The Annals of Frontier and Exploratory Science

Any information displayed here is the propriatary information in the area of "Wrong and Inadequate None-physical "Solutions" of Many-body (and n-body) Problems in COHP Holding Back Contemporary Science and Mankind in General. Physics 2"

As any physical and mathematical definition and statement for Many-Body Problem (MBP) demands for recognition of this kind of physical tasks as the Two-phase Two-scale (2P2S), at least, task that involves requirements for its physical and mathematical statement and solution the use of the concepts and methods of HSP, which in turn outlines this hypothesis.

The main body of Hypothesis about statements and possibility of the correct physically and mathematically MBP solution is that the correct solution of the MBP (physical) should be obtained only within HSP for, at least, the statement of 2P2S for MBP.

The electric field applied as in this Figure below to the 3D regular medium of equal spherical particles arranged as the matrix

and for this Heterogeneous spatial media of Many-body type researched many One-scale - Lower scale problems and obtained still limited, but large amount of Lower scale data with again not fully described Limited and/or INCORRECT data for the Upper scale physics.

The insufficiencies of the COHP MBPs are always communicated to the One phase formulation mathematics for dynamics of bodies (particles) supported by the frivolous summation of the pair-wise mathematical (based on the pair-wise experiments) formulation of the inter-particle force, emerging of the EM, gravitation, or other physical source of interaction.

The fundamental difference between the summed pair-wise and collective interactions couldn't be even disclosed and understood by physicists in previous centuries based on the only COH physics understandings and concepts.

There were no polyphase, 2- or more scale physics and mathematics in XVII - XX (first half) before ~1970s. Nevertheless, up to now - 2010s - COH physicists can not apprehend the basics of HSP due to lack of special education, lack of mathematical background, that should be extended for ~3 years in the universities.

We are watching this resistance and coercion for obsolete, more on that, to wrong understanding and methods with which COH physics still try to persue wrongly stated the One-phase MBPs.

While with the 2P2S MBP physical and mathematical statement the problem obtains the needed features of fully defined conditions for the only singular solution. More of that, the Two-scale Hierarchical mathematics it is the way to discover and include in the set of physical phenomena pertained to MBPs the completely new to COHP description of related phenomena - the phenomena that appeared as existing while are visible only via the Two- (or more) scale physics consideration of the MB problem [1-10].

That also means that the solutions of the One-scale Bottom-Up (BU) MBPs with even a low number of bodies are incomplete or simply wrong for most of the problem types due to the lack of accounting for the existing physical Polyscale phenomena [1-6,11-28].

While these One-scale solutions will be decisively wrong for the Top-Down (TD) MBPs. For example, in the astrophysical, nuclear, biological, medicinal, ecological events, phenomena.

When the Top-Down designations and values of the physical phenomena fields (variables in mathematics) and fluxes should be corresponding correctly from one scale to another in the same way as of the BU communications. Which is not the case in COHP. While physicists in COHP prefer not knowing about this.

The fundamental imbalance in the COHP statements for MBPs is that in their modeling equations included the pair-wise Local interaction functions - that implies then - that the collective Non-local interaction is not achievable in principle in COHP.

Even in the infinite limits of the computational interactive methods. They don't understand this. Because in these mathematical modeling equations - see the statements for Many-body and n-body problems in COHP literature, there are absent the needed terms reflecting the various interaction mechanisms in the equations [1-3,6,8,11-16] etc.

This means in the COHP mathematical statements for MBPs are absent some terms, while in the HSP equations they are present. So - both sets of governing equations are a priori different - for the same reasons will be different and their solutions - as we demonstrated in numerous HSP problem solution cases [1-3,6,8,10-19] etc.

We would like to mention here again that the separation of "n-body Problems" into a diverse group of physical problems we do not acknowledge and support. The topic and methodology used for qualification of the"n-body Problems" and Many-Body Problems are the same may be said.

And you know why COH physics insists on providing for education the separation of the categories of Many-Body Problems and n-body Problems in spite that their ideology and even modeling development procedures are almost identical - mainly because COH physics of sub-atomic scales dreams on continuing the deception of students and public on the so-called "existance" of Point-Mass-Charge-Spin (PMCS) "particles" - that is their "bread and butter" in COH physical sciences.

That is why we place in here and in other similar spots the figures of the sub-atomic particles as the Volumetric objects with the Mass, Charge, and Spin individual properties. So - the particles as particles not dot-myths.

While development of correct Collective Interaction physical and mathematical models (statements) for MBPs by COH physics is not capable for a few reasons - one of these reasons is not the correct mathematics of them.

When we following Scaled physics and Hierarchical mathematics of HSP, for example, as ascribed in [1-40] with special attention into [1,2,36], we understand why the pretty simplified and incorrect One-phase One-scale statements for the MB and n-body problems that developed in COH physics during the last ~400 years are not reflecting on the desirable effects and modeling only the Homogeneous physics for these MB problems - which is incorrect. While they are usually the Heterogeneous and Two-phase Two-scale at least.

Then we should understand that these COHP descriptions and pseudo-solutions for MBPs are not corresponding to physics of the natural world around.

This situation to some degree explains why the science and total efforts of humanity are held back since the beginning of the XX century. The so-called MBPs as the tremendously important part of physics, chemistry, and biology, existing in any chapter of them, make their input wrong being stated in COHP as described above whatever they are right now in Conventional Homogeneous physics.

Acknowledgements:

We would like to sincerely express our acknowledgment to T.J.Champion for the support in providing this work.

References

1. Travkin, V.S., "What Classical Mechanics of XVIII Provided in XX Has Done Wrong to the Base of Mechanical Science Including the Classical Mechanics of Continuum Particles and Conventional Orthodox Homogeneous Particle Physics", http://travkin-hspt.com/rottors/classmechwrong/classmechwrong.htm, (2014)

2. Travkin, V.S.,"The Major Forces Have Been Missing From Governing Equations for Dynamics of Sub-atomic and Continuum Particles, Bodies in XVIII - XX ", http://travkin-hspt.com/rottors/forcemissing/forcemissing.htm, (2014)

3. Travkin, V.S., Physics of Many-body Continuum Media Problems. Not Only Mathematics. Physics 2, http://travkin-hspt.com/elastic2/manybody/manybody.htm, (2016)

4. Travkin, V.S., Physics of Many-body Particulate Media Problems. Not Only Mathematics. Physics 2, http://travkin-hspt.com/parphys2/manypartibody/manypartibody.htm, (2016)

5. Travkin, V.S., Physics of Many-body Atomic Media Problems. Not Only Mathematics. Physics 2, http://travkin-hspt.com/atom2/manyatombody/manyatombody.htm, (2016)

6. Travkin, V.S., "When the 2x2 is not going to be 4 - What to do?" "http://travkin-hspt.com/eldyn/WhatToDo2.htm, (2002-2004)

7. Travkin, V.S., "Two Scale EM Wave Propagation in Superlattices - 1D Photonic Crystals Two Scale Exact Solution, " http://travkin-hspt.com/eldyn/photcrys1.htm, (2004)

8. Travkin, V.S., "Globular Morphology Two Scale Electrostatic Exact Solutions," http://travkin-hspt.com/eldyn/glob1.htm, (2004)

9. Travkin, V.S., "Two Scale Two-Phase Straight Bars (Capillaries) Electrostatic Exact Solution," http://travkin-hspt.com/eldyn/pores1.htm, (2004)

10. Travkin, V.S., "Effective Coefficients in Electrodynamics," http://travkin-hspt.com/eldyn/edeffectivecoeff.htm, (2007)

11. Travkin V.S., Classical Problems in Fluid Mechanics, http://travkin-hspt.com/fluid/03.htm, (2003)

12. Travkin V.S., Classical Problems in Thermal Physics, http://travkin-hspt.com/thermph/02.htm, (2003)

13 . Travkin, V.S., "Scaled Modeling of Interaction and Interscale Hidden in COHP Forces and Effects in the Sub-Atomic and Continual Particles Arrays (Clouds). Physics 2," http://travkin-hspt.com/classmechht/classmbpinteract/classmbpinteract.htm, (2017)

14 . Travkin, V.S., "Interscale Hidden in COHP Forces upon Interacting Sub-Atomic or/and Continual Particles (They are Always Interact) - in a Cloud of Identical Particles. Physics 2," http://travkin-hspt.com/classmechht/hidforcesidenpart/hidforcesidenpart.htm, (2016)

15 . Travkin, V.S., "Two-phase Two-scale (2P2S) Two Coordinate System (2^3PSC) Dynamics of Interaction of Rotating/Spinning Arrays of Particle and/or Bodies. Physics 2," http://travkin-hspt.com/classmechht/2p2s2cdyninterpart/2p2s2cdyninterpart.htm, (2016)

16. Travkin, V.S., "Conceiving and Formulating a Few Classical problems in Two-phase Two-scale Many-Body Problems (MBP) That are Solvable as the Previous Tasks in Two-phase Heterogeneous Physics in 1980-90s," http://travkin-hspt.com/classmechht/classmechhtcltasks/classmechhtcltasks.htm, (2016)

17. Travkin, V.S., What's Wrong with the Pseudo-Averaging Used in Textbooks on Atomic Physics and Electrodynamics for Maxwell-Heaviside-Lorentz Electromagnetism Equations, http://travkin-hspt.com/eldyn/maxdown/maxdown.htm, (2009)

18. Travkin, V.S., Incompatibility of Maxwell-Lorentz Electrodynamics Equations at Atomic and Continuum Scales, http://travkin-hspt.com/eldyn/incompat/incompat.htm, (2009)

19. Travkin, V.S., Electrodynamics 2 - Elements 3P (Polyphase-Polyscale-Polyphysics), http://travkin-hspt.com/eldyn2/index.htm, (2013)

20. Travkin, V.S., "Spinning or "Torsion" Mechanics in "Homogeneous" Media? Is it Possible?" http://travkin-hspt.com/rottors/torsmechhom/torsmechhom2.htm, (2015)

21. Travkin, V.S., "Scaled Presentation of "Torsion" Mechanics in Polyphase Media", http://travkin-hspt.com/rottors/tormechpoly/tormechpoly.htm, (2014)

22. Travkin, V.S., "Top-Down and Bottom-Up Hierarchical Processes in the E-Cat Nuclear Reactor. Physics 2 ," http://travkin-hspt.com/coldlenr/ecathier1/ecathier1-ab.htm, (2012-2013)

23. Travkin, V.S., "Interscale Magnetism Between the Sub-Atomic ("vacuum0") - Mesoscale (Continuum) - and Bulk Micrometer Scale Polydomain Characteristics. Magnetic Motors Phenomenon Applications," http://travkin-hspt.com/fermag/abstracts/magnet3sc-ab.htm, (2013)

24. Travkin, V.S., Linear Acousto-Elasticity in Porous Medium, http://travkin-hspt.com/acoustics/02.htm, (2007)

25. Travkin, V.S. and Bolotina, N.N., How not to Scale-Down...or -Up.. ..Analysis of Current Studies on Scaled, Collective Phenomena in Biology Fields Presented as the One-Scale Concepts, http://travkin-hspt.com/bio/biopapersop.htm, (2009)

26. Travkin, V.S., "Concepts: HSP-VAT Conceptual Vision and Methods Applied to Biology," "http://travkin-hspt.com/bio/conceptsbio/conceptsbio.htm, (2013)

27. Travkin, V.S. and Bolotina, N.N., "Quantum Chemistry, Physical Chemistry, Molecular Dynamics Simulation, DFT (Density Functional Theory), and Coarse-Graining Techniques Applied in Structural, Cellular Biology, Polymer Science and Implication for Scaleportation," Journal of Alternative Energy and Ecology, No. 2, pp. 58-75, (2011a)

"Quantum Chemistry, Physical Chemistry, Molecular Dynamics Simulation, DFT (Density Functional Theory), and Coarse-Graining Techniques Applied in Structural, Cellular Biology, Polymer Science and Implication for Scaleportation"(757K)

28. Travkin, V.S. and Bolotina, N.N., "Pseudo-Scaled and Scaled Description and Scaleportation of Inorganic and Organic Polymer and Polymer Composites Properties," Journal of Alternative Energy and Ecology, No. 1, pp. 62-77, (2011b)

"Pseudo-Scaled and Scaled Description and Scaleportation of Inorganic and Organic Polymer and Polymer Composites Properties"(818K)

29. Travkin, V.S. and Bolotina, N.N., Heterogeneous Scaled Biophysics (HtScBp). Fundamentals, "http://travkin-hspt.com/biophysics/index.htm (2010)

30. Travkin, V.S. and Bolotina, N.N., Bacteriology Heterogeneous PolyScale (BHS), "http://travkin-hspt.com/biobact/index.htm (2005)

31. Travkin, V.S. and Bolotina, N.N., Cellular Biology HS ^v , "http://travkin-hspt.com/biocell/index.htm (2009)

32. Travkin, V.S., Structural Biology Based on Homogeneous Physics (SBH) and Elements 3P (Polyphase-Polyscale-Polyphysics) of Structural Biology 2 (SB3P) - as Hierarchical, Heterogeneous, Multiscale Science, "http://travkin-hspt.com/biostruc2/index.htm (2014)

33. Travkin, V.S. and Bolotina, N.N., Virology - is the Heterogeneous Hierarchical Science ^v, "http://travkin-hspt.com/virology/index.htm (2011)

34. Travkin, V.S., "Nuclear Energy, Polyscale Polyphase Structure of Heat Generation. HtHr Modeling," http://travkin-hspt.com/nuclearen/index.htm, (2009)

35. Travkin, V.S., Elements of the 2nd Physics at the beginning of XXI , Elements of the 2nd Physics at the beginning of XXI , (1978-2015)

36. Travkin, V.S., "Classical Mechanics Attempts for Description of Atomic Physics (ClM One-scale One-phase Homogeneous Atomic Physics - ClMO2HAP) Phenomena ," http://travkin-hspt.com/parphys2/clmechonesc1/clmechonesc1.htm, (2014)

37. Travkin, V.S., "Two-Scale Three-Phase Regular and Irregular Shape Charged Particles (Electrons, Photons) Movement in MHL Electromagnetic Fields in a Vacuum0 (Aether)," http://travkin-hspt.com/parphys2/abstracts/twoparticlesshort-ab.htm, (2013)

38. Travkin, V.S. and Bolotina, N.N.,"Two-Scale Two-Phase Formation of Charged 3D Continuum Particles - Sphere and Cube From Electrons in a Vacuum0 (Aether). An Example of Scaleportation of Charge from the Sub-Atomic to Continuum Charged Particles, Conventional MD Cannot be Applied," http://travkin-hspt.com/parphys2/abstracts/subtocontin-ab.htm, (2013)

39. Travkin, V.S. and Bolotina, N.N., "One Structured Electron in an Aether (Vacuum0) Electrodynamics, Many Electrons in an Aether Fixed in Space - the Upper Scale Galilean Electrodynamics ," http://travkin-hspt.com/parphys/abstracts/stillelectrons-ab.htm (2011)

40. Travkin, V.S. and Bolotina, N.N., "Electrons and CMBR (Cosmic Microwave Background Radiation) Flux of Photons in a Vacuum0 (Aether) - Two-Scale Galilean Theory ," http://travkin-hspt.com/parphys/abstracts/elcmbr-ab.htm (2010)

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