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

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

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 $\Lambda$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.Comment: This version was accepted for publication in the International Journal of Modern Physics D; revised version of an essay that won Honorable Mention in the Gravity Research Foundation 2016 Awards for Essays on Gravitation. 10 pages, 3 figures. arXiv admin note: text overlap with arXiv:1509.0928

The Missing Mass Problem as a Manifestation of GR Contextuality

In Newtonian gravity, mass is an intrinsic property of matter while in general relativity (GR), mass is a contextual property of matter, i.e., matter can simultaneously possess two different values of mass when it is responsible for two different spatiotemporal geometries. Herein, we explore the possibility that the astrophysical missing mass attributed to non-baryonic dark matter (DM) actually obtains because we have been assuming the Newtonian view of mass rather than the GR view. Since an exact GR solution for realistic astrophysical situations is not feasible, we explore GR-motivated ansatzes relating proper mass and dynamic mass for one and the same baryonic matter, as justified by GR contextuality. We consider four GR alternatives and find that the GR ansatz motivated by metric perturbation theory works well in fitting galactic rotation curves (THINGS data), the mass profiles of X-ray clusters (ROSAT and ASCA data) and the angular power spectrum of the cosmic microwave background (CMB, Planck 2015 data) without DM. We compare our galactic rotation curve fits to modified Newtonian dynamics (MOND), Burkett halo DM and Navarro-Frenk-White (NFW) halo DM. We compare our X-ray cluster mass profile fits to metric skew-tensor gravity (MSTG) and core-modified NFW DM. We compare our CMB angular power spectrum fit to scalar-tensor-vector gravity (STVG) and $\Lambda$CDM. Overall, we find our fits to be comparable to those of MOND, MSTG, STVG, $\Lambda$CDM, Burkett, and NFW. We present and discuss correlations and trends for the best fit values of our fitting parameters. For the most part, the correlations are consistent with well-established results at all scales, which is perhaps surprising given the simple functional form of the GR ansatz.Comment: 18 pages text. Twice revised per referee/reviewer comments. Fit of CMB angular power spectrum and dark matter halo fits adde

Impact Of The Regulation Flexibility Act On The Implementation And Judicial Review Provisions Of The Magnuson-Stevens Fishery Conservation And Management Act

Through the Magnuson-Stevens Fishery Conservation and Management Act (Magnuson-Stevens Act), Congress has delegated to the Secretary of Commerce the broad authority to manage and conserve coastal fisheries. The Magnuson-Stevens Act creates eight independent regional fishery management councils to prepare fishery management plans for each region. However, the regional councils do not have authority over all species because the Magnuson-Stevens Act assigns responsibility to the Secretary of Commerce for non-Pacific Ocean highly migratory species. Highly migratory species are defined under the Magnuson-Stevens Act to include tuna species, marlin, ocean sharks, sailfishes, and swordfish. In preparing and implementing all fishery management plans under the Magnuson-Stevens Act, the Secretary must consider factors that are aimed at conserving and protecting the fishing industry, including minimizing the disadvantage to domestic fishermen. Further, the Secretary must comply with ten national standards, applicable to all fishery management plans under the Magnuson-Stevens Act, that require consideration of competing environmental and economic concerns. The Secretary must also comply with the Regulatory Flexibility Act (RFA), which was enacted to prevent the inequitable impact of agency rules on small businesses. Small businesses tend to incur regulatory compliance costs that are disproportionately higher than the costs associated with larger businesses for the same regulatory compliance. Under the RFA, agencies are required to analyze their proposed rules and attempt to reduce their impact on small businesses prior to passage of the rules. The RFA requires agencies to prepare and publish in the Federal Register an Initial Regulatory Flexibility Analysis (IRFA) describing the effect of a proposed rule on small businesses and discussing significant alternatives that might minimize adverse economic consequences. Publication of the IRFA provides small businesses with an opportunity to publicly comment on the analysis. If an agency decides that a significant impact on small businesses likely exists, then the agency must explore alternatives to the rule that would lessen the potential economic severity. However, if a significant impact is not foreseeable, then the agency may issue the rule, prepare a Final Regulatory Flexibility Analysis (FRFA), and publish it in the Federal Register. The agency may exempt itself from this process by certifying that the final rule will not have a significant economic impact on a substantial number of small entities. Both the RFA and the Magnuson-Stevens Act provide for judicial review of the Secretary\u27s regulatory actions pursuant to the Administrative Procedures Act (APA). Agency actions under both the RFA and the Magnuson-Stevens Act are to be reviewed for compliance in accordance with the arbitrary and capricious standard under the APA. The United States Court of Appeals for the First Circuit has held, under the RFA, that judicial review should be a determination of whether the S6cretary employed a reasonable, good-faith effort in his consideration of alternative regulation. Essentially, a court reviewing an agency action under the arbitrary and capricious standard must determine whether the agency has examined the pertinent evidence, considered the relevant factors, and articulated a satisfactory explanation for its action, including a rational connection between the facts found and the choice made by the agency

Marathon Oil Co. v. United States: The Rising Costs Of Domestic Oil Production

The Outer Continental Shelf Lands Act of 1953 (OCSLA) was enacted by Congress to establish exclusive federal jurisdiction over submerged lands on the continental shelf beyond three miles from the coastline. Pursuant to the OCSLA, the Secretary of the Interior is authorized to sell oil and gas leases on outer continental shelf (OCS) lands through a competitive bidding process. The Act was amended in 1978 to provide for the expeditious and orderly development, subject to environmental safeguards, of resources on the OCS consistent with the maintenance of competition and other national needs. Lessees must seek approvals from various federal and state agencies before each stage of exploration, development, andproduction. Considerable controversy can develop between the lessee and the federal and state governments. In one recent decision, Marathon Oil Co. v. United States, the United States Court of Appeals for the Federal Circuit held that the government\u27s refusal to issue oil and gas exploration permits for the OCS to the lessee did not constitute a material breach of a lease As a result, lessees were not entitled to restitution of over $156 million in up-front contract bonuses. In ruling that the government had not breached the lease, the court upheld a means by which the federal government may withdraw federal rights based on state objections without returning the federal consideration. Moreover, the legislative policy behind the OCSLA has been undermined as OCS development under the current law will neither be expeditious nor orderly as long as the federal government does not have to operate under rules of fair dealing. Viewing the OCSLA from an equitable perspective leads to the conclusion that the process is flawed and should be changed. This Note argues that lessees do not engage in a fair process when conflicting legislation exists and judicial determinations are unable to take this into account in decision making. This Note suggests that the structure of the OCSLA provides the answer in that more discussion should be centered upon the lease sales rather than allowing state objections to effectively destroy an exploration project post-sale

Marathon Oil Co. v. United States: The Rising Costs Of Domestic Oil Production

The Outer Continental Shelf Lands Act of 1953 (OCSLA) was enacted by Congress to establish exclusive federal jurisdiction over submerged lands on the continental shelf beyond three miles from the coastline. Pursuant to the OCSLA, the Secretary of the Interior is authorized to sell oil and gas leases on outer continental shelf (OCS) lands through a competitive bidding process. The Act was amended in 1978 to provide for the expeditious and orderly development, subject to environmental safeguards, of resources on the OCS consistent with the maintenance of competition and other national needs. Lessees must seek approvals from various federal and state agencies before each stage of exploration, development, andproduction. Considerable controversy can develop between the lessee and the federal and state governments. In one recent decision, Marathon Oil Co. v. United States, the United States Court of Appeals for the Federal Circuit held that the government\u27s refusal to issue oil and gas exploration permits for the OCS to the lessee did not constitute a material breach of a lease As a result, lessees were not entitled to restitution of over $156 million in up-front contract bonuses. In ruling that the government had not breached the lease, the court upheld a means by which the federal government may withdraw federal rights based on state objections without returning the federal consideration. Moreover, the legislative policy behind the OCSLA has been undermined as OCS development under the current law will neither be expeditious nor orderly as long as the federal government does not have to operate under rules of fair dealing. Viewing the OCSLA from an equitable perspective leads to the conclusion that the process is flawed and should be changed. This Note argues that lessees do not engage in a fair process when conflicting legislation exists and judicial determinations are unable to take this into account in decision making. This Note suggests that the structure of the OCSLA provides the answer in that more discussion should be centered upon the lease sales rather than allowing state objections to effectively destroy an exploration project post-sale