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Nature of Reality According to Einstein’s

Statistical-Thermodynamic

and Geometrical ideas

Prof. O. Goloubjeva. Prof. A.Soukhanov

Russia, Moscow ogol@oldi.ru

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I. General introduction• At present time we have all the possibilities for the complete

comprehension of Einstein’s scientific legacy. The most important point here is to elucidate the role of Einstein’s ideas in the creation of modern concepts about the nature of physical reality.

• To evaluate Einstein’s contribution in the world science and culture one must consider not only his papers on Physics but his achievements as a thinker and philosopher. He did not write pure philosophical works but in spite of it his comprehensive reflections about physics reality enriched humanity by new universal views on the Nature

• Einstein always preferred in the Physics the most universal systems of views on the reality because he thought of as a picture of World must be entire. He was impressed by so-called “Theories of Principle” based on general features of phenomena. Such theories for him were the geometry and thermodynamics in the most wide sense of these notions ( according to Einstein, “Physics = Geometry + Experience”).

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• The concepts of geometry attracted him by the possibility of the invariant description of Nature without any specification of the coordinate system. These concepts were realized in Einstein’s works on special and general relativity theories.

• The concepts of thermodynamics are the most close

to experience. They were also highly evaluated by Einstein due to their generalization , i.e. independence upon specific physical models. To develop and apply the thermodynamics were only needed the most general ideas about the interrelations between the material object and it’s environment, i.e. between the system and the thermal bath. At the same time the thermodynamics deals with macroscopic observables which may be obtained from experience

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II. General Estimate of Einstein’s Heritage

• Philosophical and scientific ideas of Einstein were closely bound. But to understand his world outlook we start from estimating his scientific legacy. When one say about Einstein – physicist the most often one refers to his world-famous relativistic theories. But according to well known scientist M. Born “Einstein should be referred to as one of the greatest physicist of all times even in the case when he should write nothing on the relativity theory”. We full agree upon this opinion (despite to the latest own Einstein’s statements).

• So let us make no mention of his relativity theories and concern Einstein’s works on the statistical theories. They contain some pioneer basic ideas of modern essential part of Physics - the Statistical Thermodynamics which were developed by his nearest followers (Fuhrth, Laue, Szilard).

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III. Short review of Einstein’s statistical theories

• Chronologically the first of these statistical theories was the Statistical Mechanics in the phase space, which was worked out by Einstein simultaneously with and independent of Gibbs. As a “byproduct” of the statistical mechanics there appeared the fluctuations of some macro-parameters. But to these ones didn’t belong intensive characteristics like a temperature and an entropy, having no mechanical analogues.

• The second original and in fact most important statistical theory by Einstein, was the true statistical thermodynamics operating in the space of all macro-parameters in which he carried out a generalization of the zeroth law of thermodynamics. Einstein put forward the following fundamental statements:

• a temperature of any object in a thermal equilibrium state is only equal to a temperature of a thermal bath on the average and it has an ability to fluctuate alongside with other macro-parameters.

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• On this basis he established a fundamental sense and an universal formula for Boltzmann's constant that applied to macro-objects of any type; calculated fluctuations of the internal energy and the inverse temperature of a macro-system that allows us to write a thermodynamic uncertainties relation between them depended on Boltzmann's constant; formulated Boltzmann's principle and a developed the fluctuations theory of any macro – parameters.

• The third his statistical theory was the theory of Brownian motion, or the generalized diffusion theory, which includes the Einstein – Fokker – Planck equation. According to modern views, it is a fully independent from Statistical Mechanics theory, where coordinate and momentum obtain the sense of macro- parameters.

• Finally, the fourth statistical theory was his Quantum Theory of radiation etc. Predicted by him a spontaneous radiation is an analogous to the spontaneous decay of the nucleus. This event opened the era of the development of stochastic notions on the microscopic level of the description of Nature.

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IV. Entering of fundamental constants

• Einstein's ideas have begun an independent description of the Nature at the macro –level. He provided the stochastic description of Nature as on the microscopic as well macroscopic levels. Nevertheless, Einstein appeared to be the ancestor of qualitatively new – non-classical – views of the Nature, where the central point is the concept of the stochasticity of all natural processes.

• Note that each of his theories (as relativistic as statistical) is connected with one (or more than one) of world constants. In particular constant c (velocity of light) is in corresponding to SRT, G (constant of gravitation)- to GRT, ђ (Planck’s constant) appeared due to photon hypotheses and at last kB (Boltzmann’s constant) has an direct relationship to fluctuations theory. Moreover Einstein’s radiation theory joins three constants ђ, c and kB. . So it must be admitted that they all them had got the status of universal constants due to Einstein!

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V. The goal of Physics

• Let us recall that just the formation of the Physics Picture of World as a whole description is the uttermost goal of physics – such was the opinion of many outstanding physicists and thinkers like Leibnitz, Mach, Planck and Einstein himself. That is another matter how entire this PPW might be in the final. Before Einstein Physics looked like a mosaic of theories sometimes even contradicting each other. All the work of Einstein in relativity theory as well as in thermodynamics was intended on the overcoming of this disconnection of various views on the Nature. He was sure that PPW must be entire.

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• The main methodological achievement of Einstein was demonstrating the fundamental role of two universal views on the Nature – i.e., geometry and thermodynamics in the most wide sense of these concepts. The geometrical way of Einstein’s thinking allowed him to realize the concept of integrity in the classical version of PPW, in which fluctuations are absent. In turn, the thermodynamic way of Einstein’s thinking created the possibilities for the realization of the integrity concept in the non-classical version of PPW in which there are the fluctuations as extensive as intensive characteristics.

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VI. Zellmanov’s cube • The results of Einstein’s studies continue to play the outstanding

role in the acknowledgment of the integrity of contemporary PPW. First of all the question is in the discovery of conceptual structure of Physics. Many scientists were interested in this problem and suggested its different versions. Several of them were grounded on the basis composed of fundamental constants and connected with them theories.

• In the thirties of XX century was realized the three- parametrical model of Zellmanov. The model was formulated in terms of only three fundamental constants − c, G, ħ. It gave some possibility for analysis of the interrelations between existing physical theories and stimulated the searching of the missing elements of the model. The model was referred to as “Zellmanov’s cube” because it had got an obvious geometrical image in the form of cube.

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• In our opinion, the main shortcoming of this model consists in abandonment from consideration the fundamental Boltzmann’s constant kB which status according Planck’s mention (1899) is not lower than of preceding three constants. It means that in this model Physics was only reduced to the microscopic description.

• In this way, from the very beginning was excluded the thermodynamics as an independent fundamental and universal physical theory. Up to now the all intellectual efforts to construct a full model didn’t bring the expected results.

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• Now to construction a PPW we suggest starting from admitting on equal rights of all four fundamental physical constants. The main bulk of physical knowledge in our opinion may be classified according to two foundations – the first are versions of PPW, while the second – the levels of the Nature description.

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• Starting from the first foundation we obtain two versions of PPW– the classical and non-classical ones.

• Starting from the second foundation we suggest that there are two levels of the description of Nature – the microscopic and macroscopic ones.

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• On this basis the special and general relativity theories are classical ones, whereas statistical thermodynamics and quantum dynamics are the non-classical ones.

• On this way we take into account Einstein’s viewpoint on fluctuations as an important property of Nature objects. So these versions differ in the following respect: do or do not play the significant role the fluctuations of all the physical quantities (as well as correlations between them) in these theories.

• Noticed, Micro- and macro- levels are equally fundamental and independent. By macroscopic description the outstanding role are played by such quantities as temperature and entropy.

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VII. The tetrahedron

• The main difficulty on this way – looking for adequate geometrical image for this structure. As the first step it may be schematically shown by the aid of planar table, consisting of four cells. Accordingly we have four sets of fundamental physical theories, which are qualitatively different. The constants c and G correspond to classical theories but constants ђ and kB correspond to non-classical ones.

• But much more informative will be obtained by means of some obvious spatial image. For all this construction it should be the tetrahedron – the minimal Plato’s body.

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• Every face of this body corresponds to one of the cells of the planar table and, consequently, to one of fundamental constants.

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• The tetrahedron suggested is the image of some integral physical picture of the world (IPPW). All the faces of the body, unifying sets of physical theories, together describe the Nature as a whole. It may be well admissible that the future development of physics will come towards the deepening of the interrelations between the theories on every face as well as between the different faces. This prognosis in our opinion is adequate to entire Nature.

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VIII. Elaboration of Einstein’s ideas

• Einstein’s creative heritage suggests the possibility also for the next step toward the integrity of PPW. In fact, the question is to generalize and to give a real content to the Mach’s principle which was highly rated by Einstein. In our opinion, the generalized Mach’s principle is equivalent to the following statement:

• any physical object besides the local characteristics possess also the global ones, and just these last ones reflect in some generalized way the influence of the environment on the object.

• Striking examples of the global characteristics are the temperature in statistical thermodynamics (non-classical version of PPW) and the energy-momentum tensor in general relativity theory (classical version of PPW). Einstein explained us their physical sense and role in Nature’s description.

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• In this connection, grows the significance of another Einstein’s favorite method - the Geometry in the wide sense. Nowadays geometrical ideas are wide used for generalization of thermodynamics.

• Finally, one more tradition laid down by Einstein consists in the use of so-called “thermodynamic envelope” when developing the quantum views. This may be considered as the prologue to the creation of modern quantum field theory (QFT) with belonging to this theory universal concept of vacuum.

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• At the same time successfully developing are some versions of QFT at finite temperatures – in the first place the thermo-field dynamics (TFD), which allows to combine in harmonic way the significant features of standard QFT and statistical thermodynamics. This version of QFT relies on the universal notion of the thermo-field vacuum, which combines the usual notions of “cold vacuum” and the thermal bath.

• As a result, one may foresee the following possible development of theoretical physics in the current post-Einstein century. In our opinion, there should happen the combination and unification of the ideas originally inherent in Einstein’s creative and seminal work – i.e., his ideas in geometry, quantum field theory and statistical thermodynamics.

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IX. Conclusion

• As a conclusion let us present some formula, which symbolizes the future integrated theory of physics. This formula is well known about thirty years, but it was not yet analyzed in such a context: we mean the Beckenstein – Hawking formula for the entropy S of the black hole.

• Assume for simplicity the hole as being not charged and not rotating; then the standard form of this formula is the following:

• S= kB(A/4L 2PL), A=4πR2 ;

• here kB – is the Boltzmann’s constant; LPL − is the Planck length;

• R– is the radius of the black hole.

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• If one rewrites this formula, expressing Rbh through M – the mass of the black hole and using further only the fundamental constants, one obtains S=4π M2 ( ).

• It is not difficult to see in this formula on quite equal rights enter all the four fundamental constants. It seems us this is a very beautiful expression!

• Following to Einstein, such fact hardly may be considered as simply accidental one!

cGk

B