2,911 research outputs found
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 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 is related to graphical proper distance
by the equation , where the inner product can differ from its usual
trivial form. The modified Regge calculus model (MORC), EdS and 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
versus gives a correlation of
0.9955 and a sum of squares error (SSE) of 1.95. By comparison, the best fit
CDM gives SSE = 1.79 using = 69.2 km/s/Mpc, = 0.29
and = 0.71. The best fit EdS gives SSE = 2.68 using =
60.9 km/s/Mpc. The best fit MORC gives SSE = 1.77 and = 73.9 km/s/Mpc
using = 8.38 Gcy and kg, where is the
current graphical proper distance between nodes, is the scaling factor
from our non-trival inner product, and is the nodal mass. Thus, MORC
improves EdS as well as 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
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
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 and any field \K, the
space of -marked groups such that the group algebra \K[G] is
stably finite is compact.Comment: 21 page
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
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