Modified Regge calculus as an explanation of dark energy

Using Regge calculus, we construct a Regge differential equation for the time evolution of the scale factor $a(t)$ in the Einstein-de Sitter cosmology model (EdS). We propose two modifications to the Regge calculus approach: 1) we allow the graphical links on spatial hypersurfaces to be large, as in direct particle interaction when the interacting particles reside in different galaxies, and 2) we assume luminosity distance $D_L$ is related to graphical proper distance $D_p$ by the equation $D_L = (1+z)\sqrt{\overrightarrow{D_p}\cdot \overrightarrow{D_p}}$, where the inner product can differ from its usual trivial form. The modified Regge calculus model (MORC), EdS and $\Lambda$CDM are compared using the data from the Union2 Compilation, i.e., distance moduli and redshifts for type Ia supernovae. We find that a best fit line through $\displaystyle \log{(\frac{D_L}{Gpc})}$ versus $\log{z}$ gives a correlation of 0.9955 and a sum of squares error (SSE) of 1.95. By comparison, the best fit $\Lambda$CDM gives SSE = 1.79 using $H_o$ = 69.2 km/s/Mpc, $\Omega_{M}$ = 0.29 and $\Omega_{\Lambda}$ = 0.71. The best fit EdS gives SSE = 2.68 using $H_o$ = 60.9 km/s/Mpc. The best fit MORC gives SSE = 1.77 and $H_o$ = 73.9 km/s/Mpc using $R = A^{-1}$ = 8.38 Gcy and $m = 1.71\times 10^{52}$ kg, where $R$ is the current graphical proper distance between nodes, $A^{-1}$ is the scaling factor from our non-trival inner product, and $m$ is the nodal mass. Thus, MORC improves EdS as well as $\Lambda$CDM in accounting for distance moduli and redshifts for type Ia supernovae without having to invoke accelerated expansion, i.e., there is no dark energy and the universe is always decelerating.Comment: 15 pages text, 6 figures. Revised as accepted for publication in Class. Quant. Gra

Expansive actions on uniform spaces and surjunctive maps

We present a uniform version of a result of M. Gromov on the surjunctivity of maps commuting with expansive group actions and discuss several applications. We prove in particular that for any group $\Gamma$ and any field \K, the space of $\Gamma$-marked groups $G$ such that the group algebra \K[G] is stably finite is compact.Comment: 21 page

The Relational Blockworld Interpretation of Non-relativistic Quantum Mechanics

We introduce a new interpretation of non-relativistic quantum mechanics (QM) called Relational Blockworld (RBW). We motivate the interpretation by outlining two results due to Kaiser, Bohr, Ulfeck, Mottelson, and Anandan, independently. First, the canonical commutation relations for position and momentum can be obtained from boost and translation operators,respectively, in a spacetime where the relativity of simultaneity holds. Second, the QM density operator can be obtained from the spacetime symmetry group of the experimental configuration exclusively. We show how QM, obtained from relativistic quantum field theory per RBW, explains the twin-slit experiment and conclude by resolving the standard conceptual problems of QM, i.e., the measurement problem, entanglement and non-locality

An Adynamical, Graphical Approach to Quantum Gravity and Unification

We use graphical field gradients in an adynamical, background independent fashion to propose a new approach to quantum gravity and unification. Our proposed reconciliation of general relativity and quantum field theory is based on a modification of their graphical instantiations, i.e., Regge calculus and lattice gauge theory, respectively, which we assume are fundamental to their continuum counterparts. Accordingly, the fundamental structure is a graphical amalgam of space, time, and sources (in parlance of quantum field theory) called a "spacetimesource element." These are fundamental elements of space, time, and sources, not source elements in space and time. The transition amplitude for a spacetimesource element is computed using a path integral with discrete graphical action. The action for a spacetimesource element is constructed from a difference matrix K and source vector J on the graph, as in lattice gauge theory. K is constructed from graphical field gradients so that it contains a non-trivial null space and J is then restricted to the row space of K, so that it is divergence-free and represents a conserved exchange of energy-momentum. This construct of K and J represents an adynamical global constraint between sources, the spacetime metric, and the energy-momentum content of the element, rather than a dynamical law for time-evolved entities. We use this approach via modified Regge calculus to correct proper distance in the Einstein-deSitter cosmology model yielding a fit of the Union2 Compilation supernova data that matches LambdaCDM without having to invoke accelerating expansion or dark energy. A similar modification to lattice gauge theory results in an adynamical account of quantum interference.Comment: 47 pages text, 14 figures, revised per recent results, e.g., dark energy result

Why the Tsirelson Bound? Bub's Question and Fuchs' Desideratum

To answer Wheeler's question "Why the quantum?" via quantum information theory according to Bub, one must explain both why the world is quantum rather than classical and why the world is quantum rather than superquantum, i.e., "Why the Tsirelson bound?" We show that the quantum correlations and quantum states corresponding to the Bell basis states, which uniquely produce the Tsirelson bound for the Clauser-Horne-Shimony-Holt quantity, can be derived from conservation per no preferred reference frame (NPRF). A reference frame in this context is defined by a measurement configuration, just as with the light postulate of special relativity. We therefore argue that the Tsirelson bound is ultimately based on NPRF just as the postulates of special relativity. This constraint-based/principle answer to Bub's question addresses Fuchs' desideratum that we "take the structure of quantum theory and change it from this very overt mathematical speak ... into something like [special relativity]." Thus, the answer to Bub's question per Fuchs' desideratum is, "the Tsirelson bound obtains due to conservation per NPRF."Comment: Contains corrections to the published versio

Answering Mermin's Challenge with Conservation per No Preferred Reference Frame

In 1981, Mermin published a now famous paper titled, "Bringing home the atomic world: Quantum mysteries for anybody" that Feynman called, "One of the most beautiful papers in physics that I know." Therein, he presented the "Mermin device" that illustrates the conundrum of quantum entanglement per the Bell spin states for the "general reader." He then challenged the "physicist reader" to explain the way the device works "in terms meaningful to a general reader struggling with the dilemma raised by the device." Herein, we show how "conservation per no preferred reference frame (NPRF)" answers that challenge. In short, the explicit conservation that obtains for Alice and Bob's Stern-Gerlach spin measurement outcomes in the same reference frame holds only on average in different reference frames, not on a trial-by-trial basis. This conservation is SO(3) invariant in the relevant symmetry plane in real space per the SU(2) invariance of its corresponding Bell spin state in Hilbert space. Since NPRF is also responsible for the postulates of special relativity, and therefore its counterintuitive aspects of time dilation and length contraction, we see that the symmetry group relating non-relativistic quantum mechanics and special relativity via their "mysteries" is the restricted Lorentz group.Comment: 18 pages, 9 figures. This version as revised and resubmitted to Scientific Report