Space-time structure

The persistent correlation that recurs between number patterns and physical structures indicates a similarity between the structure of space-time and number. Like numbers and chiral growth, matter has a symmetry-related conjugate counterpart. The mystery about this antimatter is its whereabouts in the universe. By analogy with numbers, the two chiral forms of fermionic matter may be located on opposite sides of an achiral bosonic interface. In the case of numbers this interface is the complex plane, in the physical world it is the vacuum. An equivalent mapping has classical worlds located in the two surfaces and the quantum world, which requires complex formulation, in the interface. 

Like numbers and their conjugates, matter and antimatter would merge naturally if the two conjugate surfaces constituted the double cover of a 

Mobius strip. In this way the antimatter mystery disappears matter and antimatter are one and the same thing, which merely appear to be different depending on their position in the double cover. In more dimensions the Mobius model is replaced by a projective plane, obtained from an open hemisphere on identifying points on opposite sides of the circular edge. Topologically equivalent constructs are known as a Roman surface or a Klein bottle. 

This space-time model is a conjecture that has been described in detail [28] and will be reconsidered in chapter 7. A new aspect thereof, which derives from number theory, is that the general curvature of this space-time manifold [26, 29] relates to the golden mean. This postulate is required to rationalize the self-similar growth pattern that occurs at many levels throughout the observable universe. 

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An intriguing possibility thus presents itself. If some kind of a primordial information, and not higher-level constructs such as mass, energy, spin, and so forth, is indeed the real substance out of which all stuff is made - leaving aside for the moment, the question of form of that information - is it not natural to suppose that a discrete space-time structure, our heretofore pre-defined and static dynamical mediator, is itself built out of the same substance i.e. to suppose that space-time is not just a backdrop for information processing, there only to define what is local and what is not and where to and where from information is allowed to flow, but is itself a construct of primordial information This supposition is not entirely without precedent. 

MSN. 107. 1. Prigogine, Irreversibility and space-time structure, in Proceedings, International Conference on Fluctuations and Sensitivity in Nonequilibrium Systems, Austin, 1984, W. Horsthemke and K. D. K. Kondepudi, eds., Springer, Berlin, 1984, pp. 2-9. 

MSN.118. I. Prigogine, Irreversibility and space—time structure. Res Mechanica 21 (1987). 

A. Riiger, Atomism from cosmology Erwin Schrodinger s work on wave mechanics and space-time structure, Hist. Stud. Phil. Sci., 18 (1988) 377 - 401. 

The second part of the book re-examines the traditional concepts of chemistry against the background of physical theories adapted for chemistry. An alternative theory is formulated from the recognition that the processes of chemistry happen in crowded environments that promote activated states of matter. Compressive activation, modelled by the methods of Hartree-Fock-Slater atomic structure simulation, leads to an understanding of elemental periodicity, the electronegativity function and covalence as a manifestation of space-time structure and the golden ratio. 

Each of the three theories accounts for some, but not all aspects of elemental periodicity. The common ground among the three may well reveal the suspected link with space-time structure. What is required is to combine aspects of the wave-mechanical model of hydrogen, the structure of atomic nuclei and number theory. 

Chemical behaviour depends on chemical potential and electromagnetic interaction. Both of these factors depend on the local curvature of space-time, commonly identified with the vacuum. Any chemical or phase transformation is caused by an interaction that changes the symmetry of the gauge field. It is convenient to describe such events in terms of a Lagrangian density which is invariant under gauge transformation and reveals the details of the interaction as a function of the symmetry. The chemically important examples of crystal nucleation and the generation of entropy by time flow will be discussed next. The important conclusion is that in all cases, the gauge field arises from a symmetry of space-time and the nature of chemical matter and interaction reduces to a function of space-time structure. 

Central to the discussion of space-time structure is the notion of a vacuum. As argued before (5.9) the physical vacuum is not a void. Because... 

The new theories that spring from the application of Bohmian mechanics to chemical problems reveal a close connection between chemical phenomena and the attributes of space-time. The most fundamental principle of chemistry is the periodic classification of the elements in terms of natural numbers. Examined against the background of number theory a deeper level of periodicity that embraces all nuclides is revealed and found to relate on a cosmic scale to an involution in space-time structure. 

Thermodynamics had been studied both in far-from-equilibrium and in near-equilibrium situations. A near-equilibrium world is a stable world. Fluctuations regress. The system returns to equilibrium. The situation changes dramatically far from equilibrium. Here fluctuations may be amplified. As a result, new space-time structures arise at bifurcation points. We considered the possibility of oscillating reactions as early as in 1954, many years before they were studied systematically. We introduced concepts such as selforganization and dissipative structures, which became very popular. In short, irreversible processes associated to the flow of time have an important constructive role. Therefore, the question that arises is how to incorporate the direction of time into the fundamental laws of physics, be they classical or quantum. 

Eq. (15) follows by using tlie exponential model for the space-time correlation defined in Fig. 1. Three spatial scales and an Eulerian relaxation time characterize the space-time structure of, t Because the Green s function for the wall eddy is locally convected by the mean axial velocity, the effect of the smoothing approximation employed above is to replace the coordinates, X.) in. with where represents an average convection velocity for the wall eddy. Thus, t jjin Eq. (16) is... 

Fig. 1.10 Chemical waves and space-time structural patterns studied in the BZ-AOT reaction system (Adopted from Ref. [12])...

It is the aim of this book to give a readable introduction to present-day thermodynamics starting with its historical roots as associated with heat engines but including also the thermodynamic description of far-from-equilibrium situations. As is well known today, far-from-equilibrium situations lead to new space-time structures. For this reason the restriction to equilibrium situations hides, in our opinion, some essential features of the behaviour of matter and energy. An example is the role of fluctuations. The atomic structure of matter leads to fluctuations. But at equilibrium or near equilibrium, these fluctuations are inconsequential. 

Indeed a characteristic feature of equilibrium thermodynamics is the existence of extremum principles. For isolated systems entropy increases and is therefore maximum at equilibrium. In other situations (such as constant temperature) there exist functions called thermodynamic potentials which are also extrema (maxima or minima) at equilibrium. This has important consequences. A fluctuation which leads to a deviation from equilibrium is followed by a response which brings back the system to the extremum of the thermodynamic potential. The equilibrium world is also a stable world. This is no longer so in far-from-equilibrium situations. Here fluctuations may be amplified by irreversible dissipative processes and lead to new space-time structures which... 

Here again the recent extension of thermodynamics to situations far from equilibrium is essential. Irreversible processes lead then to new space-time structures. They play therefore a basic constructive role. No life would be possible without irreversible processes (Chapter 19). It seems absurd to suggest that life would be the result of our approximations We therefore cannot deny the reality of entropy, the very essence of an arrow of time in nature. We are the children of evolution and not its progenitors. 

It all hangs together. To account for such consilience, Plichta [6] conjectured that numbers have real existence in the same sense as space and time. A more conservative interpretation would link numbers, through the golden ratio, to the curvature of space-time. A common inference is that the appearance of numbers as a manifestation of the periodicity of atomic matter is due to a spherical wave structure of the atom. A decisive argument is that the fiiU symmetry, implied by the golden ratio, incorporates both matter and antimatter as a closed periodic function with involution, as in Fig. 9, in line with projective space-time structure. 

Cosmic self-similarity has been documented and discussed many times with reference to atomic nuclei, atomic structure, the periodicity of matter, covalence, molecular conformation [26], biological structures, planetary and solar systems [27], spiral galaxies and galactic clusters [28]. The prominent role of the golden ratio in all cases can only mean that it must be a topological feature of space-time structure. 

Closed or open systems on the macroscopic level turn out to be characterized by relatively few collective macroscopic observable quantities, also denoted here as grossvariables or macrovariables. Examples are pressure, density entropy, energy- and particle-fluxes, correlation functions and further parameters characterizing the macroscopic state or dynamic space-time structure of fields and particles. 

I take it that current physics is committed to developing a complete theory formulated in terms of the categories of energy, field and space-time structure. Now, it seems reasonably plausible to me that no such theory is possible, because of as yet unknown physical effects that cannot be accounted for in terms of these current categories, and that therefore a genuinely complete theory (PHYSICS) will need to appeal to further explanatory categories. What seems unlikely to me is that these further categories should include mental ones. [Papineau, 1991,... 

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