Transcript I. General introduction

Nature of Reality
According to Einstein’s
Statistical-Thermodynamic
and Geometrical ideas
Prof. O. Goloubjeva.
Prof. A.Soukhanov
Russia, Moscow [email protected]
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I. General introduction
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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 socalled “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 worldfamous 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.
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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 macroparameters.
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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.
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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.
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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 nonclassical 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.
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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.
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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.
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Assume for simplicity the hole as being not charged
and not rotating; then the standard form of this formula is
the following:
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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
k G
S=4π M2 (  c ).
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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!
B
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