Foundational physical theories

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 ... 

Perhaps we ought to infer from this limited scope of actual applicability of foundational physical theories a denial of their purported universality. Perhaps we ought to think of the world s ontology, its natures, as being as diverse and pluralistic as the rich world of special sciences, with their idiosyncratic concepts and laws of limited applicability, that we use actually to describe and explain nature s behavior. 

But, it has been trenchantly argued, if the domain of a theory is properly taken to be the class of happenings in the world the theory can actually desctibe and explain, then foundational physical theories have no such universal scope. First, consider the fact that for most of what we want desctibed and explained in the world, such theories have no applicability at all. Who ever provided a description of the behavior of a chimpanzee, say, in terms of relativistic quantum field theory, and who ever explained failure of competitive equilibrium in markets with natural monopolistic aspects, say, by reference to the elementary particles of the world and their dynamics in spacetime ... 

Niels Bohr s 1913 hydrogen atom paper demonstrates the traditional interest of some physicists in placing the facts and laws of chemistry within a broader framework of foundational principles laid out by physicists. During the course of the next two decades, a number of physicists who became known as quantum physicists developed physical theories and mathematical techniques that they claimed would create a mathematical and theoretical chemistry. However, few of them had much chemical knowledge beyond a general understanding of the periodic table of the elements and familiarity with the Lewis-Langmuir theory of the electron duplet and octet. 

Hendry and Vemulapalli nicely frame the space for the work taken up in the next section. Fundamental physical theories such as quantum mechanics raise difficult foundational questions that have demanded the efforts of many powerful minds in physics and the philosophy of physics. As chemistry is not reducible to physics, there is an autonomous space for chemical theory and for foundational issues in chemical theory. Three such issues are raised in this section. Joseph Earley examines the role of symmetry in chemistry and argues for closer attention to group theory on the part of his fellow chemists. Ray Hefferlin seeks to extend the idea of a periodic law from elements to compounds. Jack Woodyard takes on the fundamental obstacles that get in the way of a more straightforward application of quantum theory to molecules. 

The equation of state for rubber elasticity, embodied by any of equations (6-53) through (6-60), is important not only because it is historically the first quantitative treatment of molecular theories for elastomers but also because it laid a conceptual foundation for theories for the physical properties of polymers in general. Some of these have been discussed in detail in previous chapters. Perhaps the single most significant contribution is its recognition of the role of... 

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 ... 

I have asserted that important methodological observations have sometimes led to extreme conclusions. Thus the observation that the applicability of our foundational physics to really predict and explain the behavior of actual systems is confined to a very limited set of such systems in the world has led, falsely, I think, to the conclusion that these theories are not applicable in any sense to the whole world and to versions of ontological pluralism. Again, the observation that the application of our foundational theories to real systems generally rests upon the need to idealize these systems in order that they can be dealt with by the foundational theories might lead, once more falsely, I think, to such claim as that the foundational theories are meant to apply only to abstract models and not to the real systems themselves. 

At this point I want to take up a related claim. Suppose we admit that all of our predictions and explanations concerning real systems that rest on foundational or nonfoundational physical theories require substantial... 

Not so basic. It may appear superfluous in such a book presenting a new physi-cal theory, to reformulate such primary and well-known mathematics as done here. The reason is that behind these apparently purely mathematical objects is hidden a physical meaning that constitutes foundation of many physical theories. The role of the multiplicative property of wave functions is crucial in quantum mechanics and the duality between multiplicative/additive properties is the seed for proposing exponential functions in many domains. In support of this insistence, one may invoke Feynman s judgment, who does not hesitate to present Euler s formula as the most beautiful formula ever written (Feynman 1964). 

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 theorist s goal in studying molecular properties has been to use fundamental physical theory to deduce, calculate, or extract specific molecular properties not already known. The theoretical foundation for accomplishing this is a solid one and supports the layers of sophisticated computational treatments that have been built atop it. These were spurred on by dramatic improvements in computing machinery. There is now tremendous capability in many laboratories for directly computing a host of molecular properties for small and large molecules. That is the focus of this chapter. 

D. O. Shah and W. C. Hsieh, Microemulsions, Liquid Crystals and Enhanced Oil Recovery, in Theory, Practice, and Process Principles for Physical Separations, Engineering Foundation, New York, 1977. 

The purpose of this chapter is to provide an introduction to tlie basic framework of quantum mechanics, with an emphasis on aspects that are most relevant for the study of atoms and molecules. After siumnarizing the basic principles of the subject that represent required knowledge for all students of physical chemistry, the independent-particle approximation so important in molecular quantum mechanics is introduced. A significant effort is made to describe this approach in detail and to coimnunicate how it is used as a foundation for qualitative understanding and as a basis for more accurate treatments. Following this, the basic teclmiques used in accurate calculations that go beyond the independent-particle picture (variational method and perturbation theory) are described, with some attention given to how they are actually used in practical calculations. 

Linear response theory is an example of a microscopic approach to the foundations of non-equilibrium thennodynamics. It requires knowledge of tire Hamiltonian for the underlying microscopic description. In principle, it produces explicit fomuilae for the relaxation parameters that make up the Onsager coefficients. In reality, these expressions are extremely difficult to evaluate and approximation methods are necessary. Nevertheless, they provide a deeper insight into the physics. 

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. ... 

During the nineteenth century the growth of thermodynamics and the development of the kinetic theory marked the beginning of an era in which the physical sciences were given a quantitative foundation. In the laboratory, extensive researches were carried out to determine the effects of pressure and temperature on the rates of chemical reactions and to measure the physical properties of matter. Work on the critical properties of carbon dioxide and on the continuity of state by van der Waals provided the stimulus for accurate measurements on the compressibiUty of gases and Hquids at what, in 1885, was a surprisingly high pressure of 300 MPa (- 3,000 atmor 43,500 psi). This pressure was not exceeded until about 1912. 

Following a brief section on Units and Dimensions (Section 4.2), Sections 4.3 and 4.4 review some of the key physical and chemical properties, respectively. Three important conservation laws are presented in Section 4.5. Basic engineering principles are discussed in Section 4.6, to present a foundation for the theory underlying the proper design and operation of a chemical process. 

The work on gas theory had many extensions. In 1865 Johann Josef Loschmidt used estimates of the mean free path to make the first generally accepted estimate of atomic diameters. In later papers Maxwell, Ludwig Boltzmann, and Josiah Willard Gibbs extended the rrratherrratics beyorrd gas theory to a new gerreralized science of statistical mechanics. Whenjoined to quantum mechanics, this became the foundation of much of modern theoretical con-derrsed matter physics. 

Frieden s theory is that any physical measurement induces a transformation of Fisher information J I connecting the phenomenon being measured to intrinsic data. What we call physics - i.e. our objective description of phenomenologically observed behavior - thus derives from the Extreme Physical Information (EPI) principle, which is a variational principle. EPI asserts that, if we define K = I — J as the net physical information, K is an extremum. If one accepts this EPI principle as the foundation, the status of a Lagrangian is immediately elevated from that of a largely ad-hoc construction that yields a desired differential equation to a measure of physical information density that has a definite prior significance. 

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