W. M. Stuckey

The nature of time : geometry, physics and perception

Preface. List of participants. Group photo. 1: Internal Times and Consciousness. An Overview S. Grondin. The Human Sense of Time: Biological, Cognitive and Cultural Considerations A.D. Eisler. The Parallel-Clock Model: a Tool for Quantification of Experienced Duration H. Eisler. Time in the Cognitive Process of Humans R. Nikolaeva-Hubenova. Studying Psychological Time with Webers Law S. Grondin. Time and the Problem of Consciousness M. Binder. Temporal Displacement G.B. Vicario. Discrimination and Sequentialization of Events in Perception H. Atmanspacher, T. Filk. Time, Consciousness and Quantum Events in Fundamental Spacetime Geometry S. Hameroff. How Time Passes G. Franck. Reality, and Those Who Perceive It J. Sanfey. The Conscious Universe M. Kafatos, S. Roy, M. Draganescu. 2: Mathematical Approaches to the Concept of Time. An Overview M. Saniga. Geometry of Time and Dimensionality of Space M. Saniga. Time in Biology and Physics J.D.H. Smith. Analysis of the Relationship Between Real and Imaginary Time in Physics G. Jaroszkiewicz. Clifford Algebra, Geometry and Physics M. Pavsic. The Programs of the Extended Relativity in C-Spaces: Towards Physical Foundations of String Theory C. Castro. Time Measurements, 1/F Noise of the Oscillators and Algebraic Numbers M. Planat. Internal Time and Innovation T. Antoniou, Z. Suchanecki. Quantum Computing: a Way to Break Complexity V. Di Gesu, G.M. Palma. On the Relational Statistical Space-Time Concept V.V. Aristov. Self-organization in Discrete Systems with Fermi-Type Memory D.B. Kucher, A.G. Shkorbatov. 3: The Physicists View ofTime. An Overview W.M. Stuckey. Thermodynamic Irreversibility and the Arrow of Time R.M. Kiehn. Time from Quantum Uncertainty Z. Jacobson. The Arrow of Time in Quantum Theories G. Vitiello. Conformal Time in Cosmology T.T. Shevchenko. Acausality and Retrocausality in Four- and Higher-Dimensional General Relativity B. Lukacs. Time, Closed Timelike Curves and Causality F. Lobo, P. Crawford. Is There More to T? A.C. Elitzur, S. Dolev. Global Causality in Space-Time Universe A.A. Chernitskii. Time at the Origin of the Universe: Fluctuations Between two Possibilities V. Dzhunushaliev. Q uantum Cellular Automata, the EPR Paradox and the Stages Paradigm J.S. Eakins. Planck Scale Physics, Pregeometry and the Notion of Time S. Roy. Causality as a Casualty of Pregeometry W.M. Stuckey. 4: Integrative Sciences Views of Time. An Overview R. Buccheri. The Aristotelian Relation of Time to Motion and to the Human Soul C.C. Evangeliou. The Dynamics of Time and Timelessness: Philosophy, Physics and Prospects for our Life A. Grandpierre. Spacetime Holism and the Passage of Time F.-G. Winkler. The Intelligibility of Nature, the Endophysical Paradigm and the Relationship Between Physical and Psychological Time R. Buccheri. Potential and Actual Time Concepts G. Darvas. Paradigms of Natural Science and Substantial Temporology A.P. Levich. Appendix. Time Questionnaire G. Jaroszkiewicz. Index.

The observable universe inside a black hole

A Schwarzschild radial coordinate R is presented for the Friedmann dust‐filled cosmology models. It is shown that a worldline of constant Schwarzschild radial coordinate in the dust‐filled universe is instantaneously null at Rn=2GM/c2, where M is the Schwarzschild mass inside the sphere R=Rn. It is also shown that Mp=3τc3/4G, where Mp is the proper mass inside R=Rn and τ is the age of the universe. The Rn=2GM/c2 result in Friedmann dust‐filled cosmology is made physically significant by abandoning the cosmological principle and adjoining segments of Friedmann dust to segments of Schwarzschild vacuum. In the resulting cosmology model, the observable universe may lie inside a black or white hole.

Being, Becoming and the Undivided Universe: A Dialogue Between Relational Blockworld and the Implicate Order Concerning the Unification of Relativity and Quantum Theory

In this paper two different approaches to unification will be compared, Relational Blockworld (RBW) and Hiley’s implicate order. Both approaches are monistic in that they attempt to derive matter and spacetime geometry ‘at once’ in an interdependent and background independent fashion from something underneath both quantum theory and relativity. Hiley’s monism resides in the implicate order via Clifford algebras and is based on process as fundamental while RBW’s monism resides in spacetimematter via path integrals over graphs whereby space, time and matter are co-constructed per a global constraint equation. RBW’s monism therefore resides in being (relational blockworld) while that of Hiley’s resides in becoming (elementary processes). Regarding the derivation of quantum theory and relativity, the promises and pitfalls of both approaches will be elaborated. Finally, special attention will be paid as to how Hiley’s process account might avoid the blockworld implications of relativity and the frozen time problem of canonical quantum gravity.

An Argument for 4D Blockworld from a Geometric Interpretation of Non-relativistic Quantum Mechanics

We use a new, distinctly “geometrical” interpretation of non-relativistic quantum mechanics (NRQM) to argue for the fundamentality of the 4D blockworld ontology. We argue for a geometrical interpretation whose fundamental ontology is one of spacetime relations as opposed to constructive entities whose time-dependent behavior is governed by dynamical laws. Our view rests on two formal results: Kaiser (1981 & 1990), Bohr & Ulfbeck (1995) and Anandan, (2003) showed independently that the Heisenberg commutation relations of NRQM follow from the relativity of simultaneity (RoS) per the Poincare Lie algebra. And, Bohr, Ulfbeck & Mottelson (2004a & 2004b) showed that the density matrix for a particular NRQM experimental outcome may be obtained from the spacetime symmetry group of the experimental configuration. This shows how the blockworld view is not only consistent with NRQM, not only an implication of our geometrical interpretation of NRQM, but it is necessary in a non-trivial way for explaining quantum interference and “non-locality” from the spacetime perspective. Together the formal results imply that contrary to accepted wisdom, NRQM, the measurement problem and so-called quantum non-locality do not provide reasons to abandon the 4D blockworld implication of RoS. But rather, the deep non-commutative structure of the quantum and the deep structure of spacetime as given by the Minkowski interpretation of special relativity (STR) are deeply unified in a 4D spacetime regime that lies between Galilean spacetime (G4) and Minkowski spacetime (M4). Taken together the aforementioned formal results allow us to model NRQM phenomena such as interference without the need for realism about 3N Hilbert space, establishing that the world is really 4D and that configuration space is nothing more than a calculational device. Our new geometrical interpretation of NRQM provides a geometric account of quantum entanglement and so-called non-locality free of conflict with STR and free of interpretative mystery. In section 2 we discuss the various tensions between STR and NRQM with respect to the dimensionality of the world. Section 3 is devoted to an explication of the Kaiser et al. results and their philosophical implications. Likewise, the Bohr et al. results and their implications are the subject of section 4. In section 5, we present our geometric interpretation of quantum entanglement and “non-locality.”

The Schwarzschild black hole as a gravitational mirror

The gravitational field outside of a nonrotating black hole is described using the Schwarzschild metric. The geodesic equations of the Schwarzschild metric are derived and those describing null and circular timelike orbits are discussed. Some numerical solutions of the null geodesic equations are shown. These depict photon trajectories which circle the black hole one or two times and then terminate at their emission points. Thus a sequence of ring‐shaped mirror images is produced. An equation which gives the angle between the photon’s trajectory and the radial direction at the emitter is derived and applied to the numerical solutions. These results serve to illustrate how an observer ‘‘passes through’’ his or her mirror image at r=3 MG/c2, as he or she moves toward a Schwarzschild black hole.

Can galaxies exist within our particle horizon with Hubble recessional velocities greater than c

A simple, global picture of photon exchange in the flat, matter‐dominated universe is presented using relativistic cosmology. Equations for the photon’s recessional velocity and position relative to the receiver are derived. The results are discussed in the context of the ‘‘raisin bread universe.’’ Contrary to intuition, it is shown that the Hubble recessional velocity of the emitter can exceed the speed of light for sources within the particle horizon of the receiver. The model used to obtain these results can be used by introductory astronomy students to obtain the proper distance and the time‐of‐flight distance to sources with large redshifts.

Causality as a Casualty of Pregeometry

In Wheeler’s pregeometry, one attempts to derive properties of the spacetime manifold, such as metric, continuity, dimensionality, topology, locality, symmetry, and causality from an otherwise structureless set [1]. Requardt & Roy refer to this methodologically reductionist attempt to model the properties of spacetime as “bottom up pregeometry” [2]. In an early attempt to derive spacetime dimensionality, Wheeler assigned probability amplitudes to the members of a Borel (structureless) set to stochastically establish spacetime adjacency [3]. Wheeler abandoned this idea, in part, because “too much geometric structure is presupposed to lead to a believable theory of geometric structure” [4]. In particular, he considered the manner in which probability amplitudes were assigned, and a metric introduced, to be ad hoc. However, recent models by Nagels [5], Antonsen [6], and Nowotny & Requardt [7] employing graph theory have, arguably, surmounted these objections.

End of a dark age

We argue that dark matter and dark energy phenomena associated with galactic rotation curves, X-ray cluster mass profiles, and type Ia supernova data can be accounted for via small corrections to idealized general relativistic spacetime geometries due to disordered locality. Accordingly, we fit THINGS rotation curve data rivaling modified Newtonian dynamics, ROSAT/ASCA X-ray cluster mass profile data rivaling metric-skew-tensor gravity, and SCP Union2.1 SN Ia data rivaling

The Relational Blockworld Interpretation of Non-relativistic Quantum Mechanics

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Uniform Spaces via Topological Groups and Non-Locality

CDM without non-baryonic dark matter or a cosmological constant. In the case of dark matter, we geometrically modify proper mass interior to the Schwarzschild solution. In the case of dark energy, we modify proper distance in Einstein-deSitter cosmology. Therefore, the phenomena of dark matter and dark energy may be chimeras created by an errant belief that spacetime is a differentiable manifold rather than a disordered graph.