The Principle Of Coservtion Of Informtion As The Evidence Of Existence Of God

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  • 1. THE PRINCIPLE OF CONSERVATION OF INFORMATION AS THE EVIDENCE OF EXISTENCE OF GOD Prof.dr hab. Inż Jerzy Lechowski International Academy of Sciences AIS Departament of Cybernetics RESUME This work is intended to prove that the rightness of the second principle of thermodynamics results out of the principle of conservation of information which proof had been carried out in this work. It had been ascertained that in the universe as, we know it, that principle must be limited by the nature of its carrier (material or energetic) but is at the same time infinite as it may be transformed into another one like the mass or energy. The way to calculate the maximum volume of information contained in the whole matter of the universe, as we know it, has been presented. It was proved that the water is most perfect antientropic material of all living creatures. 1.Relation between the principle of conservation of information and the second principle of thermodynamics The second principle of thermodynamics is considered to be one of the most important in physical and chemical sciences. Its rightness might have been questioned by “Maxwell’s demon”, sly and intelligent being, were it not for the principle of conservation of information in isolated patterns published the first time in 1972, which, in decisive way, expelled the demon out of thermodynamics. The second principle of thermodynamic is connected with the notion of proficiency p . Proficiency . is defined as the quotient of useful work Wu and performed work Ww = Wu + Wr Ww: , and because: , where: Wu η= Ww Wr –is diffused work (swapped for heat)), hence: Ww − Wr Q1 − Q2 mcw ∆T1 − mcw ∆T ∆T − ∆T2 (T1 − T ) − (T2 − T0 ) η= = = = 1 = Ww Q1 mcw ∆T1 ∆T1 T1 − T0 Assuming T0 = 0 K we have
  • 2. T1 − T2 Q1 − Q2 η= = T1 Q1 hence T2 Q 1− = 1− 2 T1 Q1 so T2 Q2 = T1 Q1 or Q1 Q2 = T1 T2 hence Q1 Q2 − =0 T1 T2 Assuming that: T1 = T2 = T and: Q2 S2 = T2 We arrive at: ∆Q ∆S = S1 − S 2 = =0 T In isolated patterns (we can assume that the universe represents isolated pattern) and in reversible processes (happening in the nature) entropy remains unchanged. So does the volume of information defined as negentropy, that is, decrease of entropy [10]. This problem may be reversed allowing to affirm that out of the principle of conservation of the volume of information in reversible processes and in isolated patterns results the rightness of the second principle of thermodynamics. i.e.n S = 0. This problem is linked strictly to the intellectual experience of L.Szilard of 1928 [6] who founded himself on suggestions articulated by M. Smoluchowski in 1906 referred to in the second principle of thermodynamics. L. Brillouin commented this fact in 1956 as follows: „When we discover notable similarity between information and entropy- the physics comes in
  • 3. question. This similarity was noted long time ago by Szilard in his work of 1929 which is believed to be a precursor of the actual theory of information. That work was really a pioneering penetration of a new territory which we are thoroughly investigating right now”.[1,s.20]. Out of experience of M. Smoluchowski – Szilard comes out that the entropy of the system must be changing when subject to data collection if the second principle of thermodynamics is to be reaffirmed. The collection of certain information about the system is possible only when entropy of both the system and its environment is changing, as during data collection of one system about another one – the change of entropy in both systems and their environment is taking place. In order to reveal this fact, that below experience of Smoluchowski-Szilard is provided [5,6]. The cylinder containing one molecule is partitioned on two parts, i.e. two volumes respectively V 1 and V2. Let the partition serve as a piston sliding up and down inside the cylinder. We are assuming that a man would be able to observe the said molecule and depending on its actual position, either in V1 or in V2, , could have switched the piston with the help of coupled lever making the molecule to perform a work in isothermal process lifting, for example, some weight and loosing its energy. Depending on the position of the molecule we should distinguish two ingredients of entropy S1 and S2, such, that S = p1S1 + p2 S 2 where:: p1 i p2 –the respective probabilities defined by the formula below: V2 p2 = V1 + V2 , At the same time , during the process of isothermal inflation of gas its entropy is decreasing by s1 caused by the observation of the molecule and collection of data about its position. _ s Average value of entropy with andi and average value of entropy, produced by observation (data collection) is negative and makes up for:
  • 4. V2 s2 = k lg V1 + V2 _ s Without the second principle of thermodynamics could not be fulfilled due to “Maxwell’s demon”. Demon could have sorted all the molecules into those of smaller and greater energy, and then, it would be possible to avail oneself of the heat of the pattern without the difference of temperature T1 i T2 If the second principle of thermodynamics is to be fulfilled in open patterns, the following condition must be fulfilled: _ _ S+ s ≥ 0 Therefore, the second principle of thermodynamics arises out of the principle of conservation of information in isolated patterns. However, two conditions must be fulfilled. condition I: p1 + p2 = 1 condition II: S1 S2 − − e k +e k ≤1 The condition I is fulfilled by definition of probability, since the molecule may be present only either in V1, or in V2.
  • 5. The condition II is also fulfilled because: S2 = −k ln p2 , hence: S2 − = ln p2 k and , therefore: S2 − e k = p2 and . In each case of separate events – inequality: S2 − = ln p2 k is right and that is why inequality: V2. S1 S2 − − e k +e k ≤1
  • 6. is also right. . Out of the second condition is evident that if S1 will be low at will, then S2 must be respectively of high value and vice versa. Each measurement is being saddled with an error because it is disturbing to the lesser or the greater extend the measured subject, hence, it is good example to support the principle of conservation of information. This fact becomes evident because during the measurement certain entropy equal to the information collected is being introduced into the pattern along with provided energy. If the pattern is providing information sending off some energy to the environment, the entropy may remain in this environment and the information may be taken over by another pattern. It is linked directly to the principle of indetermination by Heisenberg which says that we cannot measure exactly, and, at the same time, impetus( speed) and position of the body: when mp is decreasing, then, d x is rising, so, the below condition must always be fulfilled: : ∆E ⋅ ∆t ≥ h or It happens that not only taking measurement is responsible for introducing information and the entropy to the pattern and its environment. So is our intention to collect some information about the pattern through calculation, because, when doing it, certain energy must be used up increasing the entropy of that environment to compensate for the collected information. 2.The examples removing doubts over the evidence of the principle of conservation of information 1. Why a lecturer while passing over free information to the listeners is not loosing it himself? A lecturer to deliver a lecture had to capture from the environment both energy and information. Consuming food products he had to get out of the environment both energy, in digesting process, and essential for life as well as the linked information inherent in food products increasing their entropy.[10] 2.Why, while availing themselves of information sources such as books, CD and others we are not draining them up ?. Moreover, often different beneficiaries are getting different information from the same sourcing depending on the level of their erudition and actual necessities. To answer that question it is enough to carry out the reasoning similar to that which led to the discovery of the principle of saving electric charge. That principle was accepted in spite of alleged evidence that electric charges of different poles are tending do disappear when colliding. Moreover, that principle was accepted in physics as one of utmost importance of saving, even more important that the principle of saving mass, which, according to the theory of relativity, is changing in function of speed. Brilloun [1] citing
  • 7. Szilard [6] and underlining the fundamental importance of his work, drew attention to the fact, that any collected information must be “paid for” with entropy. In each case of collecting information from any sourcing, energy is needed, which is dissipating, increasing the entropy of the environment [10]. 3.To read a book, a light source is necessary to light up the text. Light energy is being dissipated increasing the entropy of the environment, which becomes “the price” paid for information collected from the text. In any other case of collecting information from a source, certain energy is always needed, which, dissipating, increases the entropy of the environment. 4.It might be said that destroying information source one is destroying information itself contained in it. That situation is similar to fuel combustion, making free the energy, which had been dissipated, though the principle of saving energy is still valid. Information contained in destroyed source is saved like the energy of fuel combustion. What is changed is the form of information. Information continues to exist what is underlined in a word “in-forma”, that is, in the other form.10] 5.Information like God alone is eternal and infinite. It may transform itself infinitely from one form to another one. 6.The way a Maxwell’s demon” had been expelled from thermodynamics the same way the forgery will be expelled from the human minds and the truth will make man free. 3. Calculation of the potential and information power of the system In principle, any physical value becomes information potential, which gradient is a stimulus forcing the flow of information carrier, and along with it, the information itself. Therefore, also gravitation power falling on the unit of mass may be considered as information potential, in other words, intensity of gravitation field, that is gradient of gravitation potential like the other gradients: temperature, pressure, concentration, electric field, magnetic field etc. However, according to the accepted definition of information potential [4,5,9] W∞ V= q , W∞ In order to determine its value we must assume the value q (information charge of one bite) and (the work needed to transpose one bite of information along with its minimum carrier from infinity to the fixed point A, in which, there is already another bite of information) equal:
  • 8. W1 = kT ln 2 (for T = 1K).Information potential of point A in which there is already another bite of information accounts for: J J V1 = 0,7 ⋅1,38 ⋅10−23 = 0,966 ⋅10−23 Bit B The work to transpose subsequent bites from infinity to the given material point with radius r o is determined by formula ∞ ∞ (n − 1)q ⋅ q (n − 1)q 2 W∞ = ∫ dr = ∫ r −2 (n − 1)q 2 dr = ro r2 ro ro . As may be seen, the work is rising in linear way along with transposed information. Information potential will also have upward linear trend in that point. In general, it may be put down that: Wn = n ⋅W1 , (n – natural number corresponding to the subsequent information bites transposed to the physical point, or otherwise – to the elementary information carrier with radius ro, in which there is one bite of information). Let’s fix VnA as information potential of the point A, in which there are n bites of information. That potential makes up for:: n ⋅W1 J VnA = = n ⋅10−23 q B [Vi ] =  J    B Assuming the definition of information volt as : , information potential of point A will make up for: n.10-23 Vi. Information potential of the given point will represent value 1Vi, if at this point 1/6 mole of
  • 9. information bites will be found. Farade of information Fi may be determined on the basis of the formula: Q B C=   U Vi  Material and energetic carriers may be identified as mass end energy are bound by the formula (E = mc2). The mass may always be recounted on energy, which ( as an elementary carrier of information) next may be recounted on information, transposed by the carrier. The carrier of information cannot equal 0. Theoretically it is possible to calculate maximum volume of information contained (bound information) or transposed (free information ) of the given mass or energy. Example: let’s calculate maximum volume of information which may be contained in one gram of the matter. That maximum volume of bound information in structure of the system may be calculated by the formula mc 2 n= [ B] kT ln 2 , where: m – mass of the system c – speed of light J k = 1,38 ⋅10−23 K k - Boltzmann’s constant () T – temperature by Kelwin There is also formula to calculate maximum volume of free information the system can emit without abruptly changing its internal structure, as below ε ⋅ S ⋅σ ⋅ T 4 ⋅ t n= hν ,
  • 10. where: ε - coefficient of emission capacity of a given body S – surface of the system W σ = 5,67 ⋅10−8 m2 K 4 - constant by Stefan – Boltzmann () t – time of emission of the information, h – constant of Planck (h = 6,62.10-34Js J - frequency of emitted quantum . Max. Volume of bound information contained in one gram of the matter depends, visibly, on temperature. Assuming we have reached the temperature of 1 K, then, in one gram of the matter there is: m 1g (3.108 ) 2 mc 2 s n= = ≈ 1036 bitów k ln 2 0.7 ⋅1,38 ⋅10−23 J K It is easy to calculate that one electron cannot contain more than 8,4.109 bites. Assuming that in the whole universe, known to us, there is about 1080 atoms, it can be estimated that it cannot contain more than 10100 bites of information. Qi Ui = Ci Each system, apart from maximum of bound information which may possess has also information potential[10], as well as information power . Information potential of the system, depends, electric potential likewise, on capacity, according to the formula : . Therefore, solely information power of the system is decisive for its quality. Often, however, excess of
  • 11. information creates a problem, because we do not know which information is most important . Well, the most important is that one which has the greatest information power, i.e. has higher product of “draft-lift power” [4,9] and higher flow speed. What advantage can we get from information which is stored and cannot be transposed?. In such case the only and the most important advantage is the fact that it creates the specific structure of the system which remains unproductive for arranging the environment, unless, it constitutes an element somewhat important of the system. Free information of great power have capacity to overcome information resistance because of their higher speed of flow v. The power is expressed by the formula W F ⋅s P= = = F ⋅v t t , According to M. Mazur [7] the power of the system is determined by the formula: P = a ⋅ c ⋅ν where: a – quality of material, c – volume of material. c - unit power of material, i.e., information power proper to the system The quality of material, or otherwise, information power proper to the system is bound with its resistance to increase of entropy. Water is the material resistant to the increase of entropy due to hydrogen inherent in it. Hydrogen features one of the highest proper temperature and is probably why both hydrogen and water are the main ingredients of all living creatures. This fact certifies that it was God Creator of life who put up the best material to build up living organism, not the casual natural selection glorified by the theory of evolution. 4.Antientropic material of living creatures. kJ 4,9 kg ⋅ K
  • 12. The best material for building life has liquid form, neither solid nor gas. Liquid substance certainly represents the richest variety of physical resources as well as dynamic and organizational possibilities. Water proved to be the best building material of life because of many reasons. First and most important reason is that water has, after helium and hydrogen, the highest specific heat out of all other substances present in nature. It is probably owing to hydrogen , which is the lightest. Specific heat of hydrogen makes up for: , and that of water . The specific heat of helium ; is really higher than that of water, but helium, being noble gas, is not reacting with other elements. It is not accidentally that hydrogen, having the highest specific heat, is inherent to all chemical compounds. Apart, it is worth noting, that all traced microelements found in living organism have relatively high specific heat. It is easy to prove making review of traced microelements present in living organism. Why just specific heat feature is so important for selection of building material of life? This feature is bound to the principle of conservation of information and to entropy conception. It is turning out that the substances of high specific heat are resistant to the increase of entropy, that is to a mess, that is, to deficient organizational order.[10]. Isn’t great having the body resistant to a mess? The increase of entropy in living bodies leads to death destroying their structure and organization. The growth of entropy, as is known, is determined by the formula: ∆Q  J  m ⋅ cw ⋅ ∆T ∆S = = T K    T . Out of this formula is noted that the lower specific heat of the body the smaller quantum of heat is needed to warm up given mass m by 1 K ,and vice versa, the higher specific heat, the more heat should be provided to rise body temperature by 1 K. Hence the conclusion that living bodies with high specific heat are resistant to the increase of entropy, that is, are more fit to retain their organization against destructive activity of the environment. Some scientist point out that we owe our life to the evolution and to random natural selection. However, out of the principle of conservation of information follows that it is Creator who had designed this wonderfully organized universe for us. Determinism (which assumes existence of basic natural laws) and random (which prizes statistical methods as the basic instrument for understanding of interdependencies) take us to the same way of understanding of the universe. Therefore, they do not differ much except for the method chosen and initial assumptions assorted. There is no room for casualty in the universe. Only a man unfamiliar with complexity of natural laws may think otherwise. So, we can, with conviction say that all began with information. Moreover, the information is and always will be present and decisive (though limited in view of its material and energetic carrier) and infinite (in view of the process of permanent transformation we are the witness of).
  • 13. Bibliografy [1] Brillouin L., Nauka a teoria informacji Warszawa, 1969. [2] Gabor D., CommcuniationTheory and Physics, Phil. Mag. 41, 7, 1950. [3] Lechowski J., Modelowanie elektryczne pola informacyjnego w strukturach biologicznych, Materiały III Sympozjum PTFM, Zabrze 1972. [4] Lechowski J., Analiza możliwości modelowania elektrycznego przepływu informacji w środowisku, Postępy Cybernetyki, 3, 1983. [5] Smoluchowski M., Granice stosowalności drugiej zasady termodynamiki, [W:] Wkład polskich uczonych do fizyki statystyczno-molekularnej, PWN, Warszawa 1962. [6] Szilard L., Űber die Entropieverminderung in einem termodynamischen System bei Eingriffenin intelligenter Wessen, Zeitschrift fur Physik, Bd 53, Berlin 1928. [7] Mazur M., Cybernetyczna teoria układów samodzielnych, PWN Warszawa 1966. [8] Mitiiugow W. W., Fizyczne podstawy teorii informacji, PWN, Warszawa 1980. [9] Lechowski J., Zastosowanie zasady zachowania informacji w układach izolowanych, Postępy Cybernetyki, 3, 1987. [10] Lechowski J., Analiza możliwości modelowania elektrycznego przepływu informacji w organizmie człowieka i jego otoczeniu, Praca habilitacyjna, AIS, San Marino 1994.