Physical Theories

Like Euclidean geometry the perception that we live in a three-dimensional world went unchallenged for millenia. The first indication that the perception could be wrong followed the formulation of the special theory of relativity. 

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A physical theory about the effect of the eddy current on the impedance of the solenoid can be established by a simple way when we develop the fundamentals principles... 

Caiien H B 1960 Thermodynamics, an Introduction to the Physical Theories of Equilibrium Thermostatics and Irreversible Thermodynamics (New York Wiiey)... 

John von Neuman, one of the greatest mathematicians of the twentieth century, believed that the sciences, in essence, do not try to explain, they hardly even try to interpret they mainly make models. By a model he meant a mathematical construct that, with the addition of certain verbal interpretations, describes observed phenomena. The justification of such a mathematical construct is solely and precisely that it is expected to work. Stephen Hawking also believes that physical theories are just mathematical models we construct and that it is meaningless to ask whether they correspond to reality, just as it is to ask whether they predict observations. 

Apphcations of ultrasound to electrochemistry have also seen substantial recent progress. Beneficial effects of ultrasound on electroplating and on organic synthetic apphcations of organic electrochemistry (71) have been known for quite some time. More recent studies have focused on the underlying physical theory of enhanced mass transport near electrode surfaces (72,73). Another important appHcation for sonoelectrochemistry has been developed by J. Reisse and co-workers for the electroreductive synthesis of submicrometer powders of transition metals (74). 

In this expression, p(H) is referred to as the prior probability of the hypothesis H. It is used to express any information we may have about the probability that the hypothesis H is true before we consider the new data D. p(D H) is the likelihood of the data given that the hypothesis H is true. It describes our view of how the data arise from whatever H says about the state of nature, including uncertainties in measurement and any physical theory we might have that relates the data to the hypothesis. p(D) is the marginal distribution of the data D, and because it is a constant with respect to the parameters it is frequently considered only as a normalization factor in Eq. (2), so that p(H D) x p(D H)p(H) up to a proportionality constant. If we have a set of hypotheses that are exclusive and exliaus-tive, i.e., one and only one must be true, then... 

The simplified failure envelopes are not derived from physical theories of failure in which the actual physical processes that cause failure on a microscopic level are integrated to obtain a failure theory. We, instead, deal with phenomenological theories in which we ignore the actual failure mechanisms and concentrate on the gross macroscopic events of failure. Phenomenological theories are based on curve-fitting, so they are failure criteria and not theories of any kind (the term theory implies a formal derivation process). 

Ultimately physical theories should be expressed in quantitative terms for testing and use, but because of the eomplexity of liquid systems this can only be accomplished by making severe approximations. For example, it is often neeessary to treat the solvent as a continuous homogeneous medium eharaeterized by bulk properties such as dielectric constant and density, whereas we know that the solvent is a molecular assemblage with short-range structure. This is the basis of the current inability of physical theories to account satisfactorily for the full scope of solvent effects on rates, although they certainly can provide valuable insights and they undoubtedly capture some of the essential features and even cause-effect relationships in solution kinetics. Section 8.3 discusses physical theories in more detail. 

In a solution of a solute in a solvent there can exist noncovalent intermolecular interactions of solvent-solvent, solvent-solute, and solute—solute pairs. The noncovalent attractive forces are of three types, namely, electrostatic, induction, and dispersion forces. We speak of forces, but physical theories make use of intermolecular energies. Let V(r) be the potential energy of interaction of two particles and F(r) be the force of interaction, where r is the interparticle distance of separation. Then these quantities are related by... 

Dack (4) has suggested that solvents be elassified on the basis of the product ep., the electrostatic factor. There seems to be no theoretical basis for this function [indeed, the dipole moment appears as ix in physical theory, as in Eqs. (8-10) and (8-6)], but ep. does contain more information than either of the quantities alone,... 

A theory is the more impressive the greater is the simplicity of its premises, the more different are the kinds of things it relates and the more extended is its range of applicability. Therefore, the deep impression which classical thermodynamics made upon me. It is the only physical theory of universal content which I am convinced, that within the framework of applicability of its basic concepts, will never be overthrown. 

Viewing things from the perspective of his physical theory of contact electricity, Volta was intrigued by the apparently endless power of the battery to keep the electric fluid in motion without the mechanical actions needed to operate the classical, friction, electrostatic machine, and the electrophorus. He called his batteiy alternately the artificial electric organ, in homage to the torpedo fish that had supplied the idea, and the electromotive apparatus, alluding to the perpetual motion (his words) of the electric fluid achieved by the machine. To explain that motion Volta relied, rather than on the concepts of energy available around 1800, on his own notion of electric tension. He occasionally defined tension as the effort each point of an electrified body makes to get rid of its electricity but above all he confidently and consistently measured it with the electrometer. 

If a physical theory is complete" then every element of physical reality must have a counterpart in that physical theory. 

We must next consider more precisely the connection between the description of bodily identical states by the two observers (the requirements of Postulate 1). Quite in general, in fact, a physical theory, and quantum electrodynamics in particular, is fully defined only if the connection between the description of bodily identical states by (equivalent) observers is known for every state of the system and for every pair of observers. Since the observers are equivalent every state which can be described by 0 can also be described by O. Given a bodily state of the same system, observer 0 will ascribe to it a state vector Y0> in his Hilbert space and observer O will attribute to it a state vector T0.) in his Hilbert space. The above formulation of invariance means that there exists a one-to-one correspondence between the vectors Y0> and Y0.) used by observers 0 and O to describe bodily the same state.3 This correspondence guarantees that the two Hilbert spaces are in fact isomorphic. It is, therefore, possible for the two observers to agree to describe states of the system by vectors in the same Hilbert space. A similar statement can be made for the observables there exists a one-to-one correspondence between the operators Q0 and Q0>, which observers 0 and O attribute to observables. The consistency of the theory (Postulate 2) demands, however, that the two observers make the same prediction as the outcome of the same experiment performed on bodily the same system. This requires the relation... 

The complexity of even the simplest organic compounds in terms of physical theory well endows the field of physical organic chemistry with the frustrations of approximations. The quantitative correlations employed in this field vary from purely empirical operational formulations to the approach of applying physical principles to a workable model. The most common procedures... 

RT = 1.35kcal/mol at room temperature. This is an important thermodynamic relation, as it relates microscopic physical theories (which serve as the basis for computational models) to experimentally measurable quantities. 

The energy of interaction of the central ion with its ionic atmosphere depends on the potential of this atmosphere t /atm(0) at a point where the central ion is located (r = 0). Therefore, it is the main task of the physical theory of ion-ion interaction to calculate the potential of the ionic atmosphere, j/a,ni. 

Time is a fundamental property of the physical world. Because time encompasses the antinomic qualities of transience and duration, the definition of time poses a dilemma for the formulation of a comprehensive physical theory. The partial elimination of time is a common solution to this dilemma. In his mechanical philosophy, Newton appears to resort to the elimination of the transient quality of time by identifying time with duration. It is suggested, however, that the transient quality of time may be identified as the active component of the Newtonian concept of inertia, a quasi occult quality of matter that is correlated with change, and that is essential to defining duration. The assignment of the transient quality of time to matter is a necessary consequence of Newton s attempt to render a world system of divine mathematical order. Newton s interest in alchemy reflects this view that matter is active and mutable in nature... 

Particularly spectra and quantum theory seemed to indicate an order. A planetary model almost suggested itself, but according to classical physics, the moving electrons should emit energy and consequently collapse into the nucleus. The 28-year-old Niels Bohr ignored this principle and postulated that the electrons in these orbits were "out of law". This clearly meant that classical physics could not describe or explain the properties of the atoms. The framework of physical theory came crashing down. Fundamentally new models had to be developed.1... 

With real data, a more scientifically valid approach would be to correct the nonlinearity from physical theory. In the current case, for example, a scientifically valid approach would be to convert the data to transmission mode, subtract the stray light and reconvert to absorbance the nonlinear wavelengths would have become linear again. There are, of course, several things wrong with this procedure, all of them stemming from the fact that this data was created in a specific way for a specific purpose, not necessarily to be representative of real data ... 

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