Weitere Kapitel dieses Buchs durch Wischen aufrufen
A Zero-Energy Universe Scenario (ZEUS) is portrayed and its implications are examined and clarified. The formulation is based on the algebra of observables, e.g. the momentum-energy and their canonical conjugate partner space-time. Operators represent them in quantum theory and classical canonical variables in nonquantum applications. Conjugate operator/variable arrays impart a united edifice for a zero-energy universe scenario, which corresponds to using a non-positive definite metric for the manifestation of unstable states as recently employed in the field of chemical physics. Analogous formulations within a general complex symmetric setting provide a compelling analogy between Einstein’s theory of general gravity and Gödel’s first incompleteness theorem. This scenario brings together up-to-date theories in chemical physics with modern research in biology, physics, and astronomy. This unification establishes an edifice for the various arrows of time as well as authenticates Darwin’s Paradigm of Evolution from the microscopic realm to the cosmological domain.
Bitte loggen Sie sich ein, um Zugang zu diesem Inhalt zu erhalten
Sie möchten Zugang zu diesem Inhalt erhalten? Dann informieren Sie sich jetzt über unsere Produkte:
The notion of “zero-energy universe” has been coined before, see note added in proof.
In quantum theory the Dirac bra-ket is an abstract set of vectors and dual vectors in a general mathematical theory, subject to the axioms of linear algebra, i.e. the scalar product bra-ket depends linearly (antilinearly) on the ket (bra). In the case above the abstract vector space symbolizes a lower level description that consistently portrays the singularity associated with Gödel’s proposition.
Note that the probability function/operator p in this paragraph should not be confused with the absolute value of the momentum variable of previous sections.
This extension rests on a rigorous mathematical theory, i.e. the Balslev-Combes theorem [ 21], see also Simon [ 22], and it is vital to understand and appreciate non-Hermitian quantum mechanics and its consequences for the dynamics of resonance states embedded in the continuum and their properties for higher order dynamics.
The concept of ODLRO, although developed after the famous Bardeen-Cooper-Schrieffer theory of super-conductivity, is a formulation with focus on the collective properties of matter at sufficiently low temperatures. For a material system at zero temperature with a non-degenerate ground state the entropy is zero. Under specific conditions the system may develop superconductivity.
Regarding reference [ 30], Coleman makes the following quote in [ 27]: “This article, which was based on Sasaki’s Report 77 (1962) Quantum Chemistry Group, Uppsala, was actually submitted in 1962 but was inadvertently misplaced by the publisher. It was in this paper that, independently of Yang, Sasaki observed that it is for AGP type functions that the largest possible eigenvalues of the 2-matrix occur.”
The classical mirror theorem as reformulated by Löwdin [ 9] is a much underrated and underused idea. It affects the measurement dilemma through the precise quantum mechanical relations between the system and the gauging device before decoherence. Here it opens a possibility to go beyond the rigidity of the Born-Oppenheimer approximation. For an account of some novel trends in theoretical and experimental quantum phenomena, see Karlsson and Brändas [ 35].
“Complex enough” is an unprecise statement that is prompted by the need to go from teleomatic to teleonomic processes. For more on the rules of evolving organization processes, see note added in proof.
Tegmark M (2003) Parallel Universes. Sci Am
Greene B (2011) Hidden reality parallel Universes and the deep laws of the Cosmos. Alfred A. Knopf, New York
Green MB, Schwarz JH, Witten E (2012) Superstring theory: volume 2, Loop amplitudes, anomalies and phenomenology. Cambridge University Press, Cambridge
Gödel K (1931) Über Formal Unentscheidbare Sätze der Principia Matematica und Verwandter Systeme I. Monatshäfte für Mathematik und Physik 38:173–198 CrossRef
Brändas EJ (2011) Gödelian structures and self-organization in biological systems. Int J Quantum Chem 111:1321 CrossRef
Brändas EJ (2012) Examining the limits of physical theory: analytical principles and logical implications (Adv. Quantum Chem.). In: Nicolaides CA, Brändas EJ (eds) Unstable states in the continuous spectra, part II: interpretation, theory, and applications, vol 63. Elsevier, Amsterdam, p 33
Brändas EJ (2012) The relativistic Kepler problem and Gödel’s Paradox. In: Nishikawa K, Maruani J, Brändas EJ, Delgado-Barrio G, Piecuch P (eds) Quantum systems in chemistry and physics, vol 26. Springer, Dordrecht, p 3
Kerr RP (1963) Gravitational field of a spinning mass as an example of algebraically special metrics. Phys Rev Lett 11:237 CrossRef
Löwdin P-O (1998) Linear algebra for quantum theory. Wiley, New York
Feferman S (2009) Gödel, Nagel, minds and machines. J Philos 106(4):201
Turing AM (1937) On computational numbers, with an application to the Entscheidungsproblem. Proc London Math Soc 42(2):230; ibid. 43:544
Brändas EJ (2013) Some biochemical reflections on information and communication. In: Hotokka M, Maruani J, Brändas EJ, Delgado-Barrio G (eds) Quantum systems in chemistry, physics and biology, vol 27. Springer, Dordrecht, p 75
Penrose R (1994) Shadows of the mind: a search for the missing science of consciousness. Oxford University Press, Oxford
Domcke W, Yarkony DR (2012) Role of conical intersections in molecular spectroscopy and photoinduced chemical dynamics. Ann Rev Phys Chem 63:325 CrossRef
Brändas EJ (2013) Arrows of time and fundamental symmetries in chemical physics. Int J Quantum Chem 113:173 CrossRef
Löwdin P-O (1967) Program. Nature of quantum chemistry. Int J Quantum Chem 1:1
Primas H (1983) Chemistry, quantum mechanics and reductionism. Perspectives in theoretical chemistry. Springer, Berlin CrossRef
Sklar L (1993) Physics and chance philosophical issues in the foundations of statistical mechanics. Cambridge University Press, Cambridge CrossRef
Nicolaides CA, Brändas EJ (eds) (2010) Unstable states in the continuous spectra, part I: analysis, concepts, methods, and results. Adv Quantum Chem 60:1–549
Moiseyev N (2011) Non-hermitian quantum mechanics. Cambridge University Press, New York CrossRef
Balslev E, Combes JM (1971) Spectral properties of many-body Schrödinger operators with dilatation-analytic interactions. Commun Math Phys 22:280 CrossRef
Simon B (1973) The definition of molecular resonance curves by the method of exterior complex scaling. Ann Math 97:247 CrossRef
Hehenberger M, McIntosh HV, Brändas E (1974) Weyl’s theory applied to the Stark effect in the hydrogen atom. Phys Rev A 10:1494 CrossRef
Brändas E, Froelich P (1977) Continuum orbitals, complex scaling and the extended Virial theorem. Phys Rev A 16:2207 CrossRef
Howland JS (1983) Complex scaling of ac Stark Hamiltonians. J Math Phys 24:1240 CrossRef
Löwdin P-O (1955) Quantum theory of many-particle systems. I. Physical interpretations by means of density matrices, natural spin orbitals, and convergence problems in the method of configuration interaction. Phys Rev 97:1474 CrossRef
Coleman AJ, Yukalov VI (2000) Reduced density matrices. Coulson’s challenge. Lecture notes in chemistry, vol 72. Springer, Berlin
Yang CN (1962) Concept of off-diagonal long-range order and the quantum phases of liquid helium and of superconductors. Rev Mod Phys 34:694 CrossRef
Coleman AJ (1963) Structure of fermion density matrices. Rev Mod Phys 35:668 CrossRef
Sasaki F (1965) Eigenvalues of fermion density matrices. Phys Rev 138B:1338 CrossRef
Brändas EJ, Chatzidimitriou-Dreismann CA (1991) On the connection between certain properties of the second-order reduced density matrix and the occurrence of coherent-dissipative structures in disordered condensed matter. Int J Quantum Chem 40:649 CrossRef
Prigogine I (1980) From being to becoming. Freeman W. H. Freeman and Company, San Fransisco
Obcemea CH, Brändas EJ (1983) Analysis of Prigogine’s theory of subdynamics. Ann Phys 151:383 CrossRef
Brändas E, Hessmo B (1998) Indirect measurements and the Mirror Theorem: a Liouville formulation of quantum mechanics. In: Bohm A, Doebner H-D, Kielanowski P (eds) Irreversibility and causality. Semigroups and rigged hilbert spaces. Lecture notes in physics, vol 504, p 359
Karlsson EB, Brändas EJ (1998) Modern studies of basic quantum concepts and phenomena, In: Karlsson EB, Brändas E (eds) Proceedings nobel symposium, vol 104. World Scientific Publishing, Singapore, p 7
Brändas E, Elander N (eds) (1989) Resonances: the unifying route towards the formulation of dynamical processes—Foundations and applications in nuclear, atomic and molecular physics. Lecture notes in physics, vol 325. Springer, Berlin, pp 1–564
Mayr E (1974) Teleological and teleonomic: a new analysis. Boston Studies in the Philosophy of Science 14:91 CrossRef
Mayr E (2004) What makes biology unique?. Cambridge University Press, New York CrossRef
Löwdin P-O (1965) Quantum genetics and the aperiodic solid. Some aspects on the biological problems of heredity, mutations, aging, and tumours in view of the quantum theory of the DNA molecule. Adv Quantum Chem 2:213
Brändas EJ (1995) Relaxation processes and coherent dissipative structures. In: Lippert E, Macomber JD (eds) Dynamics during spectroscopic transitions. Springer, Berlin, p 148 CrossRef
Brändas EJ (1995) Applications of CSM theory. In: Lippert E, Macomber JD (eds) Dynamics during spectroscopic transitions. Springer, Berlin, p 194 CrossRef
Zubarev DN (1960) Double-time green functions in statistical physics. Sov Phys Usp 3:320 CrossRef
Kandel ER (2006) In search of memory the emergence of a new science of mind. W. W. Norton & Company, New York
Brändas EJ (2012) Time asymmetry and the evolution of physical laws. In: Hoggan PE, Brändas EJ, Maruani J, Piecuch P, Delgado-Barrio G (eds) Advances in the theory of quantum systems in chemistry and physics. Progress in theoretical chemistry and physics, vol 22. Springer, Berlin, p 3
Rinaldi M (2012) Aspects of quantum gravity in cosmology. Mod Phys Lett A 7:1230008 CrossRef
Berman MS (2009) On the zero-energy universe. Int J Theor Phys 48(11):3278 CrossRef
Maruani J (2013) The Dirac electron as a massless charge spinning at light speed: implications on some basic physical concepts. In: Hotokka M, Maruani J, Brändas EJ, Delgado-Barrio G (eds) vol. 27. Springer, Dordrecht, p 53
- A Zero Energy Universe Scenario: From Unstable Chemical States to Biological Evolution and Cosmological Order
Erkki J. Brändas
Neuer Inhalt/© ITandMEDIA