Interaction non-local

It is seen that the symmetry of the non-coulombic non-local interaction in the bulk phase forces the symmetry of the localized interaction with the wall. If we omitted the surface Hamiltonian and set / = 0 we would still obtain the boundary condition setting the gradient of the overall ionic density to zero. The boundary condition due to electrostatics is given by... 

The theories that should feature prominently in the understanding of chemical effects have been summarized in this volume, without demonstrating their application. The way forward has been indicated by Primas [67] and in the second volume of this work the practical use of modern concepts such as spontaneous symmetry breaking, non-local interaction, bohmian mechanics, number theories and space-time topology, to elucidate chemical effects will be explored. The aim is to stimulate renewed theoretical interest in chemistry. 

There does, however, appear to be a statistically significant correlation between the rate constants for folding of single domain proteins and the average sequence separation between contacting residues in the native state. Proteins that have primarily local contacts (i.e., have a low contact order) tend to fold more rapidly than those that have more non-local interactions (i.e., have a high contact order).81,82... 

M. Niggemann and B. Steipe, Exploring local and non-local interactions for protein stability by structural motif engineering,... 

The interaction potential model, originally proposed by Shan and Chen,37 and henceforth referred to as the S-C model, introduces k distribution functions for a fluid mixture comprising of k components. Each distribution function represents a fluid component and satisfies the evolution equation. The non-local interaction... 

In 1952 David Bohm rediscovered aspects of earlier proposals by de Broglie and Madelung, which had been rejected years before, and established the concept of non-local interaction via the quantum potential. It appears to provide fundamental answers for the understanding of chemistry, but remains on the fringes, while awaiting recognition by the establishment. 

The possibility of non-local interaction within quantum systems, so vividly illustrated here for a holistic electron, was first recognized by Einstein and others [46]. To avoid conflict with the theory of special relativity the effect was interpreted to mean that quantum theory was incomplete. More recently... 

The biological activity of proteins generally depends on a unique three-dimensional conformation, which in turn is inherently linked to its primary sequence. Protein folding, the conversion of the translated polypeptide chain into the native state of a protein, is the critical link between gene sequence and three-dimensional structure. Mechanistically, folding is believed to proceed through a predetermined and ordered pathway, either via kinetic intermediates or by direct transition from the unfolded to the native state [99]. In both cases, local and non-local interactions alike stabilize transient structures along the pathway and funnel the intermediates towards the native state. 

The argument so far is premised on the assumption that there is no interaction possible between the correlated atoms at the time that the measurement is done. However, should there be an undisclosed interaction between the two particles, disturbance of A, caused by the measurement could communicate itself to B, causing a simultaneous disturbance at that position as well. This interaction may result in orientation of the spin at B in a direction opposite to that of A. Not surprisingly Einstein, the father of special relativity, did not even consider such a possibility since it requires instantaneous non-local interaction. 

In this case the two systems evidently behave independently. Situations like this are fairly common in chemistry, generally associated with an approach to the classical limit in which the quantum potential becomes negligible and non-local interactions insignificant. Although the basic law therefore refers inseparably to the whole universe, it tends to fragment into numerous independent parts, each constituted of further sub-units that are non-locally connected internally. The key to this fragmentation is the lack (or nature) of chemical interaction between sub-units, which can be treated in the traditional way. 

There are two important conclusions to be drawn from this insight, namely the additive nature of many molecular properties and the existence of nonlocal intramolecular interactions. Charge distribution and conformation of molecules are determined holistically by non-local interaction. All local features are consequences of the whole. However, molecules of any complexity are rarely the product of a one-step reaction that starts from the constituent atoms, but are more likely built up from intermediate fragments that retain some of their own molecular properties on incorporation into a bigger whole. This mechanism explains the large number of additivity rules that have been discovered empirically in molecular systems [51]. Diverse addi-... 

The previous conclusion immediately clarifies the mystery of non-local interaction through the space-like nature of the quantum potential field. All theories actually agree that superluminal motion occurs in the interior of the electron as first discovered by Dirac, but a non-local connection is not restricted to the interior of an electron it can occur in any region of high quantum potential, for instance in the interior of an atom or a small molecule. As the quantum potential is inversely proportional to mass, non-local interaction within more complex and more massive bodies becomes less significant. External classical potentials also have a disruptive influence on non-local interaction claims that such connections exist over galactic distances might be inflated, but within the domain of chemical reactions they must be of decisive importance. 

To calculate the quantum potential it is first necessary to find R, which by equation 9 is clearly a function of all particle coordinates, because of nonlocal interaction in terms of the molecular quantum entanglement inferred before. Even when all particle coordinates and velocities (v = 0) are identical in the two states, the state S must therefore still be at a lower energy. The difference can only be attributed to the quantum potential which differs for the two states. The force that holds the molecule together is therefore seen to be a special case of non-local interaction within the molecule. 

The standard representation of special relativity in terms of Minkowski space, as in figure 3.2, acquires significant new meaning in the Thierrin scheme. As in figure 6 the light cone now defines allowed directions of the u-axis of material objects and u itself represents the world-line of special relativity. The objection against non-local interaction disappears. Instead, the... 

The only factor of some chemical importance that features prominently in the theories of cosmology is the synthesis of small nuclides such as deuterium and helium. Unfortunately, the initial conditions that are considered to be crucial in these models are purely conjectural. There is little hope of a meaningful test against chemical reality and, in the present climate, no chance for the growth of a mathematically based alternative cosmology. However, the simple qualitative model of a non-orientable universe provides interesting insight into the nature of matter, non-local interaction and quantum theory. 

The special effects associated with materials made up of nanosized particles are also due to non-local interactions. Such effects were first noticed in the field of micro-electronics during efforts to decrease the size of devices to quasi one-dimensional or zero-dimensional structures [236]. One possibility for obtaining zero-dimensional structures is the inclusion of spherical semiconductor particles in a transparent dielectric medium. Such isolated microcrystals, typically of nanometer size are known as quantum dots. Best-known examples include particles of CdS and CdSe isolated in silicate glasses. 

Frishman, D. and Argos, R, Incorporation of non-local interactions in protein secondary structure prediction from the amino acid sequence, Prot. Eng., 9, 133, 1996. 

Molecular quantum potential and non-local interaction depend on molecular size and the nature of intramolecular cohesion. Macromolecular assemblies such as polymers, biopolymers, liquids, glasses, crystals and quasicrystals are different forms of condensed matter with characteristic quanmm potentials. The one property they have in common is non-local long-range interaction, albeit of different intensity. Without enquiring into the mechanism of their formation, various forms of condensed matter are considered to have well-defined electronic potential energies that depend on the nuclear framework. A regular array of nuclei in a structure such as diamond maximizes cohesive interaction between nuclei and electrons, precisely balanced by the quantum potential, almost as in an atom. 

The mysterious behaviour of bio-macromolecules is one of the outstanding problems of molecular biology. The folding of proteins and the replication of DNA transcend all classical mechanisms. At this stage, non-local interaction within such holistic molecules appears as the only reasonable explanation of these phenomena. It is important to note that, whereas proteins are made up of many partially holistic amino-acid units, DNA consists of essentially two complementary strands. Nonlocal interaction in DNA is therefore seen as more prominent, than for proteins. Non-local effects in proteins are sufficient to ensure concerted response to the polarity and pH of suspension media, and hence to direct tertiary folding. The induced fit of substrates to catalytic enzymes could be promoted in the same way. Future analysis of enzyme catalysis, allosteric effects and protein folding should therefore be, more ambitiously, based on an understanding of molecular shape as a quantum potential response. The function of DNA depends even more critically on non-local effects. 

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