Sixty-Six Theses: Next Steps and the Way Forward in the Modified Cosmological Model

The purpose is to review and lay out a plan for future inquiry pertaining to the modified cosmological model (MCM) and its overarching research program. The material is modularized as a catalog of open questions that seem likely to support productive research work. The main focus is quantum theory but the material spans a breadth of physics and mathematics. Cosmology is heavily weighted and some Millennium Prize problems are included. A comprehensive introduction contains a survey of falsifiable MCM predictions and associated experimental results. Listed problems include original ideas deserving further study as well as investigations of others' work when it may be germane. A longstanding and important conceptual hurdle in the approach to MCM quantum gravity is resolved. A new elliptic curve application is presented. With several exceptions, the presentation is high-level and qualitative. Formal analyses are mostly relegated to the future work which is the topic of this book. Sufficient technical context is given that third parties might independently undertake the suggested work units.

(306 pages)

[v1] 2022-06-27
[v2] 2022-07-26
[v3] 2023-04-19
[v4] -2023-07-26

The Time Travel Interpretation of the Bible

We describe the Biblical work of ages as a time travel program for saving humanity from extinction. God's existence is proven as a consequence of the existence of time travel, which is supposed. We present the case that Abraham's grandson Jacob, also called Israel, is Satan. We make the case that the Israelites are described as God's chosen people in the Bible despite their identity as the children of Satan because God's Messiah is descended from Abraham through Satan. They are chosen as the ancestors of the Messiah rather than as Satan's children. We propose an interpretation in which God commanded Abraham to kill his son Isaac to prevent Isaac from becoming the father of Satan. We suggest that God stayed Abraham's hand above Isaac because preventing the existence of Satan would also prevent the existence of Satan's descendant the Messiah. The history of the Israelites is summarized through Jesus and Paul. This paper is written so that the number of believers in the world will increase.

(110 pages)

[v1] 2021-04-11
[v2] 2021-05-21
[v5] 2021-12-21
[v6] 2023-04-16

On Certain Aspects of American Economics Relevant to 2021

We discuss contemporary socioeconomic issues in a frame of rhetoric beyond the Overton window. We analyze certain policies such as the minimum wage and federal tax structures. We describe a new set of wage and tax policies called normal policies and argue for their superiority over the comparable policy agenda framed by the Overton window. Coronavirus (COVID), racism, fascism, and nationalism are considered. While war followed by total reformation is certainly the best (only) solution to the present overarching societal malaise, for the purposes of scholarship we approach much of the material herein from a good faith vantage point assuming that the entrenched powers might ever permit any changes for the better to occur.

(40 pages)

[v1] 2021-03-01
[v2] 2021-04-07
[v3] 2021-05-21

Zeros of the Riemann Zeta Function Within the Critical Strip and Off the Critical Line

In a recent paper, the author demonstrated the existence of real numbers in the neighborhood of infinity. It was shown that the Riemann zeta function has non-trivial zeros in the neighborhood of infinity but none of those zeros lie within the critical strip. While the Riemann hypothesis only asks about non-trivial zeros off the critical line, it is also an open question of interest whether or not there are any zeros off the critical line yet still within the critical strip. In this paper, we show that the Riemann zeta function does have non-trivial zeros of this variety. The method used to prove the main theorem is only the ordinary analysis of holomorphic functions. After giving a brief review of numbers in the neighborhood of infinity, we use Robinson's non-standard analysis and Eulerian infinitesimal analysis to examine the behavior of zeta on an infinitesimal neighborhood of the north pole of the Riemann sphere. After developing the most relevant features via infinitesimal analysis, we will proceed to prove the main result via standard analysis on the Cartesian complex plane without reference to infinitesimals.

(22 pages)

[v1] 2019-12-02
[v2] 2020-03-11

Fractional Distance: The Topology of the Real Number Line with Applications to the Riemann Hypothesis

Recent analysis has uncovered a broad swath of rarely considered real numbers called real numbers in the neighborhood of infinity. Here we extend the catalog of the rudimentary analytical properties of all real numbers by defining a set of fractional distance functions on the real number line and studying their behavior. The main results of are (1) to prove with modest axioms that some real numbers are greater than any natural number, (2) to develop a technique for taking a limit at infinity via the ordinary Cauchy definition reliant on the classical epsilon-delta formalism, and (3) to demonstrate an infinite number of non-trivial zeros of the Riemann zeta function in the neighborhood of infinity. We define numbers in the neighborhood of infinity as Cartesian products of Cauchy equivalence classes of rationals. We axiomatize the arithmetic of such numbers, prove all the operations are well-defined, and then make comparisons to the similar axioms of a complete ordered field. After developing the many underling foundations, we present a basis for a topology.

(141 pages)

[v1] 2019-06-13
[v2] 2020-04-04
[v3] 2020-06-16
[v4] 2020-09-11
[v5] 2020-11-01
[v6] 2021-05-21
[v7] 2023-07-28
[v8] 2023-08-08

Quick Disproof of the Riemann Hypothesis

In this brief note, we propose a set of operations for the affinely extended real number called infinity. Under the terms of the proposition, we show that the Riemann zeta function has infinitely many non-trivial zeros on the complex plane and off the critical line.

(5 pages)

[v1] 2019-06-13
[v2] 2019-06-27 (unavailable)
[v3] 2019-07-06
[v4] 2020-06-05

Real Numbers in the Neighborhood of Infinity

We demonstrate the existence of a broad class of real numbers which are not elements of any number field: those in the neighborhood of infinity. After considering the reals and the affinely extended reals, we prove that numbers in the neighborhood of infinity are ordinary real numbers of the type detailed in Euclid's Elements. We show that real numbers in the neighborhood of infinity obey the Archimedes property of real numbers. The main result is an application in complex analysis. We show that the Riemann zeta function has infinitely many non-trivial zeros off the critical line in the neighborhood of infinity.

(32 pages)

[v1] 2018-11-14
[v2] 2018-11-16
[v3] 2018-11-18
[v4] 2018-11-23
[v5] 2018-12-10
[v6] 2019-06-27
[v7] 2019-08-17
[v8] 2019-10-27

Proof of the Limits of Sine and Cosine at Infinity

We develop a representation of complex numbers separate from the Cartesian and polar representations and define a representing functional for converting between representations. We define the derivative of a function of a complex variable with respect to each representation and then we examine the variation within the definition of the derivative. After studying the transformation law for the variation between representations of complex numbers, we will show that the new representation has special properties which allow for a modification to the transformation law for the variation which preserves, in certain cases, the definition of the derivative. We refute a common proof that the limits of sine and cosine at infinity cannot exist. We use the modified variation in the definition of the derivative to compute the limits of sine and cosine at infinity.

(48 pages)

[v1] 2018-09-11
[v2] 2018-09-13
[v3] 2018-09-14
[v4] 2018-09-20
[v5] 2018-11-06
[v6] 2019-06-27
[v7] 2019-08-03

Time Arrow Spinors for the Modified Cosmological Model

We construct time arrow spinor states and define for them a Stern--Gerlach analogue Hamiltonian. The dispersion relations of the allowed modes are derived in a few special cases. We examine experimental data regarding negative frequency resonant radiation and show that the energy shift of the negative frequency mode is on the characteristic scale of the energies of the new Hamiltonian. We describe the similitude of the modified cosmological model (MCM) and the Stern--Gerlach apparatus, and we also show how the Pauli matrices are well-suited to applications in MCM cosmology. Complex and quaternion phase are combined in the wavefunction to generate new multiplectic structures. The principles described in this paper are oriented toward a time circuit application so we briefly describe an electrical circuit whose constructive elements elucidate the requirements needed for a working time circuit. The algebraic graph representation of electrical nodes with different electric potentials is replaced with time nodes that have different times in the time circuit graph.

(24 pages)

[v1] 2018-07-26

The Golden Ratio in the Modified Cosmological Model

The golden ratio Phi is very important in the modified cosmological model (MCM). In previous work, we have inserted it artificially rather than showing where it comes from. Where the real numbers are extended to the complex numbers for routine physical applications, we extend the complex numbers to the hypercomplex numbers and show that Phi is inherent to the transfinite structure. We formalize the transfinite concept of continuation beyond infinity. We improve upon previous motivations for deriving general relativity and the fine structure constant in the MCM, and we propose an origin for the Yang-Mills mass gap.

(17 pages)

[v1] 2018-07-06
[v2] 2018-07-26

On Relativity and Absolutism in Morality

We demonstrate that it is impossible for humans to implement moral absolutism. The resolution to any moral proposition is, in all cases, an implementation of moral relativity.

(1 page)

[v1] 2018-06-14
[v2] 2018-07-06

Derivation of the Limits of Sine and Cosine at Infinity

This paper examines some familiar results from complex analysis in the framework of hypercomplex analysis. It is usually taught that the oscillatory behavior of sine waves means that they have no limit at infinity but here we derive definite limits. Where a central element in the foundations of complex analysis is that the complex conjugate of a C-number is not analytic at the origin, we introduce the tools of hypercomplex analysis to show that the complex conjugate of a *C-number is analytic at the origin.

(5 pages)

[v1] 2018-06-08
[v2] 2018-06-09
[v3] 2018-07-26

The General Relevance of the Modified Cosmological Model

The modified cosmological model (MCM) has been an active research program since 2009 and here we summarize the highlights while providing background and insights as they demonstrate mathematical merit. The main "modification" that underpins this work is to consider the principle of greatest action, not least, but cosmological energy functions do not appear. To accommodate infinite action, we develop a transfinite analytical framework *C In the first chapter, we define the MCM system as the union of two Kaluza--Klein theories disconnected by a topological obstruction. We identify a detail overlooked by Feynman in his "many double slits" thought experiment with which we directly motivate the principle of maximum action. Chapter two is mostly a review of fundamental concepts including twistors and quaternions. Much attention in chapter three is given to what are perceived as criticisms of the MCM mechanism for the unification of the theories of gravitation and quanta, and we closely examine the derivation of Einstein's equation from unrelated MCM concepts. The main technical result in chapter three is to demonstrate that dark energy and expanding space are inherent to the MCM metric and we examine the role of the advanced electromagnetic potential in "hyperspacetime." Chapter four is a tour de force starting with a review of the foundations of the MCM. We extend Dirac's bra-ket to an MCM inner product for *C. We continue with a study of conformal infinity and the transfinite extension into the region "beyond conformal infinity." The double slit experiment gives an example of the empirical/philosophical utilities of the MCM principles and we examine their extension into the realm of numerical analysis before deriving the main result: a new formulation for the mass-energy budget of the universe that agrees perfectly with Lambda-CDM.

(284 pages)

[v1] 2017-12-25
[v2] 2018-01-04
[v3] 2018-05-21

On The Riemann Zeta Function

We discuss the Riemann zeta function, the topology of its domain, and make an argument against the Riemann hypothesis. While making the argument in the classical formalism, we discuss the material as it relates to the theory of infinite complexity (TOIC). We extend Riemann's own (planar) analytic continuation R->C into (bulk) hypercomplexity with C->*C. We propose a solution to the Banach--Tarski paradox.

(13 pages)

[v1] 2017-03-07
[v2] 2017-03-25
[v3] 2017-03-30
[v4] 2018-05-21

Infinitudinal Complexification

To the undoubted displeasure of very many detractors, this research program has heretofore focused on aspects of physics so fundamental that many of said detractors do not even acknowledge the program as physics. This paper responds to detractors' criticisms by continuing the program in the same direction and style as earlier work. We present one new quantitative result regarding the big bang and we find a particularly nice topic from fluid dynamics for qualitative treatment. A few other topics are discussed and we present quantitative results regarding the fine structure constant and the differential operator form of $\hat{M}^3$. This paper is somewhat reiterative as it calls attention to directions for further inquiry and continues to leave the hashing out of certain details to either a later effort or the eventual publication of results by those who have already hashed it out, possibly several years ago by now.

(14 pages)

[v1] 2016-08-21
[v2] 2016-08-22
[v3] 2016-09-10
[v4] 2017-03-06

On Certain Aspects of American Economics Relevant to 2016

This paper seeks to shine a light on some glaring economic problems of contemporary society. Too often economic issues are framed in the context of moral wedges that divide people. Here we select issues for discussion that likely can be solved and do not strictly require the resolution of any difficult moral quandaries. We show that certain popular debates are not so interesting because sufficient evidence exists to identify the relevant premises as true and false. We suggest an economic program based in part on hypothetical new energy resources that should guide the United States and the Earth's other national states towards a more equitable valley in the space of all economic configurations. This paper is intended to be persuasive and not purely expository.

(19 pages)

[v1] 2016-05-14
[v2] 2016-05-21

On Wick Rotation

Wick rotation produces numbers that agree with experiment and yet the method is mathematically wrong and not allowed by any self-consistent rule. We explore a small slice of wiggle room in complex analysis and show that it may be possible to use QFT without reliance on Wick rotations.

(1 page)

[v1] 2016-03-27
[v2] 2016-04-15

The Truth About Evolution

The purpose of this report is to debunk Darwin's theory of evolution and any variant theory that relies on the natural rate of mutation to explain the origin of new genes. We construct a model of DNA and show that the minimum rate of mutation needed to produce humans within the geological age of the Earth is too high. It is much higher than any realistic model of random mutations. The calculation presented here should end the evolution debate, at least in its Darwinian limit. Other problems with evolution are discussed.

(13 pages)

[v1] 2016-02-11
[v2] 2016-02-14

Quantum Gravity

This paper uses a small set of mathematical principles to describe a very wide swath of physics. These principles define a new theory of quantum gravity called the theory of infinite complexity. The main result is that Einstein's equation for general relativity can be derived from unrelated, mathematically novel quantum phenomena. That the theory takes no free parameters should be considered strong evidence in favor of a real connection between physics and mathematics.

(7 pages)

[v1] 2015-06-07

A New Ontology

(No Abstract)
Unpublished, unfinished draft.

(25 pages)

[v1] 2015-05-26

Infinitely Complex Topology Changes with Quaternions and Torsion

We develop some ideas that can be used to show relationships between quantum state tensors and gravitational metric tensors. After firmly grasping the math by $\alpha$ and Einstein's equation, this is another attempt to shake it and see what goes and what stays. We introduce slightly more rigorous definitions for some familiar objects and find an unexpected connection between the chirological phase $\Phi^n$ and the quaternions $\bm{q}\in\mathbb{H}$. Torsion, the only field in string theory not already present in the theory of infinite complexity, is integrated. We propose a solution to the Ehrenfest paradox and a way to prove the twin primes conjecture. The theory's apparent connections to negative frequency resonant radiation and time reversal symmetry violation are briefly treated.

(15 pages)

[v1] 2015-05-17
[v2] 2015-06-07

On the Higgs Boson

(No Abstract)
This paper was a Reddit post in which I made a nice point about lattice computations.

(1 page)

[v1] 2014-10-11
[v2] 2014-10-11

Kerr-Newman, Jung, and the Modified Cosmological Model

Where physical theory normally seeks to describe an objective natural world, the modified cosmological model (MCM) seeks to describe an observer's interaction with that world. Qualitative similarities between the psychological observer, the MCM, and the Kerr-Newman black hole are presented. We describe some minimal modifications to previously proposed processes in the MCM. Inflation, large-scale CMB fluctuations and the free energy device are discussed.

(5 pages)

[v1] 2014-05-27

On Bell's Inequality

We show that when spin eigenfunctions are not fully orthonormal, Bell's inequality does allow local hidden variables. In the limit where spin eigenfunctions are Dirac orthonormal, we recover a significant extremal case. The new calculation gives a possible accounting for alpha_MCM-alpha_QED.

(1 page)

[v1] 2013-12-21
[v2] 2014-01-26
[v3] 2014-04-27

Ontological Physics

Ambiguity in physics makes many useful calculations impossible. Here we reexamine physics' foundation in mathematics and discover a new mode of calculation. The double slit experiment is correctly described by the new mode. We show that spacetime emerges from a set of hidden boundary terms. We propose solutions to problems including the limited spectrum of CMB fluctuations and the anomalous flux of ultra-high energy cosmic rays. A fascinating connection between biology and the new structure should have far reaching implications for the understanding and meaning of life.

(8 pages)

[v1] 2013-12-21
[v2] 2014-01-27

The Truth About Climate Change

Climatology occupies the intersection of science policy and public understanding of science. In such a prominent position, the wide spectrum of climate opinions is remarkable. Society has achieved a paradigm in which global warming subscribers and non-subscribers are largely segregated by political affiliation. Since science is non-political, only a misunderstanding of the science can facilitate such a segregation. In the first section we analyze a recent study by Cook \emph{et al.} finding overwhelming scientific endorsement for the greenhouse theory of anthropogenic global warming (AGW). We find the popular reporting on Cook's result is not accurate. The aim of the following section is to clarify the science behind the most popular climate arguments and introduce the reader to some evidence that is not widely publicized. Even the astute non-climatologist should come away from this report with an enhanced understanding of relevant issues in modern climate science.

(21 pages)

[v1] 2013-09-10

The Truth About Geometric Unity

In May of 2013 a pair of articles appeared on the Guardian newspaper website featuring a new candidate "theory of everything" called Geometric Unity. A cursory reading of each article gives the impression that Geometric Unity was developed by Eric Weinstein, but a closer reading reveals that Weinstein is not credited as such. The truth about Geometric Unity is that it was authored by this writer in several papers beginning in 2009. This article will describe the development and prominent features of the new theory.

(7 pages)

[v1] 2013-07-16
[v2] 2013-07-18
[v3] 2013-07-24 (unavailable)
[v4] 2013-08-10
[v5] 2013-08-15

Quantum Structure

The logical structure of the standard model is isomorphic to the geometric structure of the modified cosmological model (MCM). We introduce a new particle representation scheme and show that it is invariant under CPT. In this representation spin arises as an ordinary physical process. The final character of the Higgs boson is predicted. Wavefunction collapse, the symmetry (anti-symmetry) of the wavefunction and some recent experimental results are discussed.

(5 pages)

[v1] 2013-02-06
[v2] 2013-02-07
[v3] 2013-02-16
[v4] 2013-05-24

Modified Spacetime Geometry Addresses Dark Energy, Penrose's Entropy Dilemma, Baryon Asymmetry, Inflation and Matter Anisotropy

A model of modified spacetime is discussed. Implications for causality regarding modern anomalies and paradoxes are made. Topics include a dark energy candidate without induced gravitational screening. The dynamics of the repulsive force of quantum geometry allow the validity of the second law continuously through a universe's death and rebirth. The baryon asymmetry is explained without addressing the Sakharov conditions. Inflation and anisotropies in an FLRW universe are also attributed to quantum bounce phenomena. No attempt at quantification is made.

(3 pages)

[v1] 2013-02-04

Geometric Cosmology

The modified cosmological model (MCM) is explored in the context of general relativity. A flaw in the ADM positive-definiteness theorem is identified. We present an exposition of the relationship between Einstein's equations and the precessing classical oscillator. Kaluza theory is applied to the MCM and we find a logical motivation for the cylinder condition which leads to a simple mechanism for AdS/CFT.

(4 pages)

[v1] 2013-01-06
[v2] 2013-01-08
[v3] 2013-01-09
[v4] 2013-04-14
[v5] 2013-05-24
[v6] 2013-07-24

Tempus Edax Rerum

A non-unitary quantum theory describing the evolution of quantum state tensors is presented. Einstein's equations and the fine structure constant are derived. The problem of precession in classical mechanics gives an example.

(4 pages)

[v1] 2012-09-04
[v2] 2012-09-04
[v3] 2013-02-16
[v4] 2013-05-25

Dark Energy in M-Theory

Dark Energy is yet to be predicted by any model that stands out in its simplicity as an obvious choice for unified investigative effort. It is widely accepted that a new paradigm is needed to unify the standard cosmological model (SCM) and the minimal standard model (MSM). The purpose of this article is to construct a modified cosmological model (MCM) that predicts dark energy and contains this unity. Following the program of Penrose, geometry rather than differential equations will be the mathematical tool. Analytical methods from loop quantum cosmology (LQC) are examined in the context of the Poincar´e conjecture. The longstanding problem of an external time with which to evolve quantum gravity is resolved. The supernovae and WMAP data are reexamined in this framework. No exotic particles or changes to General Relativity are introduced. The MCM predicts dark energy even in its Newtonian limit while preserving all observational results. In its General Relativistic limit, the MCM describes dark energy as an inverse radial spaghettification process. Observable predictions for the MCM are offered. AdS/CFT correspondence is discussed. The MCM is the 10 dimensional union of de Sitter and anti-de Sitter space and has M-theoretical application to the five string theories which lack a unifying conceptual component. This component unifies gravitation and electromagnetism.

(8 pages)

[v1] 2012-08-18

Derivation of the Fine Structure Constant

An alternate interpretation of Quantum Theory is given. The fine structure constant is derived. An experiment is proposed.

(3 pages)

[v1] 2012-08-18 (unavailable)
[v2] 2012-08-20