Abstract

Both energy conservation and its dissipation are integrated in biological emergence and complexification. If energy conservation and dissipation are globally synchronized in time, however, there would be neither emergence nor complexification. The emergence of the phenomenon of life on the planet earth could be associated with the events that dissipation asynchronous with conservation could have taken over dissipation synchronous with conservation due to gravity on the earth. Gravity sets a threshold beyond which dissipation asynchronous with conservation due to electromagnetism could become stable.

1 Introduction

Measurement is ubiquitous in the biological realm as in the form of signal generation, transmission and detection. At the same time, measurement is fundamentally irreversible in making distinction between before and after the events because of its legitimate incompetency in distinguishing no signal received yet from no signal to be received beforehand (Matsuno, 1989). Irreversibility is describable in terms of a pair of a force and its conjugate flux (e.g., Prigogine, 1969). What is more, the problem of measurement is intrinsic to quantum mechanics. This simplified overview raises a serious question on how measurement, irreversibility, the notion of force and quantum mechanics could be integrated especially in the face of naturally occurring dissipative structures, including biological ones.

2 Measurement Underlying Force

Recognizing the significance of measurement or communication internal to any physical systems has already had a rich history of its own. As a matter of fact, establishment of the third law presumes an actual implementation of the communication between any pair of action and reaction. It is not the external physicist but the notion of force itself which is responsible for measuring and identifying the opposed equality between action and reaction. The capacity of measurement is already latent in action and reaction. What is really significant in establishing the third law is that the communication between action and reaction remains legitimate whatever may be responsible for generating the pair of action and reaction. The third law states that the communication between action and reaction is physical. But, it stops short of identifying what the real physical nature of the communication is. A breakthrough for this matter came from Newton's another notion, that is, gravitation.

If an action-at-a-distance originating in gravitation is taken as a means of the communication between any pair of action and reaction, the counterbalance of the two implied by the third law can be accomplished instantaneously globally in a synchronized manner. Although Gottfried Wilhelm von Leibniz perceived Newton's gravitational attraction does not work by mechanical means (Leibniz, 1698) and Christiaan Huygens expressed his dissatisfaction with the notion of action-at-a-distance (Huygens, 1690), the idea of the globally synchronized updating of action and reaction has been proved to be so convincing and invincible since then at least on a conceptual basis. The idea of action-at-a-distance facilitates dissipation involved in internal identification of action and reaction to be completely compensated by total energy conservation in a globally synchronous manner. Such dissipation synchronous with conservation rests upon Newtonian absolute time that remains globally synchronous without recourse to anything external.

Gravitation due to exchange of gravitons between a pair of massive bodies is dissipative in emitting gravitons. But, synchronization between emitting and absorbing gravitons solely within the pair makes the overall effect consistent with conservation of energy. Action-at-a-distance is thus considered to be a form of dissipation synchronous with conservation. Each party of the pair internally dissipates or emits energy by the amount of the force acting there multiplied by light velocity per unit time, because any variation in the gravitational force propagates at light velocity. Furthermore, internal energy dissipation by one party is associated with internal measurement taking place there due to the fact that measurement, that is irreversible, is energetically dissipative. At this point, one can see a possible connection between a force associated with dissipation and measurement proceeding in quantum mechanics.

3 Force and Its Conjugate Flux in Gravitation

In order to fathom the relationship between internal energy dissipation and internal measurement of a quantum mechanical nature, let us suppose an arbitrary material system, whether a molecule or a molecular organization, is involved in measuring its outside at every time interval of dt. Each internal measurement is accompanied with the energy de specified by the energy-time uncertainty principle

in which h is Planck's constant divided by 2p. Since each measurement by the measuring system would locally disturb the outside to be measured energetically by the amount of de at every time interval dt, the energy flow w from the measuring system towards its outside turns out to satisfy

Implicit in the energy dissipation is the presence of energy sources to be dissipated on the part of the measuring system. As the time interval of successive internal measurement increases, the energy flow of dissipation would decrease. Conversely, the time interval of internal measurement cannot be made arbitrarily small, otherwise there would be no energy sources to meet the associated dissipation.

One of the most ubiquitous sources of energy is gravitation. If the gravitation on the surface of the earth is the case, the gravitational force f_g acting upon the most stable fundamental unit of mass, that is, a hydrogen atom leads to f_g~10^-21erg/cm based upon the atomic mass unit of ~10^-24g and the gravitational acceleration on the surface of the earth ~980cm/s². Since the gravitational force is mediated by graviton propagating at light velocity c (Penrose, 1989), the hydrogen atom measuring the earth as a whole dissipates energy at the rate

internally. The energy flow of dissipation due to internal measurement through the gravitation with the earth cannot become less than w_g because the hydrogen atom is the minimum mass unit available there. Of course, the hydrogen atom pulling the earth is pulled back by the earth. The dissipated energy is synchronously compensated by the earth pulling the hydrogen atom (Penrose, 1989; Conrad, 1991).

On the other hand, quantum mechanics of the hydrogen atom measuring the earth observes that the measurement would proceed at every time interval of dt_g given by

because the energy flow of dissipation due to internal measurement updated at every interval of dt_g yields w_g~h/(dt_g)². However, the internal measurement accompanied with energy dissipation caused by gravitation may be taken over if other internal measurement to be updated at the time interval smaller than dt_g would appear.

4 Biological Takeover of Dissipative Force

As a matter of fact, various naturally occurring dissipative structures on the earth are not exclusively of gravitational origin. Electrostatic and magnetic interactions are the likely possibility. In order to see the likelihood of natural dissipative structures that could occur through other than gravitational interaction, it would be asked to examine any possibility for internal measurement to be updated at the time interval smaller than dt_g.

One such example of internal measurement facilitated by electrostatic and magnetic interactions is available from an actin-myosin complex in the presence of ATP molecules as a fundamental functional unit of muscle contraction that is ubiquitous in the biological realm. Electrodynamic interactions involved in the hydrolysis of an ATP molecule at the actomyosin complex are certainly responsible for both the generation of force and the occurrence of the sliding movement of the actin filament. In view of the observed fact that the generated force f_AM is about 2x10^-7dyne per myosin head (Kishino and Yanagida, 1988; Finer, Simmons and Spudich, 1994) and the sliding velocity of the actin filament v_AM is about 4x10^-4cm/s (Harada et al, 1990), the rate of energy dissipation w_AM is found

The time interval dt_AM of successive internal measurement due to electrodynamic interactions there is

because of the uncertainty relationship. This value is certainly smaller than the time interval due to gravity upon a hydrogen atom, dt_g~5.8x10^-9s.

It is an undeniable fact that electrodynamic interactions are ubiquitous and far stronger than gravitational interactions under normal conditions realizable on the earth. Nonetheless, gravitational interactions can exert a significant influence upon the occurrence of internal measurement, or dissipative structures (Conrad, 1993). Electrostatic interaction, though far stronger than gravitational one, is quite short-ranged in comparison because of the imposed condition of electric neutrality.

On the other hand, if internal measurement accompanied by its inevitable energy dissipation is to occur, both the source and the sink of energy would have to be prepared. Otherwise, internal measurement could not take place. If there is neither the source nor the sink to be prepared externally, this stipulation would result in that the time interval for measurement proceeding internally would effectively diverge, that is, quantum mechanics of a unitary transformation accompanied by no measurement. It is at this point where gravitational interaction enters (Penrose, 1989). Although it is very weak compared to electrostatic interaction, gravitational interaction can facilitate internal measurement by preparing both the energy source and sink for its completion in a self-consistent manner (Conrad, 1991, 1993).

Electrostatic interaction can take over gravitational interaction in framing internal measurement and the accompanied energy dissipation only when the rate of facilitated dissipation is quantized and the unit is made greater than the minimum dissipation rate specified by the gravitational interaction. Quantum mechanics of internal measurement (Matsuno, 1985, 1989), which is necessarily irreversible, can materialize dissipative structures by means of electrodynamic interactions only when the associated dissipation is maintained above a certain minimum level.

Prerequisite to the appearance of dissipative structures through electrodynamic interactions is quantization of dissipation in the face of gravity. One implication of the quantization of dissipation is the homeostatic capacity of dissipation in maintaining its rate above the minimum quantum level. Unless such homeostatic capacity of approaching energy sources spontaneously from the inside is available, an indefinite sustenance of dissipation could not hold as facing and tolerating adverse conditions exerted temporarily from the outside. In fact, heterotrophic activity associated with biological phenomena ever since the origin of life on the earth about 3.8 billion years ago (Matsuno, 1995) witnesses the case that dissipation is quantized in its rate.

5 Concluding Remarks

Emergent phenomena in the biosphere on the earth are undoubtedly under the influence of gravity. Gravitation on the earth contributes to two factors. One is energy dissipation synchronous with conservation, and the other is facilitation of measurement on material grounds. Although each internal measurement is irreversible, net contribution of energy dissipation due to measurements proceeding internally vanishes in the action of gravity. There could be neither emergence nor complexification solely within gravitational interactions on the earth because dissipation synchronous with conservation prevails. Still, the gravitation sets the time interval of internal measurement. Only when dissipation asynchronous with conservation that can materialize internal measurement updated more frequently than that due to the gravitation, the accompanied dissipation and internal measurement could establish and uphold unique dissipative structures of their own.

The role of gravity is at most indirect in influencing biological emergence and complexification on the earth. A crucial moment for evolutionary processes on the earth was when electrostatic and magnetic interactions could have replaced gravitational counterpart as a principal agent for recruiting the energy to be dissipated while implementing measurement internal to material bodies.

References

1. Conrad, M., 1991. Transient excitations of the Dirac vacuum as a mechanism of virtual particle exchange. Phys. Lett. A 152, 245-250.
2. Conrad, M., 1993. The fluctuon model of force, life, and computation: a constructive analysis. Appl. Math. Comp. 56, 203-259.
3. Finer, J. T., Simmons, R. M., and Spudich, J. A., 1994. Single myosin molecule mechanics: piconewton forces and nanometer steps. Nature 368, 113-119.
4. Gunji, Y.-P., 1993. Form of life: unprogrammability constitutes the outside of a system and its autonomy. Appl. Math. Comp. 57, 19-76.
5. Harada, Y., Sakurada, K., Aoki, T., Thomas, D. D., and Yanagida, T., 1990. Mechano-chemical coupling in actomyosin energy transduction studies by in vitro movement assay. J. Mol. Biol. 216, 49-68.
6. Huygens, C., 1888-1950. Oeuvers Completes, Publ. Soc. Holl. des Sciences, 22 vols., Nijhoff, The Hague, Vol. 9, p. 538. Letter to Leibniz of November 18, 1690.
7. Kishino, A., and Yanagida, T., 1988. Force measurements by micromanipulation of a single actin filament by glass needles. Nature 334, 74-76.
8. Leibniz, G. W., 1966. In: E. Cassirer (ed.) Hauptschriften zur Grundlegung Philosophie, Meiner, Hamburg, p. 371. Letter to Bernouilli, 1698.
9. Leydesdorff, L. 1994. Uncertainty and the communication of time. Syst. Res. 11, 31-51.
10. Matsuno, K., 1985. How can quantum mechanics of material evolution be possible?: symmetry and symmetry-breaking in protobiological evolution. BioSystems 17, 179-192.
11. Matsuno, K., 1989. Protobiology: Physical Basis of Biology, CRC Press, Boca Raton Florida.
12. Matsuno, K., 1995. Consumer power as the major evolutionary force. J. Theor. Biol 173, 137-145.
13. Penrose, R., 1989. The Emperor's New Mind - Concerning Computers, Minds and the Laws of Physics, Oxford University Press, New York.
14. Prigogine, I., 1969. Introduction to Thermodynamics of Irreversible Processes, Interscience, New York.

Address: Koichiro Matsuno Department of BioEngineering Nagaoka University of Technology, Nagaoka 940-21, Japan

e-mail: kmatsuno@voscc.nagaokaut.ac.jp