Foundational physical theories problems

What are some of the problems encountered when we ask how we can actually employ foundational physical theories to describe, predict, and explain the phenomena of our real world And what are some of the extreme conclusions that might be leapt to by those who explore these problematic aspects of the place of theories in our world-picture ... 

Distinctive in nature, but again directed to problems arising out of specific theories and research programs, are the explorations of the special sciences. How are the explanatory accounts of biology and of psychology related to the kind of explanations we expect to find in the physical sciences And how are the special sciences related to the foundational physical sciences in that complicated, somewhat hierarchical, structure that we think of as scientific understanding as a whole ... 

A far more difficult problem arises in externally validating an ITS. Even with a firm theoretical foundation for the field, ITS systems must still be validated with respect to the real world in the same way that a completely elaborated physics theory (such as a unified field theory) must be proven out experimentally before it is folly accepted. ITS has borrowed its external validation methodologies from psychology and education. Unfortunately, many of these methodologies are not easily ad ted to the requirements of ITS validation. 

The development of the structural theory of the atom was the result of advances made by physics. In the 1920s, the physical chemist Langmuir (Nobel Prize in chemistry 1932) wrote, The problem of the structure of atoms has been attacked mainly by physicists who have given little consideration to the chemical properties which must be explained by a theory of atomic structure. The vast store of knowledge of chemical properties and relationship, such as summarized by the Periodic Table, should serve as a better foundation for a theory of atomic structure than the relativity meager experimental data along purely physical lines. ... 

Finite-additive invariant measures on non-compact groups were studied by Birkhoff (1936) (see also the book of Hewitt and Ross, 1963, Chapter 4). The frequency-based Mises approach to probability theory foundations (von Mises, 1964), as well as logical foundations of probability by Carnap (1950) do not need cr-additivity. Non-Kolmogorov probability theories are discussed now in the context of quantum physics (Khrennikov, 2002), nonstandard analysis (Loeb, 1975) and many other problems (and we do not pretend provide here is a full review of related works). 

Whereas many scientists shared Mulliken s initial skepticism regarding the practical role of theory in solving problems in chemistry and physics, the work of London (6) on dispersion forces in 1930 and Hbckel s 7t-electron theory in 1931 (7) continued to attract the interest of many, including a young scientist named Frank Westheimer who, drawing on the physics of internal motions as detailed by Pitzer (8), first applied the basic concepts of what is now called molecular mechanics to compute the rates of the racemization of ortho-dibromobiphenyls. The 1946 publication (9) of these results would lay the foundation for Westheimer s own systematic conformational analysis studies (10) as well as for many others, eg, Hendrickson s (11) and Allinger s (12). These scientists would utilize basic Newtonian mechanics coupled with concepts from spectroscopy (13,14) to develop nonquantum mechanical models of structures, energies, and reactivity. 

From the conceptual point of view, there are two general approaches to the molecular structure problem the molecular orbital (MO) and the valence bond (VB) theories. Technical difficulties in the computational implementation of the VB approach have favoured the development and the popularization of MO theory in opposition to VB. In a recent review [3], some related issues are raised and clarified. However, there still persist some conceptual pitfalls and misinterpretations in specialized literature of MO and VB theories. In this paper, we attempt to contribute to a more profound understanding of the VB and MO methods and concepts. We briefly present the physico-chemical basis of MO and VB approaches and their intimate relationship. The VB concept of resonance is reformulated in a physically meaningful way and its point group symmetry foundations are laid. Finally it is shown that the Generalized Multistructural (GMS) wave function encompasses all variational wave functions, VB or MO based, in the same framework, providing an unified view for the theoretical quantum molecular structure problem. Throughout this paper, unless otherwise stated, we utilize the non-relativistic (spin independent) hamiltonian under the Bom-Oppenheimer adiabatic approximation. We will see that even when some of these restrictions are removed, the GMS wave function is still applicable. 

To solve these problems the formulations chemist must have a good grasp of physical and colloid chemistry. He must use many of the theories and principles that are the foundation of physical and colloidal chemistry. 

In the beginnings of classical physical chemistry, starting with the publication of the Zeitschrift fUr Physikalische Chemie in 1887, we find the problem of chemical kinetics being attacked in earnest. Ostwald found that the speed of inversion of cane sugar (catalyzed by acids) could be represented by a simple mathematical equation, the so-called compound interest law. Nernst and others measured accurately the rates of several reactions and expressed them mathematically as first order or second order reactions. Arrhenius made a very important contribution to our knowledge of the influence of temperature on chemical reactions. His empirical equation forms the foundation of much of the theory of chemical kinetics which will be discussed in the following chapter. 

Most of modern physics and chemistry is bast d on three fundamental ideas first, matter is made of atoms and molecules, very small and very numerous second, it is impossible in principle to observe details of atomic and molecular motions below a certain scale of smallness and third, heat is mechanical motion of the atoms and molecules, on such a small scale that it cannot be completely observed. The first and third of these ideas are products of the last century, but the second, the uncertainty principle, the most characteristic result of the quantum theory, has arisen since 1000. By combining these three principles, we have the theoretical foundation for studying the branches of physics dealing with matter and chemical problems. 

The theory of chemical processes today is based on theoretical physics. In this sense, physics supplies the foundation of chemistry. But chemistry also has analysis. If you have a strange substance and you want to know what it is, you go through a long and complicated process of chemical analysis. You can analyze almost anything today, so I am a little late with my idea. But if the physicists wanted to, they could also dig under the chemists in the problem of chemical analysis. It would be very easy to make an analysis of any complicated chemical substance all one would have to do would be to look at it and see where the atoms are. The only trouble is that the electron microscope is one hundred times too poor. (Later, I would like to ask the question Can the physicists do something about the third problem of chemistry - namely, synthesis Is there a physical way to synthesize any chemical substance ... 

Contact problems have their origins in the works of Hertz (1881) and Boussinesq (1885) on elastic materials. Indentation problems are an important subset of contact problems (17,18). The assessment of mechanical properties of materials by means of indentation experiments is an important issue in polymer physics. One of the simplest pieces of equipment used in the experiments is the scleroscope, in which a rigid metallic ball indents the surface of the material. To gain some insight into this problem, we consider the simple case of a flat circular cylindrical indentor, which presents a relatively simple solution. This problem is also interesting from the point of view of soil mechanics, particularly in the theory of the safety of foundations. In fact, the impacting cylinder can be considered to represent a circular pillar and the viscoelastic medium the solid upon which it rests. 

In modem physics, there exist alternative theories for the equilibrium statistical mechanics [1, 2] based on the generalized statistical entropy [3-12]. They are compatible with the second part of the second law of thermodynamics, i.e., the maximum entropy principle [13-14], which leads to uncertainty in the definition of the statistical entropy and consequently the equilibrium probability density functions. This means that the equilibrium statistical mechanics is in a crisis. Thus, the requirements of the equilibrium thermodynamics shall have an exclusive role in selection of the right theory for the equilibrium statistical mechanics. The main difficulty in foundation of the statistical mechanics based on the generalized statistical entropy, i.e., the deformed Boltzmann-Gibbs entropy, is the problem of its connection with the equilibrium thermodynamics. The proof of the zero law of thermodynamics and the principle of additivity... 

Today it is difiicult to imagine the complacency of the physicist of 1890. Classical physics was a house in order mechanics, thermodynamics, kinetic theory, optics, and electromagnetic theory were the main foundations—an imposing display. By choosing tools from the appropriate discipline any problem could be solved. Of course, there were one or two problems that were giving some trouble, but everyone was confident that these would soon yield under the usual attack. There were two parts in this house of physics the corpuscular and the undulatory, or the domain of the particle and the domain of the wave. Matter was corpuscular, light was undulatory, and that was that. The joint between matter and light did not seem very smooth. 

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