-range con-ections within and among ecosystems. Once the phase of a givenoherent system is fixed to a particular value its internal molec-lar dynamics is determined. As described in Brizhik et al. (2009)he e.m.f. trapped within the water CDs is able to attract all the

olecules able to resonate with its own frequency; the chemi-al energy released in the molecule reaction is assumed by the.m.f. and changes its frequency of oscillation and hence its phase,hanging consequently the molecule species which get attracted.n this way the phase dynamics is able to govern the sequence ofhemical events occurring in the system. The signals mediated byhe e.m.f. potentials discussed above are also changing the phasef the e.m.f. so that they are able to induce the same phenom-na produced by contact chemical interactions. In this way theynamics of ecosystems and living systems is able to be governed

n a two-fold way: by chemical contact interactions and by the

ction at a distance started by events occurring far away and trans-orted by the electromagnetic potentials. This two-fold way canccur only in systems governed by the phase, namely in non-inertystems.

lling 222 (2011) 2869– 2877

4. Ratchet dynamics of charge carriers

We have discussed so far how the phase of a coherent systemgets modified by an event occurring very far away. The change ofthe phase, as said in the above section, produces a change of the bio-chemical sequences, which in turn produce energy. An extremelyimportant feature of living systems is a very efficient way of energytransportation. Usually the output energy of chemical reactions isdissipated in a thermal way, by release of heat. However the diffu-sive dissipation implies the loss of a large fraction of the releasedenergy, which therefore cannot be used totally for performingwork. Experimental evidence shows that living organisms presenta highly efficient energy transportation. This efficiency is connectedwith the existence of a coherent medium, such as coherent water,in living organisms. It has been shown (Del Giudice et al., 1985) thatin coherent mediums energy is transported in a non-thermal wayby very localized energy packets, named solitons. The importanceof solitons for energy propagation without losses has been firstlystressed by Davydov (Davydov, 1979). Moreover solitons play therole of giving a directionality to the supplied energy, according tothe so called “ratchet effect” (Reinmann, 2002). A ratchet is definedby Wikipedia as a device that allows continuous linear or rotarymotion in only one direction while preventing motion in the oppo-site direction. A ‘ratchet phenomenon’ consists in the appearanceof a directed current (drift) under the action of stochastic or deter-ministic unbiased (zero mean-value) forces oscillating in time. Theratchet phenomenon is a part of the general process occurring inliving systems where a chaotic supply of energy produces an effecthaving a well defined direction.

In this section we describe the effects of periodic e.m.f.s, suchas those originating in the environment and affecting organisms,on charge transport processes mediated by solitons that occur inliving organisms during their respiration or photosynthesis, andin interfacial water, water CDs in biological tissues and in ecosys-tems (in oceans, atmosphere, etc.). According to Davydov (1985),charge transport on molecular chains is provided by solitons whichdescribe bound states of charge carriers with self-induced localdeformation of the molecular chain. As any solitons in other nonlin-ear systems, solitons in molecular chains are exceptionally stabledue to the compensation of wave dispersion and nonlinearity, theirenergy is lower than the energy of free charge carriers.

Propagating along molecular chain solitons are subjected to apotential (relief) generated by the discrete structure (lattice) of thechain; this structure usually exhibits regularities that produce apotential characterized by oscillations, termed wells in the phys-ical jargon. These potentials have in general several wells, but inthe simplest case a double-well potential is considered for chainswith two atoms per unit cell. In macromolecules and DNA this is theso-called Peierls-Nabarro potential (Brizhik et al., 2000), in waterchains this is a relief, formed by double-well potentials for a pro-ton in hydrogen bonded water molecule chains (Davydov, 1985).Both Peierls-Nabarro potential and double-well relief in water sys-tems can play the role of the ratchet potential for the appearanceof the ratchet phenomenon. Here we show that this phenomenoncan also take place in charge transport systems, described above,under the action of an external field, of a local trans-membranepotential in a living cell, of a coherent electromagnetic field ofthe whole organism (endogenous electromagnetic field) (Brizhikand Eremko, 2003), etc. Since ratchet phenomenon can essentiallychange dynamics of charged solitons and their stability proper-ties, it can affect in its turn the metabolism of living organisms inparticular and ecosystems in general.

In the general case soliton dynamics in a molecular lattice isdescribed by the system of non-linear coupled equations for theelectron wave function and lattice displacements (Davydov, 1985).In the continuum approximation this system can be reduced to to

Modelling 222 (2011) 2869– 2877 2875

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he Schrödinger equation for the electron wave function in the self-onsistent deformation potential. This potential is proportionalo the electron probability at a given place and time so that thechrödinger equation contains a cubic nonlinearity and is knowns the discrete nonlinear Schrödinger equation. In the leading orderpproximation it has the soliton solution

(x, t) = 12

√g

exp(ikx − iEt/h)cosh{g[x − R(t)]/2a} (3)

here x is the atom position along the molecular chain, E is thenergy, R(t) is the c.m. coordinate of the soliton, a is lattice constant,

is the wave-vector of the soliton, and g is the nonlinear couplingonstant, that determines the width of the soliton:

= �2

2Jw(4)

ere � is the strength of electron coupling with the lattice, J ishe resonant interaction energy between the nearest sites, w ishe elasticity of the chain. In molecular chains it is determined byhe electron exchange interaction, chain elasticity and strength oflectron coupling with the lattice.

In a molecular chain the dynamic equation for the c.m. coordi-ate of the soliton, R(t), under the external force, F(t) = eE(t), taking

nto account the energy dissipation and the presence of the poten-ial relief U(R), arising from the lattice discreteness, takes the form:

sR = �R − dU(R)dR

+ eE(t) (5)

here

s = m + Mdef ; Mdef = mM�4

6h2w2(6)

s the effective mass of the soliton, ‘dressed’ with phonons. Here is the mass of a unit cell. The friction coefficient, � , in Eq. (5)

s proportional to the constant of energy dissipation in the sys-em. Eq. (5) belongs to the class of equations which under givenonditions admit solutions which describe the ratchet dynamicsReinmann, 2002), i.e., describe a motion unidirectional in averageratchet dynamics) of a particle whose trajectory is a limit cyclehose phase is locked to the external periodic drive E(t). Direc-

ion of the drift of a particle is determined by the interplay ofhe superposition of the periodical oscillating processes, caused byatchet potential and external field. Indeed, numerical solutions ofhe discrete equations for an electron in a diatomic molecular chain

anifest ratchet behavior under the action of an external periodicnbiased force (Brizhik et al., 2010).

In a chain with one atom in a unit cell the potential relief iseriodical with the period of the lattice, U(R) = U cos(2�R/a), in aiatomic molecular chain the potential relief can be written as sumf two terms

(R) = U1 cos(

2�R

a

)+ U2 cos

(4�R

a+ �

)(7)

here � is a phase which determines the asymmetry of the poten-ial arising from the difference of atoms in a unit cell. The height ofhe barrier depends on the square of the electron–phonon coupling, determined in Eq. (4) (Brizhik et al., 2000). The presence of such

potential causes the possibility of the charge drift in the unbiasedeld, provided that its intensity and period exceed some criticalalues (Brizhik et al., 2008, 2010), as has been shown by computerodeling of the initial system of discrete equations and as it can

e seen by solving numerically Eq. (5) with the potential (7) for aeriodic unbiased field E(t) = E0 sin(2�t/T) (Brizhik et al., 2010).

In a hydrogen-bonded water chain the double-well potentialelief is symmetric. Therefore, one can expect the possibility of the

Fig. 2. Position of c.m. of the soliton as function of time in an external biharmonicfield at E0 = .08, = .6, ϕ = �/2, T = 1000 in a chain with the following values of thenonlinear coupling constant g = .36 (upper curve); g = .32 (lower curve).

proton drift in the external unbiased field asymmetric respect totime; in the simplest case the field could be the biharmonic one:

E(t) = E0

(sin

(2�t

T

)+ sin

(4�t

T− ϕ

))(8)

Indeed, numerical simulations of the discrete system of nonlin-ear equations, which in the continuum approximation using thecollective coordinate representation are reduced to Eq. (5) (Brizhiket al., 2008), have shown that the unbiased biharmonic field causesa directed (in average) motion of solitons in the symmetrical chains.In Fig. 2, we show an example of such a drift in the biharmonic field(8). Here the intensity of the field is measured in units ea/J, time ismeasured in units of h/J and the friction coefficient is chosen to be0.2.

The velocity of the soliton drift is determined by the chainparameters, intensity of the field E0, and extent of energy dissipa-tion. Necessary conditions for the soliton drift are determined bythe fact that in molecular chains periodical lattice potential playsthe role of the ratchet potential. Therefore, solitons can drift withinfields, whose intensity is bigger than some critical value to allowsolitons to overcome the pinning by the potential barrier. Also thefrequency of the field should not be too high, so that the latticedeformation could follow oscillations of the electron. According tostudy of the dynamics of solitons in external field (Brizhik et al.,1998), solitons have some characteristic frequency ω0

ω0 = gVac

�, (9)

where

Vac = a

√w

m(10)

is the sound velocity in a chain. When a periodic field is applied,solitons oscillate with the frequency of the applied field, ω, buttheir effective mass depends on the frequency of the field. Namely,

at ω < ω0 deformation of the chain follows oscillations of a charge,and soliton dynamical mass includes the mass of the chain defor-mation, as defined by Eq. (6), Ms,dyn = Ms. At high frequency of thefield, ω > ω0, the deformation remains at rest and soliton dynami-

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876 L.S. Brizhik et al. / Ecological

al mass equals effective mass of a free charge, Ms,dyn = m. Since theresence of the ratchet potential is a necessary condition for theatchet dynamics, one can expect, that such ratchet dynamics cane possible in low-frequency regime. The numerical simulationsBrizhik et al., 2008) confirm this result indeed. Soliton drift is pos-ible due to the absorption of energy from the external field, andakes place as the result of the superposition of periodical processesn a nonlinear system.

According to the analytical study (Brizhik and Eremko, 2003),olitons emit sound and electromagnetic waves in both directionsuring oscillations. The amplitude of this emission is proportionalo the square of the average velocity of solitons. Therefore one canxpect that in the external periodical field electromagnetic radia-ion emitted by solitons, is modified, and that the intensity of theoliton induced radiation increases with increasing the intensity ofhe external field.

Similar to the deterministic fields considered here, symmetrichite noise (Luczka et al., 1995, 1997) also can cause drift of solitons

n low-dimensional molecular systems. Therefore, in living organ-sms and aqueous systems the presence of a symmetric stochasticoise can result in the formation of a directed current of solitons,hich affects the charge transport processes.

. Conclusions

Any living organism or ecosystem is impossible without water.he unique properties of water make it possible to be self-organizednd to be ultra-sensitive to external stimuli having an extremelyow intensity (Tiezzi et al., 2010). In organized domains, like inter-acial water, exclusion zones, CDs, coherent ensembles of CDs, etc.,ater can support nonlinear charge transport, mediated by soli-

ons. In the presence of externally applied periodic electromagneticelds the dynamics of solitons changes. Solitons attain additionalscillations with the frequency of the field, and the mass of soli-ons, which is dynamically determined, acquires a dependence onhe field frequency as well. Moreover, a non-biased oscillating fieldan cause drift of solitons. Variations of the oscillation frequencynd average velocity (per period) of the soliton are able to changehe soliton resonant frequency and the frequency of their own elec-romagnetic radiation. This affects the charge transport processesn particular, the metabolism of organisms and the functioning ofcosystems in general. These results can explain the mechanismf the sensitivity of water systems to changes in solar electromag-etic activity, which is confirmed by experimental observations,

ncluding also the results reported here.

cknowledgements

We dedicate this paper to the memory of Enzo Tiezzi. The pas-ionate discussions we have had with him have helped us veryuch to shape our point of view. His ideas will be present in the

uture and will keep inspiring us.

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