Nature of Reality

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• Nature of Reality
• According to Einsteins
• Statistical-Thermodynamic
• and Geometrical ideas
• Prof. O. Goloubjeva.
• Prof. A.Soukhanov
• Russia, Moscow ogol_at_oldi.ru

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I. General introduction

• At present time we have all the possibilities for
  the complete comprehension of Einsteins
  scientific legacy. The most important point here
  is to elucidate the role of Einsteins ideas in
  the creation of modern concepts about the nature
  of physical reality.
• To evaluate Einsteins 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 Einsteins 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
  its 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 Einsteins 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
  Einsteins statements).
• So let us make no mention of his relativity
  theories and concern Einsteins 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 Einsteins 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 didnt
  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, ? (Plancks constant)
  appeared due to photon hypotheses and at last kB
  (Boltzmanns constant) has an direct relationship
  to fluctuations theory. Moreover Einsteins
  radiation theory joins three constants ?, 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
  Einsteins 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 Einsteins 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. Zellmanovs cube

• The results of Einsteins 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, h. 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 Zellmanovs 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 Boltzmanns
  constant kB which status according Plancks
  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 didnt 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 Einsteins
  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 ?
  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 Platos 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 Einsteins ideas

• Einsteins 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
  Machs principle which was highly rated by
  Einstein. In our opinion, the generalized Machs
  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
  Natures description.

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• In this connection, grows the significance of
  another Einsteins 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
  Einsteins 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), A4pR2
  
• here kB is the Boltzmanns 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 S4p 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!