biological physics and the physics of the real world

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BioSyslerns, ll (1979) 323--327 323 © Elsevier/North-Holland Scientific Publishers Ltd. BIOLOGICAL PHYSICS AND THE PHYSICS OF THE REAL WORLD EFIM LIBERMAN* lnstitu te of the Problems of Information Transmission, Moscow, USSR 1. Introduction Any mind (~uman mind or computer with programmes) using physical laws is itself a part of the physical world. There- fore, a correction of physical laws is nec- essary to take into account the influence of the work of a real computer on the outer world. If we suppose that the world is regular in a sense to be defined, correction is neg- ligible and the possibility of calculating the connection between physical and bio- physical constants arises from the conditions for the optimal work of a limited molecular computer (m.c.). At best our real world is constructed in such a way that it is maximally physically regular, in the sense that the variables which describe it are connected by formulas. Here the word "world" means any physical reality. This includes on what we carry out experi- ments, what we calculate and the means by which we calculate: stars, stones, devices, computers and people. The word "maximun" has its usual mathematical meaning involving a description of reality with numbers. How- ever, the word "physical regularity" is not determined. Until now, the conception of scientific physical regularity is not generally used in a precisely defined sense. This state- * This note was prepared by Dr. Liberman in re- sponse to comments on his paper (Liberman, 1979) which appeared in the BioSystems Special Issue on Macromolecules anti the Evolution of Information Processing (BioSystems, Volume II, No. 2,3). It should be read in conjunction with that paper. ment may seem strange, since many physical laws are known which at first sight are deter- mined very well, such as Ohm's law, New- ton's laws, Einstein's theory, Dirac's equation. In all these cases physical values are exactly determined by measurement, and mathe- matical formulas connecting these values with each other are available. This is just the sense in which the words "physical regularity" are used. However, it is neces- sary to make more precise the real sense of the words "to substitute the physical values into mathematical formulas". The substitution into formulas is the introduction of numerical or symbolic values by means of a real physical process in a human brain or a computer, both of which are also real physical devices consisting of elements belonging to the same world. Studies of molecular computers (m.c.) lead to the conception of a limited calculat- ing device that expends a minimum of free energy for solving particular problems and thus does not alter the system under study. Im- agine that a maximally effective "limited mind" (i.e., a thermally optimal, limited problem solving and measuring regulator) studies a physical world which is (at most) regular for it. The system (M) is a device restricted in space and consisting of the same elements as the physical world it studies. What physical laws are necessary if the world is at most regular for M? In such a world any fundamental physical value can be measured with definite accuracy and its future behavior at any given time can be predicted by M with definite accuracy.

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Page 1: Biological physics and the physics of the real world

BioSyslerns, l l (1979) 323--327 323 © Elsevier/North-Holland Scientific Publishers Ltd.

B I O L O G I C A L PHYSIC S A N D T H E P H Y S I C S OF T H E R E A L W O R L D

EFIM LIBERMAN*

lnstitu te of the Problems o f Information Transmission, Moscow, USSR

1. I n t r o d u c t i o n

Any mind ( ~ u m a n mind or c o m p u t e r wi th p r o g r a m m e s ) using phys ica l laws is i tself a pa r t of the phys ica l world . There- fore, a co r r ec t i on of phys ica l laws is nec- essary to t ake into a c c o u n t the inf luence of the w o r k o f a real c o m p u t e r on the ou t e r world. I f we suppose t ha t the wor ld is regular in a sense to be def ined , co r rec t ion is neg- ligible and the possibi l i ty o f ca lcula t ing the c o n n e c t i o n be t ween phys ica l and bio- phys ica l cons t an t s arises f r o m the cond i t i ons for the o p t i m a l work o f a l imi ted mo lecu l a r c o m p u t e r (m.c.) .

At bes t our real wor ld is cons t ruc t ed in such a w a y tha t it is m a x i m a l l y phys ica l ly regular , in the sense t ha t the var iables which descr ibe it are c o n n e c t e d by formulas . Here the word " w o r l d " means any phys ica l real i ty . This includes on w h a t we car ry ou t experi- men t s , w h a t we calcula te and the means by which we calcula te : stars, s tones , devices, computers and people. The word "maximun" has its usual m a t h e m a t i c a l mean ing involving a desc r ip t ion of real i ty wi th num ber s . How- ever, the word " p h y s i c a l r egu la r i t y " is n o t d e t e r m i n e d . Unti l now, the c o n c e p t i o n o f scientif ic phys ica l regular i ty is no t general ly used in a precisely de f ined sense. This state-

* This note was prepared by Dr. Liberman in re- sponse to comments on his paper (Liberman, 1979) which appeared in the BioSystems Special Issue on Macromolecules anti the Evolution of Information Processing (BioSystems, Volume II, No. 2,3). It should be read in conjunction with that paper.

m e n t m a y seem strange, since m a n y phys ica l laws are k n o w n which a t f irst sight are deter- m ined very well, such as O h m ' s law, New- t o n ' s laws, Eins te in ' s t h e o r y , Di rac ' s equat ion . In all these cases phys ica l values are exac t ly d e t e r m i n e d by m e a s u r e m e n t , and ma the - mat ica l f o rmu la s c o n n e c t i n g these values wi th each o the r are available. This is jus t the sense in which the words " p h y s i c a l r egu la r i ty" are used. However , it is neces- sary to m a k e m o r e precise t he real sense o f the words " t o subs t i tu te the phys ica l values into m a t h e m a t i c a l f o r m u l a s " . The subs t i t u t ion in to fo rmu la s is the i n t r o d u c t i o n of numer i ca l or s y m b o l i c values by means of a real phys ica l process in a h u m a n brain or a c o m p u t e r , b o t h of which are also real phys ica l devices consis t ing of e l emen t s be longing to the same wor ld .

Studies of m o l e c u l a r c o m p u t e r s (m.c.) lead to the c o n c e p t i o n of a l imi ted calculat- ing device t h a t e x p e n d s a m i n i m u m of free ene rgy fo r solving par t icu la r p r o b l e m s and thus does no t a l te r t he s y s t e m unde r s tudy . Im- agine t h a t a m a x i m a l l y ef fec t ive " l im i t ed m i n d " (i.e., a t h e r m a l l y op t ima l , l imi ted p r o b l e m solving and measu r ing regula tor ) s tudies a phys ica l wor ld which is (a t m o s t ) regular fo r it. T h e s y s t e m (M) is a device res t r ic ted in space and consis t ing of the same e l emen t s as the phys ica l wor ld it studies. What phys ica l laws are necessary if the wor ld is at m o s t regular fo r M? In such a wor ld a n y f u n d a m e n t a l phys ica l value can be measu red wi th def in i te accu racy and its fu tu re behav io r at a n y given t i m e can be p red i c t ed b y M wi th def in i te accuracy .

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If such requirements are imagined, one must immediately refrain from using in- finitely small and infinitely large magnitudes. M would not write or calculate such quan- tities with any accuracy.

2. The physical and biophysical limitations of counting

There is no quant i ty greater than some final one, i.e. there is the largest possible quanti ty . Any real counting process is limited. We shall explain a physical sense of this statement. One can count only on a real physical device; for instance on a macro- machine consisting of molecular computers or on a modern computer in which there are ~101° simple memory elements, or on an excellent machine of the distant future in which there might be 1030 elements. (I represent the human brain or animal brain as macromachines from cell m.c.'s in which there are 102o elementary mole- cular elements). These elements must al- ways consist of real physical particles and contain real physical devices which count particles or radiation quanta. If we consider numbers of the first class, each of them can be represented by a suitable quant i ty of objects or any distinguishable physical values for which a measuring method is indicated, described, and realized. Such numbers in the real world cannot be greater than a real physical device can "wr i te" , for instance, by putting into a "sack" ~ radiation quanta or o ther elementary particles. Such a counting process of the first class starts f rom the indivisible unit • ("a leph", Hebrew) and it can be successfully cont inued only until the number of particles starts to change significantly due to the existence of the real physical interactions between them. We shall denote a limiting number of the first class as m ( " m e m " for the end of a word, Hebrew). For a count with elect- rons and fight quanta, limitations of ~ will arise because of physical properties of the

"sack", for instance, of a resonator and in any case because of birth and destruction of particles under the action of electro- magnetic forces. A rough estimate gives

r-10 ~° (in usual numerical writing). A count with nucleons (neutrons or protons) has an upper limit due to action of gravita- tional forces. The count is limited also by means of the magnetic field or the moment of momentum. If one supposes that a maxi- mum magnitude ~ in all cases is the same, we shall obtain an interrelation of the different fundamental magnitudes.

Any number of the "first class" can be writ ten in a measuring and solving compute r device (m.s.d.) by means of numbers of the "second class". An example of the number of the second class is a positional number writ ten on the paper or by means of the molecule-words of DNA or RNA. For such writing a definite dimensional disposition of the real physical objects and at least two distinguishable objects in sufficient quant i ty are necessary. The limitation of the number quant i ty of the "first class" imposes limitations on the number quanti ty of the "second class" n =?, where n is the number of the different signs for writing.

This limitation is not quite essential for a full description of the fundamental physical magnitudes of the world if our postulation is correct. The full description of any physical constant requires only several hundreds of binary signs. Therefore, a not very complex m.s.d, can describe the fundamental laws of the macroworld exactly wi thout affecting the world by the physical process of the calculation and number writing.

When I paid at tent ion to the effect of the calculation process on the physical object, the future behaviour of which we wanted to predict (Liberman, 1975), an impression was produced that there were no supreme, limited laws. " In format ion physics" which would predict the future behaviour of the physical object on the basis of measure- ments and calculations by real m.s.d.'s would be different for various numbers of para-

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meters and for various m.s.d.'s. However, one can suppose that this is not so because the physical worH is at most possibly cogniz- able in the sense of maximum possible pre- dictability for a cognitive system, constructed from elements of the same real physical world.

3. The upper limitation o f the physical magnitudes leads to the c o m m o n theory of relativity.

As any physical--magnitude has a terminal value in such world, so the limitation of the speed of light becomes an ordinary consequence of our postulate ions. Argu- ments on why just speed, rather than other physical magnitudes, has the easily measured upper limit c (speed of light in the vacuum) will be presented. In order to obtain a special theory, of relativity, besides the existence of the superior limit of speed, c, one must suggest that the laws of mechanics are iden- tical in all coordinate systems. At first sight, this suggestion i~,~ a consequence of the prin- ciple of the maximum regularity of the world. However, an m.s.d, which moves slowly in relation to the object to be mea- sured has other possibilities for description than an m.s.d, which moves in a straight line in relation to this object at the rate of the order of c. Consequently, the physical laws are different for them, though the difference is not large for rates (v) which are not too close to c. If a system moves in a circle, like particles in a ring accelerator, there will be no such in-principle difficulty. The physical laws seem to be identical for a supreme limited m.s.d, in all moving systems only in a world closed due to the existence of a strong enough gravitational field. At the same time a requirement of the superior limitation of the fundamental physical magnitude, length, is fulfilled in such a world. Thus, the superior limitation of the physical magnitudes results in the special theory of relatively in the world limited in space and time.

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4. The inferior limitation of physical mag- nitudes and the requirement for maximum narrowness boundaries of counting result in quantum mechanics

From the requirement of regularity of the physical world for M the inferior limit- ation of all the fundamental physical magni- tudes also follows, the minimum value of action, h, included. The occurrence of action quanta is not sufficient for the transition from Newton's mechanics to quantum mech- anics. But the necessity of the wave proper- ties of matter also follows from the principle of the maximum regularity of the world for a limited m.s.d. Indeed, earlier we dis- cussed superior physical limitations of count- ing. In order to have maximally narrow counting boundaries one must be able to count with the accuracy up to one quanta and one particle. This possibility arises just from the wave properties of quanta and particles.

The principle of maximum regularity of the physical world for an M constructed from elements of the same world also sets limitations on the physical constants of the elementary particles. In fact, not only is the most simple world for M mecessary, but such physical elements from which the optimal limited m.s.d, is obtained are also necessary.

5. On the possibility of obtaining new relationships between physical constants by the requirement o f the optimal action of m.c.

If one suggests that m.s.d, is a macro- machine built from molecular computers, then the main requirement is to have suit- able elements for m.c.; i.e., elements of the minimum size and with optimal links allow- ing the carrying out a search by means of chaotic thermal movement. The covalent bonds in the molecule-words must be as stable as possible and the temperature which determine the Brownian search rate must

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be as high as possible. But proteins to which a demand is made to recognize the address and to break suitable covalent bonds account for a minimum port ion of the free energy and cannot funct ion at high temperature. All this sets limitations on parameters ac- counting for covalent, Van der Waals, ionic and hydrogen bonds. Finally, all the para- meters can be expressed by fundamental constants: electron charge, proton mass, Planck's constant, the speed of light and so on. Thus the principle of the maximum regularity of the physical world can provide a basis for constructing quantum, "relat ive" physics in which all physical values are limited as well as for calculating fundamental constants f rom theoretical considerations. If this programme could be fulfilled, the results obtained could be compared with experiment. However, such description of the principle will require new mathematics. Formulas of mathematical physics are pro- grammes for calculating parameters in which the operator must take part. These formulas are taken from "unin te r rupted {continuous) mathematics" and do not contain an indi- cation of the method which must be used for calculation or when this calculation must be terminated. Formulas of physics for limited cases should indicate the method of calculation and the principle of a com- puter. In particular, it is necessary to stip- ulate when the calculation must be termin- ated, because the cont inuat ion of this cal- culation, which always requires the outlay of an "ac t ion" , will change the physical world, so that prediction will be less accurate than the case in which the calculation is finished "in t ime". This will have an espec- ially impor tant effect on the "condi t ional ly cor rec t" laws of physics for the interaction of several tens or hundreds of atoms when we have measured their initial state and want to have t ime to predict and to check their behaviour in the future. For instance, protein enzymes are such objects. And the living cell is a device, in which the measure- ment and the calculation proceed in the

same place so that the calculating effect cannot be neglected.

But two limited cases form the basis of physics: (1} dynamics, when the effect of calculation is at a minimum and at some time this effect can be completely removed as a result of the suitable world structure; and (2) statistics, in which detailed calcul- ation of the interaction of many particles becomes so cumbersome that one gives it up and replaces this calculation by Brownian search for the answer according to codes of the problem in the m.s.d. The length of the codes is known to be proport ional to log N or, more precisely, to

N - ~ Pi log Pi

i=1

This formula is very similar to that for en- t ropy. However, in future physical theory ent ropy and information will have to be clearly divided; with en t ropy for the physical world and information for code length, in- volving free energy and time operations in the limited m.s.d, which is studying the physical world.

The dynamic laws can be described by the principle of minimum action and un- controlled influence o f a limited calculating system because the interaction of this system with the world which is studied and controlled by it is just a physical action: it requires both energy and time. The suggestion is that for a decrease in uncontrol led influence of M there are such properties in the con- struction of the physical world which are successfully described by the special theory of relatively, quantum mechanics and quan- tum chromodynamics and "possibly the existence of minimum elements of space and time. The principle of the min imum action and uncontrolled influence is not accidentally integral: when the influence of calculation cannot be ignored, then sum- mation takes place in the course of the m.s.d, action. The principle of the minimum action puts requirements on symmetry

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of the e l emen ta ry particles. In the frame- work o f these l imita t ions the second prin- ciple result ing f rom the m a x i m u m possible regular i ty o f the world for M - the principle o f the most possible a s y m m e t r y o f the e l emen ta ry part icle - must allow for the cons t ruc t ion oF the most diversif ied and c o m p a c t elemerLts o f M. Tha t is why unusual molecules con t ro l the func t ion o f the living cell. It is possible tha t N-molecules , hypo- thet ical nuclear s t ructures of the min imum size, consist ing of dif ini te sequences o f the e l emen ta ry parficles could in principle also provide such elements . If the hypo thes i s abou t the par t ic ipa t ion of h y p e r s o u n d mole- cular generators in the func t ion of the cell molecular c ompu te r s is t rue (Liberman et al., 1978) , it will be interest ing to check

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w h e th e r ou r personal self iconsciousness works on superdense nuclear s t ruc ture of this type . Such s t ruc ture might con ta in %102o elemen- t a ry part icles and could be viewed as a heavy a tom with the connec t ion with m.c. im p lem en ted by means of h y p e r s o u n d oscil- la t ions at f requencies o f the order o f 10 l'~-- I012 Hz.

References

Liberman, E.A., ]975, Molecular cell computer. VII. Cell biophysics and realistic or informative physics (1). Biofizika 20, 432--436.

Liberman, E.A.S.V. Minima and N.E. Shklovski, 1978, The study of diffusion modelling system of neuron. Biofizika 23, 630--636.

Liberman, N., 1979, Analog-digital molecular cell computer. BioSystems 11, 111--124.